K-12, College, Graduate Level Tutoring

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Teacher Credentials


City: Santa Rosa, CA 95405
Cell/Text: (707)235-4095
Email: mark.c.stansberry@gmail.com
Available: Days, Evenings, Weekends
At: Your Home, Coffee Shop or Library
Economical Rates: As Low as $25.00 Hour (Sliding Hourly and Subject Scale)

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Experience and Background
Over 10 Years Tutoring in Sonoma County (2004)
Bachelor Science Electrical Engineering(BSEE, San Jose State)
California CBEST Teacher Credential
California CSET Geometry and Statistics Credential
Over 15 years as a technical writer and electronics engineer

QuickNotes Driven Instruction and Exam Notes

BookMarkTutoring develops and produces QuickNotes, a series of formula and study guides customized to the needs of its students.  The series of online notes allows students to rapidly learn and review the critical material needed to score consistently higher on quizzes, midterms and exams.

QuickNotes can be customized for your specific course and textbook into seven major subject areas: Business, Engineering, Graphic Design, Mathematics, Science, Technology and Test Preparation.  

The Business Series of QuickNotes cover  Microsoft’s line of office products. Get the concise information you need to learn Excel, Word and PowerPoint quickly and the needed material for business courses such as business calculus, finite mathematics, economics and macroeconomics.

The Electrical Engineering Series of QuickNotes focus on electronics technology for technicians, electricians, electronic engineers and hobbyists: Analog Circuit Analysis, Digital Logic, Integrated Circuit Design, Microcontrollers, Microprocessors and more.

The Graphic Design Series of QuickNotes cover the essentials to get up and running using Adobe’s line of graphic design products. Become a pro with Adobe Illustrator, Photoshop, Flash, Indesign and eaver.

The Mathematics Series of QuickNotes encompass the spectrum of high school and college level math including algebra, calculus, differential equations, finite mathematics, geometry, linear algebra, statistics and trigonometry.

The Marketing Series of QuickNotes give online businesses the information they need to know to grow their businesses and market their products. Provides listings of top retail online stores to distribute products through, newswire aggregators and newswire listings, leading online business directories, fastest growing companies, high income demographics, statistical sampling techniques, SEO strategies and more.

The Science Series of QuickNotes give you comprehensive coverage of the chemistry and physics formulas, procedures and facts that you need for high school and college courses including AP Chemistry and AP Physics.

The Test Preparation series of QuickNotes cover the basics needed for scoring high on college entrance exams (ACT and SAT) teacher credentials ask about our CBEST and CSET QuickNotes and are other state specific credential exam QuickNotes.

The Technology Series of QuickNotes cover computer science, information technology and web development. For web development QuickNotes are available for HTML5, CSS and JavaScript. For computer science find notes for basic, C++, C# and Visual Studio. 

Other BookMark Publications

The Very Best Algebra Notes, 2013, View on Amazon
EHow, Demand Studies, Over 500 How Tos on math, science, art, electronics and engineering
The Art of Perspective Illustration, 2007
Over 100 publications written on electronic and computer technology for leading high technology trade magazines and corporations.

Algebra I Review Guide 2014 - Preliminary


For more detailed publication lists and background information visit Mark Stansberry's linkedin page

BookMark offers

1) A Step-by-Step, How-To Instruction Approach

2) Formula and Review Study Guides for All Subjects

3) Customized Curriculum Design for Home Schools and Businesses

4) Compliance with California and Federal Common Core Educational Standards

5) Flexible Scheduling

About BookMark

BookMark offers individual tutor lessons and group tutor sessions on subjects that range from mathematics to art and architecture. We offer tutoring services to all ages and training services to businesses. BookMark also develops educational software tools and apps. This software includes our Infinity Machine, an online graphic design software program used to help students understand the relationships between art, mathematics and science.

BookMark has the Experience

With over 15 years in academic tutoring and corporate training BookMark has the experience needed for students to reach their academic and career goals.

BookMark has tutored hundreds of high school and college students throughout Santa Rosa and Sonoma County. From this experience, BookMark knows where students have problems and Santa Rosa high schools and colleges. BookMark also knows educational trends in Sonoma County, California and in the United States and knows the coming course changes dictated by the Common Core National Education Standards.

BookMark's broad based experience in the academic and corporate world gives it the perspective to balance teaching so you and your children can successfully prepare yourself to fulfill not just academic requirements but the demands of the professional marketplace.

BookMarks experience extends from the academic world to the corporate world. BookMark has trained high technology employees in semiconductor and electronic circuit design technology, computer programming, statistics, business process management, electronic design automation, cloud computing technology, graphic design, web site analytics, web design, and animation. In these roles, BookMark provides one-on-one and group instructions as well as complete training materials from PowerPoint Slides to in-depth training manuals through complex engineering design manuals.

About Mark Stansberry

Mark Stansberry, the principle of BookMark Tutoring, has written scores of technical articles, books and reports on almost every technical topic imaginable. As a technical writer, electrical engineer and instructor, he has written for high technology companies, leading trade press magazines, market research firms and educational companies. With a focus on leading edge technology, Mark's writing has enlightened thousands on the technology and applications of alternative energy, business process managements, computer science, electronics, mathematics, medical technology, physics, semiconductor technology, His broad base of knowledge, his skill at concisely conveying procedural steps and explaining technical concepts in an easy to understand format, gives students not only the instruction they need to learn a subject quickly, but also the insight into how to apply problem solving techniques to other subjects and to problems encountered in the corporate world.

Mark has tutored students enrolled in engineering, mathematics and science courses at Santa Rosa Junior College, Sonoma State and the high schools throughout Santa Rosa. BookMark is familiar with the courses and prerequisites for fast track programs at Santa Rosa High School, Maria Carillo High School, Montgomery High School, Rancho Cotati High School and others. As well BookMark is familiar with the content in Santa Rosa Junior College and Sonoma States engineering, science and mathematics courses.

Mark Stansberry has a Bachelor of Science Degree in Electrical Engineering from San Jose State University. In his efforts to develop a graphic design automation program he has completed numerous courses in graphic, fashion and architectural design.

Mark is currently is developing a series of graphic design automation programs based on non-recursive and recursive mathematical equations. These programs include 2D and 3D graphic design automation programs used for the development of patterns, shapes and forms. He is also developing a series of architectural, graphic and fashion design composition tools. Prototypes of these tools are often used in the city design and illustration classes he teaches.


Why Tutoring Works

Statistics about education indicate that students with tutors achieve the highest academic and community level achievements levels. And that's because students that have tutors get concise explanations about necessary procedures, immediate answers to their questions and the educational supplementary material needed to perform well in academically challenging subjects, The end result is that students with tutors don't struggle with homework and are much more organized. This means more free time for the student to focus on extracurricular activities and more time for the student to apply their academic knowledge


Builds Skills for Advanced Studies and College

Tutors provide a path to not only improved high school grades, but a path to sustained higher grades. The stronger subject foundation that a student obtains with a tutor allows a student to approach more advanced subjects with greater confidence, a stronger set of skills and a studying methodology that overcomes hurdles.

The approaches to learning, research and test taking that tutors emphasize and teach, facilitates the process by which a student can become an independent learner. Although independent learning is often necessary and the most efficient way to address solutions to many problems other times it is more efficient to communicate with professors, coworkers and others in the community. BookMark emphasizes the importance of not only utilizing and finding high quality research resources, but also emphasizes the importance of students working together in groups and collaborating on solving problems Through group tutor sessions and group projects, BookMark provides the guidance students need to work together effectively and organize the results of their work as a group. .


Concise to the Point Explanations and Visuals

BookMark's students have found that improving a grade is not strictly a question of study time, but more a question of how concise and comprehensive the explanations is. At BookMark the emphasis is on providing the student the key information that unlocks the students ability to solve problems and understand concepts.

Supplemental Educational Materials that Makes Studying Easier

So that students save time organizing, reviewing and in the actual problem solving processed, tutors often provide supplementary educational material that is specifically designed to make the students life easier.

BookMark is no exception. BookMark makes a dedicated effort to ensure that its supplementary educational material makes the learning process more efficient. Our educational materials, which include study guides, formula sheets, problems and solutions databases and educational apps are designed to minimize problem solving time, reduce research time and provide the organizational format students need to review for tests and obtain a deeper conceptual understanding of their subjects.

BookMark's study guides summarize the formulas and critical facts and points that are needed to excel in all levels of mathematics, chemistry, physics, statistics, computer science, writing and graphic design. These guides not only provide the critical formulas, rules and points for specific subject, but also provide a reference for the student to use throughout the course and as a comprehensive checklist for mid-term and final exam reviews.

At BookMark tutoring we create our study guides and supplementary educational course materials and educational apps around the new Common Core National Educational Standards, California high school standards and California university accrediting standards. Because we cater to the needs of Sonoma State University, Santa Rosa Junior College and the numerous high schools in Santa Rosa and Sonoma County, our educational supplemental material also emphasizes the focus that these schools have built their curriculums around.

At BookMark we not only have study guides for specific academic subjects, courses, tutor sessions, homework sessions and final reviews, but also have study guides and checklists for high school standards testing, scholarship testing, advanced placement testing such as CLEP, AP and International Baccalaureate testing, as well as study guides for college entrance exams for ACT, SAT, MCAT, CBEST, CSET and GMAT testing,


BookMark researches the latest text books, educational web sites, educational apps and videos so that students know which are the best educational resources available to them. BookMark compiles problems and solutions into well-organized problem and solution databases. Our problem and solutions databases lists problems and their solutions by specific topic categories so that students can not only find relevant examples for the problems quickly, but obtain a total perspective on different approaches to problem solving and different approaches to explaining solutions.

BookMark has an ongoing effort in the design of educational apps as part of its educational software development program. So far to date, we have developed educational apps used in graphic design automation, fashion composition and computer science. These applications are designed to show students different approaches to the solving of graphic design problems, to improve technical illustration skills and to show students the inherent relations between graphic design, geometry, architecture and advanced mathematics.

The graphic design automation apps, which are based on high level mathematical algorithms developed at BookMark, are fundamental for teaching computer science skills in our special studies tutoring sessions. Through our special studies programs, students apply math and science to create computer software. We show students how to code math and science formulas to create computer programs for their own use and for the development of software products. In special projects sessions, we introduce students to computer algorithms used in the development of video games, computer aided design systems and simulators. In computer science project sessions students also learn the basics of computer programming and how to create graphical user interfaces and the design criteria for the creation of a successful graphic user interface.

BookMark produces its own course material such that it emphasize the standards required in California Universities and Sonoma County and Santa Rosa high schools. We also produce course material that has been specifically created for courses taught at all Sonoma County colleges including Santa Rosa Junior College and Sonoma State University. Our instructional materials are also relevant to course materials and the types of problems solved in the University of California and California State University classes. BookMark Tutoring's literature development process include student feedback which allows us to continually improve our course material to changing academic demands.

BookMark Tutoring subject specific formula and summary sheets are one of its most powerful learning tools. These subject specific study guides provide the student a road map to the course knowledge needed for proficiency. The formula and summary sheets save students organization time. And that's because they provide all the basic information that the student will need to study for the subject's mid-terms and final exams.

The Very Best Algebra Notes is one of our latest publications. It is available as an Ebook for tablets, the Kindle, smart phones and PCs. through Amazon.

Very Best Algebra Notes

Bookmark Tutoring develops its course material for the needs of Santa Rosa and Sonoma County high school and college students. At a tutoring session, we note any unique formulas and topics each teacher focuses on. The students often add input into what they need in the course material and summary sheets to reduce studying time and improve comprehension and test grades.

BookMark knows which problems students most often have the most difficulty with and which of these they will absolutely need to have absolutely proficient to achieve high scores in college courses.


Improved Academic Attitudes With Better Grades and Better Skills

A tutor can be one of the better scholastic investments for more than just grades. Studies have not only indicated a relation between higher grades and tutoring, but have also shown a correlation between tutoring, positive attitudes and level of scholastic enthusiasm.

Often the enthusiasm is because students soon realize that study and research time is reduced with a tutor and it takes less time to learn new material. .A well-prepared tutor also provides time-saving course material that directly address the course needs of the student and gives them insight into the most important concepts related to a specific subject.

Students with tutors learn that the teaching method, the books used and the supplementary materials are just as important in learning as student study time is. Tutors know and teach their students that different books, different teaching methods and different teaching materials will effect not only the time it takes to learn a subject, but also the level of understanding of the subject.

Because tutors that teach in a one-on-one environment are able to more effectively interact with students, a student with a tutor learns the importance of asking questions and obtaining a well-thought out explanation to their problems solutions quickly. Because tutors know what problems students are most likely to have difficulty with and which are the most important concepts in a course, a student with a tutor doesn't miss out on critical information that is not only important for success in the course but also on concepts and procedures that are necessary for success in more advanced courses.


Research Skills Improve

BookMark emphasizes the development of research skills and the use of research material for the solving of problems, writing of reports and the expansion of creativity. BookMark in its sessions points out the critical sources of information that professionals and top performing students use. These resources include online resources such as patent databases, professional conference papers, educational applications, book depositories, business wires, graphic and art databases as well as online calculators that are used to make solving problems and versifying solutions easier and more efficient.

.BookMark has years of experience in writing technical and market research reports and knows the importance of the right facts and having all the right facts. BookMark brings this to its students and shows them how to apply this research to give them the academic and professional career edge.

New Teaching Methodologies Accelerate Academic Learning Rate

There are several ways that a tutor can ensure that they convey concepts and explain procedures so that the student's level of understanding increases quickly. One of the most important is continual tutor training, training that involves learning new teaching procedures, the adoption of effective educational computer technology and continued writing and improvement of course material.

At BookMark Tutoring skills are continually updated. As part of our tutor improvement program, our tutors develop their own course material, formula sheets, flash cards and continually review the new text books, new teaching software and new teaching methods that increase learning productivity.

California Scholastic Standards Are Met

BookMark Tutoring makes a point to be up to date with the course standards and course topics in California at the grade school, middle school, high school, junior college and university levels Because of this familiarity, BookMark knows where to place the emphasis on in learning.

Santa Rosa Charter and Home School Curriculum Planning

Today many parents in Santa Rosa have taken the home school and charter school option. Often they feel a better education and one more relevant to their children's needs can be obtained.

For those with children in home school, Bookmark can develop curriculums specific to your requirements and one that meets California education code Federal Common Core standards.

Many Santa Rosa charter school students do extremely well. They often attend Santa Rosa Junior College and earn college credits in high school. Top colleges and universities often seek out Santa Rosa's charter school students. And that's because they often are better educated in subject areas that range from the arts to science, are known to perform well in college, are independent learners and often are active participants in school and community activities.

However, the charter school chosen will effect how well your children are prepared to take college entrance exams and their eligibility for different colleges. BookMark's chartered tutoring programs takes the anxiety and worry out of charter school. With our charter school programs, we examine the charter school curriculum for performance in critical key areas. First we look for standards compliance, then we look at instructional materials that the school produces.

A good charter school will often have the best books, and the best course and curriculum writers on staff. They will also be familiar with standards and can demonstrate there familiarity with the standards through the course materials that come with the course. What makes charter schools exceptional is that they often give students the ability to excel to near professional levels. The right charter school can provide even better instruction and more interesting assignments than even the most expensive private schools.

At BookMark Tutoring, we offer Santa Rosa and Sonoma County's charter school students and their parents everything extra they will need to ensure academic excellence in any one of the scores of charter schools found here. With BookMark's standards knowledge, our standards summary and formula sheets, our computer programming tools and online educational tool development and years of tutoring experience, you won't have to second guess if your student is well-prepared and qualified for the college or the career of their choice.

BookMark Tutoring not only can give you an assessment of your charter school's curriculum and validate that your child has standard requirements covered, but also tutor your child according to California standards for Algebra, Geometry, Intermediate Algebra, Statistics, Chemistry and Physic and more.


Santa Rosa Private Schools Tutor Programs

Those that attend Santa Rosa private schools often want their children to have the best education and become well-prepared for university and professional career paths. Because BookMark knows California standards, BookMark can determine just how your private school stacks up in meeting the standards requirements that your children will have to demonstrate a knowledge of.

Our private school academic tutoring programs prepare students so that they can start earning college credit courses in high school, and start preparing for AP, PSAT early testing, SAT and Advanced SAT testing well before the test dates. At BookMark Tutoring we integrate the salient points that AP and SAT tests focus on within the context of everyday subject tutoring. Having both AP and SAT analytical capability in high school helps students achieve higher grades in their high school classes and helps them focus their attention on specific topics that directly relate to what they will have to know for the SAT.

College Scholarship and Funding Resource Information

Planning for the best education and staying within a fixed budget can be a challenge if you are not well-informed about the wide range of scholarship options, loans and grants available and when to apply. Fortunately though with planning you can greatly reduce college costs without compromising the quality of education. In fact, if you are well prepared you can greatly improve your own and your children's education and reduce costs at the same time.

BookMark Tutoring can help you plan for a high quality education and at the same time lower academic costs, locate financial resources and help ensure acceptance to the school of your choice.

At Bookmark, we also offer tutor programs that prepare students to successfully compete for scholarships, low-interest loans and find work in areas that help them build their academic skills.

BookMark focuses on international, national, state and local sources for scholarship and grant funding. In Santa Rosa, there are a number of foundations that specifically support scholarship funding. Foundations can be found at most Santa Rosa and Sonoma high schools as well as Santa Rosa Junior College and Sonoma State University. Sonoma Academy is also a resource for scholarship information.

The scholarship and student academic foundations in Santa Rosa include the Santa Rosa High Foundation, The Montgomery High School Foundation and the Santa Rosa Junior College Foundation. The Santa Rosa Junior College Foundation supports scholarship funding through cooperation with private businesses, organizations and individuals.

The Santa Rosa High Foundation, a foundation that is dedicated to the improvement in education for Santa Rosa high school students and career opportunities is another place to look at and get involved with if you want to find out more about finding funding for specific education pursuits.

