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Gopi M.

Tutor for Science, Technology, Engineering and Math: K-College

Riverside, CA (92506)

Travel radius
40 miles
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My name is Gopi M. I have a Masters' degree in Chemical Engineering and I enjoy teaching, tutoring and coaching students to make them successful in life.

I am a chemical engineer/scientist with 34+ years of experience in the pharmaceutical/food/nutrition industry. I also teach part-time at Chaffey Community College, Rancho Cucamonga and I am an Adjunct Faculty at the University of Redlands and Visiting Professor at DeVry University- teaching all levels of Math (Basic Algebra to MBA Statistics) and Science (Chemistry, Physics, Biology, Life Sciences, Environmental Science and Nutrition) at DeVry University in Colton, CA.

I am happy to teach K-12 and College Math, Science, Engineering and Technology. My goal is to make everyone successful and show them how and why the subject being studied can be applied in day-to-day life and to pursue a successful career. This is extremely important, I think, to enjoy your studies, increase your knowledge and give a "fuller meaning" to one's life. Achieving the highest potential possible with every student in Math and Science is my goal.

Best regards,
Gopi M.

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Gopi’s subjects

ACT Math, Algebra 1, Algebra 2, Calculus, Differential Equations, Geometry, Linear Algebra, Prealgebra, Precalculus, Probability, SAT Math, Trigonometry
English, Public Speaking, Reading, SAT Reading, SAT Writing, TOEFL, Vocabulary, Writing
Mathematica, Microsoft Excel, Microsoft PowerPoint, Microsoft Word
Elementary Education:
Elementary Math, Reading, Study Skills, Vocabulary
Career Development, Finance, GMAT, GRE, Marketing, Microsoft Excel, Microsoft PowerPoint, Microsoft Word, Public Speaking
Algebra 1, Algebra 2, Biology, Calculus, Chemistry, English, Geometry, Physics, Prealgebra, Precalculus, Reading, SAT Math, SAT Reading, Study Skills, Writing
Test Preparation:
ACT Math, Career Development, GMAT, GRE, SAT Math, SAT Reading, SAT Writing, TOEFL
Corporate Training:
Career Development, Finance, GMAT, Microsoft Excel, Microsoft Word, Public Speaking

Algebra 1

This class is a study of the language, concepts, and techniques of Algebra that will prepare students to approach and solve problems following a logical succession of steps. Skills taught in the course lay groundwork for upper level math and science courses and have practical uses. Algebra I is offered 8th through 12th grade. The majority of students take Algebra I as 9th graders.


I have 34 years of work experience in Pharmaceutical/Food and Nutrition related to Botanical plants and have grown, harvested and processed plants for Nutrilite for 20 years. I have several patents on plants (botanical vegetables, fruits and herbal plants) for process development and also for new products from botanical plants. Also, I have launched these products world-wide as part of my work as a Scientist at Nutrilite. I have also published papers on processing of botanical plants for nutraceuticals.

Career Development

I am a professional Chemical Engineer with a Master's Degree in Chemical Engineering and 34 + years of Industrial Experience. I teach various classes as a Certified Kepner-Tregoe Specialist, Certified Green Belt for Operational Excellence, Certified Career Development Speaker for last 10 years at High Schools and Colleges: Chaffey Engineering College, Rancho Cucamonga, CA., UC Riverside and Adjunct Professor at the University of Redlands (since 2009).

Chemical Engineering

I have a Bachelor's and Master's Degree in Chemical Engineering. My Bachelor's degree is from University of Baroda, India (A+ Distinction) and my Master's degree is with a GPA of 3.3/4.0 from Oklahoma State University.
I have over 34 years of experience in the field of Chemical Engineering with 2 years working for US EPA; 9 years for GSK Company, NC; 2 years with Uncle Ben's Inc., Greenville, MS; and 21 years at Nutrilite/Amway, California.


High School chemistry looks at complex scientific concepts that may become tedious to study with the wrong approach. The curriculum must be detailed, while finding creative ways to illustrate the subject matter. Begin with atoms as the building blocks and show how these become molecules, compounds and elements and interact with each other in the world.

