AP Calculus BC, one topic at a time

AP Calculus BC score calculator: enter your section results and see an estimated 1–5 score.

1. Unit 1 · 4–7%

   Limits and Continuity

   Introducing Calculus: Change at an Instant · Defining Limits and Using Limit Notation · Estimating Limit Values from Graphs · Estimating Limit Values from Tables · Determining Limits Using Algebraic Properties · Determining Limits Using Algebraic Manipulation · Selecting Procedures for Determining Limits · Determining Limits Using the Squeeze Theorem · Connecting Multiple Representations of Limits · Exploring Types of Discontinuities · Defining Continuity at a Point · Confirming Continuity over an Interval · Removing Discontinuities · Infinite Limits and Vertical Asymptotes · Limits at Infinity and Horizontal Asymptotes · Working with the Intermediate Value Theorem

2. Unit 2 · 4–7%

   Differentiation: Definition and Fundamental Properties

   Average and Instantaneous Rates of Change · Defining the Derivative · Estimating Derivatives at a Point · Connecting Differentiability and Continuity · Applying the Power Rule · Constant, Sum, Difference, and Constant Multiple Rules · Derivatives of cos x, sin x, eˣ, and ln x · The Product Rule · The Quotient Rule · Derivatives of tan x, cot x, sec x, and csc x

3. Unit 3 · 4–7%

   Differentiation: Composite, Implicit, and Inverse Functions

   The Chain Rule · Implicit Differentiation · Differentiating Inverse Functions · Differentiating Inverse Trigonometric Functions · Selecting Procedures for Calculating Derivatives · Calculating Higher-Order Derivatives

4. Unit 4 · 6–9%

   Contextual Applications of Differentiation

   Interpreting the Derivative in Context · Straight-Line Motion · Rates of Change in Applied Contexts Other Than Motion · Introduction to Related Rates · Solving Related Rates Problems · Local Linearity and Linearization · L'Hospital's Rule

5. Unit 5 · 8–11%

   Analytical Applications of Differentiation

   Using the Mean Value Theorem · Extreme Value Theorem and Critical Points · Intervals of Increase and Decrease · The First Derivative Test · The Candidates Test for Absolute Extrema · Concavity · The Second Derivative Test · Sketching Graphs of Functions and Their Derivatives · Connecting f, f′, and f″ · Introduction to Optimization Problems · Solving Optimization Problems · Behaviors of Implicit Relations

6. Unit 6 · 17–20%

   Integration and Accumulation of Change

   Exploring Accumulations of Change · Approximating Areas with Riemann Sums · Riemann Sums and Definite Integral Notation · The Fundamental Theorem and Accumulation Functions · Accumulation Functions and Area · Properties of Definite Integrals · The Fundamental Theorem and Definite Integrals · Antiderivatives and Indefinite Integrals · Integrating Using Substitution · Long Division and Completing the Square · Integration by Parts · Linear Partial Fractions · Improper Integrals · Selecting Integration Techniques

7. Unit 7 · 6–9%

   Differential Equations

   Modeling with Differential Equations · Verifying Solutions to Differential Equations · Sketching Slope Fields · Reasoning with Slope Fields · Euler's Method · General Solutions by Separation of Variables · Separation of Variables with Initial Conditions · Exponential Models · Logistic Models

8. Unit 8 · 6–9%

   Applications of Integration

   Average Value of a Function · Position, Velocity, and Acceleration with Integrals · Accumulation in Applied Contexts · Area Between Curves · Area Between Curves as Functions of y · Curves That Intersect More Than Twice · Cross Sections: Squares and Rectangles · Cross Sections: Triangles and Semicircles · Disc Method Around the x- or y-Axis · Disc Method Around Other Axes · Washer Method Around the x- or y-Axis · Washer Method Around Other Axes · Arc Length

9. Unit 9 · 11–12%

   Parametric Equations, Polar Coordinates, and Vector-Valued Functions

   Differentiating Parametric Equations · Second Derivatives of Parametric Equations · Arc Length of Parametric Curves · Vector-Valued Functions and Their Derivatives · Integrating Vector-Valued Functions · Motion with Parametric and Vector Functions · Polar Coordinates and Derivatives · Area of a Polar Region · Area Bounded by Two Polar Curves

10. Unit 10 · 17–18%

    Infinite Sequences and Series

    Convergent and Divergent Series · Geometric Series · The nth Term Test for Divergence · Integral Test · Harmonic Series and p-Series · Comparison Tests · Alternating Series Test · Ratio Test · Absolute and Conditional Convergence · Alternating Series Error Bound · Taylor Polynomial Approximations · Lagrange Error Bound · Radius and Interval of Convergence · Taylor and Maclaurin Series · Representing Functions as Power Series

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  Same sections, time limits and calculator rules as the May exam. Every set and mock updates your predicted 1 to 5.