High School Math Curriculum
AP Calculus AB
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Limits
1
Introduction to 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
Trig Limits and Strategies for Finding Limits
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7
Limit 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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Derivatives
1
Basics of Derivatives
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2
The First Principle Definition of the Derivative
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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 Logarthmic Functions
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Derivatives of Composite, Implicit, and Inverse Functions
1
Differentiating Composite Functions
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2
Differentiating Exponential, Logarithmic, and Inverse Functions
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3
Implicit and Logarithmic Differentiation
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4
Differentiating Inverse Trigonometric Functions
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5
Finding Higher-Order Derivatives
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Applications of Derivatives
1
Interpreting Derivatives in a Context
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2
Related Rates
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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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6
Optimization
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Antiderivatives and Definite Integrals
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
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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
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8
Method of Substitution
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9
Fundamental Theorem of Calculus
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Differential Equations
1
Slope Fields
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2
Finding Solutions
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3
Modeling using Differential Equations
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Applications of Integration
1
Area Under a Curve Using Definite Integrals
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2
Total Area and Regions Below the Axis
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3
Areas of Symmetric Regions
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4
Area Between Two Curves
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5
Areas of Composite Regions
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6
Volumes and Solids of Revolution
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