AP Calc AB Review

Limits

100

Evaluate:

lim⁡x→3  (2x+1)

What is 7?

200

Evaluate: 

lim⁡x→2  (x2+4x−1)

What is 11?

300

Evaluate:

lim⁡x→0 (sin⁡x)/x

What is 1?

400

Evaluate:

lim x→1 (x²-1)/(x-1)

What is 2?

500

Find the horizontal asymptote of:

f(x)= (3x²+1)/(x²-4)

What is y=3?

Derivatives

100

Find the derivative of:

f(x) = x³

What is 3x²?

200

Find the derivative of:

f(x) = 5x⁴-2x

What is 12x³-2?

300

Differentiate:

f(x) = sinx

What is cosx?

400

Differentiate:

f(x) = e^x

What is e^x?

500

Use the product rule to differentiate:

f(x) =x²cos x

What is 2xcosx-x²sin x?

Applications of Derivatives

100

If f'(x) > 0 on an interval, the function is this.

What is increasing?

200

If f"(x) > 0, the graph is described as this.

What is concave up?

300

A point where the derivative equals zero or is undefined is called this.

What is critical point?

400

Find the slope of the tangent line to:

f(x) =x²+1

at x = 3

What is 6?

500

A particle's position is:

s(t) = t³-6t²+9t

Find the velocity at t = 2.

What is -3?

Intergals

100

Evaluate

Intergal 4x³dx

What is x⁴+C?

200

Evaluate

Intergal cosxdx

What is sinx+C?

300

Evaluate

Integral xdx

a=0 b=2

What is 2?

400

Find the area under:

f(x) = x²

from x = 0 to x = 1.

What is 1/3?

500

Evaluate

Integral (3x²-4x+1)dx

What is x³-2x²+x+C?

Differential Equations

100

If:

dy/dx= 3x²

find y.

What is x³+C?

200

A differential equation that includes dy/dx is used to describe this.

What is rate of change?

300

Find the particular solution if:

dy/dx=2x

and y = 3 when x = 0.

what is y=x²+3?

400

Solve:

dy/dx= 1/x

What is y=ln|x|+C?

500

A population grows according to:

dP/dt= 0.2P

This type of growth is called this.

What is exponential growth?