AP Calculus AB Math Tests with Answer Keys
22 chapter tests for AP Calculus AB, 176 questions in all, each test scored out of 20 points with a full answer key.
- 155 US Letter pages
- 22 chapter tests
- 176 scored questions
- PDF to print
- Cards accepted without a PayPal account
- Instant download, up to 3 devices
About this book
Each test checks one chapter of the course, from introducing limits to average value, area and volume. The scoring notes make it easy to grade a test the way a teacher would.
Each test lists its time (45 minutes) and its total of 20 points on its first page, then mixes short questions and multi-part problems, like Justifying an extremum in the Optimization test. Part 2, from page 75, holds the answer keys: worked solutions and a scoring note for every question.
For a student taking AP Calculus AB, a parent, or a teacher who wants chapter tests ready to print. Pair it with the AP Calculus AB Math Worksheets with Answers to go back to the lesson when a problem gets stuck.
Detailed contents
The 22 AP Calculus AB tests, their questions, points and time, and the titles of the first questions.
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1
Introducing Limits
- Estimating from a table
- Reading a graph
- Piecewise function
- Parameter for a limit
- Instantaneous speed
- Unbounded behavior
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2
Evaluating Limits Algebraically
- Substitution and limit laws
- Factoring
- Rationalizing
- Trigonometric limit
- Squeeze Theorem
- Difference quotient limit
-
3
Continuity and the Intermediate Value Theorem
- Three conditions
- Classifying discontinuities
- Repairing a function
- Continuity at two points
- IVT and a root
- IVT guarantees
-
4
Infinite Limits and Asymptotes
- One-sided infinite limits
- Vertical asymptotes
- Limits at infinity
- Both directions
- Reading asymptotes
- All asymptotes
-
5
The Derivative as a Limit
- Average and instantaneous rate
- Limit definition, polynomial
- Limit definition, reciprocal
- Tangent line
- Differentiability of a piecewise function
- Recognizing a derivative
-
6
Power, Sum and Basic Function Derivative Rules
- Polynomial derivative
- Roots and reciprocals
- Trig, exponential and log
- Tangent line
- Horizontal tangents
- Normal line
-
7
Product Rule, Quotient Rule and Trig Derivatives
- Product rule
- Quotient rule
- Trig and product
- Tangent line
- Table of values
- Horizontal tangents
-
8
The Chain Rule
- Power chain
- Trig chain
- Exponential and log chain
- Three layers
- Tangent line
- Composite from a table
-
9
Implicit Differentiation
- Implicit derivative
- Slope on an ellipse
- Chain rule in y
- Horizontal and vertical tangents
- Tangent line
- Second derivative
-
10
Derivatives of Inverse Functions
- Inverse from a table
- Inverse of a cubic
- Inverse trig derivatives
- Inverse trig and a root
- Second derivative
- Acceleration
-
11
Rates of Change in Context and Straight-Line Motion
- Interpreting derivatives
- Position, velocity, acceleration
- Direction from a sign chart
- Geometric rates
- Velocity from a table
- Reading a velocity graph
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12
Related Rates
- Circle area
- Ladder
- Cone volume
- Rectangle
- Shadow
- Distance between boats
-
13
Linearization and L'Hopital's Rule
- Linearization
- Tangent line estimate
- Over or under
- Using a table
- Hopital 0 over 0, second form
- Hopital infinity form
-
14
Mean Value Theorem and Extreme Value Theorem
- Verify the MVT
- Hypotheses fail
- MVT conclusion
- Critical numbers
- Absolute extrema
- Speed and the MVT
-
15
Increasing, Decreasing and the First Derivative Test
- Intervals of monotonicity
- First derivative test
- Reading the derivative graph
- No sign change
- Absolute extrema
- Justification
-
16
Concavity and the Second Derivative
- Concavity intervals
- Inflection point
- Second derivative test
- Graph of the derivative
- Reading a summary table
- Justify a statement
-
17
Optimization
- Maximum product
- Pen against a wall
- Open box
- Closest point
- Revenue
- Can design
-
18
Riemann Sums and the Definite Integral
- Riemann sums for a line
- Table estimate
- Over or under
- Geometry and integrals
- Properties
- Accumulated change
-
19
Fundamental Theorem of Calculus and Antiderivatives
- Indefinite integral
- Definite integral
- FTC with the chain rule
- Accumulation from a graph
- Initial value problem
- Motion with integrals
-
20
Integration by Substitution
- Indefinite substitution
- Definite substitution
- Exponential substitution
- Trigonometric substitution
- Logarithm form
- Long division
-
21
Differential Equations and Slope Fields
- Verify a solution
- Slope field analysis
- Euler's method
- Separation of variables
- Exponential growth
- Matching a slope field
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22
Average Value, Area and Volume
- Average value
- Motion
- Area between curves
- Area with a crossing
- Cross sections
- Washer method
Sample pages
Three pages from the AP Calculus AB Math Tests with Answer Keys, exactly as you will print them. Click to enlarge.
How to use these tests
Set a timer
Give each test the time printed on its first page, 45 minutes for most AP Calculus AB chapters, to work in real conditions.
Grade with the key
The scoring note of each question says how the points are awarded, so a parent can give partial credit on the 176 questions of AP Calculus AB.
Retest a weak chapter
A low score on Evaluating Limits Algebraically? Review that chapter, then take the test again a week later.
Go further
Frequently asked questions
How many tests are in the AP Calculus AB test book?
22 AP Calculus AB tests, one per chapter, with 176 questions in all. Each test is worth 20 points and takes 45 minutes.
How are the AP Calculus AB tests graded?
Part 2 gives an answer key for each AP Calculus AB test, with worked solutions and a scoring note for every question, so you can grade out of 20 the same way every time.
Do I need the AP Calculus AB Math Worksheets with Answers along with the test book?
No, the AP Calculus AB Math Tests with Answer Keys stands on its own. But both books follow the same 22 chapters of AP Calculus AB; together they make a complete course, practice then test.
How do I receive the AP Calculus AB Math Tests with Answer Keys?
Right after paying with PayPal or a card, you reach your download page, where the AP Calculus AB Math Tests with Answer Keys is waiting. An email with the link is sent too.
Can I print the AP Calculus AB test book and open it on several devices?
Yes: the 155-page PDF of the AP Calculus AB Math Tests with Answer Keys prints as often as you need and opens on three devices (computer, tablet, phone). It carries your name at the bottom of the pages.
More answers on the shop page, or through our contact form.