AP Calculus AB Study Guide
Created by Cathy J.
AP Calculus AB Test Topics:
Precalculus Review
Module 2
2.1 - Tangent and Velocity
2.2 - Limit of a Function
2.3 - Limit Calculations with Limit Laws (& Squeeze Theorem)
2.4 - Limits at Infinity and Horizontal Asymptotes
2.5/6 - Continuity (& IVT)
Module 3
3.1 - Derivatives and Rate of Change
3.2 - Derivative as a Function
3.3 - Derivatives of Polynomials & Exponential Functions
3.4 - Product & Quotient Rule
3.5 - Derivatives of Trigonometric Functions
3.6 - Chain Rule
3.7 - Implicit Differentiation and Inverse Functions
3.8 - Derivatives of Logarithmic Functions
3.9 - Applications of the Derivative
3.10 - Related Rates
3.11 - Local Linearity
Module 4
4.1 - Maximum & Minimum Values, EVT
4.2 - MVT
4.3 - How Derivatives (First and Second) Affect the Shape of a Graph
4.4 - L'Hôpital’s Rule
Module 5
5.5 - Optimization
5.6 - Antiderivatives
Module 6
6.1 - Riemann Sums and Approximations
,6.2 - Definite Integrals
6.3 - Fundamental Theorem of Calculus (Part I & II)
6.4 - Properties of the Definite Integral
6.5 - Substitution Rule
6.9 - Integrand Manipulation
Module 8
8.1 - Area Between Curves
8.2 - Volume of a Solid: Revolution
8.4 - Volume of a Solid: Cross Sections
Module 7
7.1 - Modeling with Differential Equations
7.2 - Separable Differential Equations, Exponential Growth/Decay
7.3 - Slope Fields
,Precalculus Review
6.1: Conic Sections
Eccentricity (e) is the measure of circular deviation
𝑐
𝑒= 𝑎
; c = distance from center/vertex to focus; a = distance from center to
vertex
● Parabola: e = 1
2
(𝑦 − 𝑘) = 4𝑝(𝑥 − ℎ) → Horizontal Orientation
Vertex: (ℎ, 𝑘)
Focus: (ℎ + 𝑝, 𝑘)
Directrix: 𝑥 = ℎ − 𝑝
Opens Right: 𝑝 > 0
Opens Left: 𝑝 < 0
2
(𝑥 − ℎ) = 4𝑝(𝑦 − 𝑘) → Vertical Orientation
Vertex: (ℎ, 𝑘)
Focus: (ℎ, 𝑘 + 𝑝)
Directrix: 𝑦 = 𝑘 − 𝑝
Opens Up: 𝑝 > 0
Opens Down: 𝑝 < 0
● Ellipse: 0 < e < 1
- a → major axis value, larger value
- b → minor axis value, shorter value
2 2 2
- c → 𝑐 = 𝑎 − 𝑏
2 2
(𝑥−ℎ) (𝑦−𝑘)
2 + 2 = 1 → Horizontal Orientation/Major Axis
𝑎 𝑏
Center: (ℎ, 𝑘)
Vertices: (ℎ ± 𝑎, 𝑘)
Co-vertices: (ℎ, 𝑘 ± 𝑏)
Foci: (ℎ ± 𝑐, 𝑘)
, 2 2
(𝑥−ℎ) (𝑦−𝑘)
2 + 2 = 1 → Vertical Orientation/Major Axis
𝑏 𝑎
Center: (ℎ, 𝑘)
Vertices: (ℎ, 𝑘 ± 𝑎)
Co-vertices: (ℎ ± 𝑏, 𝑘)
Foci: (ℎ, 𝑘 ± 𝑐)
● Hyperbola: e > 1
- a → positive axis value
- b → negative axis value
2 2 2
- c → 𝑐 = 𝑎 + 𝑏
2 2
(𝑥−ℎ) (𝑦−𝑘)
2 − 2 = 1 → Horizontal
𝑎 𝑏
Center: (ℎ, 𝑘)
Vertices: (ℎ ± 𝑎, 𝑘)
Co-vertices: (ℎ, 𝑘 ± 𝑏)
Foci: (ℎ ± 𝑐, 𝑘)
2 2
(𝑦−𝑘) (𝑥−ℎ)
2 − 2 = 1 → Vertical
𝑎 𝑏
Center: (ℎ, 𝑘)
Vertices: (ℎ, 𝑘 ± 𝑎)
Co-vertices: (ℎ ± 𝑏, 𝑘)
Foci: (ℎ, 𝑘 ± 𝑐)
6.2: Parametric Equations
● Parametric equations are given the variable t for time, and the output is
location: (x, y)
1. Convert parametric equation to rectangular (substitution/system)
2. Find the intersection (graphing/system)
3. Compare time (plug x-values into parametric for t)
4. Conclusion (therefore… the objects don’t collide)
● Remember to add parametric arrows signifying positive flow of time
Created by Cathy J.
