Conquering ACT Math and Science 4th

Steven W. Dulan, Amy Dulan

Chapter 9

Practice Test 4 with Explanations

Educators


Problem 1

Katie plans to purchase a motorcycle that costs $\$ 4,600 .$ In addition, she has to pay $\$ 450$ for insurance and $\$ 320$ for taxes. If Katie has $\$ 3,200$ saved, what amount must she borrow to be able to buy the motorcycle and pay the expenses?
A. $\$ 630$
B. $\$ 1,400$
C. $\$ 1,850$
D. $\$ 2,170$
E. $\$ 7,800$

Lily A.
Numerade Educator

Problem 2

What is the greatest common factor of the monomials $18 x^{2}, 27 x^{4}$, and $30 x^{3} ?$
F. $3 x^{2}$
G. $3 x^{4}$
H. $9 x^{2}$
J. $18 x^{2}$
K. $30 x^{3}$

Lily A.
Numerade Educator

Problem 3

$6 a^{7} \times 9 a^{3}$ is equivalent to:
A. $54 a^{21}$
B. $54 a^{10}$
C. $54 a^{4}$
D. $15 a^{21}$
E. $15 a^{10}$

Lily A.
Numerade Educator

Problem 4

In parallelogram $W X Y Z$ shown below, $\overline{W Y}$ is perpendicular to $\overline{Y Z}$, and the measure of angle $W Z Y$ is $72^{\circ} .$ What is the measure of angle $X Y W ?$
F. $12^{\circ}$
G. $18^{\circ}$
H. $36^{\circ}$
J. $58^{\circ}$
K. $72^{\circ}$

James K.
Numerade Educator

Problem 5

What is the value of the expression $\frac{20,000}{Y^{2}-12 Y+100}+5 Y$ when $Y=50 ?$
A. 130
B. 155
C. 200
D. 260
E. 310

Lily A.
Numerade Educator

Problem 6

For the variables $y$ and $z, a=3 y^{4}-z^{2}$ and $b=-5 y^{3} .$ Which of the following expressions represents the product $a b ?$
F. $-15 y^{12}+5 y z^{6}$
G. $-15 y^{7}+5 y^{3} z^{2}$
$\mathbf{H} \cdot-8 y^{7}+z^{2}$
J. $-2 y^{3}-z^{2}$
$\mathbf{K} .-2 y-z^{2}$

Lily A.
Numerade Educator

Problem 7

What is the slope of the line $12 y+4 x=17 ?$
A. 17
B. 12
C. 4
D. $\frac{17}{12}$
$\mathbf{E} \cdot-\frac{1}{3}$

Lily A.
Numerade Educator

Problem 8

Mars has much less gravity than Earth, so objects on Mars weigh about $38 \%$ of what they would weigh on Earth. If Jason weighs 175 pounds on Earth, about how many pounds would he weigh on Mars?
F. 66.5
G. 89
H. 108.5
J. 241
K. 460.5

Lily A.
Numerade Educator

Problem 9

Brad's volleyball team won 25 of its 45 games, and had 2 ties. What fraction of the 45 games did the team lose?
A. $\frac{3}{5}$
B. $\frac{5}{9}$
C. $\frac{2}{5}$
D. $\frac{1}{3}$
E. $\frac{2}{9}$

Lily A.
Numerade Educator

Problem 10

In the figure below, $\overline{M L}$ is perpendicular to $\overline{L K},$ and points $L, K$, and $J$ are collinear. If the measure of angle $L M K$ is $62^{\circ},$ what is the measure of angle $M K J ?$
F. $28^{\circ}$
G. $76^{\circ}$
H. $118^{\circ}$
J. $134^{\circ}$
K. $152^{\circ}$

James K.
Numerade Educator

Problem 11

In Boardman City, the daily low temperatures, in degrees Fahrenheit $\left({ }^{\circ} \mathrm{F}\right),$ during the first week in January were $-13,-8,10,2,23,31,$ and
30. To the nearest $1^{\circ} \mathrm{F}$, what was the mean daily low temperature for that week?
A. -3
B. 10
C. 11
D. 18
E. 25

Lily A.
Numerade Educator

Problem 12

In the $(x, y)$ coordinate plane, what is the radius of the circle $(x-1)^{2}$ $+(y+2)^{2}=8 ?$
F. 1
G. $\sqrt{2}$
H. 2
J. $\sqrt{8}$
K. 8