According to Santa Rosa's High School's Foundation's web site, "During the 2007-2008 academic year, the Foundation funded over $100,000 in academic enhancement requests, scholarships and student programs. Since the Foundation's inception in 1988, such grants now total more than $1,000,000. Additionally, the Foundation’s Permanent Endowment Fund now totals $319,000 with the receipt of estate and memorial funds. "

Santa Rosa Junior College Grants and Scholarships

The Santa Rosa Junior College Foundation provides over 700 scholarships for full-time students who will continue their education at SRJC or will transfer from SRJC to a four-year institution. These scholarships are based on scholastic achievement, financial need, academic field of study, community service, campus activities, and essay responses.

Through the Santa Rosa Junior College most students can obtain grants, scholarships or loans that will pay for books and tuition. . The Doyle ScholarShip as well as Pell Grants are available for most students. As well, many students can also obtain waivers for tuition if they don't have substantial resources.

Students can also receive scholarship funding through private organizations through Santa Rosa Junior College Foundation. The type and number of these scholarships change continually and so it is always best to check on a regular basis for new scholarships and new deadlines.

Below lists some of the scholarships that local business sponsor through the Santa Rosa Junior College: .


Agilent-BEST Scholarship: Santa Rosa Junior College Students, $500.00 for Electrical Engineering Students with a GPA, 2.75.

Agilent-BEST Scholarship: Santa Rosa Junior College Student Transferring, $1000.00 for Electrical Engineering Students, GPA 2.75.

American Indian Scholarship: Any Major, $175.00 - $750.00.

Annabel Baker Lagomarsino Scholarship - Ag/Farm Study: Agriculture major, $1250, farm work experience

Russian River Rotary: Major Culinary Arts, Viticulture or Hospitality, $500.00, Given to local high school students, GPA 2.5.

Sonoma County Abalone Network (SCAN) Scholarship: Marine Biology or Wildlife Management, $475, 3.0 GPA.

SRJC Floristry Scholarship: SRJC Floristry Certificate Program, $100 - $300, GPA 2.5

Sueños Scholarship: Any Major, GPA 2.5 or higher, Latino immigrants who are AB-540

Varenna Employees Scholarships: , Any Major, $750, Employed at Varenna, GPA 2.5.

The Santa Rosa Junior College Foundation is a non-profit that receives and administer gifts and funds from private sources. Earnings from investing contribute to the funding scholarships and programs at Santa Rosa Junior College that are designed to promote academic life of students, faculty, staff, and community.


Santa Rosa School District Academic Options

Today students must compete at the highest level to get accepted at the leading colleges and universities. In order to increase the chances of success of acceptance, Santa Rosa's school district offers various programs that will increase there chances of success. These programs are often administrated through different programs and the type of program depends on the specific high school attended.

Montgomery High School Tutoring

Montgomery High School, located near Montgomery Village in Santa Rosa, is know for its academic excel lance. The school offers students several different pathways to ensure that they are well-prepared for academic professional careers or well-prepared to find skilled work in emerging growth markets after high school.

Montgomery High School focus on academic excel lance revolves around the International Baccalaureate Program. Through this program students can earn college credits in high school that can be transferred to the best colleges and universities throughout the world.

BookMark Tutoring has developed its tutoring programs so that Montgomery High School students can succeed in the International Baccalaureate Program. With BookMarks trio of Math, Physics and Chemistry tutoring services, students can get answers to all of their academic questions from one tutor in one session. This one-stop tutoring gives parents an easy solution to solving all their children's homework problems efficiently. And it gives the student time to focus on the other projects that college admissions look for, like charity drives, community work, work experience, science fair projects, after school sports, club participation and beginning business endeavors.

Santa Rosa High School Tutoring

Santa Rosa high school is one of the better high schools in California. Santa Rosa High School has had the highest SAT scores in Sonoma County for the last 9 years. Santa Rosa High School also has a high number of students that complete college credit (through AP courses) while still in high school.

Students at Santa Rosa High School and Santa Rosa's middle schools also have more options for accelerating their academic programs. Santa Rosa middle school students that score well in honors pre algebra can often skip Algebra I at Santa Rosa High School.

In high school, Santa Rosa High students have options to take higher level calculus, physics as well as advanced computer technology and graphic design training. All the options give students at Santa Rosa High School the ability to move quickly through advanced academic requirements and put them in the best position to attend the top schools. Because Santa Rosa Junior College is just next store to Santa Rosa High School, it is often easy to take college courses for those that attend Santa Rosa high school. .

Keeping life less than overwhelming while trying to achieve academic excellence at Santa Rosa High School can be a challenge. However a tutor can make the task much easier. Students can achieve the highest grades in the most advanced classes in much less time with a tutor than without. Such time savings will not only keep your child's life more well-balanced, allowing him or her the time for the things they like to do, but also give your child a better appreciation for academic subjects.

BookMark also takes the frustration out of highly technical subjects like chemistry, physics and statistics and replaces it with easy-to-understand concise explanations all within the framework of real life interesting applications.

Physics Tutoring Program

At BookMark we tutor Santa Rosa and Sonoma County students so that they know what will be required to score well in the California Standards Physics test, the Advanced Placement Physics Test, The SAT Physics, the AP Physics and the CLEP standard physic tests. Having your child tutored in physics will increase the chances that they will earn college credit towards their college majors in high school and have more opportunities for scholarships and the best selection of universities to choose from.

At Bookmark, the physics tutoring program reviews all the fundamental concepts, equations, and calculation procedures that you need to know to solve physics problems proficiently and quickly.










BookMark offers math, science, engineering and computer science tutoring for all ages and all academic levels. BookMarks customers have included hundreds of full-time K-12 and college students as well as working adults seeking undergraduate and graduate degrees.

Our clients consistently report that they have significantly improved their grades with our tutoring services. Our clients also point out to us that their children have become much more independent learners, enjoy their school work much more and consistently score higher on their exams.


torus image picure illustrationOffer tutoring in basic Arithmetic, Algebra, Geometry, Intermediate Algebra, Trigonometry, Calculus, Differential Equations and Finite Mathematics. Tutoring programs follow California Educational Standards and Federal Common Core Standards. Experienced with college courses taught at Santa Rosa Junior College and Sonoma Statue University


Statistics Icon ButtonStatistics tutoring is available for high school AP statistics classes and statistics courses taught at Sonoma State University and Santa Rosa Junior College. Focus on descriptive and inferential statistics, probability and related topics such as z-tests, t-tests, matched pairs tests, confidence intervals, expected value, binomial, normal and Poision distributions, Chi Square tests, test of independence, one way and two way ANOVA and non parametric tests.

Also offer instruction in the use of the TI-83 andT-84 calculator, Excel and the R-Programming language to solve statistics problems.


chemistry tutoring santa rosa bookmarkChemistry: Chemistry tutoring is available for topics covered in AP Chemistry and for chemistry courses taught at Santa Rosa Junior College and Sonoma State University. Provide homework help, llaboratory report writing services and test preparation for chemistry topics that relate to atomic theory, the periodic table , bonding, thermochemistry, solids, liquids and gases, chemical equilibrium, acids and bases, electrochemistry, nuclear reactions, and organic chemistry.


Bookmark Santa Rosa Physics TutoringPhysics BookMark offers physics tutoring for AP high school physics courses and physics courses required for degree programs at Sonoma State Universality and Santa Rosa Junior College. Topics covered include single and multidimensional kinematics, static and dynamic rotational mechanics, sound and music, light and optics, electricity, magnetism, electromagnetic's, nuclear physics and quantum physics. Also provide assistance for writing physics lab reports.



Math Test Preparation: ACT, AP (Advanced Placement), CBEST, GRE, PSAT, SAT, SAT I


Electronics High school and college level electronics, digital and analog design, integrated circuit design, logic and circuit simulation


3D MathArt, Drawing and Design Lessons: Drawing, Color and Lighting, Fashion Design Basics, Geometry for Artists, Perspective for Artists

Graphic Design and Animation: Dreamweaver, Flash Professional, Illustrator, Photoshop

Technical Illustration Services and TutroingTechnical Illustration (3D): Linear Perspective, Architectural Design


Technical Writing: Research methodologies, Style Formatting


Flexible Scheduling

At BookMark we offer instruction that can meet the demands of your busy schedule. BookMark can meet with you weekdays, weekends and in the evening. We can also come to your home to teach you in person . Or we can meet you at the local library, the beautiful Santa Rosa Junior College Frank Doyle Library or at the Sonoma State University Charles M. Schultz library

Credit By Examination Program

For those that don't have the time to attend college, we can show you how you can earn transferable college credits through standard examinations such as the CLEP exams and the numerous exams offered through the testing offices of California Junior Colleges, State University and University of California educational systems. More importantly, we can provide you with the study material you will need to reduce study time and obtain a higher score on credit-by-exam tests

College Entrance Exam Preparation

We also offer tutoring for those that want to improve their score on college entrance exams such as the SAT and ACT. Or score high on high school exit and equivalency exams (GED).


CBEST and CSET Exam Preparation

For those seeking their teacher credentials, we offer complete test preparation services for the CBEST as well as the CSET multiple exam and selected CSET subject exams. We can not only teach you how to score high on these exams, but expand your knowledge of math, science and english beyond that of the CBEST and CSET with our in-depth subject specific tutorial sessions.


Results in Less Time

With BookMark Tutoring, it takes less time to earn an A and it takes less time to salvage a course from failure. Our client data suggests you can save 50 percent or more in study time with Bookmark.Not only that you will get a better grade and be more confident that you can earn better grades consistently.

Honors and International Baccalaureate Programs

For those in academic, honors, international baccalaureate or scholarship programs, BookMark offers tutoring not just for the specific content in these courses, but offers you valuable tips on how to prepare for college entrance exams, college board tests and college scholarship examinations.

Improve Your Job Skills

BookMark besides academic oriented tutoring, also provides tutoring services for those that need new job skills. Our job skills tutoring subjects include computer programming, web design and development, graphic design, animation and electronics circuit design. We not only have the software tools you need to learn new skills but we have the tutoring programs and training sessions that let you gain experience with these tools and learn them quickly.

Homework Sessions

For each tutor subject that BookMark offers it provides homework sessions as well as tutor sessions. Homework sessions focus on the solving of a students homework problems so that the student not only understands the concepts but also becomes proficient with solving the homework problems.

Focused Tutorial Sessions

Tutor sessions offers individual and focused tutor sessions on specific topics that the students need or wants to improve in. Although tutor session focus on specific topics in a subject, they are often customized to focus on the specific areas that the course focuses on.


Statistics Review and Summary Sheet

Our statistics review and summary sheet includes all the formulas and necessary short form tables and charts for you to efficiently solve problems and review for statistics tests, midterms and finals.

For the quick determination of z-scores and probabilities for given normal distribution models, the formula sheets provide easy-to-reference empirical and cumulative rules as well as critical z - values for commonly used confidence levels.

For mean and proportion tests all the formulas for the calculations of standard deviation, test statistics, confidence intervals, margin or error and sample size are listed for the most commonly used distributions.

The review sheets also include probability rules and guidelines for the selection of specific types of tests for different types of sample survey designs.

Statistics Applications and Calculators

BookMark Tutoring also develops statistics educational apps for the educational market. As part of this development effort we integrate statistics calculators into one central dashboard. We produce custom statistics dashboards that integrate different types of statistical calculators into easy-to-use statistical process and control systems that can be used to solve a wide variety of statistics problems. Our statistics dashboards can be customized to aggregate and compile real-time statistics data so that you can view statistics tables, graphs and charts can be viewed about your business or organization in real time.

Our dashboards can be designed to include custom algorithms that you need for your statistics work such as high powered decision logic. We can also build customized statistic calculators from the most basic to the most complex that interface directly with real-time corporation data, real time web traffic date or with employee and departmental data from Excel spreadsheets.


Statistics Resources

BookMark's individual and group statistics instruction combined with our supplementary educational statistics resources allow you to learn and apply statistics principles to the solving of statistics problems, the design of surveys and treatment studies and the interpretation of survey and treatment data.

Complementing our concise and to the point, how-to step-by-step explanations are our statistics problems and solutions database, our statistics summary and review sheets, our statistics online calculator databank as well as in-house statistics software.

Algebra I Supplementary Material

BookMark's Algebra I study guides, review sheets, database of problems and solutions, databank of Algebra I calculators not only make it easier to learn Algebra I , but easy to become proficient in solving the complete range of Algebra I problems.

Our Algebra I formula sheet reduces the amount of time it takes to solve Algebra I problems and provides the fastest and most efficient way to review and study for Algebra I quizzes, tests, mid-terms and final exams.

Our Algebra I checklist, which parallels California Algebra I standards and the Common Core National Education Standards for Algebra I , quickly lets us evaluate which topics you are proficient in and where you need more instruction time.

BookMark's Algebra I database of solutions and problems gives you plenty of practice problems and the solutions so you can quickly learn the procedures needed to solve the various types of Algebra problems.

Geometry Formula and Review Sheets

Studying for geometry tests, mid-terms and finals is made easier with BookMark's Geometry Formula Geometry Review Sheet and Geometry Postulate, Axiom and Theorem List.

Our review, formula and rules lists, also allow us to quickly asses your geometry knowledge and determine which geometric topics you need more instruction in.

The Geometry Postulate, Axiom and Theorem study guide lists the over 100 postulates, axioms and theorems that are used most often to solve geometrical problems and design geometric proofs. The guide focuses on the most important 30 postulate, theorems and axioms that are needed to solve geometry problems proficiently.

The geometric formulas sheets provide all the formulas that are used to solve problems and design proofs in analytical geometry. These formulas include the distance formula, midpoint of a line formula, radian to degree conversions, and the formulas for calculating geometric parameters of circles, squares, rectangles, parallelograms, rhombi, trapezoids and a variety of different types of triangles.

The geometric formula sheet also defines all the components of the different geometric shapes such as altitude, circumference, chords, diagonals, orthocenter's, radii, secants, tangents and others.

The geometry formula sheet also summarize volumes, surface areas and lateral areas of prisms, pyramids, cylinders, cones, and spheres.

The summary sheets also include all the equations and relations that are needed to solve polygon problems that involve the apothem, radius, central angle, exterior angles, perimeter and area of regular polygons and create polygon proofs..

Trigonometric Formula Sheets

In trigonometric proof tutor sessions, Bookmark provides summary sheets of common and not so common trig identities On these sheets are also listed the procedures that are most effective in simplifying and transforming identities Our identities sheet lists over 30 trigonometric identities as well as tabulates the most often used values for the sine, cosines and tangent functions of the unit circle

Trigonometry Special Studies

For those that are interested in the application of trigonometry BookMark offers its trigonometry special studies program. In this program students learn the basics of computer programming and how to apply trigonometry to create computer software programs. Students create computer programs that use trigonometry formulas to produce sounds and graphics that can be used for the development of mathematical programs, engineering simulators and computer aided design (CAD) software packages.

Physics Formula Sheets

Because physics is one of the most formula intensive sciences we provide extensive formula summary sheets for each of the major physics subject areas.

BookMark's Physics Formula and Summary Sheets summarize the equations needed for Classical Mechanics, Thermodynamics, Electromagnetism, Linear and Rotational Kinematics and Quantum Mechanics in a concise and easy to use format.

The summary sheets also includes the most often used physical constants and conversion factors that are necessary to solve physics problems quickly and easily.

BookMark's physic tutor topics includes two-dimensional force equations, rotational kinetics, atomic energy, conservation of energy for potential and rotational, translational, linear kinetic energy. BookMark's Electromagnetic Formula and Summary Sheet lists equations needed to calculate the electric fields, forces, charges, energy and magnetic fields associated with the movement of charges in free space or when exposed to electric or magnetic fields.



BookMark Tutoring Press Releases

Bookmark Tutoring announces Algebra Formula Sheet geared for Algebra I high school students.

BookMark Tutoring (Santa Rosa, CA) has announced the first in a series of formula and review sheets as part of its Excellence in Tutoring program. The new sheets (cheat sheets) are designed to simplify and expedite the learning process. According to Mark Stansberry, Instruction Director at BookMark Tutoring, “The Algebra I formula and summary sheet has been designed so that it would increase the student’s learning productivity and provide the tutor's with an easy to use instruction guide and Algebra reference sheet. The review sheet summarizes all the essential formulas and rules that the student must know to gain the highest level of proficiencies in Algebra I. Based on State Board of Education Standards (California) and the new Common Core National Education Standards, the review sheet serves not only as a easy to use reference sheet for the student to memorize and use, but it also serves as a check list of topics that the tutor must ensure that the student knows and understands.

Complemented with the tutors own knowledge of the standards and the questions for the standards test, BookMark tutors use summary sheets so that can ensure that all necessary facts are taught to ensure 100 percent standards compliance and the highest possible grade for the student.

Officially called “Algebra I: An Educational Summary, Formula and Rule Synopsis” the sheet includes the formulas for the three standard equations covered in Algebra I: the line, the parabola and the indirect variation. Formulas for calculating the slope of the line, the vertices, roots (x-intercepts) of the parabola, asymptotes, domain and range of the inverse functions (indirect variation). The summary sheet also includes the radical and exponent rules and an all important summary of the critical equations for the solving of mixture, rate and sales problems. . A short list of perfect squares was added so that students can work with and factor second degree equations quickly. Completing the square formulas, as well as common factor formulas such as the difference of squares and the sum of squares are given.

The Algebra I formula and study sheet has been specifically designed for students throughout Sonoma County that take Algebra I at Montgomery High School, Maria Carillo High School, Piner High School, Santa Rosa High School and Santa Rosa Junior College.

