AP Calculus AB

Unit 1

100

If f(t) = 3t² - 10t + 2, will f(x) = 1 on the interval [-1, 3]?

yes. f(-1) = 15 and f(3) = -1 

200

The domain of f(x) = x² - x / x

All real numbers, except zero

300

The limit as x approaches 1 for (x²-5x)/(x - 1)

Does not exist.

400

The limit as x approaches 8 for (x² + 2x - 80) / x- 8 

18

500

The limit as x approaches 2 for (x² + 6x - 16) / 2 - x

-10

Units 2 and 3

100

Another name for a derivative?

Slope/rate of change

200

What is the derivative of f(x) = 8x² - 6

16x

300

The derivative of f(x) = (x² - 5)⁴

8x(x² - 5)³

400

The derivative of f(x) = 3^x - 4cosx

3^xln3 + 4sinx

500

The simplified derivative of h(x) = (3x + 1) / 2x²

-3x - 2 / 2x³

Unit 4

100

To find the velocity function from the position function

Derivative

200

The acceleration function if x(t) = t³ - 4t² + 3

x"(t) = a(t) = 6t - 8

300

A particle is speeding up when 

v(t) and a(t) have the same sign

400

Given the position s(t) = 1/3t³ - 3t² + 8t - 5, the particle is at rest when t = 

t = 4 and t = 2

500

What law is used when a limit equals 0/0?

L'Hopital's Rule

Units 5 and 6

100

When f'(x) > 0, f(x) is

increasing

200

If f"(x) < 0, f(x) is 

concave down

300

The linear motion of an object when f'(x) changes signs

The object changes direction

400

The value of the integral of (4 - 6x) dx from -2 to 5

-35

500

The indefinite integral of 6x²(x³ + 4)⁵ dx

1/3(x³ + 4)⁶ + C

Units 7 and 8

100

The equation of the tangent line through the point (-1, -2), if dy/dx = 1 - xy

y + 2 = -1(x+1)

200

The particular solution for the differential equation where dy/dx = 6y and y = 5 when t = 0

y = 5e^6t

300

The average value of f(x) = 6 - x² on [-1, 3]

11/3

400

The formula to find the volume of a solid with semicircles cross sections

V = integral a to b of 1/2 pi r^2 dx where r is f(x) - g(x) / 2

500

The volume bounded by y = 4 - 2x, y = 0, and x = 0. Revolved about the y-axis.

16pi/3