Begin the chemistry course with instruction on the scientific method, units of measurement, significant figures and uncertainty in measurements and calculations. Teach students how to measure things in chemistry using dimensions, temperature and density, as students will be doing these things throughout the year. Review what matter is, exploring it on the level of atoms and progressing to molecules and compounds. Use Dalton's atomic theory to show the way atomic theory has evolved, beginning with the simple concept that all matter is made of atoms, which are indivisible and indestructible.

Periodic Table
Explore the periodic table and its functions and significance, along with atomic masses and chemical equations. A general overview of the periodic table should mention the logic behind its layout--elements are arranged in order of elevating mass--as well as its relevant history: Dmitri Mendeleev originally created the periodic table and left blank spaces for elements whose existence he predicted but could not yet prove; Henry Moseley corrected the table by arranging atoms by their atomic number, or number of protons in an atom, and giving each element a different symbolic name.

Elementary Math

Students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative integers; they accurately compute and solve problems. They apply their knowledge to statistics and probability. Students understand the concepts of mean, median, and mode of data sets and how to calculate the range. They analyze data and sampling processes for possible bias and misleading conclusions; they use addition and multiplication of fractions routinely to calculate the probabilities for compound events. Students conceptually understand and work with ratios and proportions; they compute percentages (eg., tax, tips, interest). Students know about pi and the formulas for the circumference and area of a circle. They use letters for numbers in formulas involving geometric shapes and in ratios to represent an unknown part of an expression. They solve one-step linear equations.


Reading Comprehension lessons are designed so students learn to actively construct meaning when reading both fiction and non-fiction passages. Interactive high-interest lessons help students master key skills including identifying main idea , comparing & contrasting, identifying supporting facts and details, making inferences & drawing conclusions, predicting outcomes, recognizing fact & opinion, recognizing realism versus fantasy, identifying cause & effect, recognizing sequence of events and identifying story elements.


Welcome to Geometry
2. Geometry is a high school mathematics course designed for students who have successfully completed Algebra 1.
3. Geometry is a high school mathematics course designed for students who have successfully completed Algebra 1. This course emphasizes understanding the relationships among geometric figures and using those relationships along with your ____________ to solve problems.
4. Geometry is a high school mathematics course designed for students who have successfully completed Algebra 1. This course emphasizes understanding the relationships among geometric figures and using those relationships along with your ____________ to solve problems. algebra skills
5. STUDENT REQUIREMENTS You are expected to:
6. Have demonstrated mastery of Algebra 1 material with a final grade of ____________. STUDENT REQUIREMENTS You are expected to:
7. Have demonstrated mastery of Algebra 1 material with a final grade of ____________. STUDENT REQUIREMENTS C (or better) You are expected to:
8. Have demonstrated mastery of Algebra 1 material with a final grade of ____________. Attend class daily, participating in class discussions and activities. STUDENT REQUIREMENTS C (or better) You are expected to:
9. Have demonstrated mastery of Algebra 1 material with a final grade of ____________. Attend class daily, participating in class discussions and activities. Complete homework assignments. STUDENT REQUIREMENTS C (or better) You are expected to:
10. Have demonstrated mastery of Algebra 1 material with a final grade of ____________. Attend class daily, participating in class discussions and activities. Complete homework assignments. Study materials presented in class, online, and from the textbook. STUDENT REQUIREMENTS C (or better) You are expected to:
11. COURSE MATERIALS : Basic Text, Geometry, Concepts and Applications . Glencoe / McGraw-Hill, 2006.
12. COURSE MATERIALS : Basic Text, Geometry, Concepts and Applications . Glencoe / McGraw-Hill, 2006. TOOLS - Scientific Calculator, compass, protractor, ruler and straightedge three-ring binder, paper, and pencil(s).
13. COURSE MATERIALS : Basic Text, Geometry, Concepts and Applications . Glencoe / McGraw-Hill, 2006. TOOLS - Scientific Calculator, compass, protractor, ruler and straightedge three-ring binder, paper, and pencil(s). NOTE: If you should choose to purchase a graphing calculator, I recommend the TI-84 Plus.


GRE stands for graduate record examination. The GRE or Graduate Record Exam is required for admission to most U.S., Canadian, and UK graduate schools. Most students attend graduate business school for pursuing a Master degree. In addition, GRE can also be used for admission to PhD program. Graduate record examination GRE is a computer based examination and is administered and conducted worldwide by educational testing service (ETS). Graduate record examination GRE is a multiple choice test which tests a student’s verbal, mathematical and writing abilities for applicants to graduate schools.

