AP Calculus AB (12th Grade) Math Worksheets, Lessons and Tests (Free PDF)
These ap calculus ab worksheets follow the College Board course chapter by chapter: each chapter has a lesson, a worksheet of at least 20 exercises with solutions, a timed test with its answer key and an online quiz, all with a free PDF.
AP Calculus AB follows the College Board course: limits and continuity, the derivative and its rules, the chain rule and implicit differentiation, related rates and optimization, the analysis of functions, antiderivatives and definite integrals, differential equations and applications of integration.
Ap calculus ab worksheets: all chapters
1. Introducing Limits
Understand a limit · Estimate a limit from a table · Understand one-sided limits · Understand a reliable method
2. Evaluating Limits Algebraically
Understand the limit laws · Handle square roots · Understand the Squeeze Theorem · Understand a clean written method
3. Continuity and the Intermediate Value Theorem
Make a piecewise function continuous · Understand the Intermediate Value Theorem
4. Infinite Limits and Asymptotes
Understand an infinite limit · Understand limits at infinity · Find limits at infinity of rational functions · Find every asymptote of a rational function
5. The Derivative as a Limit
Understand the derivative · Compute a derivative from the definition
6. Power, Sum and Basic Function Derivative Rules
Understand the basic derivative rules · Differentiate roots and fractions · Understand a good order of work · Find tangent and normal lines
7. Product Rule, Quotient Rule and Trig Derivatives
Understand the product rule · Understand the quotient rule · Understand the derivatives of the other trig functions · Use the rules together
8. The Chain Rule
Understand the chain rule · Apply the chain rule step by step · Understand the most common chain rule patterns · Use the chain rule with a table of values
9. Implicit Differentiation
Understand implicit differentiation · Do it step by step
10. Derivatives of Inverse Functions
Differentiate an inverse function · Understand the derivatives of inverse trig functions · Understand higher-order derivatives · Choose a method
11. Rates of Change in Context and Straight-Line Motion
In context, a derivative is a rate of change measured in output units per input unit.
12. Related Rates
Understand a related rates problem · Set up a ladder problem
13. Linearization and L'Hopital's Rule
Understand a local linear approximation · Understand L'Hôpital's Rule
14. Mean Value Theorem and Extreme Value Theorem
Understand the Mean Value Theorem · Understand the Extreme Value Theorem · Understand critical numbers · Find absolute extrema on a closed interval
15. Increasing, Decreasing and the First Derivative Test
Build a sign chart · Understand the First Derivative Test · Read a graph of f′
16. Concavity and the Second Derivative
The second derivative f″ shows concavity: f is concave up where f″ is positive and concave down where f″ is negative.
17. Optimization
Understand an optimization problem · Set up and solve one · Justify a maximum or minimum
18. Riemann Sums and the Definite Integral
Understand accumulation of change · Understand a Riemann sum · Understand the trapezoidal sum · Understand a definite integral
19. Fundamental Theorem of Calculus and Antiderivatives
Understand an accumulation function · Understand an antiderivative · Evaluate a definite integral · Understand an initial value problem
20. Integration by Substitution
Understand integration by substitution · Choose u
21. Differential Equations and Slope Fields
Understand a differential equation · Understand a slope field · Understand Euler's method · Solve by separation of variables
How to use these ap calculus ab worksheets
Pick a chapter, read its one-page lesson, then solve the worksheet on paper and check every answer with the solutions page. Take the ten-question quiz to see what is still unclear, and finish with the timed test. Every page can be printed from its PDF button, and the quick practice at the bottom of each page gives ten new questions at every visit.
AP Calculus AB math: common questions
What is AP Calculus AB?
AP Calculus AB is a college-level calculus course taught in high school, usually in 12th grade, ending with the AP exam in May.
What units are in AP Calculus AB?
Eight units: limits and continuity, differentiation, composite and implicit functions, contextual applications, analytical applications, integration, differential equations, and applications of integration.
Are there AP Calculus AB practice tests?
Yes. Each chapter has a 45-minute test with point values and its solutions.
Is a calculator allowed?
The tests here are written to be done without a graphing calculator unless a question says otherwise.