Conquering ACT Math and Science 4th

Educators

Problem 1

$(4 x-5)(3 x+1)$ is equivalent to:
A. $7 x-4$
B. $12 x^{2}-5$
C. $7 x^{2}+11 x-4$
D. $12 x^{2}-11 x-5$
E. $16 x+20$

Lily A.

Problem 2

The square root of a certain number is approximately $3.316 .$ The certain number is between what 2 integers?
F. 3 and 4
G. 5 and 6
H. 9 and 12
J. 25 and 30
K. 33 and 39

Lily A.

Problem 3

Adam attempted 33 field goals throughout the football season and made 26 of them. Approximately what percentage of his field goals did he make during the season?
A. $27 \%$
B. $33 \%$
C. $66 \%$
D. $72 \%$
E. $79 \%$

Lily A.

Problem 4

What $(x, y)$ pair is the solution to the system of equations below?
$$\begin{array}{l}-2 x+4 y=-18 \\4 x-5 y=30\end{array}$$
F. (5,-2)
G. (3,3)
?. (0,0)
J. (-3,-3)
K. (-5,2)

Lily A.

Problem 5

If the measure of each interior angle in a regular polygon is $90,$ how many sides does the polygon have?
A. 8
B. 6
C. 5
D. 4
E. 3

Lily A.

Problem 6

For all positive integers $x,$ what is the greatest common factor of the numbers $256 x$ and $144 x ?$
F. 12
G. 16
H. $x$
J. $16 x$
K. $24 x$

Lily A.

Problem 7

Kathleen and Natalie are putting new carpet in their apartment. Kathleen used $22 \frac{3}{4}$ square yards of carpet in the living room, and Natalie used $12 \frac{1}{2}$ square yards of carpet in the dining room. If 50 square yards of carpet was purchased, how many square yards were left after laying down new carpet in both rooms? A. $12 \frac{3}{4}$
B. $14 \frac{1}{4}$
C. $14 \frac{1}{2}$
D. $14 \frac{\overline{3}}{4}$
E. $16 \frac{1}{4}$

Lily A.

Problem 8

In the figure below, parallel lines $q$ and $r$ are intersected by line $s .$ What is the value of $x ?$
F. 9
G. 16
H. 20
J. 40
K. 55

James K.

Problem 9

The equation of a circle is $x^{2}+y^{2}=81$. If this circle is graphed in the standard $(x, y)$ coordinate plane, what will be the $y$ intercepts?
A. (0,3) and (0,-3)
B. (0,9) and (0,-9)
C. (0,12) and (0,-12)
D. (0,18) and (0,-18)
E. (0,27) and (0,-27)

Lily A.

Problem 10

A new rectangular soccer field is being constructed at John Adams High School. The length of the field must be $(4 x-3)$ yards, and the width must be $5 x$ yards. Which of the following expressions in terms of $x$ gives the number of square yards of grass needed to cover the field?
F. $x-3$
G. $9 x-3$
H. $20 x-15 x^{2}$
J. $15 x^{2}+9 x$
K. $20 x^{2}-15 x$

Lily A.

Problem 11

In the geometric sequence
$4,10,25,62 \frac{1}{2}, N, \ldots$
what is the 5 th term, $N ?$
A. $144 \frac{3}{4}$
B. $148 \frac{1}{2}$
$\mathrm{C} \cdot 156 \frac{1}{4}$
D. $156 \frac{1}{2}$
E. $162 \frac{\overline{1}}{4}$

Lily A.

Problem 12

What are the values for $x$ that satisfy the equation $(x+y)(x+z)=0 ?$
F. $y$ and $z$
G. $y$ and $-z$
$\mathbf{H} \cdot-y z$
J. $-y$ and $z$
$\mathbf{K} .-y$ and $-z$

Lily A.