About BookMark Tutoring

Bookmark Tutoring, based in Santa Rosa, California, offers in-person and online tutoring for mathematics, chemistry, physics as well as support subjects such as computer science, graphic design, animation and technical illustration.  The company also produces course material and study guides for Santa Rosa and Sonoma County students to use to further improve their learning productivity.



























































References and Resources

Effect of Tutoring on Scholastic Performance Educational Outcomes of Tutoring: A Meta-analysis of Findings, American Education Research Journal

Peer Tutoring, A Teachers Guide

Effectiveness of Before and After-school Tutoring Programs as Measured by the Mississippi Curriculum Test ... By Patricia Marie Goyette, The University of Southern Mississippi

Science Content Standards for California Public Schools


Santa Rosa High School Foundation

Montgomery High School Foundation

Doyle Scholarship



Site Map Links









Directory of Santa Rosa Directories

Santa Rosa Junior College Mathematics Tutoring

Santa Rosa Junior College Calculus 1, Math 1A Tutoring

Calculus Problem and Solutions Database

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Wikipedia Discrete Probability Distribution, http://en.wikipedia.org/wiki/Probability_distribution







































































































QUICKNOTES (Cheat Sheets)

In support of its educational services, BookMark Tutoring produces and publishes the QuickNotes Series of Formula and Review Guides. These concise subject overviews provide BookMark's clients with the well-organized notes they need to consistently save time and score high on exams.



BookMarkTutoring blends computer science with math, science and graphics. Students not only learn the basics needed for their computer classes, but also how to apply the knowledge to make their academic and professional life more enjoyable, interesting and practical. At Bookmark students create online calculators, graphing progams, graphic designs all in a framework that builds on and complements their academic foundation.


BookMark's Online Instructional Design Board

Ms Goose's Calculator - Try it Out

Ms. Duck's Trigonometry Calculator

Bird of Paradise Degree-to-Radian Angle Conversion Calculator

Mathematically Driven Image Generator

Actionscript 3 Projects

Dreamweaver Web Page Layout Projects

Two-Way Chat and Drawing Board

Computers have become an integral part of everyday life and everyday business. Many K-12 programs and college degree programs now require, or soon will require, computer science as part of their curriculum.

BookMark Tutoring provides tutoring for students taking computer science courses at the university level and the K-12 level. BookMark teaches basic computer science concepts, fundamental computer technology terminology and code development. It also provides assistance for high school and college level computer programming projects.

BookMark covers all the computer programming bases that today's students and professionals need to know. This includes HTML, CSS, XML and other markup languages like SVG, BookMark can show you how. BookMark also provides instruction in programming languages such as ActonScript, C++, Java, Perl, and Python. For web applications BookMark can also help you learn JavaScript, PHP, MySQL, Ruby, VBScript.


Computer Programming for Kids

For kids, BookMark makes learning computer technology interesting, fun and relevant. Besides the basics students need to get up and running, BookMark shows students how to write code that solves math problems, draws geometrical figures and calculates projectile position.

Geometry Special Studies

In our geometry special studies program students apply geometry principles and formulas to create computer programs. Students also learn the basics of computer programming and how to apply geometry to create computer generated graphic designs. The program is designed to reinforce geometry principles and show students how geometry is used to create software products, games and apps



In support of the computer tutoring program, BookMark produces code databases. These code databases allow students to start producing working code quickly and develop large scale programs using an object oriented or modular approach.



Office Automation: Microsoft Office, Excel, PowerPoint, Word, Google Docs, Adobe Acrobat Pro

BookMark Educational Apps

Through BookMark's educational apps development program, BookMark develops and codes its own apps. BookMarks apps development program currently focuses on the development of paint and drawing systems, mathematically generated paint brushes and mathematically driven image generators.

One such image generator is used to generate flower, video game icon, iris and 3D virus images.


Bookmark provides everything you need to know to design, implement and maintain your web site. Learn how to create web site graphics with Adobe Illustrator and PhotoShop, design web pages with Adobe Dreamweaver and create animations with Adobe Flash. As part of web sited development tutoring, you can also learn what you need to know about web programming languages such as JavaScript, HTML5, PHP, MySQL, SVG, XML, CSS and VBScript.


BookMark's tutor sessions give you the flexibility to meet your busy schedule. At BookMark, you can drop in for just a one hour homework or review session, schedule a series of sessions or select a subject you want to learn about from our growing offering of tutorial sessions.

BookMark besides individualized tutor sessions, offers specific topic oriented tutor sessions. These sessions, built on California State Education Board standards, prepare students for future courses as well as high school and college credit-by-exam tests.

The content taught in the tutorial sessions parallels educational content found in the standards of the California State Board of Education, the Common Core National Education Standards, the College Board, Santa Rosa Junior College , Sonoma State University and San Francisco State. For high school and middle school students our tutor sessions focus on the course content that is taught in Montgomery High School, Santa Rosa High School and Sonoma Academy.


Statistics Tutorial Session Descriptions

Statistics Icon ButtonStatistics: Statistics involves the making of conclusions about populations based on sample data such as market survey data opinion surveys and treatment variables. In business, surveys are often used to determine what products and services have the best chance for success. In medicine, statistics are used to determine if a type of medication is effective or not. In law, statistics are used to draw conclusions and develop successful legal prosecution and defense strategies.

BookMark Tutoring statistics tutoring sessions are designed to meet the needs of students and working professionals.Our tutoring session are designed to support statistics taught in Santa Rosa high schools, Santa Rosa Junior College, Sonoma State University,San Francisco State and various online statistics courses including the Brigham Young University statistics course. the Walden University online course as well as courses from DeVry University, Phoenix University, and the American Public University.

BookMark offers its statistics tutoring sessions for all different levels of students including middle school, high school students and college students.

Besides individualized tutoring for statistics, BookMark also offers complete statistics preparation programs that allow students to obtain college credits through examination and score high on the AP statistics test, the Statistics CLEP exam, and online statistics courses.

For those that are seeking white, green and black belt statistics certificates needed for employment, our instruction and course materials will give the basic statistic skills you must know and allow you to implement Six Sigma Quality standards for manufacturing, marketing, sales, engineering, information, financial and other business processes.

Statistics Tutoring Sessions

BookMark's divides statistics instruction into distinct statistics tutoring sessions topics Major statistics tutor sessions include

Descriptive Statistics Tutorial Session

Statistics Graphs and Tables Tutorial Session

Probability and Counting Tutorial Session,

Discrete Probability Distributions Tutorial Session

Normal Distribution Tutorial Sessions

Sampling Distribution Tutorial Sessions,

Confidence Interval and Survey Sample Size Tutor Session

Hypothesis Tests Tutorial Sessions

Linear Regression Tutorial Session

Chi-Square Distribution and Tests Tutorial Session

Analysis of Variance Tutorial Sessions

Non Parametric Statistics Tutorial Sessions,

Statistical Process Control Tutorial Session,

Sampling and Simulation Tutorial Sessions

TI-83/84 Statistics Graphing Calculator Tutorial Session.


Statistics Survey Fundamentals Tutorial Session

At the heart of statistics is the survey. From surveys, data is gathered about a sample population for determination of a population characteristic. For a business, these surveys may be focused on questions that relate to the acceptance of businesses product or service. In medicine, surveys may include results of medical tests that indicate the effects of a specific medical treatment.

Today, businesses and organization use web traffic statistics to analyze market trends and interests. These surveys are often automated through IP robots and can gather and analyze statistical data about the demographics and characteristics of a wide number of populations.

Sophisticated statistics programs are available that use IP addresses and IP address personality databases to determine characteristics of web site visitors such as s income, gender and ethnicity, These computer programs then automatically aggregate that data into statistical survey summaries that are displayed to the business, sales and marketing staff at the company for further analysis and use in the decision making process.

Statistics Survey Tutorial Sessions

In BookMark's survey tutor sessions we focus on the different types of survey designs and discuss their relative strengths and weakness. Sampling techniques are also discussed and defined in relation to the validity of survey results. Sampling techniques often discussed in tutor sessions include random sample, simple random sample, convenience sampling, systematic sampling and stratified sampling.

Descriptive Statistics Tutorial Session

Fundamental to statistics is data characterization. Data characterization involves the summarization of data through a set of descriptive statistics (numbers that represent the key characteristics of the population).

Descriptive statistics that are used to most often describe a set of data values are the mean (average), the variance, the standard deviation, the range, the median, the mode and the shape of the distribution or data curve. Outliers, data values that are unusually high or low, also are used to describe or summarize sets of sample data.

In BookMark's descriptive statistic tutor sessions the different types of descriptive statistics are clearly defined in relation to how they are used and how to interpret their meaning. Discussed are measures of center (mean, median, mode , midrange and distribution skew), measures of variation (range, standard deviation, variance, range rule, empirical rule), chebyshev's theorem, coefficient of variation), and measure of relative standing ( z-scores, percentiles, quartiles and box plots and 5 number summaries).


Statistic Graphs and Tables Tutorial Session

Displaying of statistics data in an easy to understand and explain format is essential to making persuasive arguments, conclusions and statistics reports.

In BookMark's statistics graphing tutor sessions the fundamentals needed to construct your own statistics charts and how to generate statistics charts from graphing calculators and statistics software packages.

BookMark the most popular statistics charts and tables used in business and science including frequency tables, histograms, standard line and bar graphs, stem-and-leaf plots, scatter plots and box-and-whisker plots (5 number summary).


Probability and Counting Techniques Tutorial Session

Probability is an important business and scientific tool. In business logistics probability is used to determine the best shipment routes. In financial risk management probability is used to time business investments so optimum yields are obtained. In chemistry, probability can be used to determine the odds of a chemical reaction or whether a medical treatment will be effective. In physics probability is central to an understanding of modern atomic theory.

Probability, as opposed to statistics, allows one to calculate the likelihood of the occurrence of a specific event or specific events based on a total set of possible events.


In BookMark's probability tutor sessions the basics of probability are discussed. These basics are then applied to business, medical, and engineering problems.

Basics covered in probability tutorial sessions include fundamental definitions, such as the definition of an event, independent and dependent events as well as the meaning and use of probability nomenclature and symbols.

In the probability tutor sessions we also show you how to use different probability methods and formulas to solve specific classes of probability problems. In these tutor sessions you will learn how to calculate sample space from the number of symbol-token arrangements, how to use counting methods such as trees to determine probability of dependent events, and how to use permutations and combinations formulas to calculate probabilities of specific sets of events from large number of possible events,.

In the probability tutor session we also demonstrate independent and dependent definitions with examples that incorporate probability rules (probability with replacement and without placement).

Probability rules explained and used in working examples include the addition rule, the multiplication rule, the complements rule, mutual exclusive and disjoint rules and conditional logic rules. The use of the Venn diagram is also covered specifically within the context of conditional probability.


Discrete Probability Distributions Tutorial Session

Discrete probability distributions involve discrete random number variables (variables that have data values that can only be whole numbers).

Examples of discrete probability distributions include the tossing of a coin and the rolling of a die. In both examples, each random variable outcome can be be represented with a random variable (zero for tails and one for tails and a number for each of the faces of the die).

A discrete probability distribution can be represented with a table or a graph. In a table, the probability of the occurrence of a random variable is listed in one row and the value of the random variable is listed in the other row (in the case of a die, the numbers on the face of the die are listed in one row and the probability of the occurrence of each face in the other, 1/6).

Common discrete probability distributions used in statistics include the binomial probability distribution, the Poisson distribution. the Bernoulli distribution,the geometric distribution, and the negative binomial distribution.

In BookMark's discrete probability tutor sessions, generalized distribution formulas for the calculation of the mean, standard deviation and variance for each type of discrete probability distribution.

The discrete binomial probability distribution is one focus of the session. The binomial distribution is defined along with the requirements that must be met to use it. Additionally, the formulas needed to calculate the the mean, standard deviation and variance of a binomial distribution are given and calculations explained in working examples. . Additionally, how to use the TI-83/84 binomial statistics functions to calculate binomial probabilities is illustrated.

The Poision distribution is another discrete probability distribution covered in this tutor session. Applications and use of the Poision distribution formulas as applied to interval based data, such as rate data, are illustrated in the context of a variety of statistics problems.


Normal Distribution Tutorial Sessions

Normal distributions are used when the random variable is continuous (the variables can have decimal values) and the requirements for a normal distribution, such as normality, are met.

In normal distribution tutor sessions, the normal distribution and standard normal distribution is defined. Examples are discussed that illustrate how to find probabilities using the standard normal distribution tables, the TI-83/84 calculator and Excel software. In the session, you also learn how to calculate z-scores and use these z-scores to determine probabilities for different z-score ranges. As well, you are also shown how to calculate z-scores from known probabilities.

The central limit is also a major topic in normal distribution tutor sessions. The central limit theorem allows you to quickly assess whether the mean of a small sample provides evidence for or against a claim.

Small variations in the mean of small samples can indicate quickly whether market trends, political opinions manufacturing processes or demographics are changing. In BookMark's statistics tutor sessions, we show you how to calculate the standard deviation of a small sample with the central limit theorem formula. And we show you how to use the results to test a claim about market trends, political opinion, manufacturing processes and demographics.

The normal distribution tutor session also covers the use of the normal distribution for applications that would normally require the use of the binomial distribution. Requirements for the use of the normal distribution for a binomial distribution are summarized and applied to several different types of statistics problems.

Confidence Interval and Survey Sample Size Tutor Sessions

Determining the right sample size for a survey allows you to lower survey costs and increase the probability that your survey results match that of the population characteristic under test. However, minimizing the sample size will lower the precision in which you are able to quantify the population parameter under test. Knowing the probable error of your sample statistics requires that you always construct a confidence interval for your survey statistics.

In our confidence interval and sample size tutoring sessions, BookMark Tutoring presents the most often used sample size formulas, explains the variables in the formulas and shows you step-by-step how to use the formulas to compute your needed sample size.

The procedural steps to calculate a confidence interval that is the error range obtained for a specific sample size are also presented in survey sample size tutorial sessions. In general, larger sample sizes let you estimate the value of the population parameter under study with higher precision (the population parameter will fall within a smaller prediction range).

The procedure to calculate sample sizes and confidence intervals is covered for surveys that are used to predict the mean and proportion population parameters.

The calculation of confidence intervals and sample sizes requires that you understand confidence levels, margin of error and critical z score vales. In this tutor session, these terms are further explained within the context of surveys, sample size and confidence interval calculations.

How to calculate confidence intervals using formulas for the TI-83 / 84 calculator for the standard normal distribution (z) and the student distribution (t) are illustrated. Also explained are the conditions that must be evaluated to select whether the confidence interval should be calculated using the z or t confidence intervals.

This statistics tutor session also provide tips and guidelines on survey design so that your sample will better reflect the general population parameter you are trying to determine.

Hypothesis Test Tutorial Sessions

Hypothesis tests are part of the branch of statistics known as inferential statistics. In inferential statistics, a conclusion is made about a characteristic of a population based on sample survey data.

In hypothesis testing, the mean, proportion, standard deviation or variance is calculated from survey data and compared against an existing claim about a population parameter. For example, a consumer advocate group might collect data on the gas mileage of a specific type of car and compare it against the manufacturers' claimed gas mileage (the null hypothesis). If the survey data suggests that the sampled data is different than the manufacturers claim, the consumer group would make an alternative hypothesis and then use a hypothesis test to determine the probability that the null hypothesis (the population claim) is true.

In hypothesis tutor sessions, we show you how to quickly and confidently determine the null hypothesis and the alternative hypothesis. As well, we show you how to calculate the probability that a null hypothesis is true based on the sample data's statistics.

In the hypothesis sessions we also show you how to do complete hypothesis tests quickly using the TI-83 / 84 calculator or using normal distribution tables and formulas. Also learn how to make quick estimates of the validity of a claim without calculators or statistics formulas and tables.

BookMark's hypothesis tutor session covers all the basics of hypothesis testing for mean, proportion and variance hypotheses for either single or two population sample studies. We show you how to perform each step in hypothesis testing: calculation of the test statistic, determination of the critical values and regions, calculation of the p-value and the selection and conversion of the significance level to a p-value or critical z score. Procedures required for p-value based methods for single-tail and two-tail test are also not forgotten.

Other topics covered in the hypothesis tutor session are Type I and Type II errors and the Power of a Hypothesis.

The hypothesis tutor sessions offer complete step-by-step how to examples for statistics problems that require you to test a claim about a mean, a proportion, a standard deviation, the difference of two means, difference of two two proportions or the difference of two standard deviations or variances. We also explain the how to select the right type of hypotheses test, such as z or t test selection.

There are several different methods for the testing of a hypotheses. In the hypotheses tutoring session we cover the critical value method and the p-value method. Additionally, we show you how to implement each of the different methods using the standard statistic formulas and tables, using the TI-83/84 hypothesis testing calculator functions or using Excel's hypothesis testing functions (for mean, proportion, standard deviation and variance claims).

Linear Regression Tutorial Sessions

Linear regression is used to determine if a linear relationship (straight line relationship) exists between two variables. In agriculture, farmers use linear regression to predict the yield of crops based on different weather and soil conditions. In medicine, researchers use linear regression to determine if there is a relation between the dosage level and healing time. In science, researchers use linear regression to determine if there is mathematical relationship between two variables.

In elementary statistics linear regression of two variables is often emphasized. In higher level course, multivariable and curvilinear regressions are taught.

BookMark Tutoring can help you understand linear regression as well as multiple regression. We can also teach you the basics about linear equations if you missed that in your algebra courses.

In our linear regression tutor sessions, students are shown how to construct scatter, linear regression and residuals plots by hand with the TI-83/84 calculator and with Excel software.

We also explain how to interpret linear regression results from the calculator or your software. This includes an explanation of linear correlation coefficients, coefficient of determination and residuals, and the identification of outliers

Also covered in linear regression tutor sessions are the procedures for regression based hypothesis tests such as the hypothesis test for correlation (using the r test statistics or the p-value methods).

Rules for using regression equations for predictions are also emphasized along with how to interpret linear regression plots and residual plots.

Variation and prediction intervals are also covered in college level statistics courses about regression. BookMark also covers these topics in its tutor sessions. Prediction intervals are similar to confidence intervals. For the calculation of prediction interval, as with confidence intervals,one must also be able to calculate the standard error of the estimate


Chi-Square Distribution and Tests Tutorial Session

Chi-Square tests are not only used to test if the variances of two populations are equal, but also if a specific sample distribution matches another type of distribution.

