Every AP Calculus AB test on Math Made Easy ships with an answer key and a scoring guide, so a teacher or parent can grade it in minutes. The 8 tests match the chapters, from limits and continuity to areas, volumes and accumulated change, and follow the College Board AP Calculus AB framework.
Tests follow the AP format of multiple-choice style items plus free-response problems, and the scoring guide awards points the way the College Board rubrics do.
Tests in this set include
- Chain Rule, Implicit Differentiation and Inverse Functions
- Derivatives in Context: Motion and Related Rates
- Integration and Accumulation of Change
- Differential Equations
- Limits and Continuity
Take a test after the lesson and worksheet for the same chapter, working alone and without the key. Then use the scoring guide to see which AP Calculus AB problems lost points, and finish with the chapter quiz to confirm the fix. Domains tested in AP Calculus AB: limits, derivatives, integrals and differential equations. Chapters such as the definition of the derivative and related rates and motion make good checkpoints.
Chapter 1 · AP Calculus AB · AP Calculus AB Unit 1
Limits and Continuity: Approaching a Value
Find limits from graphs, tables, and algebra, including one-sided limits and limits at infinity, and use the squeeze theorem, continuity, and the Intermediate Value Theorem. You will classify jump, removable, and infinite discontinuities and read asymptotes. Do the lesson, then the worksheet and answer key, then the scored test on limits; the short quiz gives a fast check on the way.
- One-sided limits
- Continuity
- Discontinuities
Chapter 2 · AP Calculus AB · AP Calculus AB Unit 2
Derivative Definition and Differentiation Rules
Move from average to instantaneous rate of change, write the limit definition of the derivative, and test differentiability. Then apply the power, product, and quotient rules and the derivatives of sin x, cos x, e^x, and ln x. Lesson first, worksheet next: the answer key confirms each derivatives result, and the quiz and test with scoring guide close the chapter.
- Limit definition
- Power rule
- Product and quotient rules
Chapter 3 · AP Calculus AB · AP Calculus AB Unit 3
Chain Rule and Implicit Differentiation
Differentiate composite functions with the chain rule, use implicit differentiation, and find derivatives of inverse and inverse trigonometric functions and higher-order derivatives. For x^2 + y^2 = 25, you will show dy/dx = -x/y. Read the lesson on advanced differentiation, solve the worksheet and check it with the answer key, then take the quiz and the test.
- Chain rule
- Implicit differentiation
- Inverse derivatives
Chapter 4 · AP Calculus AB · AP Calculus AB Unit 4
Motion, Related Rates and Linearization
Interpret a derivative with units, connect position, velocity, and acceleration, and solve related rates and linearization problems, plus L'Hopital's rule. A ladder sliding down a wall at 2 feet per second is a classic related-rates setup. Work through the derivative applications lesson, test yourself on the worksheet with its answer key, and finish with the quiz and the scored test.
- Motion
- Related rates
- Linearization
Chapter 5 · AP Calculus AB · AP Calculus AB Unit 5
Using Derivatives to Analyze Graphs and Optimize
Apply the Mean Value and Extreme Value Theorems, use first and second derivative tests, read increasing, decreasing, and concavity, sketch curves, and optimize. Maximizing the area of a rectangle with 100 feet of fence gives a 25 by 25 square. Mathbot suggests the lesson first, then the worksheet with answer key, and finally the quiz and test to prove your function analysis skills.
- Mean Value Theorem
- Derivative tests
- Optimization
Chapter 6 · AP Calculus AB · AP Calculus AB Unit 6
Integrals, Riemann Sums and Accumulation
Build Riemann sums with left, right, midpoint, and trapezoidal rules, define the definite integral, and use the Fundamental Theorem of Calculus with antiderivatives and u-substitution. You will interpret an integral of a rate as accumulated change. Every page pairs a lesson with a worksheet and answer key, plus a quiz and a test whose scoring guide shows where integration points were earned.
- Riemann sums
- Fundamental Theorem
- u-substitution
Chapter 7 · AP Calculus AB · AP Calculus AB Unit 7
Modeling Change with Separable Equations
Model situations with differential equations, sketch and read slope fields, verify solutions, and solve by separation of variables, including exponential growth and decay. From dy/dx = 0.2y with y(0) = 50 you will build y = 50e^(0.2x). Read, solve the worksheet, grade it with the answer key; the quiz is a quick check on differential equations, and the test comes with a scoring guide.
- Slope fields
- Separation of variables
- Growth and decay
Chapter 8 · AP Calculus AB · AP Calculus AB Unit 8
Applications of Integration: Area and Volume
Use integrals for average value, motion, net change, and area between curves, then find volumes by cross sections and by the disc and washer methods. Rotating y = x from 0 to 2 about the x-axis gives a cone-shaped volume of 8 pi/3. Learn integral applications in the lesson, build speed on the worksheet, correct mistakes with the answer key, and confirm mastery with the quiz and test.
- Area between curves
- Disc and washer
- Average value
Grade 12 AP Calculus AB Tests with Answer Keys and Scoring Guides: frequently asked questions
Does every AP Calculus AB test have an answer key and a scoring guide?
Yes. All 8 AP Calculus AB tests come with a separate answer key and a scoring guide that lists the points for each problem. Partial credit is described for correct setup on problems about related rates and motion.
What does an AP Calculus AB test cover?
Each test covers one chapter, such as the definition of the derivative, related rates and motion or accumulation and Riemann sums. AP Calculus AB problems start with direct skills and finish with a multi-step or context problem.
How is an AP Calculus AB test scored?
The AP Calculus AB scoring guide assigns points to each problem and shows what earns full and partial credit. Points are awarded for correct setup on the definition of the derivative and for the final answer.
When should a student take an AP Calculus AB test?
Take it after finishing the lesson and the worksheet for the same AP Calculus AB chapter, with the answer key closed. Rework each missed problem on accumulation and Riemann sums before moving on.
Are the AP Calculus AB tests aligned with standards?
The tests align with the College Board AP Calculus AB course framework, which sets out the course units on limits, derivatives, integrals and differential equations. The eight chapters line up with those units in order, so each AP Calculus AB test maps to one unit.