Free AP Calc AB Readiness Check

1.

Solve for

x

:

3(2x - 4) = 5x + 1

2.

Which of the following is a factor of

x^2 - 5x + 6

?

A.

x - 1

B.

x - 2

C.

x + 2

D.

x - 6

3.

Evaluate without a calculator:

\left(\dfrac{1}{16}\right)^{-3/4}

4.

Simplify:

\dfrac{x^2 - 9}{x^2 - 3x}

A.

\dfrac{x+3}{x}

B.

\dfrac{x-3}{x}

C.

\dfrac{3}{x}

D.

x + 3

5.

What are the solutions of

2x^2 - x - 6 = 0

?

A.

x = 2

and

x = -\tfrac{3}{2}

B.

x = -2

and

x = \tfrac{3}{2}

C.

x = 3

and

x = -1

D.

x = 6

and

x = -\tfrac{1}{2}

6.

If

f(x) = 2x + 1

and

g(x) = x^2

, find

f(g(3))

.

7.

What is the domain of

f(x) = \dfrac{1}{x-2} + \sqrt{x+3}

?

A.

x \ge -3

and

x \ne 2

B.

x \ge -3

C.

x > -3

D.all real numbers except

2

8.

Let

f(x) = \dfrac{2x+1}{x-3}

. Find

f^{-1}(3)

.

9.

Compared with the graph of

y = f(x)

, the graph of

y = f(x - 2) + 3

is shifted…

A.right 2 and up 3B.left 2 and up 3C.right 2 and down 3D.left 3 and up 2

10.

Let

f(x) = \begin{cases} x^2 & x < 1 \\ 3x - 2 & x \ge 1 \end{cases}

. Find

f(1)

.

11.

Suppose

\sin\theta = \dfrac{3}{5}

and

\theta

lies in Quadrant II. Evaluate

5\left(\sin\theta + \cos\theta\right)

.

12.

Evaluate:

\cos(\pi)

13.

For

0 \le \theta < 2\pi

, the solutions of

\tan\theta = 1

are…

A.

\theta = \tfrac{\pi}{4}

and

\theta = \tfrac{5\pi}{4}

B.

\theta = \tfrac{\pi}{4}

onlyC.

\theta = \tfrac{\pi}{4}

and

\theta = \tfrac{3\pi}{4}

D.

\theta = \tfrac{\pi}{2}

and

\theta = \tfrac{3\pi}{2}

14.

For every value of

x

,

\sin^2 x + \cos^2 x

equals…

A.

1

B.

0

C.

\sin(2x)

D.it depends on

x

15.

Solve for

x

:

2^x = 32

16.

Evaluate:

\ln(e^3)

17.

Solve for

x

:

9^{\,x} = 27^{\,x-2}

18.

As

x

gets closer and closer to

2

, what value does

\dfrac{x^2 - 4}{x - 2}

approach?

19.

As

x

grows without bound, what value does

\dfrac{1}{x}

approach?

20.

In calculus, the limit of

f(x)

as

x

approaches

a

describes…

A.the value

f(x)

gets closer and closer to as

x

approaches

a

B.the value of

f(a)

C.the slope of

f

at

x = a

D.the largest value

f

ever reaches