The GRE® General Test is your gateway to graduate programs and an essential early step along your career path.

Each year, more than 600,000 prospective graduate school applicants from approximately 230 countries take the GRE General Test. Applicants come from varying educational backgrounds and countries, and the GRE General Test provides the only common measure for comparing their qualifications.

The GRE General Test is accepted at more than 3,200 graduate and business schools as well as departments and divisions within these schools.

Graduate programs and business schools use GRE® scores to evaluate your readiness for graduate-level work. The GRE General Test measures verbal reasoning, quantitative reasoning, critical thinking and analytical writing skills that are not related to any specific field of study.

• Analytical Writing — Measures critical thinking and analytical writing skills, specifically the test taker's ability to articulate complex ideas clearly and effectively

• Verbal Reasoning — Measures reading comprehension skills and verbal and analogical reasoning skills, focusing on the test taker's ability to analyze and evaluate written material

• Quantitative Reasoning — Measures problem-solving ability, focusing on basic concepts of arithmetic, algebra, geometry and data analysis

The new graduate record examination GRE from October 2007 will consist of 3 main sections:
• GRE Verbal
GRE Math/ Quant
• GRE Essay/ AWA
There are seven sub-sections to the GRE General Test:

Two Verbal Sections (38 questions and 30 min each)
Two Quantitative Sections (30 questions and 30 min each)
Two Analytical Sections (25 questions and 30 min each)
One Experimental Section (30 min)

The Experimental section is not scored, nor is it identified in the exam booklet. It may be of a verbal, quantitative, or analytical nature.

There are some important facts to remember when taking the GRE General Test. First, each question is worth the same number of points, no matter how hard or easy it is. Second, in each section except the reading comprehension questions (in the Verbal Section), the questions tend to go from easy to difficult. Therefore, it is foolhardy to spend too much time on early questions when you know that later ones will probably take even longer. You have somewhere around one minute or less to answer each question (on the average), so budget your time effectively. Finally, when in doubt, guess. Do not leave a question unanswered. There are no penalties on the General Test for wrong answers.

Your raw score (number of correct answers) is converted to a score on a scale of 200-800. If you miss all the questions, you still score 200. An 800 score can be achieved even if you miss one or two questions. The average scores for the GRE are about 470 for Verbal and 570 for Quantitative.
The Verbal, Quantitative, and Analytical scores are reported separately as scaled scores - you will also receive a percentile rank (indicating the percent of total examinees scoring below your score). Scores are mailed to you about six weeks after the test date.


I grew up in India and studied in Mumbai and New Delhi till I finished my Bachelors' degree in Chemical Engineering. Hindi and English are associate languages of India and one has to study and speak Hindi to get along in India,

Hindi was my second language and I took it all the way from Kindergarden to second year of college. I am fluent in speaking, writing and reading Hindi.


I have over 34 years of experience in Pharmaceutical/Food and Nutrition Marketing of botanical plant extracts. The last ten years I have worked to market and launch Botanical Extracts in Asia: Thailand, India, Malaysia, Philippines and Singapore. I have presented the advantages of nutrition from botanical plants and marketed products globally. I have extensive experience in Technical Marketing expertise in answering Frequently Asked Questions (FAQ's) related to marketing and consumption of nutraceutical products.

Microsoft Excel

Microsoft Excel 2000 and Microsoft Excel 2001 for Mac are very similar programs in many ways. For example, they share a common file format and they share most of the same features. However, there are some important differences that you may want to know when you work with both Excel 2000 and Excel 2001 for Mac.

In Excel 2001 for Mac, you cannot insert a Microsoft Data Map into a worksheet. There is no Map tool on the Standard toolbar, and the Map menu command does not appear on the Insert menu.
Convert from Excel 2000

If you open a workbook that contains a map that was created in Excel 2000, the map is imported as a picture and appears in black and white. If you double-click the map in Excel 2000, you receive the following error message:
Cannot start the source application for this object. There may not be enough memory available.
If you open a workbook that contains a map, make changes to the workbook, save it, and then reopen the workbook in Excel 2000, the map still works correctly.

