High School Math Curriculum
AP Calculus AB
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Limits
1
Graphical estimation of limits
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2
One-sided and infinite limits
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3
Numerical estimation and oscillating behavior
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4
Limits by Direct Substitution and Limit Laws
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5
Evaluating Limits Algebraically
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6
Trigonometric limits and strategies for finding limits
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7
Limits of piecewise and composite functions
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8
Squeeze theorem
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9
Limits at infinity
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Continuity
1
Introduction to Continuity
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2
Analytically Determining Continuity
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3
Properties of Continuous Functions
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4
Intermediate Value Theorem
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Basics of Differentiation and Derivatives
1
Basics of Derivatives
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2
First Principle Definition of Derivatives
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3
Differentiability of a Function at a Point
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4
Continuity and Differentiability
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5
Laws of Derivatives
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6
Trigonometric Derivatives
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7
Derivatives of Natural Exponential and Logarithmic Functions
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8
Basics of Derivatives
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Derivatives of Composite, Implicit, and Inverse Functions
1
Differentiate Composite Functions
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2
Differentiating Exponential and Logarithmic Functions with Different Bases
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3
Derivatives of Inverse Functions
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4
Differentiating Implicitly
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5
Finding Derivatives using Logarithmic Manipulation
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6
Differentiating Inverse Trigonometric Functions
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7
Finding Higher Order Derivatives
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Applications of Differentiation
1
Interpreting Derivatives in a Context
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2
Related Rates Problems
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3
Tangents and Normals
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4
Linear Approximations
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5
L’Hospital’s Rule
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Analysis of Functions Using Derivatives
1
Finding Extrema
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2
Extreme Value and Mean Value Theorems
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3
First Derivative Test
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4
Concavity and Second Derivative Test
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5
Graphing Functions Using Calculus
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Optimization Problems
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Basics of Integral Calculus
1
The Area Problem
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2
The Intuition Behind Net Change
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3
Riemann Sums
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4
Definite Integrals (Notation and interpretation)
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5
Properties of Definite Integrals
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6
Using Antiderivatives to Evaluate Definite Integrals
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7
Indefinite Integrals (Notation and interpretation)
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8
Definite Integrals (Notation and interpretation)
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9
Method of Substitution
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10
Fundamental Theorem of Calculus
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Differential Equations
1
Modeling Situations with Differential Equations
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2
Verifying Solutions for Differential Equations
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3
Sketching Slope Fields
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4
Reasoning Using Slope Fields
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5
Finding General Solutions Using Separation of Variables
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6
Finding Particular Solutions Using Initial Conditions and Separation of Variables
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7
Exponential Models with Differential Equations
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Applications of Integration
1
Finding Area Under Simple Curves-1
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2
Finding Area Under Simple Curves-2
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3
Finding Area Under Simple Curves-3
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4
Finding Area Between Two Curves-1
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5
Finding Area Between Two Curves-2
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6
Finding Volumes of Solids of Revolution
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