AP Calculus AB Test Topics:
Precalculus Review
Module 2
2.1 - Tangent and Velocity
2.2 - Limit of a Function
2.3 - Limit Calculations with Limit Laws (& Squeeze Theorem)
2.4 - Limits at Infinity and Horizontal Asymptotes
2.5/6 - Continuity (& IVT)
Module 3
3.1 - Derivatives and Rate of Change
3.2 - Derivative as a Function
3.3 - Derivatives of Polynomials & Exponential Functions
3.4 - Product & Quotient Rule
3.5 - Derivatives of Trigonometric Functions
3.6 - Chain Rule
3.7 - Implicit Differentiation and Inverse Functions
3.8 - Derivatives of Logarithmic Functions
3.9 - Applications of the Derivative
3.10 - Related Rates
3.11 - Local Linearity
Module 4
4.1 - Maximum & Minimum Values, EVT
4.2 - MVT
4.3 - How Derivatives (First and Second) Affect the Shape of a Graph
4.4 - L'Hôpital’s Rule
Module 5
5.5 - Optimization
5.6 - Antiderivatives
Module 6
6.1 - Riemann Sums and Approximations
,6.2 - Definite Integrals
6.3 - Fundamental Theorem of Calculus (Part I & II)
6.4 - Properties of the Definite Integral
6.5 - Substitution Rule
6.9 - Integrand Manipulation
Module 8
8.1 - Area Between Curves
8.2 - Volume of a Solid: Revolution
8.4 - Volume of a Solid: Cross Sections
Module 7
7.1 - Modeling with Differential Equations
7.2 - Separable Differential Equations, Exponential Growth/Decay
7.3 - Slope Fields
,Precalculus Review
6.1: Conic Sections
Eccentricity (e) is the measure of circular deviation
𝑐
𝑒= 𝑎
; c = distance from center/vertex to focus; a = distance from center to
vertex
● Parabola: e = 1
2
(𝑦 − 𝑘) = 4𝑝(𝑥 − ℎ) → Horizontal Orientation
Vertex: (ℎ, 𝑘)
Focus: (ℎ + 𝑝, 𝑘)
Directrix: 𝑥 = ℎ − 𝑝
Opens Right: 𝑝 > 0
Opens Left: 𝑝 < 0
2
(𝑥 − ℎ) = 4𝑝(𝑦 − 𝑘) → Vertical Orientation
Vertex: (ℎ, 𝑘)
Focus: (ℎ, 𝑘 + 𝑝)
Directrix: 𝑦 = 𝑘 − 𝑝
Opens Up: 𝑝 > 0
Opens Down: 𝑝 < 0
● Ellipse: 0 < e < 1
- a → major axis value, larger value
- b → minor axis value, shorter value
2 2 2
- c → 𝑐 = 𝑎 − 𝑏
2 2
(𝑥−ℎ) (𝑦−𝑘)
2 + 2 = 1 → Horizontal Orientation/Major Axis
𝑎 𝑏
Center: (ℎ, 𝑘)
Vertices: (ℎ ± 𝑎, 𝑘)
Co-vertices: (ℎ, 𝑘 ± 𝑏)
Foci: (ℎ ± 𝑐, 𝑘)
, 2 2
(𝑥−ℎ) (𝑦−𝑘)
2 + 2 = 1 → Vertical Orientation/Major Axis
𝑏 𝑎
Center: (ℎ, 𝑘)
Vertices: (ℎ, 𝑘 ± 𝑎)
Co-vertices: (ℎ ± 𝑏, 𝑘)
Foci: (ℎ, 𝑘 ± 𝑐)
● Hyperbola: e > 1
- a → positive axis value
- b → negative axis value
2 2 2
- c → 𝑐 = 𝑎 + 𝑏
2 2
(𝑥−ℎ) (𝑦−𝑘)
2 − 2 = 1 → Horizontal
𝑎 𝑏
Center: (ℎ, 𝑘)
Vertices: (ℎ ± 𝑎, 𝑘)
Co-vertices: (ℎ, 𝑘 ± 𝑏)
Foci: (ℎ ± 𝑐, 𝑘)
2 2
(𝑦−𝑘) (𝑥−ℎ)
2 − 2 = 1 → Vertical
𝑎 𝑏
Center: (ℎ, 𝑘)
Vertices: (ℎ, 𝑘 ± 𝑎)
Co-vertices: (ℎ ± 𝑏, 𝑘)
Foci: (ℎ, 𝑘 ± 𝑐)
6.2: Parametric Equations
● Parametric equations are given the variable t for time, and the output is
location: (x, y)
1. Convert parametric equation to rectangular (substitution/system)
2. Find the intersection (graphing/system)
3. Compare time (plug x-values into parametric for t)
4. Conclusion (therefore… the objects don’t collide)
● Remember to add parametric arrows signifying positive flow of time
