Search 75,587 tutors
Over 400 tutoring hours

Paul Z.

High School Math Tutor/Teacher

Wake Forest, NC (27587)

Travel radius
10 miles
Hourly fee
Email Paul Z.

You don't pay for tutoring
unless you find a good fit!

Background Check Status for Paul Z.

Paul Z. passed a background check on 6/18/12. The check was ordered by Paul through First Advantage. For more information, please review the background check information page.

After sending a message to Paul, you will be able to order a new background check for $7.99. As part of your tutor selection process, we encourage you to run updated background checks. Please also review the safety tips for hiring tutors.

Experienced high school tutor and teacher of 40 years. Twenty years teaching in public schools and twenty years teaching in private schools. B.S.Ed. and M.S.Ed. in mathematics. Comfortable with classes from arithmetic through calculus. High average SAT scores in the past twenty years. I have been tutoring individuals since college and enjoy pupils of all ages. High school mathematics is a teachable skill available to everyone and all educated citizens should be knowledgeable through Calculus I.

Methods include academic dialogue as a pedagogical technique, didactic teaching, and lots of guided practice. Few good things result from a quick application, such as readying for the SAT I or II in a month. This generally does not work well for students. This test is more about how you use what you know rather than just what you know.

A high percentage of my students graduate from college as mathematics or applied mathematical science majors. Many local schools like NCSU or UNC Chapel Hill accept my students as well as schools like Princeton or Emory.

Email Paul

Paul’s subjects

ACT English

On the ACT English test, six elements of effective writing are included in the English Test: punctuation, grammar and usage, sentence structure, strategy, organization, and style. The questions covering punctuation, grammar, and sentence structure make up the Usage/Mechanics subscore. The questions covering strategy, organization, and style make up the Rhetorical Skills subscore.
Punctuation (13%). Questions in this category test your knowledge of the conventions of internal and end-of-sentence punctuation, with emphasis on the relationship of punctuation to meaning (for example, avoiding ambiguity, indicating appositives).
Grammar and Usage (16%): Questions in this category test your understanding of agreement between subject and verb, between pronoun and antecedent, and between modifiers and the word modified; verb formation; pronoun case; formation of comparative and superlative adjectives and adverbs; and idiomatic usage.
Sentence Structure (24%): Questions in this category test your understanding of relationships between and among clauses, placement of modifiers, and shifts in construction.
Rhetorical Skills
Strategy (16%): Questions in this category test how well you develop a given topic by choosing expressions appropriate to an essay's audience and purpose; judging the effect of adding, revising, or deleting supporting material; and judging the relevance of statements in context.
Organization (15%): Questions in this category test how well you organize ideas and choose effective opening, transitional, and closing sentences.
Style (16%): Questions in this category test how well you select precise and appropriate words and images, maintain the level of style and tone in an essay, manage sentence elements for rhetorical effectiveness, and avoid ambiguous pronoun references, wordiness, and redundancy.

We shall focus on 8 test taking strategies that will maximize your score in this area of the ACT test.

ACT Math

SAT/ACT Course Description: Topics include

Digit Value and Divisibility; Consecutive Integers, Remainders, and Even and Odd Integers; Prime Numbers, Fractions, and Decimals; Percents, Percent Equations, Markup, and Discount Ratio and Proportion; Average and Distance-Rate-Time; Consumer Problems and Time; Integers, Terminology; Equations: Solving, Substitution, and Systems; More Equations and Word Problems: Age, Work-Rate, Mixture, and Word Interpretation; Exponents and Radicals; Scientific Notation and Inequalities; Plugging In, Factoring, and Solving Equations; Angles and Parallel Lines; Triangles; Special Right Triangles; Composite Figures; Perimeter, circumference, and area; More Problems Involving Circles; Volume; Graphing; Sequences and Number Theory; Counting Principles and Probability ; Statistical Averages; Graphs and Statistical Word Play; More Number Theory; Absolute Value; Exponents and Radicals; Equations; Slope; Equations of Lines; Functions; Transformations; Rational Expressions and Rational Equations; Proportions in Similar Triangles; Variation; Sets; Sequences; Mean, Median, and Mode; Misc. Geometry; Trigonometry

ACT Reading

The ACT Reading Test is a 40-question, 35-minute test that measures your reading comprehension. You're asked to read four passages and answer questions that show your understanding of: what is directly stated; statements with implied meanings
Specifically, questions will ask you to use referring and reasoning skills to: determine main ideas; locate and interpret significant details; understand sequences of events; make comparisons; comprehend cause-effect relationships; determine the meaning of context-dependent words, phrases, and statements; draw generalizations; and analyze the author's or narrator's voice and method.
The test comprises four prose passages that are representative of the level and kind of reading required in first-year college courses; passages on topics in social studies, natural sciences, prose fiction, and the humanities are included. We shall prepare to master this section using nine test strategies for scoring your best on this portion of the ACT test.

