**Professor:** Dr. Kevin L. Powell, Mathematician and Physicist

**Email:** kevin@tutorincharlotte.com

**Phone: **704-719-0956 Fax documents to: 704-909-2701 using this: cover page.

**Office Hours:** 8:00 a.m. to 3:00 p.m. No phone calls will be accepted when online tutoring is being done with the exception of in-person tutoring.

**High School Calculus AB and College Calculus I** Intensive 1 on 1 Tutoring $180.00 Per Month for 12 Hours of Online Tutoring! $260.00 Per month for 12 hours of Online Tutoring and 12 Hours of In-Person Tutoring.

**High School Calculus AB and College Calculus I** **Tutoring Description: **

**Before studying calculus, **all students should complete four years of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions . These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions . In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions.

**High School Calculus AB and College Calculus I** **Tutoring Description:**

**I. Functions, Graphs, and Limits**

**Analysis of graphs.** With the aid of technology, graphs of functions are often easy to produce. The emphasis is on the interplay between the geometric and analytic information and on the use of calculus both to predict and to explain the observed local and global behavior of a function.

**Limits of functions (including one-sided limits)**

## • An intuitive understanding of the limiting process.

## • Calculating limits using algebra.

## • Estimating limits from graphs or tables of data.

**Asymptotic and unbounded behavior**

## • Understanding asymptotes in terms of graphical behavior.

## • Describing asymptotic behavior in terms of limits involving infinity.

## • Comparing relative magnitudes of functions and their rates of change (for example, contrasting exponential growth, polynomial growth, and logarithmic growth).

**Continuity as a property of functions**

## • An intuitive understanding of continuity. (The function values can be made as close as desired by taking sufficiently close values of the domain.)

## • Understanding continuity in terms of limits.

## • Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem).

**II. Derivatives **

**Concept of the derivative**

## • Derivative presented graphically, numerically, and analytically.

## • Derivative interpreted as an instantaneous rate of change.

## • Derivative defined as the limit of the difference quotient .• Relationship between differentiability and continuity.

**Derivative at a point**

## • Slope of a curve at a point. Examples are emphasized, including points at which there are vertical tangents and points at which there are no tangents.

## • Tangent line to a curve at a point and local linear approximation.

## • Instantaneous rate of change as the limit of average rate of change.

## • Approximate rate of change from graphs and tables of values.

**Derivative as a function**

## • Corresponding characteristics of graphs of ƒ and ƒ’.• Relationship between the increasing and decreasing behavior of ƒand the sign of ƒ’.

## • The Mean Value Theorem and its geometric interpretation.

## • Equations involving derivatives. Verbal descriptions are translated into equations involving derivatives and vice versa.

**Second derivatives**

## • Corresponding characteristics of the graphs of ƒ, ƒ∙, and ƒ’’.

## • Relationship between the concavity of ƒ and the sign of ƒ’’.

## • Points of inflection as places where concavity changes.

**Applications of derivatives**

## • Analysis of curves, including the notions of monotonicity and concavity.

## • Optimization, both absolute (global) and relative (local) extrema.

## • Modeling rates of change, including related rates problems.

## • Use of implicit differentiation to find the derivative of an inverse function.

## • Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.

## • Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations.

**Computation of derivatives**

## • Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions.

## • Derivative rules for sums, products, and quotients of functions.

## • Chain rule and implicit differentiation.

**III. Integrals**

**Interpretations and properties of definite integrals**

## • Definite integral as a limit of Riemann sums .

## • Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval.

## Basic properties of definite integrals (examples include additivity and linearity).

**Applications of integrals.**

## Appropriate integrals are used in a variety of applications to model physical, biological, or economic situations. Although only a sampling of applications can be included in any specific course, students should be able to adapt their knowledge and techniques to solve other similar application problems. Whatever applications are chosen, the emphasis is on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. To provide a common foundation, specific applications should include finding the area of a region, the volume of a solid with known cross sections, the average value of a function, the distance traveled by a particle along a line, and accumulated change from a rate of change.