For additional information, click the following article number to view the article in the Microsoft Knowledge Base:
274220 MacXL: Data maps are not supported in Microsoft Excel for Mac


I have 21 years of experience in the Nutrition Industry (Senior Research Scientist) at Nutrilite/Amway) and have over 10 patents in my name in the nutrition field. I have developed more than 10 nutrition supplements and have been awarded an Excellence Award, Creativity Awards and Industrial/Association recognition.


This course includes a study of sets of real numbers, solution of first and second-degree equations, graphing on the coordinate plane, applications of algebra to data analysis and probability, patterns and functions and their applications, measurement and discrete mathematics, and basic mathematical structures.

The course includes but is not limited to the following topics:

1. Number and Operations
2. Data Analysis, Probability, and Discrete Mathematics
3. Patterns, Algebra, and Functions
4. Geometry and Measurement
5. Structure and Logic


Sequence and Content

Quarter 1
Trigonometric Functions (Chapter 5)
Unit Circle and Radian Measure
Special Angles
Basic Identities: Reciprocal, Pythagorean, Even/Odd, Cofunction
Graphs of Trigonometric Functions (Chapter 5)
Variable amplitudes
Variable Vertical Shifts
Adding Sinusoids
Graphs of Tangent, Cotangent, Secant, and Cosecant
Basic Graphs
Trig Functions of Angles (Chapter 6)
Arc Length
Areas of Sectors
Angular and Linear Speed
Solving Right Triangles with Applications
Law of Sines
Law of Cosines

Quarter 2
Analytic Trigonometry (Chapter 7)
Fundamental Identities
Proving Identities
Simplifying Trig Expressions
Addition and Subtraction Formulas
Double and Half-Angle Formulas
Sum to Product Formulas
Inverse Trig Functions
Vectors (Chapter 7 and Section 9.8)
Dot Product
Angle Between Two Vectors
Vector and Parametric Equations of Lines
Vector and Parametric Equations of Circles, Ellipses, and Hyperbolas
Conversion from Parametric Form and Vice-versa
Graphing in Parametric Form
Polar Coordinates and Parametric Equations (Chapter 9)
Polar Coordinates
Polar Graphs: Spirals, Limaçons and Cardiods, Roses, Lines, Circles
Conversions from Polar to Parametric Form
Complex Numbers in Polar Form
DeMoivre's Theorem

Quarter 3
Functions (Chapter 2)
Average Rate of Change - Increasing and Decreasing Functions
Toolkit of Functions
Extreme Values
Combining Functions
One-to-One Functions and Their Inverses
Exponents and Logs (Chapter 4)
Logarithmic Functions
Laws of Logs
Log Equations
Polynomial and Rational Functions (Chapter 3)
Polynomial Functions and Their Graphs
Dividing Polynomials
Real Zeros of Polynomials
Polynomial Inequalities
Rational Functions
Rational Inequalities
Introductions to Limits

Quarter 4
Limits: A Preview of Calculus (Chapter 12)
Definition of Limit
Right and Left Limits
Limits from a Graph
Limits That Do Not Exist
The Derivative
Tangent Lines
Rates of Change
Falling Object Applications
Extreme Value Problems
Sequences and Series (Chapter 10)
Sigma Notation
Arithmetic Sequences and Series with Applications
Geometric Sequences and Series with Applications
Counting and Probability (Chapter 11)
Basic Counting Techniques
Permutations and Combinations
Conditional with Bayes Theorem (other sources)
Binomial Theorem and Pascal's Triangle with Applications to Binomial Probability (Chapter 10 plus other sources)
Expected Value

A graphing calculator is required for this course. No particular model is required, but the TI-89 and/or TI-83 will be used for demonstrations.
It is advisable to have a notebook in which to keep homework assignments, class notes, handouts, and returned quizzes.
A pencil is the preferred writing instrument. You may take class notes and do homework with an instrument of your choosing, but it is expected that you will do all tests and quizzes in pencil.

Public Speaking

I am a Scientist/Engineer for the last 34 years and have extensively traveled abroad to do technology transfer, product development and in-market launch of various products (pharmaceutical, food and nutrition) in all USA cities and Asian countries.