ACT Science

This test assumes that students are in the process of taking the core science course of study (three years or more) that will prepare them for college-level work and have completed a course in Earth science and/or physical science and a course in biology.

The test presents seven sets of scientific information, each followed by a number of multiple-choice test questions. The scientific information is presented in one of three different formats: data representation (graphs, tables, and other schematic forms); research summaries (descriptions of one or more related experiments); conflicting viewpoints (expressions of several related hypotheses or views that are inconsistent with one another).

The questions require you to: recognize and understand the basic features of, and concepts related to, the provided information; examine critically the relationship between the information provided and the conclusions drawn or hypotheses developed; generalize from given information and draw conclusions, gain new information, or make predictions.

We shall focus on the four (4) test strategies that work best for the majority of test-takers.

Algebra 1

Algebra 1 covers the fundamental concepts of algebra, including exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, factoring quadratics, complex numbers, completing the square, and the quadratic formula. Students are ready for this class if they have mastered arithmetic with fractions, decimals, percents, and negative numbers. Most students who have completed a typical Prealgebra class are ready for this course.

Algebra 2

Algebra 2 covers quadratic equations, graphing, complex numbers, functions, sequences and series, and exponents and logarithms. Problem solving skills are emphasized throughout, and time is devoted to advanced topics like telescoping sums and piecewise functions. This course also covers quadratics, conics, polynomials, functions, logarithms, clever factorizations and substitutions, systems of equations, sequences and series, symmetric sums, advanced factoring methods, classical inequalities, and functional equations. Students are ready for this class if they have mastered square roots and fractional exponents, order of operations, linear equations and inequalities, ratio, and proportion. I recommend that students have experience with factoring quadratics prior to taking this course.

American History

This course is a study of American history from pre-colonial times until the present. Topics include: introducing the student to the character of American history and culture both as background to contemporary institutions and as a major force in world development; placing the development of American history and culture within a general historical context in order to provide the student with a perspective of America's place within the experience of mankind; fostering an understanding of the interplay of politics, economics, and cultural changes by observing the manner in which alterations in one bring on changes in the others. To teach the historical method as a means of critical thinking, including the evaluation of conflicting testimony in assessing historical fact and assisting the student in applying this historical perspective to the major trends examined.


The mathematics portion of this test measures your reasoning ability in three areas: arithmetic (number theory); algebra; and geometry. My Comprehensive Arithmetic Reasoning and Mathematics Knowledge review includes:
•The Easiest Math Review You'll Ever experience
•Solving for Variables
•Breezing Through Word Problems
•Keeping Probability Simple
•Using the Right Formulas
•Graphing for Success
•Racing Through Ratios
•Understanding Line Plotting
•Mastering Difficult Problems


Although biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy, this course is intended for the generalist.

Whether you are a high-school student or a college student facing 1500 pages of text to learn and understand, I can help you make sense of all the facts, confusing diagrams, and giant molecules that make up the majority of general biology. We'll take the study a step at a time.

Along the way, I will be showing student study- or organizational skills invaluable not only to remember the vast amount of information, but also how to tie everything together into a coherent whole.


I am a certified AP-calculus teacher, and I have been teaching this subject continuously since 1990.