**Fundamental Theorem of Calculus**

## • Use of the Fundamental Theorem to evaluate definite integrals .

## • Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined.

**Techniques of anti-differentiation**

## • Antiderivatives following directly from derivatives of basic functions.

## • Antiderivatives by substitution of variables (including change of limits for definite integrals).

**Applications of anti-differentiation**

## • Finding specific antiderivatives using initial conditions, including applications to motion along a line.

## • Solving separable differential equations and using them in modeling (including the study of the equation y’ = ky and exponential growth).

**Numerical approximations to definite integrals.** Use of Riemann sums (using left, right, and midpoint evaluation points) and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values.

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**High School Calculus AB and College Calculus I** Intensive 1 on 1 Tutoring $180.00 Per Month for 12 Hours of Online Tutoring! $260.00 Per month for 12 hours of Online Tutoring and 12 Hours of In-Person Tutoring. This also includes remedial lessons in Precalculus from these textbooks below>

## Pre-Calculus

**Sullivan: Advanced Algebra and Trigonometry, 8e-**students are lectured only on the chapters they are being tested on in school and assigned academic practice to pass their next quiz, test, and or exam.**Glencoe Precalculus-**students are lectured only on the chapters they are being tested on in school and assigned academic practice to pass their next quiz, test, and or exam.

**Program Description: What you are paying for?**

## The student receives 30 days of online tutoring including 16 hours of one on one online tutoring sessions per month.-

## The students receive 12 hours of in-person one on one tutoring per month. Any hours over 12 hours per month cost only $25.00 per hour. A maximum of 8 extra hours will be given at this price. Academic work is required from the student to receive additional hours at this reduced fee.

## The student will be assigned comprehensive practice work related to their current school work to master the skills and study habits needed to pass their next quiz, test, or exam.

**Parents may choose for their students to opt out of all academic work.**## It is assumed the student will study and complete all practice work assigned by the professor in order to do well on their next quiz, test, or exam and address their individual academic issues.

## Your student will be taught and tutored using highly recommend textbooks.

## Your student will be tested and continuously assessed as to the material learned and covered by the master tutor and or their teacher.

## We contact the student's teacher biweekly if necessary.

## No contracts or obligations. You pay month-to-month and can end services anytime with no further obligations.

## A textbook costing $17.00-$34.00 plus shipping must be purchased from Tutor Charlotte for students of mathematics and or English.

## The student is required to purchase a textbook in the subject being tutored.

## Up to four 3-6 hour invitations to in-person tutoring per month costing $20.00 each.

## Access to the Tutor Charlotte website.

## All year around continuous daily preparation for the North Carolina EOG/EOC and SAT/ACT.

## No Refunds!

## There is absolutely no refund once academic tutoring and supplemental education has begun either online or in-person or after the parent and or student is emailed the username and password to the Tutor Charlotte website. The No Refund Policy Form must be completed, signed, and returned to the office of Tutor Charlotte by fax, email, mail, or delivered in-person before online or in-person academic tutoring will begin. In addition, the Student Informational Form and the Application for Subsidized Tutoring Form must be completed and filed with Tutor Charlotte's master tutor before academic online or in-person tutoring may begin along with the student's user name and password to PowerSchool.

**High School Calculus AB and College Calculus I Details**

## A student will be assisted with their regular public and or private school homework, quizzes, tests, and exam preparation in the one subject paid for during online tutoring hours

**(Monday through Thursday 2:00 p.m. -10:00 p.m.)**through internet online communications and or cell phone using the Tutor Charlotte Website and AdobeConnect. The student and or parents are responsible for making appointment requests and the duration of any tutoring appointments can be a minimum 5 minutes to a maximum of 90 minutes per session based on the sole discretion and approval of Tutor Charlotte Inc., The Michigan Administration, and its master tutor Dr. Kevin L. Powell.## A student will be assisted during in-person 1 on 1 tutoring with their regular public and private school homework, quiz preparation, exam preparation, and test preparation in the one subject paid for between the hours of 2:00 pm and 8:00 pm on Fridays, 8:00 a.m. and 9:00 p.m. Saturdays and or Sundays by appointment only in two-hour minimum to four-hour sessions. The student and or parents are responsible for appointment requests and the duration of the appointment requests can be a minimum two hours to a maximum of four hours per session request for in-person tutoring.