In BookMark's Chi-Square Distribution and Tests tutor session we summarize the Chi-Square distribution formulas, properties and variable definitions. Included is the Chi-Square test statistic formula, the definition of degrees of freedom, methods for the determination of chi-square critical values as well as the formulas for the calculation of confidence interval for the population standard deviation and variance.

The three main types of Chi Square tests include the Goodness of Fit Test, the Chi Square Test of Independence and the Chi Square Test of Homogenous proportions. In the Chi Square statistics tutor session, each of these tests and the relationship to specific types of survey designs are emphasized.

The Goodness of Fit Chi Square test procedures that are also covered let you determine if a sample distribution matches a normal distribution, a discrete distribution or a distribution to another sample or arbitrary chosen population distribution.

The test of independence lets you determine if their is a dependency between two variables and the homogeneous proportions tests lets you determine if the population parameters have the same proportion in different sample groups.


Analysis of Variance Tutorial Sessions

Analysis of Variance or ANOVA for short is a statistical technique used to test if three or more sample population means differ when different stimulus are applied to different sample groups It is also a way to test if there is an interaction between stimulus variables ANOVA analysis are used in a number of different types of business and industry applications. In agriculture an ANOVA could be used to determine if mean yield of three different crop samples that are treated with different fertilizers are different. In human nutrition, ANOVA tests could be used to determine whether the mean weight loss from three different types of diets are the same. In environmental engineering, ANOVA tests could be used to determine whether the mean gas emissions from four different types of cars is different.

In the two-way ANOVA, the analysis of variance test is used to determine not only if the population sample means are equal when exposed to a stimulus, but whether or not selected external variables or cofactors have an effect on the mean of the population sample means.

In a two way ANOVA, you still have three or more sample populations with a unique characteristic. You also have data from subcategories (variables or cofactors) that allows you to see if the variable or cofactor effects the sample mean values. That is there is an interaction between the cofactors and the treatment. .In human nutrition, two way ANOVAs could be used to compare the mean weight of three different age populations and determine if the gender had an effect on the mean weight. In this case, the three population samples would come from three distinct age groups and the cofactor would be male or female. From the weight data you could determine if gender affected the mean weight of specific age group.

In BookMark ANOVA tutor sessions, one-way and two-way ANOVA tests are explained, standard null hypothesis are summarized and the procedural process to determine whether to reject an ANOVA null hypothesis is outlined and stepped through for different types of statistical studies.

Besides the table and formula manual methods for testing the claim, the use of Excel as well as online ANOVA calculators are detailed. Additionally, the ANOVA tutor sessions explain how to interpret the print-outs obtained from Excel ANOVA tests and online ANOVA calculators are interpreted..


Non Parametric Statistics Tutorial Sessions

Non-parametric tests are statistics tests that don't require the distribution to have a specific shape. Because non parametric tests are not dependent on the type of distribution, they are often called distribution free tests.

Non-parametric tests statistics are often calculated to test claims about a median of a single population, claims about the difference of two population medians, claims involving matched pairs, and claims about nominal data in two categories,

BookMark's non parametric tutor sessions define the terms you need to know to perform non parametric tests, summarizes the formulas used to perform nonparametric tests, lists the requirements that need to be met before a non-parametric test can be applied, and outlines the procedure for conducting a hypothesis test based on any one of the many non-parametric test statistics.

BookMark's non-parametric statistics tutor sessions explain the various non-parametric sign tests used to solve typical application problems. In the tutor session the sign test, the Wilcoxon Signed Ranks Test for Matched Pairs, the Wilcoxon Ranked-Sum Test for Two Independent Samples, the Kruskal-Wallis test, rank correlation and runs test for randomness are highlighted.

Statistical Process Control Tutorial Session

Statistical process control is central to improving the operations of organizations and businesses. The methods of statistical process control are applied to manufacturing marketing, sales, logistics, financial and end-to-end processes to minimize operating costs, achieve maximum manufacturing yields , increase customer satisfaction levels, maximize profits, and improve sales growth levels.

Statistical process control has expanded beyond manufacturing to the domains of information workers, business managers, executives, marketing and sales.

Today for company's to operate at peak efficiency rates, all types of employees must work with business process management software and evaluate statistical process control data. Statistics are used corporate wide to allow managers and executives to pin point inefficiencies in their operations and take steps or create automated procedures to eliminate inefficiencies..


Because businesses and organizations are using statistics more and more to become more efficient, more cost effective and profitable, business professionals must be able to use business process management software and understand the terminology and methodologies used in statistics process control.

These skills along with the ability to interpret statistical process control data have been statistically linked to the ability to effectively make the best business, marketing, sales, financial, manufacturing and operations decisions

The demand for statistical process control has been not only furthered becuase of advanced manufacturing automation technology, but also because of the emergence of wide-spread company networks and the Internet. Becuase of the ability to obtain and extract data from every PC connected to the Internet, companies now have the ability to monitor and aggregate real time company statistics as well as real time Internet statistics. This ability has enabled companies with tens of thousands of employees, hundreds of retail outlets, thousands of different products and hundreds of thousands of customers to significantly reduce operating costs and increase sales growth rate.

In BookMark's statistical process control tutor sessions, the fundamental principles of statistical process control are summarized and the procedures necessary to determine the stability of a process with various different types of control charts are explained in the context of either the students specific problems or examples from BookMark's statistical process control problems and solutions database.

Typical statistics problems discussed statistical process control tutor sessions involve run charts such as the R Chart (range), the X Chart (means) and the P chart (proportions) . Formulas for the calculation of the charts and associated upper and lower control limits are summarized and then illustrated in step-by-step example problems. In the tutor sessions, interpretation of the charts is detailed within the context of different application scenarios.

TI-83/84 Tutor Sessions

Different teachers and different schools emphasize different topics and slants in statistics courses. Today, many statistics classes require that the student use the TI-83/84 calculator for tests and homework. Because of this, BookMark Tutoring, offers complete TI-83/84 instruction.

In the TI calculator tutor sessions you will learn how to use the TI-83/84 to help you reduce statistics problem solving times that involve every type of statistic formula and table This includes calculations of means, proportions, standard deviations, medians, inter quartile range, test statistics, confidence intervals and hypothesis test results for all types of distributions including the binomial, z, t, chi, poision and geometric distributions.

To facilitate, the learning of the TI-83/84 statistics functions quickly, we use real-life problems and explain how they are solved using the calculator. For each problem, we show each operational step in the TI-83/84 sequence and the different parameters that need to be entered in each step. The results that the TI-83/84 displays are explained within the context of the problems solution.

Classical Methods Tutorial Sessions

Even in classes that emphasize the TI-83/84, students often still must show that they know how to perform hand-calculations and use statistics tables and formulas. For those that must use hand calculations and tables, BookMark Tutoring will show how to use the tables and formulas in the most efficient manner for the determination of a variety of statistics problems that involve sample sizes, test statistics, confidence intervals, hypothesis testing and margins of error.



Algebra I: Algebra I is essential for the development of skills necessary for the solving of basic business, engineering, architectural and science problems. The foundation that Algebra I provides is also essential to the study of higher level mathematics and the development of the skills necessary to solve complex technical problems.

BookMark Tutoring provides Algebra I tutoring so that the student not only excels in standards, honors and college level Algebra I courses, but obtains an algebra foundation so that the content of more advanced mathematical courses the student will have the skills necessary to perform better in more advanced math classes. .

BookMark divides Algebra I into several different tutor sessions topics. The exact content of these sessions are often tailored to the exact requirements of the Algebra I course that the student is taking.

BookMark's Algebra I tutor sessions include linear equations, parabolic equations and inverse variation equations sessions. In addition to these sessions we have a factoring session, an exponents session and algebraic expression simplification session.


Factoring Tutorial Sessions

Factoring of algebraic expressions is a basic an essential algebraic skill. In Algebra I students learn several different factoring methods used to factor first and second degree equations. Algebra I emphasizes the factoring of second degree equations and expands on factoring methods for first degree equations. Factoring methods emphasized in Algebra I include the factor-sum method, the quadratic formula method, the completing the square method and for some courses, the grouping method.

Students are also taught to find common factors and how to factor these out of algebraic expressions. Least common denominators rules are also used for factoring out rational algebraic expressions in Algebra I.

Exponents Tutorial Session

Exponents are used to indicate how many times a variable or number is to multiplied by itself or how many times the reciprocal of a number is to be multiplied by itself.

In BookMark's exponent tutor sessions the four basic exponent rules are summarized. The exponent multiplication, division, distribution and reciprocal rules are all used to simplify complex algebraic expressions that contain exponents.

The student also learns how to derive the exponent rules so as to ensure that they always apply exponent rules correctly.

Radical Expressions Tutorial Session

Radical expressions, algebraic expressions that contain the root symbol, must be understood in order to solve many types of algebra problems. In BookMark's radical expressions sessions, the square root, cube root and nth root radical expression notation is explained. The relation between exponent notation and radical expression is emphasized. Students are also shown how to convert between radical expressions and exponent notation. Mathematical rules of exponent and radical expressions are also summarized and explained and used to simplify algebraic expressions and solve different algebra application problems.

Polynomial Tutorial Session

Algebra I requires that the student know the definition of a polynomial, how to identify different types of polynomials as well as how to add, subtract, multiple and divide polynomial equations. These procedures are used in Algebra I to simply rational expressions and obtain the factors of a polynomial.

In BookMark's polynomial tutor sessions the definition of a polynomial is defined and the procedure to identify the type of polynomial (monomial, binomial or trinomial) the degree of the polynomial, and the coefficients of the polynomial are listed.

Emphasizing polynomial definitions and terminology ensures that the student not only knows how to work with polynomials, but also understands necessary polynomial vocabulary. Understanding the polynomial vocabulary is emphasized because it gives the student the the skills to effectively understand the content of mathematics lectures in Algebra I and in more advanced courses. .

Linear Equations Tutorial Session

In the linear equations tutor session, the three forms of a line equation are introduced, methods to plot lines illustrated and the calculation of slope and the y-intercept are detailed.

Methods and formulas used to determine if lines are parallel, perpendicular or identical are summarized and explained. Problems that require the determination of an equation of a parallel or perpendicular line are solved.

Systems of linear equations, a set of two or more linear equations, are a main topic in Algebra I. Students given a system of linear equations must be able to find the intersection point of the lines that the linear system represents.

All three methods to solve a system of linear equations, graphical, substitution and elimination, are illustrated step-by-step in the linear equations tutor sessions.

Solving systems of linear inequalities are also taught in linear equations tutorial sessions. Because the solution for a system of linear inequalities is a graphical region as opposed to a point of intersection, systems of linear inequalities are solved with the test point method. The test point method requires that the linear equations be first plotted and then test points selected within each of the graphed regions. The test point is then evaluated with each regions inequality equation to determine if the region is a solution set of the set of linear inequalities.

Indirect Variation Tutorial Session

Indirect variation equations, like line linear equations and parabolic equations, have a generalized shape. The plot of an indirect variation will reveal two curves that are symmetrical and open in opposite directions.

In indirect variation tutor sessions students are taught how to recognize the general form of an indirect variation equation, how to determine its x and y asymptotes, its axis of symmetry, origin of symmetry, the shaping constant and the horizontal and vertical translation constants.

Students are also shown how to write a indirect variation equation for a given graph based on x and y translation from the base or parent indirect equation.

How to determine the domain and range of an inverse variation equation with formulas for the domain, range and asymptote. These formulas not only provide an easy way to determine the domain, range and asymptotes, but also provide insight into the mathematical relationships between asymptotes and domains and ranges.

Parabola Tutorial Session

A quadratic (second degree) equation when graphed will always form a parabola. Parabolas, which are open ended curves, are used to solve many types of business, engineering, graphic design and architectural problems. In physics, the parabola is used to determine the path of projectile under the force of gravity. In environmental engineering , the equation of a parabola is used to determine the position of parabolic solar mirrors for optimum energy output. In business, quadratic equations are used to compute the maximum price for a product to maximize revenues or profits.

In parabola tutor sessions, the two forms of the equation of a parabola are listed and explained. Students are taught how to determine the parabola's vertex, the axis of symmetry, whether or not the parabola opens up or down, the minimum or maximum point on the parabola, and the x-intercepts (roots) of the parabola with the standard and vertex forms of the parabola equation. Students are also shown the most efficient way to plot a parabola (using x-coordinates that are symmetrical about the parabola's axis of symmetry).

Word Problem Tutorial Session

In Algebra I students must learn how to solve basic chemistry, physics graphic design, architectural and business problems using a variety of different algebraic techniques. Types of word problems that students must solve involve rates of speed, rates of work, concentration of liquid mixtures, sales levels, depreciation and simple and compound interest.

Word problems are often not a strong point with students. However, BookMark's students have relatively little difficulty with word problems. In BookMark's word problem sessions we summarize and list the most commonly used formulas for the four major types of word problems. We show how to determine which formulas are appropriate for each different type of word problem and how to extract the necessary variables from the word problems. Students who learn our techniques for solving word problems can complete word problems in much faster time than most students and with fewer or no errors.


Geometry: BookMark provides geometry tutoring lessons and programs that cover all of the California Standards for geometry including honors standards. Our geometry tutorial sessions have been specifically designed for those taking geometry in Sonoma County and Santa Rosa middle schools, high schools and colleges.

Topics covered in geometry tutor sessions include the axioms, theorems and postulates used to solve geometry problems and develop geometric proofs. The sessions also emphasize analytical geometry problems.

Bookmark's geometric tutor sessions are designed to provide the foundation for students to excel not just in the current geometry course, but also to solve problems found in architecture, graphic and fashion design, engineering and physics.

Logic Tutorial Session

Deductive, inductive and boolean logic are central to the development of skills necessary in computer science, electronic design, statistics, law and business. With logic skills, students can make decisions that involve many variables in a methodical way.

In the logic tutor session, students learn the basic definitions of logic statements. This includes the definitions of: counterexample, conjecture, converse, negation, inverse, contrapostiive and counterpositive logic statements. Students learn how to identify logic statements and derive specific logic statement types from a given logic statement,

Conditional logic statements (if then statements) are used extensively in the development of computer programs, legal analysis procedures and solving of probability problems. In the logic tutor session students learn the conditional statement structures, how to write and interpret conditional logic statements. Examples of the use of conditional logic statements to design software programs is demonstrated.

Boolean logic is a mathematical system used to solve logic problems. The ability to perform mathematical operations with Boolean logic is a necessity for the design of computer systems, electronic circuits and computer software programs. It is also an essential skill needed to solve advanced probability problems.

In the boolean logic tutor session, the basic boolean logic truth tables and operations are defined and used to solve simple boolean expressions. Boolean logic operations explained and used to solve boolean problems include the AND, OR, NAND, NOR, NOT and EXOR operations.

Area and Volume Tutorial Sessions

In BookMark area and volume tutor sessions the formulas and variables required to solve area and volume are defined and summarized. Perimeter, circumference, area, volume, lateral area, and surface area formulas for rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms and trapezoids area calculations are listed and defined. Volume and surface area formulas are also listed for a wide variety of 3D forms including prisms, pyramids, cylinders, cones and spheres. Geometric problems require that the student find out area, volume, lateral area or surface area given the dimensions or vertex coordinates of given forms. Students are also shown how to calculate form dimensions given the volume, area, surface area or lateral area of a geometric form.


Postulates, Theorems and Axioms Tutor Session

The primary postulates, theorems and axioms used to solve geometry problems and proofs are introduced in this session. the students to the primary Students receive a list of the axioms, postulates and theorems that are used most often to solve geometric problems and proofs.

In the axiom, postulate, theorems tutor session students learn all the critical axioms, postulates and theorems to solve geometry problems and prove geometry theorems to become proficient in Euclidean geometry.

Axioms, postulates and theorems for each geometric shape are highlighted. These include axioms, postulates and theorems related to points, lines, angle, angle and line constructions, triangles, rectangles, parallelograms, regular polygons, rhombi, quadrilaterals and circles.

Geometric Proof Tutorial Sessions

In BookMark's geometric proof tutor session the concepts, methods and applications of geometric proofs are discussed. The applications of proofs in architecture, higher mathematics and machine design are highlighted.

Students are shown the basic written format of a geometric proof and a logical argument. The different proof methods are shown. These include include proof by contradiction, direct proofs, indirect proof, paragraph proof and two-column proofs.

Examples of proofs illustrated and explained in the session include the proof of Pythagoreans thereon and a number of triangle proportionality proofs. Common uses of constructions to prove geometric relations are summarized.

The session emphases the basic postulates that are fundamental to all geometric proofs. These include the reflexive property, symmetric property, transitive property, addition postulate, subtraction postulate, multiplication postulate, division postulate,and partition postulate.

Planes, Parallel and Intersection Lines Tutorial Session

In this tutor session, parallel and intersecting lines are defined. The symbols and relationships between parallel lines and the angles that are cut by a transversal are summarized. Students learn how to quickly determine which angles are congruent in transverse parallel line problems and how to use these theorems to prove geometric relationships about triangles, squares and rectangles.


Other topics in this session include the triangle inequality theorem.

line in a plane,


Angles Tutorial Session

Angles are fundamental to geometry problems and geometry proofs. In the angles tutor session, the angle is defined and the definitions and characteristics of the different types of angles are summarized. Angles discussed include acute, central, obtuse, complimentary, interior, exterior, supplementary and right angles. The different types of angles are discussed in relation to the types of geometric problems and proofs they are used to solve.

The radian and degree units of measure for angles are also explained and how to convert between radians and degrees is shown. The formulas for the sum of angles in geometric shapes such as circles, triangles and polygons are emphasized.

In the angles tutor session, angle postulates, theorems, and axioms are a primary focus. BookMark's angle postulate, theorem and axiom review sheet list, defines and gives examples of their use in geometry problems and proofs. .Angle postulates, theorems and axioms are also used to prove a variety of different geometric proofs and solve typical and more different geometric problems found in geometry courses and college entrance exam tests such as the PSAT, SAT, CBEST, CSET and ACT.