This course covers limits, continuity, derivatives and their applications, definite and indefinite integrals, infinite sequences and series, plane curves, polar coordinates, and basic differential equations. At the conclusion of the course, students should have sufficient preparation to take the AP Calculus BC exam; however, "AP exam preparation" is not the main focus of the course. (Note: this exam is not offered by me -- you will have to privately arrange to take the exam at a local school if you are interested.) There are two main things I hope to accomplish (that many high-school calculus courses do not): 1) Students will gain a fundamental understanding of single-variable calculus, beyond the level of rote calculation; and 2) Students will learn how to apply calculus techniques to solve difficult problems. For better or worse, the standard high-school calculus curriculum usually only stresses #1 a little bit and #2 not at all, in favor of repeated examples of solving essentially the same problem over and over again. However, my course is not "rigorous" in the sense that a college-level Real Analysis course would be. Although we will try to gain a deeper understanding of many calculus concepts, we will not commit to rigorously proving every result.


This course is designed specifically for high school students of chemistry. We shall study atomic structure and the periodic table; bonding; rates of chemical reactions; gases; liquids, solids and phase changes; properties of solutions; acid-base equilibria in aqueous solution; chemical equilibrium; chemical thermodynamics; oxidation and reduction.

Elementary Math

This course is primarily intended for students 11 years and older.

Students will acquire number sense and perform operations with whole numbers, simple fractions, and decimals.
• Use concrete objects and visual models to add and subtract common decimals.
• Explore numbers less than zero by extending the number line and by using familiar applications such as temperature.
• Investigate the concept of ratio (e.g., the number of students to the number of teachers).

Students will use patterns and relations to represent mathematical problems and number relationships.
• Use concrete materials to build an understanding of equality and inequality.
• Explore properties of equality in number sentences (e.g., when equals are added to equals, then the sums are equal; when equals are multiplied by equals, then the products are equal).

Students will understand attributes and properties of plane geometric objects and spatial relationships.
• Analyze results of transformations (e.g., translations, rotations, reflections) on two-dimensional shapes.
• Investigate two-dimensional representations of three-dimensional objects.

Students will describe relationships among units of measure, use appropriate measurement tools, and use formulas to find area measurements.
• Investigate perimeter of rectangles and squares.
• Investigate area of trapezoids.

Students will interpret and organize collected data to make predictions, answer questions, and describe basic concepts of probability.
• Explore minimum and maximum values for a set of data.
• Explore mean, median, mode, and range.


English is a very broad term covering a wide variety of skills, and individual needs take precedence over the items described below.
Normally preliminary discussion with the student or parent is required before mapping out a curriculum.

This course will ask you to read and analyze articles on a variety of subjects. You will then be asked to interpret what the author was saying. We will select several articles or books on subjects that will interest you, and revive your joy of reading as well. The focus here is on grammar and vocabulary. The course helps you recognize the different parts of speech. These include direct objects, relative pronouns, transitive verbs, and sentence construction. There are also vocabulary exercises. This course will teach you how to write clearly. You will understand how to write a complete paragraph and express complete thoughts. Descriptive and creative writing strategies are developed. A comprehensive review of the elements of the English language, grammar, vocabulary, punctuation and the basic elements of writing are all addressed as well. This course reviews the essential skills in grammar and sentence structure necessary to write and effective paragraph. It teaches students how to choose a topic and develop their ideas, with appropriate details, as well as how to edit and revise their writing using clear, effective prose. The student will be asked to choose one of several books, such as “A Red Badge of Courage” or “A Tale of Two Cities”. After finishing the book, you will be asked to analyze the book, following the course guidelines.

European History

The study of European history introduces students to cultural, economic, political, and social developments that played a fundamental role in shaping the world in which they live. Without this knowledge, we would lack the context for understanding the development of contemporary institutions, the role of continuity and change in present-day society and politics, and the evolution of current forms of artistic expression and intellectual discourse. In addition to providing a basic narrative of events and movements, the goals of this course in European History are to develop (a) an understanding of some of the principal themes in modern European History, (b) an ability to analyze historical evidence and historical interpretation, and (c) an ability to express historical understanding in writing.


Although I tutor all sections of the GED test, some students are interested only in the math portion, described below.

