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AP Calculus AB
Jill Bell Curriculum
Unit 1. Limits, Continuity, and Definitions of Derivative
1.1 Intro to Limits - Graphical Limits
1.2 Algebraic Limits - Part 1
1.3 Algebraic Limits - Part 2
1.4 Properties of Limits and Squeeze Theorem
1.5 Trig Limits
1.6 Limits Involving Infinity - Part 1
1.7 Limits Involving Infinity - Part 2
1.8 Limits Review
1.9 Continuity - Part 1
1.10 Continuity - Part 2
1.11 Intermediate Value Theorem (IVT)
1.12 Difference Quotients
1.13 Rates of Change (AROC and IROC)
1.14 Definitions of Derivative
Unit 2. Basic Derivative Rules
2.1 Power Rule for Derivatives
2.2 Higher Order Derivatives
2.3 Slopes of Secant and Tangent Lines
2.4 Differentiability
2.5 Product and Quotient Rule
2.6 Numeric Derivatives
2.7 Straight Line Motion
2.8 Projectile Motion
2.9 Chain Rule
2.10 Differentiating Generic Functions
Unit 3. Transcendental Functions, Implicit Differentiation, Graph Analysis
3.1 Derivatives of Trigonometric Functions
3.2 Implicit Differentiation
3.3 Intro to Graph Analysis
3.4 Horizontal and Vertical Tangent Lines
3.5 Related Rates
3.6 Derivatives of Exponential Functions - Part 1
3.7 Derivatives of Exponential Functions - Part 2
3.8 Derivatives of Logarithmic Functions
Unit 4. Applications of Derivatives
4.1 Extreme Value Theorem (Abs Max and Min)
4.2 Rolle's Theorem and Mean Value Theorem (MVT) - Part 1
4.3 Rolle's Theorem and Mean Value Theorem (MVT) - Part 2
4.4 First Derivative Test - Part 1
4.5 First Derivative Test - Part 2
4.6 Concavity and Points of Inflection
4.7 Second Derivative Test
4.8 Connecting f' and f" to f
4.9 Graphing Working Backwards
4.10 L'Hospital's Rule
4.11 Antiderivatives
4.12 Derivatives of Inverse Functions - Part 1
4.13 Derivatives of Inverse Functions - Part 2
4.14 Derivatives of Inverse Trigonometric Functions
4.15 Linear Approximation
Unit 5. More Applications of Derivatives, Integration Rules
5.1 Optimization
5.2 Derivatives and Data
5.3 Graphing Knowing Relationship Between f, f', and f"
5.4 Indefinite Integrals
5.5 Riemann Sums and the Trapezoidal Rule - Part 1
5.6 Riemann Sums and the Trapezoidal Rule - Part 2
5.7 Definite Integrals using Area - Part 1
5.8 Definite Integrals using Area - Part 2
5.9 First Fundamental Theorem of Calculus
5.10 Average Value and Mean Value Theorem for Integrals
5.11 Second Fundamental Theorem of Calculus
5.12 Definite Integral as the Limit of a Riemann Sum
5.13 Functions Defined by Integrals - Part 1
5.14 Functions Defined by Integrals - Part 2
5.15 U-Substitution - Indefinite Integrals
5.16 U-Substitution - Definite Integrals
5.17 Integration using Long Division
5.18 Integration by Completing the Square
Unit 6. Applications of Integrals
6.1 Differential Equations - Intro
6.2 Separation of Variables
6.3 Slope Fields
6.4 Applications of Differential Equations
6.5 Displacement and Total Distance
6.6 Area Between Curves
6.7 Integrals as Net Change
6.8 Volumes by Cross Sections - Day 1
6.9 Volumes of Revolution - around x- and y-axis
6.10 Volumes of Revolution - around other lines
6.11 Integrals Using Data
AP Calculus Formulas
Formula Flipchart
Algebra 2 / Precalculus
Notes and Worksheets
Unit 1
1.1 Operations with Fractions
1.2 Inequalities and Absolute Value
1.3 Exponents and Radicals
1.4 Polynomial Expressions
1.5 Special Products
1.6 Factoring Part 1
1.7 Factoring Part 2
1.8 Factoring Part 3
1.9 Rational Expressions Part 1
1.10 Rational Expressions Part 2
1.11 Complex Fractions
1.12 Complex Numbers
SAT Practice Tests
Test #1
Test #2
Test #3
Test #4
Test #5
Test #6
Test #7
Test #8
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JPCalculus
5.15 U-Substitution - Indefinite Integrals
Notes
Notes - U-Substitution Indefinite Integrals.pdf
Video
Worksheet
WS 1 on substitution.pdf
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Notes - U-Substitution Indefinite Integrals.pdfWS 1 on substitution.pdfNotes - U-Substitution Indefinite Integrals.pdfWS 1 on substitution.pdf