AP Calculus AB Math Worksheets with Answers
480 exercises on the 22 chapters of AP Calculus AB, from Introducing Limits to Average Value, Area and Volume, and in Part 2 a worked answer for every one of them.
- 254 US Letter pages
- 22 chapters
- 480 exercises with answers
- PDF to print
- Cards accepted without a PayPal account
- Instant download, up to 3 devices
About this book
The workbook practices each of the twenty-two chapters: infinite limits and asymptotes, derivatives of inverse functions, straight-line motion, L'Hopital's rule, substitution and differential equations.
Part 1 holds the worksheets, about 22 exercises per chapter, each with a short title that says what it practices, like All features of a cubic in Concavity and the Second Derivative. Part 2, which starts on page 117, gives the answers in the same order, so checking takes a minute.
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 Lessons to go back to the lesson when a problem gets stuck.
Detailed contents
The 22 chapters of the AP Calculus AB workbook, the number of exercises in each, and the titles of the first ones.
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1
Introducing Limits
- Reading limit notation
- Table for a linear function
- Table with an undefined point
- Limit versus function value
- One-sided limits from a graph
- Limit at a smooth point
-
2
Evaluating Limits Algebraically
- Direct substitution
- Using the limit laws
- Substitution with a root
- Difference of squares
- Factoring a trinomial
- Factoring with a leading coefficient
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3
Continuity and the Intermediate Value Theorem
- Continuity of a polynomial
- Where is it undefined?
- Removable discontinuity
- Types from a graph
- Checking conditions from data
- Repairing a hole
-
4
Infinite Limits and Asymptotes
- One-sided infinite limits
- An even power
- Sign analysis
- Asymptote or hole?
- Asymptotes from a graph
- Equal degrees
-
5
The Derivative as a Limit
- Average rate of change
- Secant slope from a table
- Derivative at a point, x squared
- Derivative at a point, a quadratic
- Derivative of a reciprocal
- Derivative of a square root
-
6
Power, Sum and Basic Function Derivative Rules
- Constant and power
- Higher power
- Polynomial
- Polynomial with a fraction
- Root and reciprocal
- Simplify first
-
7
Product Rule, Quotient Rule and Trig Derivatives
- Product with an exponential
- Product of two polynomials
- Product with sine
- Exponential times log
- Square root times cosine
- Simple quotient
-
8
The Chain Rule
- Power of a linear function
- Power of a quadratic
- Square root of a linear function
- Reciprocal power
- Sine of a multiple
- Cosine of a power
-
9
Implicit Differentiation
- Circle
- Product of x and y
- Sum of cubes
- Mixed terms
- Sine of y
- Exponential in y
-
10
Derivatives of Inverse Functions
- Inverse derivative from values
- Inverse of a cubic
- Inverse with sine
- Inverse of the exponential
- Inverse of a fifth-degree polynomial
- Inverse from a table
-
11
Rates of Change in Context and Straight-Line Motion
- Interpreting a cost derivative
- Interpreting a temperature derivative
- Velocity and direction
- Velocity and acceleration
- Speeding up or slowing down
- Reading a velocity graph
-
12
Related Rates
- Growing ripple
- Melting ice cube
- Growing cube
- Sliding ladder
- Rectangle
- Two cars
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13
Linearization and L'Hopital's Rule
- Linearization of x squared
- Estimating a square root
- Estimating a cube root
- Estimating a reciprocal
- Exponential near zero
- Sine near zero
-
14
Mean Value Theorem and Extreme Value Theorem
- MVT with a parabola
- MVT with a cubic
- MVT with a logarithm
- MVT with a reciprocal
- Two values of c
- When the MVT fails
-
15
Increasing, Decreasing and the First Derivative Test
- Intervals for a parabola
- Intervals for a cubic
- First derivative test, quartic
- First derivative test, exponential
- A function with an asymptote
- A square root
-
16
Concavity and the Second Derivative
- Concavity of a cubic
- Concavity of a logarithm
- Exponential inflection
- Always concave down
- Sine on an interval
- Inflection where f double prime is undefined
-
17
Optimization
- Maximum product
- Minimum sum of squares
- Maximum area, fixed perimeter
- Fence against a wall
- Minimum fence, fixed area
- Open box from a square sheet
-
18
Riemann Sums and the Definite Integral
- Left Riemann sum
- Right Riemann sum
- Midpoint Riemann sum
- Trapezoidal sum
- Riemann sums from a table
- Unequal subintervals
-
19
Fundamental Theorem of Calculus and Antiderivatives
- Polynomial antiderivative
- Negative powers
- Roots
- Sine and cosine
- Exponential and reciprocal
- Trig and inverse trig forms
-
20
Integration by Substitution
- A power of a quadratic
- A square root
- Cosine of a multiple
- Exponential of a multiple
- Exponential with a quadratic
- Sine times a power of cosine
-
21
Differential Equations and Slope Fields
- Verify a solution
- Verify a second-order solution
- Reading a slope field
- Matching an equation
- Euler, two steps
- Euler for y prime equals y
-
22
Average Value, Area and Volume
- Average value of x squared
- Average value of a root
- Average value of sine
- Average temperature
- Average value from a table
- Displacement and distance
Sample pages
Three pages from the AP Calculus AB Math Worksheets with Answers, exactly as you will print them. Click to enlarge.
How to use this workbook
Try before you check
Work on FTC part 1, chain rule on scratch paper before opening Part 2: that is where progress happens.
Use the numbering
Answers carry the same chapter and exercise numbers as the 22 AP Calculus AB worksheets, so the right one is easy to find.
Target one chapter
Before a quiz on Introducing Limits, do its 22 exercises, then redo the ones you missed.
Go further
Frequently asked questions
How many exercises are in the AP Calculus AB workbook?
480 exercises on 254 pages, spread over 22 chapters. Each one has its answer in Part 2.
Where are the answers of the AP Calculus AB worksheets?
In Part 2, at the end of the AP Calculus AB workbook, starting on page 117. They are kept apart from the worksheets so a student can work without seeing them.
Do I need the AP Calculus AB Math Lessons along with the workbook?
No, the AP Calculus AB Math Worksheets with Answers stands on its own. But both books follow the same 22 chapters of AP Calculus AB; together they make a complete course, lesson then practice.
How do I receive the AP Calculus AB Math Worksheets with Answers?
Right after paying with PayPal or a card, you reach your download page, where the AP Calculus AB Math Worksheets with Answers is waiting. An email with the link is sent too.
Can I print the AP Calculus AB workbook and open it on several devices?
Yes: the 254-page PDF of the AP Calculus AB Math Worksheets with Answers 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.