This 90-minute, 50-question test has two equally weighted parts, the first of which allows candidates to use calculators, while the second forbids their use. Test-takers must use the calculators issued at the testing center, no other.
Forty of the 50 questions are multiple-choice; the other 10 use an alternate format, requiring the test-taker to record answers on either a numerical or coordinate-plane grid. Both portions of the test have questions of both types. The test booklet offers a page of common formulas as well as directions for completing the alternate-format items and using the calculator.
The test focuses on four main mathematical disciplines:
• Number operations and number sense
• Measurement and geometry
• Data analysis, probability, and statistics
Algebra, functions, and patterns


This course is dedicated to a study of the world around us. The class starts with an introduction to geography, in which students will learn the five themes of geography, the features that define the earth, the climate patterns of the earth, how to study peoples and cultures of the earth and how to use various geographic tools. From there students will use the skills they have learned to apply to the ten areas of the world we will be studying. In addition to using these skills to apply to ten areas, the students will look at the physical features of those areas (land, climate, and types of vegetation). Each area will also be addressed in terms of its culture, which includes studies of population patterns, history and government, and cultures/lifestyles. The final area to be addressed to each of the ten areas is current news about the area. This includes current living conditions, current news events, and how people there are interacting with their environment.


This course covers a full geometry curriculum, plus many advanced problem solving geometric applications not found in a standard geometry class. Topics covered in the class include triangle similarity and congruence, complicated area problems, mastering the triangle, special quadrilaterals, polygons, the art of angle chasing, construction, power of a point, 3-dimensional geometry, transformations, analytic geometry, basic trigonometry, and geometric proofs. This class is ideal for students in grades 7-10 who have mastered basic algebra. Participants should have completed Algebra 1 either in their regular school.


The GMAT exam is a computer-adaptive assessment with proven validity in predicting success in the first year of graduate management education. More than 5,400 programs use it as a consistent, objective way to compare aspiring students worldwide—no matter what their education, age, gender, or citizenship—and to evaluate whether they are prepared for the rigors of a graduate management program.

The exam assesses higher-order reasoning skills: Verbal, Quantitative, Analytical Writing, and Integrated Reasoning.

In this course we shall review all topics covered on the current revised exam or those topics that you believe you are most uncomfortable with, and practice taking computer-adapted GMAT tests. (I have paper practice tests but the GMAT exam is not administered in that format. However, the paper tests are an excellent source of authentic questions.)

I do not advocate learning "quick tricks" for any standardized tests. The test makers know these tricks and take them into account in their questions.

Government & Politics

I have been tutoring students in Government and Politics since 1987. After this course, students will be able to:
• Understand important facts, concepts and theories pertaining to U.S. government and politics
• Understand typical patterns of political processes and behavior and their consequences (including the components of political behavior, the principles used to explain or justify various government structures and procedures, and the political effects of these structures and procedures)
• Be able to analyze and interpret basic data relevant to U.S. government and politics (including data presented in charts, tables and other formats)
• Be able to critically analyze relevant theories and concepts, apply them appropriately and develop their connections across the curriculum


The GRE revised General Test, introduced in August 2011, features a new test-taker friendly design and new question types. It more closely reflects the kind of thinking you'll do in graduate or business school and demonstrates that you are ready for graduate-level work.
•Verbal Reasoning — Measures your ability to analyze and evaluate written material and synthesize information obtained from it, analyze relationships among component parts of sentences and recognize relationships among words and concepts.
•Quantitative Reasoning — Measures problem-solving ability, focusing on basic concepts of arithmetic, algebra, geometry and data analysis.
•Analytical Writing — Measures critical thinking and analytical writing skills, specifically your ability to articulate and support complex ideas clearly and effectively.

Often, students feel they are not ready in only one of the three tested areas. If that is the case, then we shall only cover the topic(s) the student needs for review.


Writing persuasively about one or more sources begins, of course, with engaged reading. We all sift the best practices to find approaches that will help a student interact with the text. Since there is so little room in the syllabus to use the best incentive for engaged reading -- personal choice -- teachers seek meaningful activities that will energize the act of reading. Literature Circles, reader response journals, two-and-three column notes, Venn Diagrams, double entries, porcupine notes, entry/exit cards, questions, highlighting, color marking -- any of these can help the reader both comprehend and interact with the material. Once the student has "something to say," then she is more interested in learning how to incorporate the sources that generated her ideas.

While the skill of documentation can be taught and learned fairly quickly, the art of selecting evidence comes through time and practice. Anyone can work through the mechanics of quotation marks, the order of internal documentation, and the sentences that lead into or out of the quotation. And these are of course crucial. But the real learning comes in knowing how to choose and present the evidence. What is the difference between paraphrase and summary? What is "mere" summary, and what is summary-as-evidence? What should be quoted, and when? What about offering no quotations at all?

