HS AP Calculus

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:

• Derivatives

• Integration

• Solving Equations

• Finding points of intersection

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)

FORMULA PACKET

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

TWO WEEK STUDY GUIDE

Week 15 (Course Review & Full Practice Exams)

Week 16 (Course Review & Full Practice Exams)

Week 17 (Course Review & Full Practice Exams)