AP Calculus BC: Practice Questions, Units, and Exam Format
All of Calculus AB plus series, parametrics, polar, and vector functions. See exactly what is on the exam, unit by unit, and practise it with a tutor that adapts to you.
Exam format
| Section | Questions | Time | Share of score |
|---|---|---|---|
| Section I: Multiple Choice | 42 | 1 hr 40 min | 50% |
| Section II: Free Response | 6 | 1 hr 30 min | 50% |
Units and exam weights
| Unit | Exam weight | Topics covered |
|---|---|---|
| Limits and Continuity | 5 to 10% | Introducing Calculus: Can Change Occur at an Instant?, Defining Limits and Using Limit Notation, Estimating Limit Values from Graphs, Estimating Limit Values from Tables, Determining Limits Using Algebraic Properties of Limits, Determining Limits Using Algebraic Manipulation |
| Differentiation: Definition and Fundamental Properties | 5 to 10% | Defining Average and Instantaneous Rates of Change at a Point, Defining the Derivative of a Function and Using Derivative Notation, Estimating Derivatives of a Function at a Point, Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist, Applying the Power Rule, Derivative Rules: Constant, Sum, Difference, and Constant Multiple |
| Differentiation: Composite, Implicit, and Inverse Functions | 5 to 10% | The Chain Rule, Implicit Differentiation, Differentiating Inverse Functions, Differentiating Inverse Trigonometric Functions, Selecting Procedures for Calculating Derivatives, Calculating Higher-Order Derivatives |
| Contextual Applications of Differentiation | 5 to 10% | Interpreting the Meaning of the Derivative in Context, Straight-Line Motion: Connecting Position, Velocity, and Acceleration, Rates of Change in Applied Contexts Other Than Motion, Introduction to Related Rates, Solving Related Rates Problems, Approximating Values of a Function Using Local Linearity and Linearization |
| Analytical Applications of Differentiation | 10 to 15% | Using the Mean Value Theorem, Extreme Value Theorem, Global Versus Local Extrema, and Critical Points, Determining Intervals on Which a Function Is Increasing or Decreasing, Using the First Derivative Test to Determine Relative (Local) Extrema, Using the Candidates Test to Determine Absolute (Global) Extrema, Determining Concavity of Functions over Their Domains |
| Integration and Accumulation of Change | 15 to 20% | Exploring Accumulations of Change, Approximating Areas with Riemann Sums, Riemann Sums, Summation Notation, and Definite Integral Notation, The Fundamental Theorem of Calculus and Accumulation Functions, Interpreting the Behavior of Accumulation Functions Involving Area, Applying Properties of Definite Integrals |
| Differential Equations | 5 to 10% | Modeling Situations with Differential Equations, Verifying Solutions for Differential Equations, Sketching Slope Fields, Reasoning Using Slope Fields, Approximating Solutions Using Euler’s Method, Finding General Solutions Using Separation of Variables |
| Applications of Integration | 5 to 10% | Finding the Average Value of a Function on an Interval, Connecting Position, Velocity, and Acceleration of Functions Using Integrals, Using Accumulation Functions and Definite Integrals in Applied Contexts, Finding the Area Between Curves Expressed as Functions of x, Finding the Area Between Curves Expressed as Functions of y, Finding the Area Between Curves That Intersect at More Than Two Points |
| Parametric Equations, Polar Coordinates, and Vector-Valued Functions | 10 to 15% | Defining and Differentiating Parametric Equations, Second Derivatives of Parametric Equations, Finding Arc Lengths of Curves Given by Parametric Equations, Defining and Differentiating Vector-Valued Functions, Integrating Vector-Valued Functions, Solving Motion Problems Using Parametric and Vector-Valued Functions |
| Infinite Sequences and Series | 15 to 20% | Defining Convergent and Divergent Infinite Series, Working with Geometric Series, The nth Term Test for Divergence, Integral Test for Convergence, Harmonic Series and p-Series, Comparison Tests for Convergence |
How Kalyta teaches AP Calculus BC
Practice that adapts to you, an explanation for every answer, and a full rehearsal before the real thing. You spend your time on the units that move your score instead of the ones you have already got.
- Adaptive practice. Questions are picked around your current level, so you are always working just past what you can already do.
- Every answer explained. See why the right answer is right and why each other choice is wrong, with figures and step by step reasoning.
- An AI tutor you can steer. Ask why something works, ask for another example, or tell it to slow down and teach the idea from the start.
- Full exam rehearsals. Sit the real format under real timing and get a predicted score, so test day feels like something you have already done.
- Progress you can see. Watch your readiness climb unit by unit, and know what is solid before you walk in.
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