My students seem to often fall into two kinds of thinkers/writers: those who document explicitly, complete with quotations, links, and examples, and those who work implicitly, playing dangerously close to summary. Rarely able to convert either to the other's camp, I have learned instead to focus on helping each become better at her preferred method. After some mini-instruction on formats, I use models from current and previous students for discussion of the effectiveness of the choices they made.

Physical Science

Physical Science is normally a broad survey primarily of physics and chemistry. Also included in physical science may be coverage of the sciences of astronomy, physical and historical geology, meteorology, earth science, and sometimes physical geography. Courses may differ but, in general, physical science may include a survey of all sciences except life science. Working with formulas is also a normal part of physical, although mathematics beyond pre-algebra or algebra is rare. Physical science is intended for both high school and college students.


What is the most important word in the English language? I suggest that the word is "relationship." Every thought and action carried out in our minds and lives boils down to a relationship between two things. We're never interested in just one thing; always in how that one thing relates to another thing. I suggest that the second most important word in the English language is "change." Once we establish a relationship between two things, like displacement and time giving us velocity, we want to know how that relationship changes, in this example, acceleration. Physics is the study of relationships, which we sometimes call equations, and how those relationships change.

This course is designed to be a non-calculus based physics course that covers a very wide range of topics, including mechanics, fluids, thermodynamics, fluids, waves and optics, electromagnetism, and atomic and nuclear physics. Students in an honors physics course in high school or AP Physics B will find this course created for their particular needs. It is important to plan out a schedule to cover the topics and stick with it. I spend a great deal of time on conceptual development and problem solving, so I do not plan for labs unless the student is being home-schooled and then I have the students do labs, and I make them count. The student needs to be able to take data, with or without high-tech probes and software, organize the data, analyze the data and sources of error, draw conclusions, and explore ways to improve or extend the experiment. I guide my students in such a way that they design the procedure of the labs themselves. I tell them what equipment they have available to them and what it is I want them to measure, and let them go. I have found my students really enjoy the freedom to be creative in the lab.


Prealgebra includes a thorough exploration of the fundamentals of arithmetic, including fractions, exponents, and decimals. I introduce beginning topics in number theory and algebra, including common divisors and multiples, primes and prime factorizations, basic equations and inequalities, and ratios. Prealgebra also includes square roots, a thorough exploration of geometric tools and strategies, an introduction to topics in discrete mathematics and statistics, and a discussion of general problem-solving strategies.


This course covers all topics needed for the study of calculus, including: Lines in the Plane; Functions; Graphs of Functions; Shifting, Reflecting, and Stretching Graphs;
Combinations of Functions; Inverse Functions; Linear Models and Scatter Plots; Quadratic Functions; Polynomial Functions of Higher Degree; Real Zeros of Polynomial Functions; Complex Numbers; The Fundamental Theorem of Algebra; Rational Functions and Asymptotes;
Graphs of Rational Functions; Quadratic Models; Exponential Functions and Their Graphs; Logarithmic Functions and Their Graphs; Properties of Logarithms; Solving Exponential and Log Models; Exponential and Logarithmic Models; Nonlinear Models; Radian and Degree Measure; Trigonometric Functions: The Unit Circle; Right Triangle Trigonometry; Trigonometric Functions of Any Angle; Graphs of Sine and Cosine Functions; Graphs of Other Trigonometric Functions; Inverse Trigonometric Functions; Applications and Models; Using Fundamental Identities; Verifying Trigonometric Identities; Solving Trigonometric Equations;
Sum and Difference Formulas; Multiple-Angle and Product-Sum Formulas; Law of Sines; Law of Cosines; Vectors in the Plane; Vectors and Dot Products; Trigonometric Form of a Complex Number; Solving Systems of Equations; Systems of Linear Equations in 2 Variables; Multivariable Linear Systems; Matrices and Systems of Equations; Operations with Matrices;
The Inverse of a Square Matrix; The Determinant of a Square Matrix; Applications of Matrices and Determinants; Sequences and Series; Arithmetic Sequences and Partial Sums; Geometric Sequences and Series; Mathematical Induction; The Binomial Theorem; Counting Principles;
Probability; Circles and Parabolas; Ellipses; Hyperbolas; Rotation and Systems of Quadratic Equations; Parametric Equations; Polar Coordinates; Graphs of Polar Equations; Polar Equations of Conics; The Three-Dimensional Coordinate System; Vectors in Space; The Cross Product of Two Vectors; Lines and Planes in Space; Introduction to Limits; Techniques for Evaluating Limits; The Tangent Line Problem; Limits at Infinity and Limits of Sequences; The Area Problem.


