AP Calculus AB Review Jeopardy

Limits, derivatives, integrals, and applications on one free AP Calculus AB review board. Project it, split into teams, and buzz in from phones.

6 categories · 30 clues · Final Jeopardy · everyone buzzes in from their phone

For college and exam prep

Copies all 30 clues into an editor of your own. Free, no account needed.

Every clue on this board

This page is public, so anyone can read the answers — copy the board and swap a few clues before game day.

Limits and Continuity

$200
The limit as x approaches 0 of sin x divided by x equals this value.
What is 1?
$400
This theorem guarantees a function continuous on [a, b] takes on every value between f(a) and f(b).
What is the Intermediate Value Theorem?
$600
This rule evaluates limits of the form 0/0 by differentiating the numerator and denominator separately.
What is L'Hopital's rule?
$800
The limit as x approaches infinity of (3x squared plus 1) divided by (5x squared minus x) is this value.
What is 3/5?
$1,000
Used to show that x squared times sin(1/x) approaches 0 as x approaches 0, this theorem traps a function between two others.
What is the squeeze theorem?

Derivative Rules

$200
The derivative of sin x is this function.
What is cos x?
$400
The derivative of e to the 3x is this function.
What is 3e^(3x)?
$600
This rule is needed to differentiate a composite function such as sin of x squared.
What is the chain rule?
$800
The derivative of the natural log of (x squared plus 1) is this function.
What is 2x/(x^2 + 1)?
$1,000
The derivative of arctan x is this function.
What is 1/(1 + x^2)?

Applying the Derivative

$200
At a relative maximum of a differentiable function, the first derivative equals this.
What is 0?
$400
A point where the graph of a function changes concavity is called this.
What is a point of inflection?
$600
This theorem guarantees some c in (a, b) where f'(c) equals the average rate of change of f on [a, b].
What is the Mean Value Theorem?
$800
A particle's position is s(t) = t cubed minus 6t squared, so its acceleration at t = 1 is this.
What is -6?
$1,000
A circle's radius grows at 2 cm per second, so when the radius is 5 cm its area grows at this rate.
What is 20 pi square centimeters per second?

Integration Techniques

$200
This is the general antiderivative of x squared.
What is x^3/3 + C?
$400
This is the general antiderivative of 1/x.
What is ln|x| + C?
$600
To integrate 2x cos(x squared), this technique sets a new variable equal to x squared.
What is u-substitution?
$800
This is the general antiderivative of secant squared x.
What is tan x + C?
$1,000
The definite integral of e to the 2x from 0 to ln 3 has this value.
What is 4?

The Fundamental Theorem

$200
The derivative with respect to x of the integral from 0 to x of f(t) dt is this.
What is f(x)?
$400
The definite integral of 2x from 1 to 3 has this value.
What is 8?
$600
The derivative with respect to x of the integral from 0 to x squared of sin t dt is this function.
What is 2x sin(x^2)?
$800
The average value of f(x) = x squared on the interval [0, 3] is this number.
What is 3?
$1,000
If F(x) is the integral from 1 to x of ln t dt, then F''(x) is this.
What is 1/x?

Differential Equations

$200
Solutions of dy/dt = ky with k greater than 0 describe this kind of growth.
What is exponential growth?
$400
This graph of short line segments shows the slope a differential equation prescribes at many points.
What is a slope field?
$600
This technique solves dy/dx = xy by moving all the y terms to one side and all the x terms to the other.
What is separation of variables?
$800
This is the general solution of dy/dx = 2y.
What is y = Ce^(2x)?
$1,000
The solution of dy/dx = y with y(0) = 3 takes this value at x = ln 2.
What is 6?

Final Jeopardy — The Big Theorem

This theorem states that if f is continuous on [a, b] and F is an antiderivative of f, then the definite integral of f from a to b equals F(b) minus F(a).

What is the Fundamental Theorem of Calculus?

How to run this board

The six columns follow the AB course: limits and continuity, derivative rules, applications of the derivative such as related rates and optimization, integration techniques, the Fundamental Theorem, and differential equations and slope fields.

Most clues take a minute of work, so give every team a whiteboard and 30 seconds before the buzzers open. The first team to buzz with a correct written answer takes the points, which rewards accuracy over speed.

A tip for the last weeks before the exam: after each clue, ask whether a calculator would have been allowed. Knowing which problems are calculator-active is half the battle on test day.

More from the library

Spotted a clue that's wrong or out of date? Tell us and we'll fix the board. Or start from a blank board and write your own.