Conquering ACT Math and Science 4th

Steven W. Dulan, Amy Dulan

Chapter 2

ACT Mathematics Diagnostic Test

Educators


Problem 1

For each of four months, the table below gives the number of games a basketball team played, the number of free throws the team attempted, and the number of free throws the team made.
$$\begin{array}{|l|c|c|c|}
\hline \text { Month } & \text { Games } & \begin{array}{l}
\text { Free Throws } \\
\text { Attempted }
\end{array} & \begin{array}{l}
\text { Free Throws } \\
\text { Made }
\end{array} \\
\hline \text { September } & 4 & 78 & 69 \\
\hline \text { October } & 6 & 107 & 93 \\
\hline \text { November } & 8 & 120 & 102 \\
\hline \text { December } & 5 & 83 & 76 \\
\hline
\end{array}$$
To the nearest tenth, what is the average number of free throws that the team made per game in November?
A. 8.5
B. 10.2
C. 12.8
D. 15.0
E. 17.3

Lily A.
Numerade Educator

Problem 2

For the polygon below, the lengths of 2 sides are not given. Each angle between adjacent sides measures $90^{\circ} .$ What is the polygon's perimeter, in centimeters?
F. 41
G. 47
H. 54
J. 62
K. 123

James K.
Numerade Educator

Problem 3

Which of the following inequalities represents the graph shown below on the real number line?
A. $-6 \leq x<1$
B. $-5 \leq x \leq 0$
C. $-5<x \leq-1$
D. $-5<x \leq 0$
E. $-4 \leq x<-1$

James K.
Numerade Educator

Problem 4

What is the value of $3^{a-b} \times 4$ when $a=1$ and $b=-2 ?$
F. -12
G. 24
H. 76
J. 94
K. 108

Lily A.
Numerade Educator

Problem 5

For integers $y$ and $z$ such that $y z=24,$ which of the following is NC a possible value of $z ?$
A. -12
B. -5
C. 6
D. 8
E. 24

Lily A.
Numerade Educator

Problem 6

The length of the base of a rectangular prism is $8 \mathrm{cm},$ and the width is $6 \mathrm{cm} .$ If the height of the rectangular prism is $4 \mathrm{cm},$ what is its volume in cubic centimeters?
F. 192
G. 124
H. 86
J. 48
K. 24

Lily A.
Numerade Educator

Problem 7

A local radio station is selling airtime spots to advertisers for the upcoming week. The station charges $\$ 150$ for one of the 85 30second spots, and $\$ 270$ for one of the 4560 -second spots. Which of the following expressions gives the total amount of money, in dollars, collected from selling all of the 60 -second spots and $S$ of the 30 -second spots?
A. $150 S+12,150$
B. $150 S+270$
C. $85 S+12,150$
D. $45 S+10,000$
E. $S+150$

Lily A.
Numerade Educator

Problem 8

In the figure below, $W, X,$ and $Y$ are collinear, the measure of angle $W X Z$ is $4 x^{\circ},$ and the measure of angle $Y X Z$ is $8 x^{\circ} .$ What is the measure of angle $W X Z ?$
F. $15^{\circ}$
G. $60^{\circ}$
H. $80^{\circ}$
J. $95^{\circ}$
K. $120^{\circ}$

James K.
Numerade Educator

Problem 9

Haylee is living in a house with 11 other people, and each person will get her own room. There are 3 bedrooms on the first floor, 5 on the second, and 4 on the third. The housemates are deciding who gets what room by drawing numbers out of a hat. If Haylee draws first, what is the probability that she will get a room on the third floor?
A. $\frac{1}{12}$
B. $\frac{1}{6}$
C. $\frac{1}{4}$
D. $\frac{1}{3}$
E. $\frac{5}{12}$

Lily A.
Numerade Educator

Problem 10

Which of the following is a solution to the equation $x^{2}-49 x=0 ?$
F. 98
G. 49
H. 21
J. 7
K. -7

Lily A.
Numerade Educator

Problem 11

A group of high school students is planning to paint one side of the solid concrete wall around the elementary school playground as a way to give back to the community. The wall is 120 feet long and 8 feet tall. Assuming that 1 can of paint covers exactly 25 square feet, what is the minimum number of cans of paint the students will need in order to put 1 coat of paint on the wall?
A. 38
B. 39
C. 42
D. 47
E. 56

Lily A.
Numerade Educator

Problem 12

If the ratio of $3 x$ to $7 y$ is 1 to $7,$ what is the ratio of $6 x$ to $7 y ?$
F. 3 to 7
G. 2 to 21
H. 2 to 7
J. 1 to 35
K. 1 to 14