The Preliminary SAT/National Merit Scholarship Qualifying Test (PSAT/NMSQT) is a standardized test administered by schools that gives students firsthand practice for the SAT and tests critical reading, math and writing skills. (U.S. citizen students in the 11th grade who take the PSAT/NMSQT are also eligible for National Merit scholarship programs.) All students who take the PSAT/NMSQT can gain access to college and career planning tools.

Of the different sections listed above, the most critical for predicting success in college are the critical reading and math section. Because some students need help in only one or two areas of the test, this course is specifically tailored to fit the student's needs.

SAT Math

SAT/ACT Course Description: Topics include

Digit Value and Divisibility; Consecutive Integers, Remainders, and Even and Odd Integers; Prime Numbers, Fractions, and Decimals; Percents, Percent Equations, Markup, and Discount Ratio and Proportion; Average and Distance-Rate-Time; Consumer Problems and Time; Integers, Terminology; Equations: Solving, Substitution, and Systems; More Equations and Word Problems: Age, Work-Rate, Mixture, and Word Interpretation; Exponents and Radicals; Scientific Notation and Inequalities; Plugging In, Factoring, and Solving Equations; Angles and Parallel Lines; Triangles; Special Right Triangles; Composite Figures; Perimeter, circumference, and area; More Problems Involving Circles; Volume; Graphing; Sequences and Number Theory; Counting Principles and Probability ; Statistical Averages; Graphs and Statistical Word Play; More Number Theory; Absolute Value; Exponents and Radicals; Equations; Slope; Equations of Lines; Functions; Transformations; Rational Expressions and Rational Equations; Proportions in Similar Triangles; Variation; Sets; Sequences; Mean, Median, and Mode; Misc. Geometry; Trigonometry

SAT Reading

The SAT doesn’t test logic or abstract reasoning. It tests the skills you’re learning in school: reading, writing and math. Your knowledge and skills in these subjects are important for success in college and throughout your life.

The critical reading section includes reading passages and sentence completions, and is considered by many professional educators to be a more accurate predictor of success in college than other parts of the exam.

In my test preparation, we shall apply several strategies to help prepare for the reading sub-section and apply a few strategies to aid in the sentence-completion portion of this part of the verbal test. Although there are no "tricks" that work on the SAT, the test is extremely predictable. Once you are sufficiently prepared, you will be able to maximize your test score.

One last word: Please do not wait until two weeks prior to the SAT before you start looking for help. Cramming makes little or no statistical difference to your score.

SAT Writing

The writing section of the SAT measures a student’s ability to recognize and conform to the conventions of standard written English. This section consists of one student-written essay and multiple-choice questions. The multiple-choice questions carry a .25-point penalty for incorrect answers. The writing section contains three types of multiple-choice questions:

•Identifying Sentence Errors
•Improving Sentences
•Improving Paragraphs

The format of the two multiple-choice sections is:

•25 minutes: 11 Improving Sentence questions, 18 Identifying Sentence Error questions, and 6 Improving Paragraphs questions
•10 minutes: 14 Improving Sentence questions

By applying appropriate strategies and incorporating sufficient practice, a student can maximize his time and score on this portion of the test. We will focus on all aspects of the writing section, including the essay.


The SSAT measures student ability. It is not an achievement test; therefore, it acts as a common denominator for schools in measuring a student’s academic capabilities, regardless of his or her school record. When used for admission by independent schools, the test is only one piece of information that is considered. SSAT scores, however, do carry some weight in varying degrees among independent schools. Consequently, you should be as prepared to take the test as possible.

Since the SSAT provides predicted 12th grade SAT scores for those students taking the test in the 7th through 10th grades, participation in this testing exercise will also provide you with valuable information regarding your educational strengths and weaknesses.