Problem 13

What fraction lies exactly halfway between $\frac{1}{3}$ and $\frac{3}{5} ?$
A. $\frac{7}{15}$
B. $\frac{2}{5}$
C. $\frac{1}{2}$
D. $\frac{\overline{2}}{3}$
E. $\frac{14}{15}$

Lily A.

Problem 14

Each night at closing time over a full workweek, Cory counted the number of customers who shopped at his store that day and recorded it in the table shown below. For that workweek, what was the average number of customers per day at Cory's store?
$$\begin{array}{|l|c|}\hline \text { Day } & \text { Number of Customers } \\\hline \text { Monday } & 20 \\\hline \text { Tuesday } & 26 \\\hline \text { Wednesday } & 21 \\\hline \text { Thursday } & 17 \\\hline \text { Friday } & 31 \\ \hline\end{array}$$
F. 26
G. 23
H. 21
J. 20
K. 18

Lily A.

Problem 15

Sasha is going to Italy over his spring break. When he arrives, he has to exchange his U.S. dollars for euros. If the exchange rate between the number of U.S. dollars $(u)$ and euros $(e)$ is expressed in the equation $0.77 u=e,$ approximately how many euros will Sasha receive in exchange for his 675 U.S. dollars?
A. 877
B. 730
C. 520
D. 493
E. 465

Lily A.

Problem 16

When doing a problem, Barb meant to divide a number by 2 , but instead she accidentally multiplied the number by $2 .$ Which of the following calculations could Barb then do to the result to obtain the result she originally wanted?
F. Divide by 4
G. Divide by 2
H. Multiply by 4
J. Multiply by 2
K. Subtract the original number

Lily A.

Problem 17

There is a bowl with 48 different marbles in it. In the bowl, there are 14 red marbles, 12 blue, 9 green, 8 yellow, and 5 white. If Corbin reaches into the bowl without looking, what is the probability that he will draw a marble that is either blue or white?
A. $\frac{21}{48}$
B. $\frac{17}{48}$
C. $\frac{12}{48}$
D. $\frac{9}{48}$
E. $\frac{5}{48}$

Lily A.

Problem 18

If $n=2,$ what is the value of $n(-6)^{n}-9 n ?$
F. 126
G. 81
H. 54
J. 18
K. -90

Lily A.

Problem 19

Which of the following is a factor of $\left(2 z^{2}-z-15\right) ?$
A. $2 z-5$
B. $2 z-15$
$\mathbf{C} \cdot z^{2}-3$
D. $z+15$
E. $z-3$

Lily A.

Problem 20

If the point with coordinates $\left(-2, y_{1}\right)$ lies on the graph of $y=-4 x+5$ what is the value of $y_{1} ?$
F. 13
G. 8
H. 3
J. 1
K. -3

Lily A.

Problem 21

If $8 y=6 x+14,$ then $x=?$
A. $y-14$
B. $\frac{8 y}{6}+14$
C. $\frac{4 y+7}{3}$
D. $\frac{4 y-7}{3}$
E. $\frac{8 y+14}{6}$

Lily A.

Problem 22

A packet of fruit snacks is filled by weight in the factory. If each fruit snack weighs about 0.04 ounce, about how many are needed to fill a packet with 1.2 ounces of fruit snacks?
F. 12
G. 30
H. 36
J. 48
K. 75

Lily A.

Problem 23

What is the difference between the mean and the median of the set \{5,7,8,12\}$?$
A. 0
B. 0.5
C. 4
D. 7.5
E. 8

Lily A.

Problem 24

The area of a circle is $121 \pi$ square units. What is the diameter, in units, of the circle?
F. $\pi$
G. 11
H. 22
J. $11 \pi$
K. 121

Lily A.
For all $x, \frac{-5(-2 x)^{3}}{10 x}$ is equivalent to:
A. $100 x^{2}$
B. $4 x^{2}$
C. $x^{3}$
D. $-4 x^{2}$
$\mathbf{E} .-100 x^{2}$