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## Description

Many high school students choose to take AP courses due to their benefits while in high school, in college applications, and beyond. According to the College Board which administers the AP tests, “AP Gives students the chance to tackle college level work while they are still in high school and earn college Credit and placement.’’

### Benefits of AP Classes:

More than a million students in America take AP classes because of the several benefits they provide. AP classes will…

1.Increase student’s chances of being admitted into top colleges.

2.Challenge students more than regular high school classes and prepare them for the demands of college.

3.Help students to obtain scholarships.

4.Enable students to receive college credit before starting college (if they score a 3 out of 5 or higher on the related exams).

5.Increase the likelihood that students will graduate earlier than normal time, thereby allowing them to save the money that extra semesters in college would cost.

### Precalculus Review

Overview

Functions and Graphing

Exponential Functions

Inverse Functions

Inverse Trigonometric Functions

Evaluating Logarithmic Functions

### Limits

The Concept of the Limit

Calculating Limits

The Squeeze Theorem

Continuity and Discontinuity

Infinite Limits and Indeterminate Forms

### Derivatives

Understanding the Derivative

Using the Derivative

Some Special Derivatives

The Power Rule

The Product and Quotient Rules

The Chain Rule

Derivatives of Trigonometric Functions

Derivatives of the Exponential Function and the Natural Logarithm

Implicit Differentiation

Differentiating Logarithms

Logarithmic Differentiation

Derivatives of Inverse Functions

### Applications of the Derivative

Position and Velocity

Linear Approximation and Newton’s Method

Optimization

Related Rates

An Introduction to Curve Sketching

Critical Points

Concavity and Inflection Points

Graphing Using the Derivative

Graphing Functions with Asymptotes

Indeterminate Quotients and L’Hospital’s Rule

Other Indeterminate Forms

### Integration

Antiderivatives

Integration by Substitution

Illustrating Integration by Substitution

The Fundamental Theorem of Calculus

Numerical Integration and Tables of Integrals

Trigonometric Substitution

### Techniques of Integration

Integrals Involving Powers of Sine and Cosine

Integrals Involving Powers of Other Trigonometric Functions

An Introduction to Integration by Partial Fractions

Integration by Partial Fractions with Repeated Factors

Integration by Parts

An Introduction to Trigonometric Substitution

Trigonometric Substitution Strategy

Improper Integrals

### Applications of Integration

Motion

Finding the Area between Two Curves

Integrating with Respect to y

The Average Value of a Function

Finding Volumes Using Cross-Sections

Disks and Washers

Shells

Work

Moments and Centers of Mass

Arc Lengths and Functions

### Differential Equations

Separable Differential Equations

Direction Fields

Growth and Decay Problems

Euler’s Method

### Parametric Equations and Polar Coordinates

Understanding Parametric Equations

Derivatives and Arc Length of Parametric Equations

Understanding Polar Coordinates

Polar Functions and Slope

Polar Functions and Area

### Sequences and Series

Sequences

Infinite Series

Convergence and Divergence

The Integral Test and p-Series

The Comparison and Limit Comparison Test

The Alternating Series Test, Absolute and Conditional Convergence

The Ratio and Root Test

Polynomial Approximations of Elementary Functions

Taylor and Maclaurin Polynomials

Taylor and Maclaurin Series

Power Series

Power Series Representations of Functions

### Inquiry Now

USA: +1 734 418 2465 | India: +91 40 4018 1306

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