ACT Math Unit 1: Preparing for Higher Math — Free with Answer Explanations

Question 1

The function $f (x) = 2^{x}$ is transformed to $g (x) = 2^{x - 3} + 5$ . Compared to $f$ , the graph of $g$ is:

A.Shifted left 3 units and up 5 unitsB.Shifted right 3 units and down 5 unitsC.Shifted right 3 units and up 5 unitsD.Stretched vertically by 5 and shifted right 3 units

Question 2

Solve for $x$ : $lo g_{3} (x) = 4$

A.

x = 12

B.

x = 7

C.

x = 81

D.

x = 64

Question 3

What is the value of $x$ if $3 x - 7 = 14$ ?

A.

x = 3

B.

x = 7

C.

x = 9

D.

x = 21

Question 4

A sphere has volume $\frac{4}{3} π r^{3}$ . If the radius is doubled, by what factor does the volume increase?

A.

2

B.

4

C.

6

D.

8

Question 5

What is the median of the data set ${4, 9, 2, 7, 5, 1, 8}$ ?

A.

4

B.

5

C.

5.14

D.

6

Question 6

The expression $sin^{2} θ + cos^{2} θ$ equals:

A.

0

B.

2

C.

sin (2 θ)

D.

1

Question 7

In right triangle $A B C$ with the right angle at $C$ , if $sin A = \frac{3}{5}$ , what is $cos A$ ?

A.

\frac{3}{4}

B.

\frac{4}{5}

C.

\frac{3}{5}

D.

\frac{5}{4}

Question 8

A circle has a radius of 5. What is its area?

A.

10 π

B.

25 π

C.

50 π

D.

5 π

Question 9

What is the slope of the line passing through $(2, 5)$ and $(6, 13)$ ?

A.

1

B.

2

C.

4

D.

\frac{1}{2}

Question 10

For what values of $x$ is the quadratic $x^{2} - 5 x + 6 < 0$ ?

A.

x < 2

or

x > 3

B.

x < - 3

or

x > - 2

C.

2 < x < 3

D.

- 3 < x < - 2

Question 11

If $f (x) = 2 x^{2} - 3 x + 1$ , what is $f (- 1)$ ?

A.

- 4

B.

0

C.

6

D.

4

Question 12

Which of the following is a solution to $x^{2} - 9 = 0$ ?

A.

x = 3

onlyB.

x = - 3

onlyC.

x = 3

or

x = - 3

D.

x = 9

or

x = - 9