# HS AP Calculus

AP Calculus AB Exam Date

**ONLINE TEST DATE: June 9, 2021**

**Week 1 (Unit 1: Limits)**

What is Calculus?

2.1 Average Rates of Change

2.1 Numerical Limit

2.2 Definition of a Limit

2.2 One Sided Limits vs. Two Sided Limits

2.2 Graphical Limits

2.3 Limit Rules

2.3 Limits Laws

2.3 Limits of Polynomials and Rational Functions pg. 97

Techniques of Finding Limits

Direct Substitution

Cancellation (Factoring)

Radical Conjugate

Algebraic Manipulation

Making use of the formal definition of an absolute value

Special Limit: lim as x-> 0 sin(x)/x = 1

**Week 2 (Unit 1: Limits)**

2.3 Squeeze Theorem pg. 101

2.2 Infinite Limits (Sign Analysis/Limit Analysis)

2.6 Limits at Infinity

Special Limit: lim as x->inf 1/x = 0

2.6 Horizontal Asymptotes

Review of Polynomial Division & Oblique Asymptotes

2.2 Vertical Asymptotes

**Week 3 (Unit 1: Limits)**

Review of Exponentials and Logarithms

Piece-wise Functions

Review of Domain and Range

2.5 Continuity

2.5 Combinations of Continuous Functions pg. 117

2.5 Library of Continuous Functions pg. 120 Theorem 7

2.5 Limits of Composite Functions

2.5 Intermediate Value Theorem pg. 122

**Week 4 (Unit 2: Derivatives)**

Public Exam #5,9,21

2.7 Derivatives by Definition

2.8 Equations of Tangent Lines

Special Cases where Derivatives fail to exist (pg. 158)

**Exam 1 MONDAY February 3, 2020 **(**Practice Exam**)

**Week 5 (Unit 2: Derivatives)**

3.1 Derivative Rules

Special Derivative: The derivative of e^x = e^x

3.2 The Product Rule

3.2 The Quotient Rule

**Week 6 (Unit 2: Derivatives)**

**3.7 (Revisit 2.7 and 2.8) to discuss position-velocity-acceleration**

3.3 Trigonometric Derivatives

3.4 The Chain Rule

**Week 7 (Unit 2: Derivatives)**

3.5 Inverse Trigonometric Derivatives

3.5 Implicit Differentiation

**These lecture notes** will be helpful to read PRIOR to beginning 3.6

Special Derivative: The derivative of ln(x) is 1/x

3.6 Derivatives of Logarithms & Logarithmic Differentiation as a technique

Equations of Normal Lines

**Unit 2 Exam Monday March 2, 2019**

**Week 8 (Unit 3: Derivatives Applications)**

3.9 Related Rates

9.2 Review: Slope Fields

Basic Calculator Use:

**Week 9 (Unit 3: Derivatives Applications) **

**EXAM 2**

3.10 Linear Approximations

4.1 Extreme Value Theorem

4.1 Critical Numbers

4.1 Extreme Values: Global (Absolute) vs. Local (Relative)

4.1/4.3 Finding Absolute Extrema

4.2 Mean Value Theorem

4.4 L'Hopitals Rule & Indeterminant Forms

4.3 First Derivative Test for Local Extrema

**Week 10 (Unit 3: Derivatives Applications)**

4.3 Second Derivative Test

4.3 Concavity

4.3 Inflection Points

4.3 & 4.5 Curve Sketching

4.7 Optimization

4.9 Anti-Derivatives

**Week 11 (Unit 4: Anti-Differentiation & Integrals)**

**Unit 3 Exam March 16, 2020**

Integral Notation

**Anti-Derivative S-V-A Word Problems**

5.1 Upper, Lower, Left-Hand, and Right-Hand Sums (Riemann Sums)

7.7 Mid-point & **Trapezoidal Sums** (The last sum approximation that we will learn. Ignore everything else in this chapter that is not the midpoint or trapezoidal rule)

**Week 12 (Unit 4: Integrals)**

6.5 Average Value of a Function

5.2 Integrals as Area

5.1 & 5.2 Summation Notation

5.2 Definite Integrals

5.2 Properties of Integrable Functions pg. 385-387

5.3 Fundamental Theorem of Calculus (Part II)

5.4 Indefinite Integrals and Net Change Theorem **Distinguish between Total (Unsigned) Area and Net (Signed) Area. (Remember, integral notation refers to signed/net area)**

**Week 13 (Unit 4: Integrals & Unit 5 Integral Applications)**

5.3 Fundamental Theorem of Calculus (Part I) [And methods for adjusting limits of integration so that FTC I applies)

5.5 Substitution (Also called u-substitution)

9.3 **Separation of Variables** (Only worry about the technique for the class example in this chapter)

**Unit 4 Exam April 3, 2020**

SPRING BREAK

**Week 14 (Unit 5 Integral Applications & Course Review)**

6.1 Area Between Curves

6.2 Volumes of Solids and Cross Sections

**Week 15 (Course Review & Full Practice Exams)**

**Week 16 (Course Review & Full Practice Exams)**

**Week 17 (Course Review & Full Practice Exams)**

**Updated 2019 AP Calculus AB Framework** and Exam Description

All assignments will be posted in VERGE daily until we return to school. If you need to talk to me, email me at bolanle_salaam@dekalbschoolsga.org or contact me through VERGE.