I have launched products in Asia going on stage, where audience numbered at rallies (Amway) from a few hundreds to a few thousands and I have delivered public speeches and motivational talks to launch health-care products.

Public speaking is second nature to me as a Technical Marketing scientist for the last ten years now,

SAT Math

SAT exam syllabus is broken down into two types of tests, the SAT subject test and SAT reasoning test. Each section will carry a score 200–800 and will be 225 minutes; the subjective test will be in the multiple choice mode and will have a time period of sixty minutes for it.

The test will cover sections like reading, math and writing which will also include an essay section. If we need to divide time per section that a student should on an average take 25 minutes or less than that to complete every section.

SAT 2012 syllabus for SAT subject test. The following subjects are covered in this section:

SAT EXAM Syllabus for SAT 2012

The critical reading
Paragraph-length critical reading: Twenty minutes
Sentence completions: Twenty five minutes
Reading comprehension: Twenty five minutes

Math section
Geometry Statistics: Twenty minutes
Algebra and functions: Twenty five minutes
Probability and Data analysis: Twenty minutes

The Writing
Essay section: Twenty five minutes
Multiple choice sections: Twenty five minutes and Ten minutes


Section Time Limit Questions Tasks
Reading* 60–80 minutes 36–56 questions Read 3 or 4 passages from academic texts and answer questions.
Listening 60–90 minutes 34–51 questions
Listen to lectures, classroom discussions and conversations, then answer
Break 10 minutes — —
Speaking 20 minutes 6 tasks Express an opinion on a familiar topic; speak based on reading and listening tasks.
Writing 50 minutes 2 tasks
Write essay responses based on reading and listening tasks; support an opinion in


The Trigonometry course is offered to students who have successfully completed
Algebra I, Algebra II, and Geometry. A practical and numerical application of the rules
of both algebra and geometry will be fundamental and a strong background in both
subject areas is necessary and recommended. Students who wish to proceed to higher
branches of pure and applied mathematics will benefit from a comprehensive study of
The Trigonometry course deals with the relationships of triangles and the theory
of the period functions connected with them and it is a basic tool used in the development
of mathematics and many sciences. The concepts studied will have applications in
surveying, navigation, engineering, physics, and chemistry. Students will learn to model
real-life problems mathematically by utilizing plane trigonometry.
The Trigonometry course will also employ computer technology to access
assisted instructional units for enrichment and to research, analyze, and calculate
trigonometry problems that address other disciplines in both the natural and physical
sciences. Students who complete the Trigonometry course will be able to continue their
studies with calculus and other advanced mathematics.
All students enrolled in the Trigonometry course will study the following Units:
1. Use trigonometry functions to solve right triangle problems.
2. Solve trigonometric equations.
3. Graph the six trigonometric functions.
4. Use the unit circle to define the six trigonometry functions.
5. Solve oblique triangles using other methods. 6. Use and graph the inverse trigonometry functions.
7. Trigonometric identities and formulas.
8. Complex numbers and polar coordinates.


College composition is an introductory course in collegiate writing that most students have to take. College composition introduces critical thinking and basic strategies of academic writing. This introductory course teaches students to refine topics, develop and support ideas, research, cite references, edit for style and word usage and write to an audience. Students will learn exposition and argument and provide a completely researched essay at the term's end.

The act of writing is actually very simple. Ironically, this simplicity is a complex skill that collegiate-level courses in writing must teach. Students majoring in English will have to take English literature courses, while students majoring in communications will more likely take creative writing or technical writing courses. Regardless, all students are required to pass basic college composition classes despite their area of study.

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M. S. University of Baroda, India

Oklahoma State University/ Southwestern Oklahoma State University (Master's)

Excellent Instructor — Mr. Gopi M. is an invaluable asset for students looking to further their understanding in difficult science subjects. I have rarely met a person with such a solid foundation in mathematics and chemistry as Mr. Gopi M. Beyond my current math courses, I will continue to rely upon his instruction to further my academic career. I recommend highly his services to any who needs a patient and extremely k ...

— David from Fontana, CA on 5/10/13

Hourly fee

Standard Hourly Fee: $45.00

Cancellation: 24 hours notice required

Discount offered for booking several sessions together at 10%.

Travel policy

Gopi will travel within 40 miles of Riverside, CA 92506.

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