Geometric Construction Tutorial Sessions

Constructions are an essential part of geometry. Geometric constructions are not only necessary for the proof of many geometric theorems but also used to prove calculus theorems Constructions learned in geometry are also used and expanded on in technical illustration, drafting and architecture courses.

Geometric constructions included in the geometry tutor session include the basic constructions as recommended from the California State Board of Education standard : angle bisectors, perpendicular bisectors and the construction of a parallel line through a given point.

In Santa Rosa High Schools students will find that the emphasis on geometric constructions can vary considerable between teachers .Where some teachers might just touch on geometric constructions, others may require students complete drafting projects that may require the student to use up to 30 different types of geometric constructions.

In addition to the standard's construction requirements, the geometric construction tutorial session gives you the option to learn any one of the many constructions that are commonly used in architecture, drafting, technical illustration, fashion design and city planning.

In the tutorial session, we can show the geometric constructions methods to copy an angle, construct 30, 60 or 90 degrees angles, divide a line into any number of line segments, construct equilateral, isosceles and right triangles, construct the centroid, incenter, orthocenter, circumcenter, circumcircle of a given triangle.

Construction problems illustrated include finding the center of a circle, construction of a circle given three points, construction of the tangent line of a circle given a point on the circumference, construction of an ellipse in a rectangle, and the location of the foci of an ellipse. For advanced animation, architectural and machine design applications, the session also demonstrates the procedures used to circumscribe and inscribe circles in and about a hexagon, pentagon, octagon. For those that want to learn the basics of 3D geometric constructions with isometric and linear perspective, BookMark also offers technical illustration tutorial sessions.


Geometric Shape Definitions, Formulas and Theorems Tutorial Session

In the geometric shapes tutor session, the fundamental shape set adopted in Euclidean geometry is discussed in detail. Each element of the Euclidian shape set, which consists of the circle, the triangle, the square, the rectangle and all other irregular and regular polygons, is discussed in detail.

The use of different shapes and combinations of shapes to create shapes that are commonly used in architecture and product design is emphasized.

Each of the geometric properties of each shape is listed, along with the shapes formula's for properties such as the perimeter, area, angle, side length, apothem, radius, chord length, arc length and diameter.

Types of problems associated with different shapes and their geometric properties are classified. Different types of SAT, ACT and Math SAT I and II that require a knowledge of shapes are examined. Difficult and easy PSAT, ACT and SAT geometry problems are discussed. The quickest ways to solve and understand these problems is emphasized.


Circle Tutorial Session

The session gives a complete discussion of the circle and each of its geometric properties: area, circumference, central angle, inscribed angle, tangent angle, radius, diameter, sector and arc length.

Circle theorems focused on in the session establish geometric congruency relations between chords that are equidistant from the center of the circle, congruent chords and congruent arcs, congruent tangent segments from the same external point to the circumference, the measure of angles inscribed in a circle, such as a right triangle in a semi-circle.


Triangle Tutorial Session

The triangle tutor session focuses on the formulas used for the calculation of triangle parameters such as side and median lengths, angle measures, area, perimeter and a number of others.

The session classifies triangles by type. Categories of triangles discussed include right triangles, isosceles triangles, special right triangles, acute triangles, obtuse triangles, equilateral triangles, similar triangles and congruent triangles.

The definition of congruent triangles and the procedure and theorems used to prove that triangles are congruent are demonstrated. These include the ubiquitous side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA) and angle-angle-side (AAS) triangle congruence theorems as well as the hypotenuse leg (HL) right triangle congruence theorem.


Similar triangles are also defined and the methods and rules associated with proving triangles are similar are also explained in triangle tutor session. The proportional relations between similar triangles are emphasized

Proofs related to congruence, similarity, corresponding parts of congruent triangles, and proportional parts of similar triangles are all solved. The triangle inequality theorem is used to determine the longest and shortest sides and angles of a triangle.

Other triangle terminology and relations discussed cover the orthocenter, centroid, incircle and circumcenter of a triangle,


Polygon Tutorial Session

In the polygon tutor session, polygon properties and geometric relations discussed include area, perimeter, interior angles, exterior angles, radius, centroid, chords, diameter, altitude, apothem, orthocenter and incenter. The session also focuses on polygon similarity and congruence.

Geometric relations of parallelograms, quadrilaterals, rectangles, squares, triangles, circles, rhombi, and regular polygons are listed. The general properties and relationships of regular polygons are a major focus. Regular polygon lessons include relations between, apothems, perimeter, exterior, central angles and interior angles of polygons.

Parallelogram proofs in the session emphasize that opposite and parallel sides of a parallelogram are congruent, the
diagonals of a parallelogram bisect each other, opposite angles of a parallelogram are congruent

For rhombi, proofs in the session emphasize that all sides of a rhombus are congruent, diagonals of a rhombus are perpendicular, bisect each other, and bisect the rhombus' internal angles.

For trapezoids, proof in the session emphasize that the trapezoid has just one pair of parallel lines, and that the base angles of an isosceles trapezoids are congruent, opposite angles are supplementary and the isosceles trapezoid has diagonals that are congruent


Trigonometric Basics Tutorial Session

Most high school and many college geometry courses introduce the student to trigonometry. At the heart of trigonometry is geometry. All trigonometric functions can be proved or verified with geometry.

In the trigonometric session, students learn how to use the sine, cosine and tangent trigonometric functions to compute all the sides and angles of a right triangle. The rules of special right triangles (30-60-90 and 45-45-90) are used to help simplify and expedite the solving of problems that involve right triangles


Geometric Rotation, Translation and Reflection

Students learn the methods requires to construct geometric figures and then rotate, translate and reflect them about an axis using the rules of geometric symmetry, rotation, translation and reflection.

The problems solved in this session not only related to the development of geometric spatial skills but also prepare the student for the geometric sections of the SAT test.

Intermediate Algebra Tutorial Sessions

Intermediate Algebra, also known as Algebra II is a year course that requires Algebra I as a prerequisite. Intermediate Algebra is taught in high schools and is sometimes called Algebra 3 and 4. In college, intermediate algebra is also taught. In college it is often referred to as college algebra and sometimes includes more advanced topics related to trigonometry and calculus.

Intermediate Algebra is the cornerstone of advanced mathematics study and fundamental to basic concepts that are further emphasized in business, physics and chemistry. Those with a good Algebra II foundation will often find that higher level math courses such as trigonometry, calculus and differential equations are easier and often approach these subjects with much more confidence. .

In many high schools, many of the topics of Algebra I are reviewed and expanded on in Algebra II. Algebra I methods such as factoring, solving systems of linear equations and linear inequalities, parabola analysis and the simplification of exponent based algebraic expression are reviewed and elaborated on in intermediate algebra.

In Algebra II problems that require methods learned in Algebra I are in general more difficult. For example, students must apply factoring methods to third and fourth degree equations instead of just first and second degree equations. As well students must be be able to solve linear systems of equations that involve three or more variables instead of just two.

Several topics are introduced in Algebra II that are not covered in Algebra I. These new topics include logarithms, exponentials, complex numbers, synthetic division, multivariable linear systems, linear programming, matrices and determinants, polynomial and rational expression, sequences, statistics, probability, conics and parametric equations. The procedures and concepts in these topics are elucidated on and used in more advanced mathematics, business, engineering and science classes such as business calculus, statistics, economics, finite mathematics, numerical analysis, physics and chemistry

Factoring Tutorial Session

In Algebra II students hone their factoring skills and learn how to factor complex algebraic equations. The emphasis in factoring in Intermediate Algebra is to improve the time it takes to factor and simplify algebraic expressions and on expanding the types of algebraic expressions that students are able to factor.

In BookMark's factoring tutor sessions, students learn how to factor second , third and fourth degree polynomials and rational expressions with two, three and four terms.

All of the different factoring methods used in Algebra I are reviewed and expanded on in Algebra II. These include the table and group factoring method. the completing the square factoring method and quadratic formula factoring method.

In the factoring tutor session, students apply factoring methods to simplify complex algebraic expressions in conjunction with conjugate operations and least common denominator. Students also learn how to identify common factors in complex algebraic expressions and pull out these factors to simplify the expressions. Factoring of transcendental, rational expressions, and trigonometric functions is introduced and the procedures and notation explained.

Linear Systems Tutorial Session

In Algebra II students must be able to calculate and solve a variety of different problems involving linear systems. They must be able to solve absolute value equations and absolute value inequalities, determine solutions of systems of linear equations with two or three variables, be able to solve linear systems through graphical methods, substitution methods, eliminations methods, through the use of matrices and determinates and row reduction methods (Gauss Jordan) .

In BookMark's linear systems tutorial session, we detail out the procedures for solving linear systems using all these methods. The focus in the tutor sessions is on linear systems with three or more variables and equations and applications specific word problems pertaining to statistics, business, economics, nutrition, fashion design, architecture, science, and engineering.


Polynomial and Rational Function Tutorial Session

In BookMark's polynomial and rational function tutor sessions, basic polynomial terminology and definitions are reviewed. Techniques and theorems are applied to find the real zeros of polynomial equations of higher degrees. The Fundamental Theorem of Algebra is also used to find the roots of polynomials.

The graphical nature of rational functions, complex fractions that have polynomials in the numerator and denominator, is also explained. Students learn the basic rules required to determine the horizontal and vertical asymptotes of a rational function and how to determine the domain and range of a rational function.

Additionally, students learn polynomial sketching rules to quickly plot the graphs of even and odd degree polynomial equations.

Polynomial division, multiplication, subtraction and addition are also reviewed in polynomial tutor sessions.

Complex Number Tutor Session

Complex numbers are another component of a comprehensive study of Algebra II. In complex number tutor sessions, students learn the definition of a complex conjugate number and how to use complex conjugate numbers to simplify complex fractions and rational expressions. Standard mathematical operations with complex numbers including addition, subtraction, multiplication and division are also explained.

Conic and Parametric Equation Tutorial Session

Conics and parametric equations are used in engineering, the sciences and computer programming. In the design of energy systems, conic equations are used to determine the point at which a parabolic mirror concentrates its heat rays. In graphic design automation computer programmers use conic and parametric equations to automatically create graphic designs used in video games and animations. In physics, conics and parametric equations are used to model satellite and planetary orbits. In architecture, conics and parametric equations are used as the basis for the design of abstract buildings that are functionally versatile and engineering marvels.

In BookMark's conic and parametric equation tutor sessions, students learn the definitions of the different conic types, their identifying equations, the mathematical properties associated with each conic type, and how to derive the standard conic equations based on their geometric definitions. Specific conics studied include the conics of a circle, ellipse, parabola and hyperbola.

How to sketch the different conics from the equation of a conic and the mathematical properties of conics (foci, eccentricity, asymptotes, centers, vertices, major axis and minor axis) are illustrated with pencil and paper and through online graphing calculators in BookMark's mathematical calculator and educational applications library.

Parametric equations are used extensively to model 2D and 3D forms, shapes and paths . Parametric equations often permit one to calculate 2D and 3D coordinates faster than with two-variable, rectangular function descriptions. In calculus, parametric equations are often easier to differentiate and integrate than two variable rectangular functions.

In parametric equation tutor sessions, the formal definition of a parametric equation is explained. How to sketch parametric equations is illustrated with pencil and paper and with parametric functions available with calculators graphing utilities and mathematical software programs.

How to convert a set of parametric equations with three variables to an equation of one variable is explained and illustrated. Determining a parametric equation from a given graph are two other skills taught in our parametric equation sessions. .

For those that want to study the use of conics and parametric equations in architecture, graphic design, and video game base computer science applications, BookMark provides advanced studies course in analytical geometry that involve the actual building of virtual conic models

Statistics and Probability Tutor Session

Statistics and probability is a part of many Algebra II courses. Although statistics and probability do not strictly fall into the Algebra subject category, the trend in middle school and high school is to place a stronger emphasis on statistics as a fundamental topic in Algebra II..

In statistics tutoring sessions counting principles, combination and permutations formulas and the binomial theorem are used to solve probability problems.

Series and Sequences Tutor Session

Series and sequences, mathematically defined patterns of numbers and sums of numbers, are also part of Algebra II curriculums and BookMark's tutor sessions.

In series and sequence tutor sessions, students learn how to distinguish between a series and a sequence, derive formulas for series and sequences, determine whether a series is a arithmetic or geometric, and obtain the sum of finite and infinite sequences.


Exponential and Logarithmic Equations and Waveforms Tutorial Sessions

The characteristics and the mathematical procedures associated with exponential and logarithmic functions are used to solve many types of problems fond in advanced mathematics classes as well as engineering, science and business classes.

Exponential and logarithmic equations are used, for example, in nutritional medicine to determine the half-lives of vitamins and minerals. In finance exponential and logarithmic functions are used to calculate return on savings investments and depreciation. In the biological sciences, exponential growth and decay equations are used to predict populations of living species. In engineering, exponential and logarithmic equations are used to perform calculations needed to design electronic circuits, physical structures and machines.

In the exponential and logarithm tutor sessions, the exponential and logarithmic functions are defined and their properties and associated graphs (waveforms, plots) are analyzed. In the session students learn how to convert logarithms from one base to another, perform logarithmic mathematical operations, simplify logarithmic expressions and convert exponential expressions to logarithmic expressions.

Word problems and application problems that require the use of logarithms and exponents to solve are emphasized. The types of logarithm and exponential logarithm word problems are classified into specific problem types along with the specific methods and formulas used to find the solution to each type of word problem .

Students are taught how to recognize different types of word problems and how to perform the procedures to solve each different type.


Trigonometric Tutroing Sine Wave Picture Image IllustrationTrigonometry: Trigonometry is fundamental to the study of architecture, physics and engineering. It is also needed for professions that are involved with musical, graphical, animation and video synthesis.

BookMark offers a large selection of standard trigonometry tutor sessions. For students, the trigonometry tutor sessions are designed to meet academic, honors, and international baccalaureate standards. The sessions beside standards content also integrate relevant content that a student can expect to see on college entrance exams, advanced placement exams and college-credit-by-test exams. .

BookMark also offers college level trigonometry tutoring and trigonometry for game designers and programmers.

Trigonometric Tutorial Sessions

BookMark divides its trigonometry instruction into distinct trigonometry tutorial sessions. These include the unit circle tutorial session, the tutor session, the unit circle tutor session, the identities and equations tutor session, the vectors tutor session, the complex number tutor session and the waveform tutor session.

Trigonometric Unit Circle Tutorial Session

In this trigonometric tutor session, the trigonometric functions are defined and then related to the unit circle. Trigonometry starts with the circle. From the circle and the right triangle, the unit circle is created and the trigonometric values of the angles of the unit circle can be calculated.

In the circle trigonometric tutor session, the unit circle is created and the trigonometric values associated with unit circle angles are calculated. Students also receive a graph of the unit circle and a unit circle table.

The Pythagorean theorem and the equilateral triangle are used to derive the values for the sine, cosine and tangent functions for the angles represented on the unit circle.

The unit circle graph and table are used to look up the sine, cosine and tangent values of angles. Students learn the two different measurement units of the circle, the radian and the degree, and how to convert between the two. Students also learn how to use the calculator to find the sine, cosine and tangent of an angle using the calculators degree mode and radian mode.

The unit circle tutor session also defines the inverse trigonometric sine, cosine and tangent functions (arcsine, arccosine and arctan). The inverse trigonometric functions are used to solve problems that require an angle be found when the length of two sides of a right triangle are given.

Trigonometric Identities and Equations Tutorial Session

Trigonometric identities, two different trigonometric expressions that graph as the same function, are on of the major topics in trigonometry courses and are the focus of the trigonometric identities tutor session.

In the trigonometric identities session, the different procedures for proving two trigonometric expressions are identical are explained. Basic procedures, such as conversion of of all trigonometric functions to cosine and sine functions, are emphasized.

The trigonometric identity session focuses on the proof of the fundamental identities and complex identities. . The proof and the application of fundamental identities in the identities tutor session include Pythagorean, the double angle, half angle, product-to-sum, sum-and-difference, sum-to-product identities.

The identities session also focuses on the simplification of trigonometric expressions through the use of identities,

Other topics covered in the identities session include the law of sines and the law of cosines.


Complex Number Tutorial Session

Complex numbers are used to represent trigonometric waveforms so that mathematical operations with trigonometric waveforms can be simplified.

In the complex number tutor session, complex numbers are defined and the relationship to the Cartesian coordinate and Polar coordinate system as well as waveforms is explained. The tutor session also covers the procedure for converting coordinates from a polar-to-rectangle format and rectangle to polar format.

In complex number tutor sessions, students learn the definition of a complex conjugate number and how to use complex conjugate numbers to simplify complex fractions and rational expressions. Standard mathematical operations with complex numbers including addition, subtraction, multiplication and division are also explained.

The tutorial session also illustrates problems that involve the use of de Moivre's theorem find the nth root of a complex number.

Imaginary and Complex Numbers

Imaginary numbers, defined as a number that represents the even root of a negative number, are at the heart of complex number tutorial sessions.

Real numbers and imaginary numbers when used together form what are known as complex numbers. Complex numbers can be converted to trigonometric waveforms through use of relatively straight forward conversion methods known as rectangular to polar conversion. Polar conversion representations of complex numbers can then be directly converted to trigonometric equations that involve the sine and cosine functions.

Vectors Tutorial Sessions

Vectors represent direction and magnitude. In science and engineering, vectors are used to simplify the computation of problems that require analysis in two or three dimensions that involve motion and forces.

In BookMarks vectors tutorial session, the components of vectors are computed with the sine and cosine trigonometric functions. Vector addition and subtraction operations are used to sum and add vectors The inverse tangent function is used to compute the angle of the vector and the Pythagorean Theorem is used to calculate the magnitude of a vector.

Unit vectors and normal vectors are defined. The cross-product and the dot-product vector operations are summarized and used in business, science and engineering application problems.

Waveform Analysis Tutorial Sessions

One of the most fundamental concepts in the study of trigonometry and physics is the mathematical relationship between a spinning circle and a waveform. When a circle spins, the plot of the position of its x-coordinate over time will be a cosine wave. It is this relationship that simplifies the mathematical equations needed to solve sound, light, radio and energy waves problems.

