AP Calculus Review Game

Derivatives

100

What is the derivative of:

y=x³ - 5x² + 7x - 4

dy/dx = 3x² - 10x + 7

200

What is the derivative of: 

y = (x² - 3x)(2x² - 4x + 3)

dy/dx = (2x - 3)(2x² - 4x +3) + (4x - 4)(x² -3x)

300

What is the derivative of: 

y = (2x-3) / (x² - 3x + 2)

dy/dx = [(2x² - 6x + 4) - (2x-3)²] / (x² - 3x + 2)²

400

What is the derivative of: 

y = (x² - 2x)³

dy/dx = 3(x² - 2x)² (2x - 2)

500

What is the derivative of:

3xy - 2x + 3y + 5 = 8

dy/dx = 2 / (3x + 3)

Limits

100

Find the limit of f(x) = 5^x / x - 5 as x is approaching infinity

What is 

Infinity

200

Find the limit of f(x) = (x + 7) / (x - 1) as x is approaching 2

What is 

3

300

Find the limit of f(x) = (20^x -7) / (5 + 9^x) as x is approaching negative infinity

what is 

-7/5

400

Find the limit of f(x) = (x - 5) / (25 - x²) as x is approaching 5

what is 

-1/10

500

Find limit of f(x) = [2 sin (x) - sin (2x)] / (x - sin  (x) as x is approaching 0

what is 

6

Integrals

100

What is the integral of 

∫ 2x - 3 dx from 0 to 5

y = 10

200

What is the integral of 

∫2e^2x - 1/x dx from 1 to 4

y = 2972.183

300

What is the integral of 

∫Sin^-1 x dx

y = x sin^-1 x + (1 - x²)^1/2 + C

400

What is the integral of 

∫(cos x - tan x)

y = sin x - ln (|sec x|) + C

500

Find y, dy/dx = (2x) (3y), on the interval (2,1/3)

y = -e^{x^2}

Trig

100

What is the Derivatives of the following functions:

Sin x = 

-Cos x = 

Tan x = 

Sec x =

-Cot x = 

Csc x =

Sin x = Cos x

-Cos x = Sin x

Tan x = Sec² x

Sec x = Tan x Sec x

-Cot x = Csc² x

Csc x = -Cot x Csc X

200

What are the Integrals of the following functions:

Cos x = 

-Sin x =

Sec² x =

-Csc² x =

-Sec x Tan x =

Csc x Cot x =

Cos x = Sin x + C

-Sin x = Cos x + C

-Sec² x = -Tan x + C

Csc² x = -Cot x + C

-Sec x Tan x = -Sec x + C

-Csc x Cot x = Csc x + C

300

∫sin(8x)sin(x)dx from 1 to 3

YOU CAN USE A CALCULATOR

What is −0.0174

400

What is the anti-derevative of 1/1+x²

What is Tan^-1 x

500

Solve the equation 2cos3x+1=0, where 0°≤x<360°.

A. x=40°,80°

B. x=40°,80°,160°,200°,280°,320°

C. x=60°,120°,180°

D. x=40°,80°,120°,160°

What is 

B. x=40°,80°,160°,200°,280°,320°

Exponential/Pi

100

What is the derevative of:

y = ln x + e^4x

dy/dy = 1/x + 4e^4x

200

You have a function, y = 3x³ - 4x² - 7x + 10, use the line tangent at (-1,10) to approximate F'(-1.8).

Tangent line equation: y = 10x + 20

y(1.8) = 2

300

find the integral 

∫Cos x - Sin x dx

y = 0

400

Find the derivative of 

y = (ln x) (ln x - e^2x) 

y' = [-2e^2x (ln x)] + (2ln x - e^2x) / 2

500

find the tangent line of 

y = e^2x - cos x + sin x at x = 0

y = 3x