This course is a complete trigonometry course and includes the following topics: Radian and Degree Measure; Trigonometric Functions: The Unit Circle; Right Triangle Trigonometry; Trigonometric Functions of Any Angle; Graphs of Sine and Cosine Functions; Graphs of Other Trigonometric Functions; Inverse Trigonometric Functions; Applications and Models; Using Fundamental Identities; Verifying Trigonometric Identities; Solving Trigonometric Equations;
Sum and Difference Formulas; Multiple-Angle and Product-Sum Formulas; Law of Sines; Law of Cosines; Vectors in the Plane; Vectors and Dot Products; Trigonometric Form of a Complex Number;


A person's vocabulary is the set of words within a language that are familiar to that person. A vocabulary usually develops with age, and serves as a useful and fundamental tool for communication and acquiring knowledge. A literate person's reading vocabulary is all the words he or she can recognize when reading. This is generally the largest type of vocabulary simply because it includes the other three. A person's listening vocabulary is all the words he or she can recognize when listening to speech. This vocabulary is aided in size by context and tone of voice. A person's speaking vocabulary is all the words he or she can use in speech. Due to the spontaneous nature of the speaking vocabulary, words are often misused. This misuse – though slight and unintentional – may be compensated by facial expressions, tone of voice, or hand gestures.

The importance of a vocabulary
• An extensive vocabulary aids expressions and communication.
• Vocabulary size has been directly linked to reading comprehension.
• Linguistic vocabulary is synonymous with thinking vocabulary.
• A person may be judged by others based on his or her vocabulary.

There are various methods and strategies for improving one's vocabulary. In this course, we will determine which type of vocabulary needs to be improved and we will employ the appropriate strategies to develop a vocabulary necessary to the use of Standard American English.

World History

Put simply, world history is macro history. Although it is important for students of world history to have a deep and nuanced understanding of each of the various cultures, states, and other entities that have been part of the vast mosaic of human history, the world historian stands back from these individual elements in that mosaic to take in the entire picture, or at least a large part of that picture. Consequently, world history studies phenomena that transcend single states, regions, and cultures, such as cultural contact and exchange and movements that have had a global or at least a transregional impact. World history is not, therefore, the study of the histories of discrete cultures and states one after another and in isolation from one another. It is also not necessarily global history. That is, world history is not simply the study of globalization after 1492. As long as one focuses on the big picture of cultural interchange and/or comparative history, then one is studying world history, which is a relatively new discipline.


What makes this writing course different from other high school English courses is its focus on rhetoric. While promoting writing in many contexts for a variety of purposes, this English Language course is the place where nonfiction texts and contexts take center stage. Here students think deeply about language as a persuasive tool and about the dynamic relationship of writer, context, audience, and argument. To best serve your students' learning, this course focuses primarily on nonfiction. This "finding of the argument" and "making of their own arguments" is often new for students, so give them time for reading, thinking, and writing. Reading time allows them to begin to recognize the various shapes and parts of an argument. Thinking time helps them explore issues, think about logical reasoning, and begin to understand appeals and rhetorical modes. Writing time provides them with the opportunity to work through the process of creating an argument. Most importantly, introduce your students to rhetorical terms and tasks: make sure they have a working vocabulary in rhetoric. Invite them to internalize Aristotle's three modes of logos, ethos, and pathos as elements that control persuasion. Ask them to refute, defend, or challenge. This course is designed with these ends in as objectives.

Read all subject qualifications »

Email Paul

back to top


University of Toledo (Mathematics Educatio)

University of Toledo (MEd)

Duke University (PhD)

Great servant to others Paul is a great tutor and servant to others. He genuinely cares for his students and wants to see them succeed. ...

— Stephen from Raleigh, NC on 4/30/14);

Hourly fee

Standard Hourly Fee: $40.00

Cancellation: 6 hours notice required

Flexible rate policies for groups and multiple-hour lessons.

Travel policy

Paul will travel within 10 miles of Wake Forest, NC 27587.

Email Paul

Usually responds in about 4 hours

Send Paul a message explaining your needs and you will receive a response by email. Have you already emailed Paul or another tutor? If so, you have an account! Sign in now

(ex: algebra, chemistry)
Please enter the tutor's email address.
Please enter the student's email address.
Please describe how you heard about us.

Receive Responses From Additional Tutors

If selected, WyzAnt will ask interested tutors to contact you by email if they are able to help. A maximum of five different tutors will email you and none of your personal information, including your email address, will be released.