Lily A.
Numerade Educator

Problem 13

What value of $x$ makes the proportion below true?
$$\frac{10}{10+x}=\frac{36}{45}$$
A. 2.5
B. 9
C. 12
D. 18
E. 27.5

Lily A.
Numerade Educator

Problem 14

$$|-5|+2|-4|-|7|=?$$
F. 10
G. 6
H. 3
J. -4
K. -20

Lily A.
Numerade Educator

Problem 15

If $18 x$ is $40 \%$ of $180,$ then $x=?$
A. 4
B. 10
C. 24
D. 38
E. 72

Lily A.
Numerade Educator

Problem 16

The expression $(6 s-2)(4 s-7)$ is equivalent to:
F. $24 s^{2}-50 s+14$
G. $24 s^{2}-34 s-14$
H. $24 s^{2}+14$
J. $10 s^{2}-50 s+14$
K. $10 s^{2}-14$

Lily A.
Numerade Educator

Problem 17

If $f(x)=5 x^{2}-3 x-27,$ then $f(-4)=?$
A. 385
B. 172
C. 65
D. 41
E. -95

Lily A.
Numerade Educator

Problem 18

If $n<0,$ which of the following best describes a general relationship between $n^{2}$ and $n^{3} ?$
F. $n^{2}<n^{3}$
G. $n^{2}>n^{3}$
H. $n^{2}=n^{3}$
J. $-n^{2}=n^{3}$
K. $\frac{1}{n^{2}}<n^{3}$

Lily A.
Numerade Educator

Problem 19

The endpoints of line $\overline{Q R}$ on the real number line are -5 and 11 . What is the coordinate of the midpoint of $\overline{Q R} ?$
A. -2
B. 0
C. 3
D. 6
E. 8

Lily A.
Numerade Educator

Problem 20

If the sine of an angle is -0.5 and its cosine is $0.7,$ what is its secant?
F. $\frac{-1}{0.5}$
G. $\frac{-0.7}{0.5}$
H. $\frac{-0.5}{0.7}$
J. $\frac{-0.5}{1}$
K. $\frac{1}{0.7}$

Lily A.
Numerade Educator

Problem 21

What is the point in the standard $(x, y)$ coordinate plane that is the center of a circle with the equation $(x+3)^{2}+(y-7)^{2}=16 ?$
A. (7,3)
B. (4,4)
$\mathbf{C} \cdot(3,-7)$
D. (-3,4)
E. (-3,7)

Lily A.
Numerade Educator

Problem 22

Through the 3 rd game of the football season, Reggie had scored 2 more touchdowns than Tom. In the 4th game, Tom scored 3 touchdowns while Reggie had none. After being injured, Tom missed the next 3 games, during which Reggie scored 5 touchdowns. Over the 8 th and 9 th games, Tom scored 4 touchdowns and Reggie scored 2 touchdowns total. In the 10 th game, Reggie scored 3 touchdowns while Tom scored 1. At the end of the 10th game, who between Tom and Reggie had more touchdowns, and by how many?
F. Tom by 4
G. Tom by 2
H. Neither
J. Reggie by 2
K. Reggie by 4

James K.
Numerade Educator

Problem 23

If $7 x-3(x-6)=2(x-7)+10,$ then $x=?$
A. 6
B. $\frac{9}{2}$
C. 2
D. -11
E. $\frac{-37}{3}$

Lily A.
Numerade Educator

Problem 24

For all $x,$ which of the following is a factor of $10 x^{2}+14 x-12 ?$
F. $(x+3)$
G. $(2 x-4)$
H. $(5 x-3)$
J. $(5 x+3)$
K. $(5 x+4)$

Lily A.
Numerade Educator

Problem 25

A group of college students started a landscaping business. The students charge $\$ 24$ per hour for a job that requires more than 5 hours. For any job that requires 5 hours or less, they charge a flat rate of $\$ 125 .$ If $h$ represents the number of hours that the job requires, which of the following expressions gives the charge, in dollars, for a job requiring more than 5 hours to complete?
A. $125 h$
B. $-24 h+125$
$\mathrm{C} \cdot 24 h-125$
D. $24 h$
E. $24 h+125$

Lily A.
Numerade Educator
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