The waveform tutor sessions defines the primary waveform equations used in trigonometry, describes the variables used in these equations (period, frequency, amplitude and phase shift) and illustrates how to graph trigonometric equations with pencil and paper and with trigonometric graphing calculators and software packages.



Physics Forumla, Review and Cheat CheatPhysics: Physics is a requirement for most all engineering and science majors. Chemists use physics to determine and analyze complex biochemical reactions, mechanical engineers use physics to design everything from cars to trains, animators use physics to construct realistic animations and video games. Musicians learn physics so that they can understand sound waveforms and how sound can be transformed and translated to produce new and refreshing sounds and to get the most from acoustic settings.

BookMark Tutoring offers individual physics tutoring for students and those that need physics for their career and professional pursuits.

We provide courses tailored to software developers and programmers that allow them to not only learn and understands physics quickly, but also to apply it to create motion , sound and special effects enhanced animations, engineering and graphic design simulators and educational apps

Physics Tutorial Sessions

The physics tutoring sessions are divided into segments that follow the topics and standards taught in high school and college undergraduate physics courses. These include tutor sessions in classical mechanics, thermodynamics, electricity, magnetism, waveform theory, sound and acoustics, light and optics, and 20th and 21st century physics, also known as modern physics (quantum mechanics, nuclear processes and relativity).

Classical Mechanics Tutorial Session

In classical mechanics students study motion and forces and the effects of forces on motion. In most high school and college courses, classical mechanics is where the study of physics begins.

The classical mechanics tutor session introduces the standard international units of mass, length and time. These units are then used in dimensional analysis to determine the validity and to devise physics equations. The introductory session also focuses on the rules of significant figures and how they are used to ensure reliable numerical calculations.

The definition and use of vectors, the calculation of vector components, vector angles and the magnitude of vectors are reviewed. Graphical vector analysis and polar and Cartesian vector analysis are used to add and subtract vectors. The use of vectors is explained in the context of moving objects, collisions of moving objects, forces on stationary and moving objects and the path of moving objects.

Motion equations (kinetic equations) are introduced and applied to one-dimensional and two-dimensional motion problems that involve the determination of acceleration, velocity, time and distance.

The classical mechanic tutor sessions also define, explain and use Newtons Laws of Motion (the first, second and third law) for the solving of problems that involve multiple forces in one and two dimensions.

The principles and formulas of linear kinematics and force are applied to solve physics problems. Problems are explained that incorporate gravitational forces, friction forces, normal forces and the use of translated coordinate systems.

Energy is another important topic covered in the classical mechanics tutor session. Work, energy, the units of work and energy, the conversation of energy, potential energy and kinetic energy are defined, explained and utilized for the solving of energy and work problems.

Energy equations are used to solve for an objects kinetic parameters (time, displacement, velocity, acceleration of a particle). The formulas for the potential energy of a spring and gravitational potential energy are used to solve elastic material and gravitational based problems.

Power (word divided by time) and work done by a force (force times distance) are defined and uses to computer power and work requirements of mechanical systems such as inclines and pulleys.

Momentum (the product of mass and velocity) is another important element of classical mechanics. In the tutor session, the principles of conservation of momentum is applied to problems that involve the calculation of mass and velocity of particles in motion and the elastic and inelastic collision of objects. One-dimensional analysis of momentum is first explained, and then methods to solve two-dimensional problems are detailed. Three-dimensional momentum problems are briefly introduced for those that are considering advanced physics classes.

Impulse, the product of force and time, is also explained and used to find the mass, velocity and acceleration of objects that have an impulse applied to them. Finally, the session discusses thrust and its use in equations to find orbital escape velocities of rockets and satellites.

Rotational motion is another element of classical mechanics that is necessary to know to understand and design machines from simple pulleys and conveyor belts to complex transmissions and energy efficient vehicles.

In the classical mechanics tutorial sessions, the rotational motion equations are defined, listed and explained. The relation between gravitation and rotation is explained, the concept of rotational equilibrium illustrated and the central ideas related to rotational dynamics emphasized.

The duality between rotational kinematics equations and linear kinematics equations is emphasized. Methods to convert angular velocity and angular acceleration to associated linear velocity and linear acceleration are used to solve physics rotational dynamics problems. Problems involving rotational motion. centripetal acceleration, planetary elliptical rotational motion (Kepler's Laws) are also detailed and explained step-by-step.

Principles of rotational equilibrium and rotational dynamics are explained along with the associated concepts of torque, rotational kinetic energy and angular momentum. Problems are solved that involve pulleys, embankments and rotating machines that require the determination of angular acceleration, velocity, torque, applied forces and inertia.

Application of the principles of classical mechanics to the analysis of the behavior of solids, gases and liquids is another aspect of the classical mechanics tutor session. Principles discussed include Archimedes and Pascal's Principles. Pressures and equations used to calculate pressure, volume and temperature of a liquid or a gas are used in typical types of machines that are used to convert chemical energy and the kinetic energy of gases to mechanical energy are explained.

Fluid fluid dynamics is introduced. The basic definitions and calculations that are used in fluid dynamics, including flow rate, surface tension, capillary action and viscous fluid flow are defined and used to solve problems.

Electricity Tutorial Session

In the electricity and magnetism tutor session, electric charges are first defined and explained. Coulombs law is used to calculate the forces between two charges at a distance The methods to draw electric fields between charges are shown, how to interpret the electric field lines is explained, and how to break down electric field vectors into horizontal and vertical components to solve electric field problems is emphasized.

Electric field, force and charge velocity calculations are made. from a charge are representations of different point charge arrangements are drawn and force calculations are made that allow the student to find the forces between charges, the direction point charges will move and the resultant magnetic fields that are created.

Magnetism Tutorial Session

In the magnetism tutorial session, the basics of magnetism and magnetic fields of magnets, the earth's magnetic field and the magnetic fields associated with electromagnetic waves and those induced with mechanical magnet based systems, such as electric motors and generators are explained. The session starts with an introduction to magnetic fields and how magnetic fields are represented graphically in two and three dimensions are illustrated.

Electricity and magnetism are two interrelated physics phenomena. Electric currents generate magnetic fields and rotation magnetic fields generate electric currents. This relationship is known as electromagnetism. Additionally, light waves have associated with them both a magnetic field and an electric field. Although many electricity problems and electronic circuit design problems don't require a knowledge of electromagnetism, solving problems in the design of communications and advanced high speed electronic circuit design does.

Magnetic fields can be created through the rotation of a current carrying wire about a magnet or through the rotation of a magnet about a current carrying wire. The basic relations between magnetic fields and current involve an understanding of the the magnetic field of a current carrying conductor, the motion of a charged particle through a magnetic fields, the magnetic forces between two current carrying wires, and the magnetic field generated through a current carrying loop.

Energy stored in a magnetic field is also emphasized in the magnetism tutor session. The tutor session also covers electromotive forces, Faraday's law of induction and Lenz's law.

The magnetic field, which is the result of the movement of a charge through an electric field, is used to explain the operation of electric motors and to calculate the current induced in a wire.

The generation of electrical energy and current from magnetic based mechanical systems, such as electrical generators, wind turbines, hydroelectric turbines and other alternative resources is also emphasized during the session. As part of the discussion on motors and generators electromagnetic basics such as the direction of a magnetic field in a straight wire or coil, induction of current from a changing magnetic field and magnetic and electric field vector analysis,


Electromagnetic Waves Tutor Session

Electromagnetic wave theory is credited with the development of the radio, satellite and television communications. The application of electromagnetic theory also led to the development of radar and cellular phone technology.

The electromagnetic spectrum is defined in terms of the specific electromagnetic waveforms that it consists of radio waves, microwaves, , infrared waves, visible light waves, ultraviolet waves, x-rays and gamma rays.

The representation of electric and magnetic fields that are generated from electromagnetic waves are illustrated and their use in the transfer and propagation of energy across space is explained.

The method and rules for the visual representation of electric, magnetic and energy and force fields of electromagnetic waves are detailed.

One, two and three dimensional vector analysis is applied to electromagnetic waves to find the field strength, field density, flux density, energy density, electric forces and magnetic forces that are inherent to electromagnetic waves.

Maxwell's and Hertz's equations are fundamentally to the solving of radio communications problems and fundamental equations for the study of electromagnetic waves. The electromagnetic wave tutor session examines all four of Maxwell's equations. These include Gauss's Law (as related to flux), Gauss's Law in Magnetism, Faraday's Law, and Ampere-Maxwell Laws. The session also emphasizes the use of Einstein's relativity equations to solve electromagnetic radiation (energy) problems.

The dual nature of atomic particles, protons and electrons, as either light waveforms or as particles (objects of mass) is discussed in relation to which types of problems are solved with particle equations, which ones are solved with wave equations and which ones are solved with both.



Electricity and Charge

The study of electrical circuits begins with a definition of the basic elements of electricity: current, voltage, power, resistance, inductance, capacitance, conductance and impedance. Current flow, the movement of electric charges, is emphasized in relation to the the electromotive forces generated from batteries and electrical generators. The characteristics, differences and similarities of the two different types of current, direct current which is obtained from batteries and solar cells, and alternating current which is generated from rotating magnets around wires or rotating wires about magnets.

Passive Components and Circuits

Formulas are used to calculate the resistance, inductance and capacitance of different materials that have specific dimensions.

The tutor session than moves ahead to cover the use of Ohms law to calculate direct current (DC), voltage, power and resistance in different types of commonly used DC circuit structures. Kirchoff's laws are used for the calculation of DC currents, power losses, voltages in a circuit that contains resistors, inductors and capacitors.

The circuit action of capacitors and inductors in DC circuits is explained in regard to the DC models of these components and the transient exponential waveforms generated when inductors and capacitors are switched in and out of live circuits.

Capacitors and inductors are discussed in regard to their design, construction and electrical characteristics. Non-ideal models of both the capacitor and inductor are explained and how the materials used and the construction of these components effect the value of capacitance and inductance and contributes to non-ideal component operation.

The capacitor is also explained from the standpoint of a voltage storing device and inductors as current storing devices. The magnetic and electric fields are also examined for capacitive and inductive circuits.

The construction and operation of transformers and their use in energy systems is diagramed. The basic properties of a transformer: turns ratio, voltage ratio and current ratio, input impedance and output impedance are defined. Formulas associated with the transformer are listed and used to solve electrical transformer problems.

Transformer characteristics are examined and the role of electromotive induction is explained in regard to the electric and magnetic fields.

Typical transformer circuits and the function they perform in power supply circuits and electric utility applications are examined.

The principles of alternating current (AC) needed for the analysis of simple AC circuits is covered. . Alternating current waveform properties are mathematically and graphical defined. These waveform properties include period, frequency, amplitude and phase. Problems in the AC tutor session detail how to calculate the AC current, voltage and power levels within circuits that contain inductors, capacitors and resistors. The frequency response of resonant circuits as well as low-pass, high pass and band pass filters are graphed and analyzed. The procedure to find the transfer function of simple filter circuits is covered.

The session also covers parallel and series resonance circuit structures, their use in radio receivers and microphones, and how to calculate voltage and current gain at resonance.

Active Components and Circuits

Semiconductor devices are a relatively recent addition to physics. Invented in the early 1950s, semiconductors today are the basic building block of all modern electronic systems. In the semiconductor tutor session, principles of current flow in a semiconductor device are explained for doped silicon and geranium semiconductors. Basic transistor circuits are examined for use in switching and amplifier applications. Basic calculations for current, voltage and power are used to analyze semiconductor circuits commonly used in electronic design.


Thermodynamic Tutorial Sessions

Thermodynamics involves the study of the conversion of thermal energy to mechanical energy and the conversion of chemical energy to thermal energy. Thermodynamics also involves the study of heat convection and heat conduction in solids, liquids and gases.

Thermodynamics is used in many different engineering and science fields. The principles of thermodynamics are needed to design household appliances such as refrigerates, stoves and fans as well as plane, truck and car engines. Architects and environmental engineers must understand thermodynamics to efficiently heat and cool buildings and homes. Electronic engineers must also know thermodynamics so that they can design cooling systems for computer systems. Environ


In the physics thermodynamics tutor sessions, the emphasis is on problems that require the conversion of thermal energy to mechanical energy and the conversion of mechanical energy to thermal energy.

Although the study of thermodynamics in physics is similar to the study of thermodynamics in chemistry, in chemistry the conversion of chemical energy to thermal energy is the primary emphasis. Thermodynamics in chemistry also places more emphasis on the concepts of enthalpy, entropy and free energy.

The physics thermodynamics tutor session lists, summarizes and explains the laws of thermodynamics within the context of kinetic energy, potential energy, free energy, the conversation of energy, heat conduction, energy efficiency and the conversion of thermal energy to mechanical energy. Each of these physics properties and processes are illustrated with worked problems that typify the procedures that students need to know to solve physics problems quickly and efficiently for exams and the laboratory. .


The Physics of Sound and Acoustics Tutorial Session

Sound and sound physics are used in a variety of different professions. Electronic engineers analyze and quantify sound so that they can design high quality audio equipment. Computer programmers study the physics of sound so that they can write computer code used in music synthesizers. Interior designers utilize their knowledge of physics to select materials that have sound acoustics to match the purpose of the room.

The sound and acoustics tutor session. revolves around the characteristics of sound waves. These include the speed of sound in different materials, the effect of materials on sound intensity, energy intensity of sound waves (decibels and logarithms), how sound wave propagates. Sound wave theory topics include the Doppler effect types of sound waves: spherical, plane waves, standing waves.

Sounds produced from vibrating strings are analyzed in the sound tutor session. The effect of the materials used, and the distance between the ends of the strings is physically related to the pitch of a sound generated in different musical instruments. Terminology such as resonance, air columns, beats and quality of sound are defined and graphically depicted.

Formulas for sound are used to compute sound wave characteristics such as amplification, constructive and destructive interference, sound intensity, sound velocity and sound direction.


Fundamentals of Waveforms, Harmonic Motion and Circular Motion

Harmonic waveforms, waveforms whose energy levels vary over time, are most often expressed as cosine and sine waves. Because springs, pendulums, rotating wheels, and electromagnetic energy levels vary with time according to cosine and sine functions, physics students must be able to draw correlations between harmonic motion and circular motion.

The harmonic tutor session summarizes, lists and defines the equations and the variables used to solve for work, energy, force, velocity, acceleration, time and distance based physics problems

In the harmonics tutor session, the spring is first discussed. The springs harmonic wave characteristics are graphed and the peaks and troughs of this waveform are used to determine the elastic potential energy and kinetic energy of the spring as it is compressed and stretched . The forces that a spring imparts is discussed in reference to hooks law.

The motion of the pendulum can also be expressed as a harmonic waveform. The potential and kinetic energy waveforms vary in a sinusoidal pattern as the pendulum swings back and forth. Because of the harmonic motion of pendulums, formulas for the velocity and the acceleration of pendulums can be and are derived. These formulas allow for the calculation of the maximum velocity of a pendulum for a given pendulum with a specific string length.

When an object moves in a circular motion, it can be defined in terms of a harmonic waveform. A graph of the x and y coordinates versus time of a wheel rotating in free space, for example, produces a cosine wave and a sine wave. In the waveform tutor session, the linear velocity, angular velocity and position of a rotating object is calculated using harmonic waveform equations.

Light and Optics Tutor Session

Photographers, opticians, graphic designers painters, electrical engineers and physicists often study light and optics. Opticians and optical scientists must often understand the principle of lights and optics so that they can design microscopes, telescopes, eyeglasses and cameras. Electrical engineers often study light and optics so that they can design light emitting diodes, light bulbs, lighting systems and light based communication systems. Photographers, graphic designers and painters will often study lights and optics so that they create special effects and add realism to their designs.

The session explains the dual nature of light and how it is treated as both a particle and a waveform to solve physics light problems. Problems that require particle equations, also known as geometrical optics equations are solved as well as problems that require waveform equations and both geometric and waveform equations.

The historically important experiments that relate to geometric optics and waveform optics are listed. The procedures, materials and equipment used to perform these experiments are detailed. How the results provide evidence that supports the theories and equations used in geometric and waveform optics is explained.

Geometric Optics Tutorial Sessions

Geometric optics explains the behavior of light in terms of Newtonian physics. Light has a speed and a direction. It will reflect in a similar fashion as a ball will deflect when it bounces off a wall (dependent on the angle at which it hits and surface irregularities.)

In the geometrics optics tutor session the fundamental principles and characteristics of light reflection, refraction, diffraction, diffusion are explained diagrammatically and illustrated with apertures, prisms, mirrors, lenses and other optical instruments.

The propagation paths of light, the projection of light and the redirection of light is analyzed for different types of materials and optical components. How optical components such as mirrors, prisms and lenses effect the direction, color and intensity of light are examined. Geometric optical equations are used to calculate the direction, color and intensity of light when light rays are directed through different optical components made of different materials and liquids, such as water and mists.

Mirrors, lenses and prisms are the three primary types of optical components studied in light particle (geometric optical) physics.

Types of mirrors discussed in the geometric optics session include flat mirrors, convex mirrors and concave mirrors. Characteristics of mirrors such as mirror aberrations are explained.

The most important properties and characteristics of mirror and lens materials reflective properties of mirrors and the refractive properties of transparent materials such as glass lenses.

How converging and diverging thin lenses are formed, the materials used in their construction and thin lens construction methods are presented. Optical and atomic properties of the materials used in traditional and modern lenses is explored. Mirror construction and materials properties are another topic.


The optical designs of microscopes, cameras, telescopes, lasers, and inferonmeters are examined and compared. Equations to calculate the magnification of projected images are used to solve mirror and lens problems. The construction of ray diagrams to solve image projection problems and prove geometric optics equations are emphasized.

Geometric optics terminology defined in the geometric optics tutor session includes focal point (focus), focal length, radius of curvature, image distance, object distance, real image and virtual image.