Lily A.
Numerade Educator

Problem 13

A recent survey of college students on a big campus was conducted to find students' preferred method of getting to class. The results showed that $35 \%$ of students walk to class, $20 \%$ take the bus, $25 \%$ ride a bike, and $15 \%$ drive; the remaining students rollerblade to class. If each student preferred only 1 method of getting to class and 75 students preferred rollerblading, how many students were surveyed?
A. 900
B. 1,250
C. 1,500
D. 1,800
E. 2,225

Lily A.
Numerade Educator

Problem 14

The ratio of 40 to 32 is the same as the ratio of 30 to what number?
F. 15
G. 20
H. 24
J. 66
K. 70

Lily A.
Numerade Educator

Problem 15

$\left(3 x^{2}-7 x+5\right)-\left(-2 x+8-x^{2}\right)$ is equivalent to:
A. $2 x^{2}-9 x+13$
B. $2 x^{2}-5 x+3$
C. $4 x^{2}-5 x-3$
D. $4 x^{2}+5 x+13$
$6 x^{2}+9 x-3$

Lily A.
Numerade Educator

Problem 16

A bleacher ticket for a high school baseball game costs $\$ 8 .$ Ryan decides to take his sister to the game as a birthday present. He gives her $\frac{1}{3}$ of the money he brought to buy two bleacher tickets and two hot dogs of equal cost. Later, Ryan decides to buy two bags of popcorn, which cost $\$ 6$ total. If $\mathrm{Ryan}$ has $\$ 34$ left, what was the price of one hot dog?
F. $\$ 6.25$
G. $\$ 5.75$
H. $\$ 5.00$
J. $\$ 3.50$
K. $\$ 2.00$

Lily A.
Numerade Educator

Problem 17

Mrs. Krantz gave her students a 15 -question pop quiz on the week's algebra lesson. Which of the following percents is a possible score for the percent of questions that a student answered correctly if each question had equal weight? (Note: No partial credit was awarded.)
A. $71 \%$
B. $73 \%$
C. $80 \%$
D. $86 \%$
E. $93 \%$

Lily A.
Numerade Educator

Problem 18

The first 4 terms of a geometric sequence are $-\frac{1}{9}, \frac{1}{3},-1,$ and $3 .$ What is the 5 th term?
F. 9
G. 3
H. -6
J. - 9
K. -12

Lily A.
Numerade Educator

Problem 19

$(5 a-2 b)^{2}$ is equivalent to:
A. $25 a^{2}-20 a b+4 b^{2}$
B. $25 a^{2}-10 a b-4 b^{2}$
C. $25 a^{2}-4 b^{2}$
D. $25 a^{2}+4 b^{2}$
E. $25 a+20 a b+4 b^{2}$

Lily A.
Numerade Educator

Problem 20

Gary had a rectangular-shaped garden with sides of lengths 32 feet and 8 feet. He changed the garden into a square with the same area as the original rectangular-shaped garden. How many feet in length is each of the sides of the new square-shaped garden?
F. 3
G. $4 \sqrt{2}$
H. 12
J. 16
K. 24

Lily A.
Numerade Educator

Problem 21

What is the solution to the equation $4 x-(-2 x+5)=-3 ?$
A. $-\frac{1}{2}$
B. $-\frac{1}{3}$
C. $\frac{1}{4}$
D. $\frac{1}{3}$
E. 1

Lily A.
Numerade Educator

Problem 22

The area of $\Delta A B C$ below is 42 square inches. If $\overline{B D}$ is 7 inches long, how long is $\overline{A C}$, in inches?
F. 9
G. 10
H. 12
J. 15
K. 21

James K.
Numerade Educator

Problem 23

Given $f(x)=3 x^{2}+6 x+11,$ what is the value of $f(-5) ?$
A. -94
B. -42
C. 56
D. 61
?. 78

Lily A.
Numerade Educator

Problem 24

Which of the following data sets has the smallest standard deviation?
F. 1,17
G. 1,2,3,4
H. 2,2,3,6,6,8
J. 15,30,40
K. 80,80,80,80,80

Lily A.
Numerade Educator

Problem 25

The table below shows the age distribution of the varsity football team at Washington High School.
$$\begin{array}{|l|c|c|c|c|}
\hline \text { Age, in years } & 15 & 16 & 17 & 18 \\
\hline \text { Percent of team } & 8 & 22 & 32 & 38 \\
\hline
\end{array}$$
What percent of the team is at least 17 years old?
A. $32 \%$
B. $38 \%$
C. $54 \%$
D. $65 \%$
E. $70 \%$

Lily A.
Numerade Educator
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