**In the High School Calculus AB and College Calculus I Tutoring Program, the "in-person hours" DO NOT ROLLOVER TO THE NEXT payment period. You must use all the hours you paid for within the 30-day payment cycle or the hours will be lost.**## Academic tutoring will also be defined as one or any of the following during a tutoring session or while the student is an active student in Tutor Charlotte:

## Academic tutoring will include interpretation of homework assignments, checking homework for accuracy, evaluating homework with the intention of offering advice to improve the quality of the required responses to the school assignment, and assistance in preparation for quizzes, tests, and exams in the selected subjected.

## The master tutor will design, explain, and give practice quizzes, exams, and tests to the student by publishing the practice quizzes, exams, and tests on the Tutor Charlotte www.tutorincharlotte.com website, or by sending emailed homework, practice quizzes, and practice tests to the student and or parent’s email address.

## The master tutor will develop homework, practice quizzes, practice exams, and practice tests that will help the student improve, understand, and acquire the knowledge necessary to master a subject or be prepared for a quiz, test, and or exam.

## The master tutor will assist the student in preparation for school quizzes, exams, and tests by providing relevant study guides, online personal one on one tutoring, online classroom tutoring, counseling, advice to the student, and act as an advocacy for the student with the student’s school and teacher(s).

## Academic tutoring will at times be given in the online classroom if necessary instead of one on one online tutoring when the subject matter or concept is universal to more than one student’s needs.

## (Note: Each and or any of these methods constitute academic tutoring and will be selected by the master tutor based on what the student needs or requests or what is available during tutoring hours.

## A missed online tutoring session will result in a $3.40 charge to the student's account and no online tutoring or in-person tutoring sessions will be approved until the fee is paid in full.

## A missed in-person tutoring session will result in a $5.46 charge to the student's account and no in-person tutoring or online tutoring sessions will be approved until the fee is paid. In addition, the hours for the missed in-person tutoring session will be deducted from the student's account.

## There will be NO CHANGES to the published schedule within 24 hours of a scheduled in-person tutoring session without a $5.46 charge to the student's account and no in-person tutoring or online tutoring will be approved until the fee is paid.

**Permanent and Temporary Termination of Academic Tutoring and Supplemental Education**

## Tutor Charlotte reserves the right to cancel and or discontinue academic tutoring and supplemental education to a student for any of the following reasons:

## Verbal or physical abuse of the master tutor online or during in-person tutoring will result in permanent termination of academic tutoring and supplemental education.

## Verbal or physical abuse of another Tutor Charlotte student online or during in-person tutoring will result in permanent termination of academic services and educational services.

## A student's refusal and or failure to comply and perform to the academic and behavior standards of Tutor Charlotte as directed by the master tutor can will result in the student being permanently or temporarily dropped from the subsidized academic tutoring program and supplemental education program.

## Nonpayment of the monthly academic fees and any other assessed fees for academic tutoring and supplemental education on the payment due date will result in temporary termination of all academic services and supplemental education.

## A student repeatedly missing approved online and or in-person tutoring sessions will be dropped from their program.

## A student's and or parent's refusal to complete a mandatory invitation to tutoring will result in the student being dropped from their academic program when their tutoring expires.

## The student has been absent from Tutor Charlotte for a period of 14 days or more will be dropped from their program and a student on the waiting list will be enrolled. You must request a 14 day hold on your student's account if you know your student is not going to do tutoring for a period of 14 days or more.