Formulas used to solve optic problems include angular reflection and refraction equations, Snel'ls equation, the thin lens equation, lateral magnification equations and several derivatives of these basic equations. The thin lens equations and ray diagrams are also used to determine focal length, virtual image distances and magnification factors of different lenses. Other solutions explained involve the calculation of index of refraction, determination of the focal length using the radius of lens curvature of the lens and angle of incidence, reflection and refraction.

The geometric optics problem solving sessions also illustrate how to determine the incidence of refraction and reflections, calculate the lens and mirror magnification factors for the projection of images, calculate projected image location and height, determine the resolution of telescopes, microscopes and glasses.


Optical Instruments

Light and light analysis is also applied and explained in the development and design of optical instruments. The operation and physics principles that govern the telescope the microscope, the camera, single slit apertures, circular apertures and the inferometer are emphasized. The sessions focuses on the camera, magnifying lenses, compound microscopes and refracting telescopes,

Wave Optics Tutor Session

In the wave optics tutor session the wave characteristics of light wave propagation are outlined. The equations used to solve wave optics problems are summarized and applied to a number of different wave optics problems. The terminology of wave optics is defined and then explained graphically.

The destructive and constructive interference characteristics of light are used to define the light wave functions. The electric and magnetic characteristics of light are used to explain the behavior or light in the presence of an electric and magnetic field.

Equations that define wave behavior of light And dispersion patterns are analyzed and calculations performed to calculate diffraction factors. The session emphasizes the historical experimental results of Young's single slit and double slit experiments to demonstrate the light wave properties of constructive and destructive interference.

The mathematical relation between the electromagnetic properties of lights waves and the orbital energy of electrons within atoms is emphasized.

Types of wave optics problems and solutions covered include the determination of the electromagnetic fields of light waveforms, calculations of the energy levels of light waveforms, determination of the dark and bright fringes in one-slit, two-slit and multi-slit diffraction grating devices, determination of color light angles emerging from a prism, polarization of light problems. phase shift of light problems,

Wave optics terminology defined in the wave optics tutor session include coherent and incoherent light, dark fringes, bright fringes, order number, diffraction. phase shift, diffraction gratings, light wave polarization, constructive interference and destructive interference.



Modern Physics

Modern physics is the study of physics that was developed for the most part in the last 100 years. Most of modern physics relates to quantum mechanics, Einstein's theory of relativity and wave theory. Topics covered in modern physics include Galilean relativity, Einstein's theory of relativity, special relativity, relativistic momentum, relative velocity, relativistic energy, speed, time and mass.

Quantum physics is another topic covered in the modern physics tutorial session. Concepts, formulas, problems and definitions that involve Planks hypothesis, blackbody radiation, the photoelectric effect, particle theory, x-rays, crystal x-ray diffraction, the Compton effect, light and matter relationships, conversion of light to matter, the wave function, and the uncertainty principle are highlighted.

For quantum physics a knowledge of atomic physics is essential. Atomic physics tutorial sessions include discussions of the different types of atomic models such as the Bohr model, the quantum mechanics of the hydrogen atom, and the Pauli exclusion principle

Nuclear physics is also a major topic covered in modern physics. In nuclear physics tutor sessions the characteristics and composition of the nucleus of atoms, the energy of atoms and the associated radioactive nature and decay processes associated with the nucleus are explained in detail. Typical problems that involve these processes are solved.

Nuclear physics also involves the analysis of nuclear fission and nuclear fusion reactions. As well it includes a study of the types of nuclear particles and antiparticles. Discussion in nuclear physics tutor sessions also revolve around special topics such as quarks and color, electroweak theory and cosmology.


Chemistry: Chemistry has always been a requirement to obtain a medical degree. Doctors, vetinarians, professional nurses, dentists and nutritionists must learn chemistry to understand the relationship between health and the chemical reactions that occur in living organisms. .

Besides the medical professions, a knowledge of chemistry is required for those entering many engineering and science fields. And that's because a knowledge of chemistry is necessary to develop nutraceuticals, pharmaceuticals, electronic devices, optical devices and new materials for building and manufacturing.

One of chemistry hallmark achievements has been in the area of alternative and solar energy. The solar cell has been made a viable source of energy because of the long-standing efforts of chemists to improve its energy efficiency. Strides in battery power efficiency ratings (weight to energy level). are also a direct results of the endeavors of chemists.

BookMark offers individualized chemistry tutoring that is geared for course work at the academic and honors high school level and the college level. We also provide research for chemistry reports for those in academia and industry.

Chemistry Tutoring Tailored for Santa Rosa

Our chemistry tutoring is designed for the coursework for academic and honors chemistry students at Santa Rosa High School and those in the Sonoma County school district. We tutor chemistry for students at Maria Carrillo, Montgomery High School as well as Santa Rosa Junior College and Sonoma State University chemistry classes.

At BookMark we will not only offer solutions to your chemistry course problems, but prepare you for lower division and upper division chemistry courses, the College Level Examination Program and AP Chemistry exams. Students who pass these exams can skip undergraduate chemistry classes and obtain chemistry college credits through the California State University, University of California or from international colleges and universities through the International Baccalaureate program.

Chemistry Tutorial Sessions

BookMarks divides its chemistry tutoring into chemistry tutor sessions and chemistry review sessions. The individual chemistry tutor sessions match the topics that are covered in high school and college chemistry courses in the California educational system.

Specific chemistry tutor sessions include atomic theory, periodic table , bonding, thermochemistry, solids, liquids and gases, chemical equilibrium, acids and bases, electrochemistry, nuclear reactions, and organic chemistry. Virtual chemistry laboratory sessions are also available for students that want to learn about the safety procedures, the equipment and the general procedures used in the design of experiments and the production of chemical compounds.

Atomic Theory

The atomic theory is central in the understanding and prediction of chemical reactions. The differences in atomic structure of elements can be used to determine and predict if a chemical reaction will occur between two or more elements or molecules.In the atomic theory session, the relation between the forces of attractions and repulsion of different elements and molecules is explained in the context of chemical reactions.

The atomic theory tutor session also covers the structure of atoms and the properties of atoms. The structure of atoms is discussed in terms of the atom's nucleus, the number of protons and the number of electrons and associated electron orbitals. Specific atomic properties of elements discussed include ionization energy, electronegativity, bonding energy, conductivity and chemical reactivity. The fundamental relations between the properties of an atomic element and its atomic structure are emphasized.

The atomic theory tutor session also covers quantum theory and the underlying physics and formulas used to predict the behavior of atoms and electronics. This includes the study of the photoelectric effect and Bohr's theory of the hydrogen atom.

Basics of quantum mechanics, quantum numbers, atomic orbitals and electron configurations of atoms are also covered. Students learn how to calculate the energy of an electron is specific electron orbitals, the significance of the Pauli Exclusion Principle and how to apply it, the definition of paramagnetism and diamagnetism and how to determine if an atom is paramagnetic or diamagnetic. Also explained is the electron shielding effect and its use in the determination of the forces of attractions and repulsion in an atom and the size of an atom, Hund's rules and its use to determine the


Periodic Table Tutorial Sessions

In the periodic table tutor session, the periodic table, the history of its developments, how it is used and how to interpret the element data within it are covered.

The periodic table session explains how to use the periodic table to determine which elements will combine to form molecules and which will not. Elements in the periodic table that are most commonly used in medicine, pharmaceuticals, nutrition, electronics and energy production are highlighted.

Element characteristics that can be determined with the periodic table include electrical conductivity, density, atomic structure, electronegativity, electron affinity and bonding energy. The periodic table also lets you quickly determine the number of electrons, neutrons and protons for each element listed and the atomic mass of the element.

The student also learns how to use the periodic table to determine the characteristic of an element from its position in the table and the elemental data given.The periodic table is divided into groups (periods) and rows. Each of the elements in the groups and rows have atomic, chemical and physical characteristics in common that allows for their chemical behavior to be explained.

In the tutor sessions, the unique characteristics of the different periods and rows of the periodic table are summarized. Industrial and medical applications of each period and row are discussed and how the elements in different rows and periods are used together in the formulation of molecular compounds is discussed.

Within the periodic table, elements are also classified according to specific element characteristic that is common to a series of elements. An element can belong to the alkali metal, alkaline earth metal, a transition metal, semimetal, nonmetal, halogen, lanthanide, actinide, transactinide or transuranium series. Element series characteristics are also discusses in the periodic table tutor session. Industrial and medical applications of each series is discussed and how the elements of each series are used to build chemical compounds and systems is discussed.

Chemical Reactions and Equations Tutorial Session

The chemical reactions and equations tutor session also summarizes the most common types of chemical reactions, the chemical groups involved in those reactions and how to classify chemical reactions from the chemical equation. Common place calculations used to solve chemical reaction problems are explained.


The chemical equation session also defines and discusses molecules and ions, molecular formulas, empirical formulas, and ionic formulas. The procedures and standards used in the naming of ionic compounds, molecular compounds, acids and bases, hydrates and inorganic compounds are summarized and applied.

The session also provides instruction on the balancing of chemical equations. This includes the balancing of molecular compound equations and ionic compounds in aqueous solutions. .

The chemical equations also discusses the characteristics of the ionic bond, how to balance ionic equations and elaborates on the principles of atomic mass, molar mass and how to calculate the percent composition of compounds, reaction yield, and how to determine the limiting reagent in a chemical reaction.

The general properties of aqueous solutions are also discussed. These include the electrolytic properties, the concentration of a solution and the ionic nature of elements within a solution. Calculations that involve the determination of the concentration of a solution and the mixtures of solutions to obtain solutions with specific concentrations are illustrated.

Types of chemical reactions are summarized along with the characteristics of these reactions and the elements involved in these reactions. Specific reactions discussed include precipitation reactions, acid-base reactions, oxidation-reduction reactions (redox reactions). Redox reactions are further classified and explained. Types of redox reactions include combination reactions, decomposition reactions, displacement reactions (hydrogen, metal, halogen, and disproportionate redox reactions).

The session steps through the process for solving acid-base titration problems. In these problems, the amount of acid or base needed to neutralize an acidic or basic solutions is calculated.

Similar problems are solved for redox titrations. In redox titration problem sessions, the procedure for determining the amount of reducing or oxidizing agent needed to reduce or oxidize a solution for difference chemical reactions are illustrated.

Terminology defined and explained in the chemical equations section include activity series, Bronsted acid, Bromated Base, half-reaction, spectator ions, hydration, salts, molarity, molecular equation, monoprotic acid, diprotic acid, triprotic acid, oxidation state, molar concentration, neutralization reaction, solute, solvent

Equations and formulas emphasized in the chemical reactions session include the molarity equation (moles/liters) and the dilution of solution equation (M1*V1 = M2*V2).

Solubility Tutorial Sessions

In the solubility tutorial session, precipitant reactions are discussed and solubility and the solubility rules of compounds are listed and qualified. Molecular and ionic equations are written and the solubility rules used to determine what compound will precipitate.


Chemical Equilibrium Tutorial Sessions

Chemical equilibrium is the point at which the concentration of reactants and products in a solution remains constant and the rates of the forward and reverse reactions are equal.

BookMark explains chemical equilibrium within the context of Le Chatelier's principle and the equilibrium constant.

In the chemical equilibrium tutor session the equilibrium constant is defined and how it is calculated from the stoichiometric coefficients of a chemical equation is explained. The use of concentrations and equilibrium partial pressures are both used to calculate the equilibrium concentration constant and the equilibrium partial pressure constant. The different equilibrium constants are calculated in problems that involve multiple equilibria. The session also provides the general rules and procedure for writing equilibrium constants.

Also in the session the relation between chemical reaction rates and the equilibrium constant are related through a set of mathematical manipulations.

The equilibrium constant is used in the sessions to solve problems that require one to predict the direction of a reaction for a set of initial concentration conditions and to determine if a chemical reaction has reached equilibrium. For this,. the reactant quotient is calculated and compared against the equilibrium constant for the chemical reactions.

Problem solving in the session focuses on calculating equilibrium constants, reactant quotients and solution concentrations at equilibrium. The session also takes a detailed look at the Haber Process for synthesizing ammonia. Terminology and concepts explained in the session also include heterogeneous equilibrium, homogeneous equilibrium and the law of mass action.


Chemical Bonding Tutorial Session

Chemical bonds allow the creation of different compounds that are critical to life and industrial processes. In chemical systems atoms and molecules are formed with different types of bonds that have varying levels of strength.

The strength of the bond determines the stability of the bond under different environmental conditions, such as pressure as and temperature. The type of bond formed and its strength is related to the atomic structure of the atoms and molecules that combine to form a bond. The ability to bond requires that the total forces of attractions of the atoms and molecules involved in the bonding to attract each others electrons into their orbits. Ionic bonds occur when one or more electronics in one atoms orbits changes its orbit from the nucleus of one atom to the another atom. In this case, the difference between the charge levels on the two atoms keeps the bonded atoms in close proximity. The other case is the covalent bond. In this case the electronics of each of the two atoms involved in bonding orbit in a path that circles the nucleuses of both atoms.

Understanding an element or molecules ability to bond with another element or molecule requires that you know the different types of bonds, the conditions that create the different types of bonds and the relative strength of different bonds (as a result of attracting and repulsive electron and proton forces and relative electronegativity, ionization energy and bonding energy for different elements and molecules.

In the chemical bonding session the different type of bonds are defined and explained. These include the ionic bond, the covalent bond,

The chemical bonding problem solving sessions focuses on solutions to chemistry bonding problems found in high school and college chemistry courses and on advanced placement exams for chemistry such as the AP Chemistry and CLEP chemistry exams.

Specific problems addressed in the problem solving sessions illustrate how to write Lewis dot structures for different ions, ionic and covalent compounds, how to determine if a bond is ionic, polar covalent, coordinate covalent, covalent, write formal charges for compounds, draw the resonance structure for ions, calculate the enthalpy for chemical reactions, use of the VSEPR model to predict the geometry of molecules and ions, determine if a molecule has a dipole moment, determination of the hybrid state of a central atom in a molecule, describe the hybridization state of different compounds, predict the properties of ions and element:d: including electron configuration, bond order, magnetic characteristics and bond length,

Relationships between bonding strength, potential energy, kinetic energy, electronegativity, ionization energy, boiling point and melting point are summarized and explained.

The session also examines the molecular shapes that are formed when atoms combine. This includes trigonals, tetrahedrals and other shapes and forms.

Other types of bonds discussed include hydrogen bonds, van der Walls bonding forces (dipole-dipole forces and London dispersion forces) , metallic bonds, organic covalent bonds, single bonds, double bonds, pi bonds, and triple bonds, In regards to atomic bonding, electron and proton forces are explained. For molecular bonding, intramolecular forces are explained.

Terminology, definitions and concepts also discussed and graphically illustrated in the bonding tutor session include antibonding molecular orbitals, bonding molecular orbitals, delocalized molecular orbitals, hybrid orbitals, sigma molecular orbitals, and homonuclear diatomic molecules

Gases and Gas Property Tutorial Sessions

In the gases and gas property tutor session, elements and molecular structures that exist as gases at room temperature are emphasized. These include hydrogen, nitrogen, oxygen, chlorine, fluorine and the noble gases as well as compounds such as hydrogen fluoride, hydrogen chloride and hydrogen sulfide.

The basic standard international units and conversion factors used in gas calculations are summarized. Pressures is defined (force/area) and problems are solved that solve for gas pressure in units of Pascals, atmospheres, Problems that involve the calculation of pressure from the height of a liquid in a manometer are emphasized.

The gas tutor session also covers the gas laws. The gas laws are summarized and used in calculations to solve for pressure, volume and temperature for gases in closed containers. The gas laws discussed and applied in the gas tutor session include Boyle's Law, Charles Law, Gay-Lussac's Law and Avogrado's Law

The ideal gas law is derived from the gas laws and in used in problems that require the determination of pressure, volume and temperature of a gas in a closed container. The modified version of the ideal gas law is used to determine the change in pressure, volume and temperature when an ideal gas is subjected to a change in volume, temperature or pressure.

For the ideal gas law, terminology discussed include STP (standard temperature and pressure), The universal gas constant, which is used in the ideal gas equation, is discussed in terms of its units and then used in pressure, volume and temperature calculations.

Emphasized in the gas tutor session is the relationship between the volume of a gas and the number of moles of a gas to produce a specific volume of gas at STP.

Dalton's Law of Partial Pressures is also derived and applied in the tutor session Problems are solved that use Dalton's law to determine the number of moles of different gases in a closed container. The vapor pressure of water and its use to determine the composition of a gas is emphasized.

The kinetic molecular theory of gases is used to explain gas behavior. The equations for solving for the kinetic energy and molecular velocity of a gas molecule are used to solve a number of molecular gas problems. The distribution of molecular speeds in a gas, the root mean square speed and the units used in the gas constant and the equations are detailed.

Other topics covered in the gas chemistry tutor session include gas diffusion and van der Walls constants and equations (used to calculate the pressure, temperature and volume of a non ideal gas). .


Chemical Solutions Tutorial Sessions

BookMark's chemical solutions tutor sessions include the definition of solute and solvent, dissolving process as a result of molecular motion, the effect of temperature, pressure and surface area on the dissolving process, calculation of the concentration of a solute in grams per liter, molarity, parts per million and percent composition. Also covered in chemical solutions tutoring is the relationship between the molality of a solute in a solution and depressed freezing and elevated boiling point. Last but not least also covered is the separation of chemicals through chromatography and distillation methods.

ThermoChemistry Tutorial Sessions

Thermochemistry, the study of heat change in chemical reactions, is used to calculate the amount of energy that is absorbed or released in chemical reaction. Nutritionists use the principles of thermochemistry to determine the amount of calories (energy) that can be derived from food, energy engineers use thermochemistry to evaluate the energy potential of different biofuels, environmental engineers use thermochemistry to evaluate the effectiveness of insulating materials, the flow of heat through buildings and through biological systems.

The thermochemistry session discusses the various types of energy found in nature. These include electromagnetic energy, radiant energy, thermal energy, chemical energy, mechanical energy, potential energy and kinetic energy. The relationships between chemical energy and other types of energy is emphasized along with the processes used to convert energy to different forms.

Thermochemical equations are used in the tutor session to calculate the enthalpy change (energy change) that occurs in a chemical reactions.

The terminology and concepts associated with the study of calorimetry are explained and used to solve a variety of calorimetry problems. Specific heat, heat and heat capacity are defined and the associated equations used to find the heat absorbed by a substance.

The construction of constant volume and constant pressure calorimetry instruments are discussed. Calorimetry instrument equations are used to solve fro molar heat of combustion and the heat change of neutralization reactions.

Other topics covered in he thermochemistry session include the standard enthalpy of formation and reaction, heat of solution and heat of dilution, and a basic introduction to the laws of thermodynamics. The first law of thermodynamics and its relation to enthalpy is emphasized.

For the determination if a chemical reaction is spontaneous or non-spontaneous the use of Gibb's free energy equation is detailed. Hess's law is another topic that is used for enthalpy calculations.


Reaction Rates Tutorial Session

Reaction rates, the rates at which the concentrations of gases, solids, liquids and ions are created and consumed, allow the chemist to determine the viability of a chemical reaction for a specific application. Reaction rate calculations are used to determine the power requirements and power production capabilities of chemical reactions. They are also necessary to use in the calculation of dosages for medical prescriptions.

The environmental variables that effect reaction rate are temperature, temperature and pressure. Catalysts can be used to increase the reaction time significantly, especially in biological systems.

The reaction rate tutor session includes a discussion on reaction rates and reaction rate problem session. The rate laws are listed and the variables used in the equations are explained. How the different rate laws are applied to different types of problems is emphasized. Reaction rates are examined and compared for commonly used chemical reactions. Catalysts are explained and the dramatic effect they have on reaction rates and activation energy quantified. Common catalysts and their uses in chemistry and biochemistry are explored.

The problem session focuses on the determination of rate expressions, the use of the rate laws to calculate formation and decomposition reaction rates, the calculation of rate constants, rate law determination, reaction completion times, half-life, calculation of activation energy, graphical determination of activation energy. The solutions use zero order, first order and second order rate formulas to perform the reaction rate calculations. The relationship between reactant concentration and time is emphasized.

Acid and Bases Tutorial Session

Acids and bases reactions in aqueous solutions are some of the most important reaction involved in biological and manufacturing processes. The balance between acids and is critical to the level of health in living systems. Manufacturing processes depend on acids and bases for the production of electronic equipment,

The acids and Bases chemistry tutor sessions, defines acids and bases in terms of Arrhenius acids and bases , Bronsted acids, Bronsted bases, Lewis acids and Lewis associated terminology such as conjugate pairs The chemical formulas for the strongest acids and bases are listed. The characteristics of acids and bases are discussed in reference to the hydrogen and hydroxide ion concentrations and the ratio and pH of a solution. The methods and calculations used in the production of of acidic, basic and neutral solutions from different combinations of strong and weak acids and bases is explained. The discussion sessions also emphasizes the acid and base properties of salts and how to determine if a salt will produce a basic solution or an acidic solution. The discussion and theory sessions also highlight the acid-base properties of oxides and hydroxides, the molecular structure and strength of acids and basis, diprotic and polyprotic acids and Lewis acids and bases.

In acids and bases problem solving sessions, problem solving procedures are explained and graphically illustrated that are used to determine the conjugate acid-base pairs in a reaction, the concentration of hydroxide and hydrogen ions in a solution, the pH of different solutions that are composed of acids and bases, direction of acid base reactions based on the strength of the acid, the acid disassociation constant given the pH and molarity of a solution, the percent ionization of a solution, the concentration of solutions at equilibrium, the percent hydrolysis of a salt, if a solution is basic, acidic or neutral, and the Lewis acid and Lewis base in reaction.

The other set of acid and base problems in the problem solving session center around acid base homogenous and heterogeneous solution equilibria. In this problem set, pH of solutions with salts are calculated, determination of buffer systems from chemical compound formulas, the calculation of the pH of a buffer system, the procedure for preparing a buffer system of a specific pH using the acid disassociation constant, calculation of pH levels at the equivalence point and at different points in the titration process and the method for selecting indicators for titration.

Problems that are focused on solubility include the determination of the solubility product from molar solubility. molar solubility of compounds given the solubility product, precipitant given the molar concentrations in the solution, concentration for a participate to form, calculation of solubility in a solution as a result of the common ion effect, the relative solubility levels of different compounds in an acidic solution and ion concentration levels due to the addition of basic and acidic solutions,


Electrochemistry Tutorial Sessions

Electrochemistry, the study of the conversion of chemical energy to electrical energy, is fundamental to the design of new and more efficient energy sources. Advances in electrochemistry have resulted in energy sources that are smaller in size and weight and have higher energy and power capacities.

In the electrochemistry tutor session reduction oxidation reactions, which are chemical reactions that involve the transfer of electrons from one substance to another, are defined. The operation of the basic electrochemical cell is graphically depicted and explained, standard reduction potentials are defined and the standard reduction potentials of different half-reactions involving different elements are compared. The spontaneity of redox reactions is explained in terms of spontaneous processes and relationship between the emf of a cell, free energy, work, voltage, and the equilibrium constant. Concentrations and their effect on cell Emf are mathematically related and used to derive the Nernst equation. The design of half cells with different concentration levels of aqueous solutions to construct concentration cells is explained in terms of La Chatelier's principles and the oxidation and reduction half-cell reactions.

The chemical constitution and construction of different types of batteries is illustrated. Batteries discussed include the dry cell battery, the mercury cell battery, the lead storage battery, the solid state lithium battery, the lithium iron magnesium battery and fuel cells. The session also includes a look at the elements that are used to construct batteries with the highest energy density ratios. The battery session also examines the anode, cathode and overall oxidation and reduction reactions for the most popular types of batteries.

Corrosion is also defined in the tutor session in terms of oxidation and reduction reactions. Electrolysis, the process of using electrical energy to cause a non-spontaneous chemical reaction to occur, is explained for the most common electrolysis processes: molten sodium chloride, water electrolysis, and the electrolysis of aqueous sodium chloride solutions. The use of anode and cathode reaction equations are used to illustrate how to calculate the quantities of metal and gas formed during the electrolysis process for a given amount of current.

In the electrochemistry problem solving tutor session, solutions to chemistry problems that are commonly encountered in the design of electrochemical cells (batteries), electrolysis and corrosion are explained and graphically illustrated. This includes problems that require the writing of balanced ionic equations that represent the oxidation and reduction of ions, the prediction of ion oxidation and reduction, the calculation of standard emfs of electrochemical cells, the use of standard reduction potential tables to calculate equilibrium constants, calculations of the free-energy change of reactions using reduction potentials of the elements involved in the reaction, determination of whether reactions are spontaneous or non-spontaneous, calculations of the molar concentrations of ions in electrochemical cells using the measured emf of the cell and the pressure of the gas in the cell, electrolysis analysis in terms of the electrode reactions, writing of half-cell reactions and the calculation of gas volumes in electrolytic cells.

Organic Chemistry Tutorial Sessions

Organic Chemistry and Biochemistry tutor lessons and topics include the study of carbon, the organic molecules formed from carbon, the sizes and shapes of carbon molecules, and the properties of carbon which make it the fundamental unit of biochemical life.

Classes of organic compounds are summarized according to their functional groups. Characteristics of the functional groups are also tabulated.

The properties and molecular structural characteristics of hydrocarbons are discussed in relation to the two main classes of hydrocarbons, aliphatic hydrocarbons and aromatic hydrocarbons. The aliphatic hydrocarbons are discussed in relation to the alkanes, alkenes, and alkynes that make up the class.

The properties of alkanes are summarized. How the International Union of Pure and Applied Chemistry nomenclature standards are used to determine the structural formula of alkanes from the IUPAC name. Type of reactions and reaction equations involve alkanes are discussed. The molecular structures and rings associated with substituted alkanes, cylcoalkanes, alkenes,

Functional groups discussed include the carbon-carbon double bond, the carbon-carbon triple bond, halogen, hydroxyl, carbonyl, carboxyl, ester and amine functional groups. Specific reactions that involve each functional group are highlighted.

The procedures for the identification of functional groups that are used to form alcohols, ketones, ethers, amines, esters, aldehydes and organic acids are listed. Additionally, the R-Group structure of amino acids is explored into its relationship to amino acids and the formation of polypeptide protein structures.


Polymers are another topic. The polymers tutor session discusses large carbon based molecules like proteins, nucleic acids and starch. The bonding characteristics of carbon that make possible the formation of hydrocarbon, polymer and biological molecules are also detailed. Amino acids are discussed in the context of proteins.

Linear hydrocarbon isomer naming conventions for single bonds and hydrocarbons with double and triple bonds is summarized. The the structure of the benzene ring is graphically illustrated and discussed in terms of its molecular structure.

The organic chemistry problem solving sessions include step-by-step methods on how to solve fundamental organic chemistry problems. Solutions to problems that involve the determination of the number of structural isomers of an organic compound, the IPUC name of an organic compound, the determination of a structural formula from an organic compounds name, if a molecule is chiral, the reaction of an organic compound in the presence of element compounds and catalysts.


Nuclear Chemistry Tutorial Sessions

The nuclear physics tutor session analyze the energy level of nuclear reactions, the functional operating characteristics and mass and energy calculations involved with nuclear reactions, as well as the biological impact of naturally occurring and man-made radioactive decay and waveforms. .

Changes within the nucleus of an atom are discussed in relation to radioactive decay of isotopes and nuclear fission and nuclear fusion reactions. Nuclear forces and their interaction with proton based electromagnetic repulsion forces are explained.

The differences between chemical reactions and nuclear reactions are summarized. Energy release is compared between nuclear reactions and chemical reactions per unit of mass of reactant. The processes in the formation of naturally occurring and nuclear reaction based radioactive isotopes are detailed. As well, the radioactive decay effects on nucleus changes are discussed.

The differences between alpha, beta and gamma radioactive decay and the energy level of each and how that energy effects biological life forms are topics in the session. Calculation of half-life for a radioactive substance and the amount of radioactive mass are solved graphically and with equations. Quarks and their role as substructures of protons and neutrons is another topic that is covered.

In the nuclear chemistry problem solving session, the methods, procedures and equations of nuclear chemistry are used to balance nuclear equations and calculate nuclear binding energy,


Historical Experiments Tutorial Session

A chemical discovery timeline is highlighted in the historical chemistry experiments tutorial session. The experiments that well known chemists performed to prove basic chemical theories and validate chemical methods and procedures are discussed. The experiments of Blaise Pascal, Robert Boyle, Antoine Lavoisier, Robert Brown, Thomas Graham, Louis Pastuer, Anders Jonas Armstrong, Francois-Marie Raoult, Marie Curie, Pierre Curie, Enest Rutheford and others are discussed.

Calculus: Calculus is a requirement for many majors including business, math, engineering, medicine and computer science. Calculus is used in almost all technical fields to perform a wide variety of calculations. In computer aided engineering, virtual shapes and forms are revolved and modified through the use of calculus based algorithms Business managers utilize calculus to determine the most cost effective methods of operation, for investment analysis and for the development of supply, demand and price models. In physics, calculus is used to determine projectile motion and the effects of forces in 2D and 3D space.

BookMark Tutoring provides calculus tutoring for high school academic and honor students as well as for college students. Calculus and differential equations tutoring is offered for undergraduate calculus courses. BookMark Tutoring also provides complete course instruction for those that are are taking online calculus courses, and those that plan to obtain Calculus college credits through CLEP testing, the AP calculus exam or need to score high in advanced SAT II college entrance exams.

BookMark provides answers and solutions to all basic Calculus questions and problems as well as the most difficult and procedurally intensive problems.

Continuity, Differentiability and Limit Tutorial Sessions

In calculus, a limit is the number which a dependent variable approaches as the independent variable approaches another value. Limits are used to prove the differential and integration properties of continuous functions.

In the limit tutor sessions, limits are found with several different procedures. These include numerical methods, graphical methods, algebraic methods, factoring methods and L'Hopital's rules. Geometric proofs are also used to solve for limits of special trigonometric functions.

In limits problem solving session limits for a wide variety of different function types, such as trigonometric, exponential, log and rational functions are explained. Problems that involve special limit cases including one sided limits, infinite limits, and limits at infinity are also solved. Limits are also used to determine whether or not a function converges or diverges.

Calculus Theorem Tutorial Sessions

continuity types, intermediate value theorem, extreme value theorem,


Derivative Tutorial Sessions

The derivative tutor session starts with a formal definition of a derivative. Procedures for the finding the derivative of a function are explained with examples.

The methods used to determine derivatives include the limit equation that defines a derivative at a point, the chain rule, the quotient rule, the power rule, implicit differentiation, and logarithmic differentiation These methods are used to find derivatives for algebraic, trigonometric, inverse trigonometric, exponential, logarithmic functions, inverse functions, composite functions and parametric functions.

The derivative tutor session also includes a discussion on the fundamental derivative theorems, Rolle's Thereon and the Mean Value Theorem. Problems that use these theorems are also illustrated.


Curve Sketching Tutorial Sessions

Instead of plotting out a function point by point, it is often easier to sketch a function by finding out the extrema, critical points, the direction of the slope in critical regions, asymptotes, inflection points and concave up and down regions of the function.

The use of limits, the first derivative and the second derivative are used in calculus to find a functions extrema (minimum and maximum values), the regions where the slope of the function is positive and negative, find a functions asymptotes, inflection points and the regions that a function is either concave up or down. With factoring methods, you can also find the roots of curves to improve your sketch of the function.

Curve sketching tutor sessions are supplemented with BookMark's sketching check list. The check list includes the 9 steps used for the sketching any type of function. using limits and the first and second derivative tests learn all the necessary calculations to determine critical points, maxima, minima, horizontal and vertical asymptotes, inflection points, concavity regions and the roots of the function.

Derivatives Applications Tutorial Sessions

In BookMark's calculus applications tutor sessions, you learn how the first and second derivative are used to solve optimization and related rate problems. BookMark also identifies the typical and more challenging types of rate and optimization problems that you will find in high school and college calculus courses, credit-by-exam courses and college entrance exams.

Integration Tutorial Sessions

Integration of a function is one of the most used mathematical procedure in calculus and the sciences. The ability to integrate functions using different integration techniques gives you the ability to solve many different classes of problems not only in calculus, but in business, engineering, biology, physics, statistics and chemistry.

In our calculus integration tutor sessions learn the integration techniques to find integrals for specific types of functions. Learn what types of integration procedures are used for rational functions, transcendental, trigonometric and conic functions. Find out which functions require algebraic substitution, integration by parts, trigonometric substitution, geometric substitution and partial expansion integration methods.

The integration tutor sessions also cover numerical methods for the calculation of a function's integral. These include Riemann's sums and Simpson Rules.

Series and Sequences Tutorial Session

In the series and sequences tutorial session, series and sequences are reviewed. Series are defined in terms of their limits and convergence and divergence properties. The major categories of series are defined, their characteristics and properties explained . Series discussed and working examples focus on the alternating series, geometric series, power series, power series, Taylor and Maclaurin series. The expansion of functions into series to solve integration problems is also explained in the tutor session.

Convergence Tutorial Sessions

Convergence and divergence of series and sequences is another major subject area in calculus. There are numerous tests that are performed on series and sequences to determine the convergence of a series. The type of test used depends in many cases on the type of series.

In calculus convergence tutoring sessions each type of convergence test is discussed with an emphasis placed on the most commonly used test which include the ratio test, the alternate series test and the comparison test. Other tests covered include the integral test and the p-series, alternation series, the harmonic series and root test.

Conics. Parametric's and Polar Coordinates Tutorial Session

Conics. polar coordinates and parametrics are used in the development of numerous types of graphic design automation programs. They are also used for the analysis of physics problems and in the design of machines.

In the conics tutor session, the primary conic equation and the types of conics it is used to represent are listed. Besides the generalized conic equation, conic equations specific to the ellipse, the parabola and the hyperbola are discussed in detail.

Proofs of the conic equations from their definitions is explained. Problems that involve finding the parameters of conics (major and minor axis, asymptotes, foci, eccentricity, area,) are explained and illustrated graphically.

In the parametric tutor session parametric equations, equations with two dependent variables and one independent variables, are covered. Characteristics and the graphs of different types of parametric equations are explained and examined.

Closely related to the topic of parametric equations are polar coordinates, coordinates that represent a point in space as an angle and a distance relative to an origin.

The polar coordinate system differs from the Cartesian coordinate system. In a Cartesian system, a point in space is represented by x and y coordinates that represent the horizontal and vertical distance from the origin of the coordinate system.

In the polar coordinates tutorial session, solutions to problems that require the conversion of a function from a polar function to a Cartesian function are explained.

Application problems center around the wheel. Problems that involve rolling wheels often require that a function and a point in space be defined in Cartesian and polar coordinate systems.

The tutor session also details the procedures for the sketching of polar functions with the polar coordinate system. Equivalent polar functions of commonly used Cartesian functions are listed along with their Cartesian graphs and polar graphs. These include the polar equations of conics, the polar equations used to represent planetary equations (Kepler's Laws) and the polar equation used to represent areas and arc length.

Vectors Tutorial Session

In the vectors tutorial session, the basics of vector analysis are covered. Typical vector operations are used to solve typical vector problems. Explained solutions utilize the vector dot product and vector cross product, vector differentiation and integration procedures to solve motion problems. The cylindrical and spherical coordinates systems, as well as 3D cartesian coordinate systems are used to solve different types of vector analysis problems.

Functions of Several Variables Tutorial Session

In the functions of several variables session, problems that are defined with two or more independent and dependent variables are solved. Students learn to solve multivariable problems that involve limits and continuity, partial derivatives, differentials, chain rules, directional derivatives and gradients, tangent planes and normal lines, extrema of functions and lagrange multipliers,



Trigonometry, Calculus,
Finite Mathematics.