# Conquering ACT Math and Science 4th

## Educators  ### Problem 1

Which of the following expressions is equivalent to $6 x+12 y-15 z ?$
A. $3(x+12 y-15 z)$
B. $3(2 x+4 y-5 z)$
C. $3(3 x+4 y)-5 z$
D. $6(x+2 y-3 z)$
E. $15(x+y-z)$ Lily A.

### Problem 2

When written in symbols, "the product of $a$ and $b$, raised to the third power" is represented as:
F. $a^{3}-b^{3}$
G. $\left(a+b^{3}\right)$
H. $(a b)^{3}$
J. $\frac{a^{3}}{b^{3}}$
K. $a b^{3}$ Lily A.

### Problem 3

Tyler took a road trip on his motorcycle. When he left, the odometer read 22,687 miles, and when he returned, it read 23,002 miles. In total, Tyler rode for 5 hours. Based on the odometer readings, what was his average speed during the trip, to the nearest mile per hour?
A. 79
B. 76
C. 64
D. 63
E. 58 Lily A.

### Problem 4

The interior dimensions of a rectangular rabbit cage are 5 feet by 4 feet by 2 feet. What is the volume, in cubic feet, of the interior of the rabbit cage?
F. 11
G. 20
H. 28
J. 40
K. 44 Lily A.

### Problem 5

If $z$ is a real number and $3^{z}=81,$ then $7 \times 2^{z}=?$
A. 14
B. 28
C. 56
D. 84
E. 112 Lily A.

### Problem 6

For the students at Bayside College, the ratio of professors to students is $2: 43 .$ There are currently 9,030 students enrolled. Which of the following statements is (are) true?
I. There are 420 professors.
II. Each professor has 43 students in his or her course.
III. Professors make up $\frac{2}{43}$ of the Bayside population.
F. I only
G. II only
H. III only
J. I and III only
K. $\mathrm{I}, \mathrm{II},$ and $\mathrm{III}$ Lily A.

### Problem 7

If the probability that a specific event will occur is $0.09,$ what is the probability that the event will NOT occur?
A. 0.00
B. 0.11
C. 0.70
D. 0.91
E. 1.00 Lily A.

### Problem 8

As shown below, the diagonals of rectangle $A B C D$ intersect at the point (-4,2) in the standard $(x, y)$ coordinate plane. Point $D$ is at $(1,-1 )$. Which of the following are the coordinates of point $B ?$
F. (1,5)
G. (-6,4)
H. (-9,-1)
J. (-9,5)
K. $(-11,6)$ James K.

### Problem 9

$|5(-3)+11|=?$
A. -4
B. 3
C. 4
D. 13
E. 26 Lily A.

### Problem 10

The expression $5 m(-3 m+6 n)-9 m n$ is equivalent to:
F. $30 m n-8 m$
G. $21 m n-15 m^{2}$
H. $15 m n-9 m^{2}$
J. $6 m n$
K. $-15 m^{2}$ Lily A.

### Problem 11

Jose recently took a history test on which certain questions were worth 3 points each, while the rest were worth 5 points each. He correctly answered the same number of 3 -point questions as 5 -point questions, and he earned a score of 72 points. How many 5 -point questions did he answer correctly?
A. 9
B. 11
C. 15
D. 24
E. 26 Lily A.

### Problem 12

A rectangular poster measures 22 inches by 16 inches. Pietro estimates that the area is 264 square inches. His estimate is what percent less than the actual area?
F. $75 \%$
G. $50 \%$
H. $45 \%$
J. $30 \%$
K. $25 \%$ Lily A.

### Problem 13

The geometric mean of 2 positive numbers is the square root of the product of the 2 numbers. What is the geometric mean of 16 and $64 ?$
A. 28
B. 32
C. 40
D. 256
E. 1,024 Lily A.

### Problem 14

A model for the braking distance $d$ feet required to stop a certain car when it is traveling $x$ miles per hour is $d=\left(\frac{x^{2}}{20}\right)+x .$ According to this model, what is the braking distance, in feet, required to stop this car when it is traveling at 30 miles per hour?
F. 30
G. 52
?. 75
J. 90
K. 102 Lily A.

### Problem 15

The expression $2 x^{2}+10 x-28$ can be written as the product of 2 binomials with integer coefficients. One of the binomials is $(x+7)$. Which of the following is the other binomial?
A. $2 x^{2}-4$
B. $2 x^{2}+4$
C. $2 x-6$
D. $2 x-4$
E. $x+4$ Lily A.

### Problem 16

The table below shows the number of miles Mandy ran each day in the last week. What is the median of the data in the table?
$$\begin{array}{|l|l|} \hline \text { Day } & \begin{array}{l} \text { Number of } \\ \text { Miles Run } \end{array} \\ \hline \text { Sun } & 15 \\ \hline \text { Mon } & 17 \\ \hline \text { Tue } & 12 \\ \hline \text { Wed } & 23 \\ \hline \text { Thu } & 13 \\ \hline \text { Fri } & 15 \\ \hline \text { Sat } & 24 \\ \hline \end{array}$$
F. 14.5
G. 15
H. 17
J. 23.5
K. 30 Lily A.

### Problem 17

Given $f(x)=\frac{x^{2}+\frac{3}{8}}{x+\frac{2}{5}},$ what is $f\left(\frac{1}{4}\right) ?$
A. $\frac{35}{52}$
B. 1
C. $\frac{52}{30}$
D. $\frac{20}{9}$
E. $\frac{9}{2}$ Lily A.

Jim has $\$ 13$more than his friend Brian, who has x dollars. Jim spends$\$25$ on Saturday, and then works on Sunday and earns $\$ 32$. Which of the following is an expression for the amount of money, in dollars, that Jim has after working on Sunday? F. 20 G.$x-7$H.$x-20$J.$2 x+7$K.$x+20$ Lily A. Numerade Educator ### Problem 19 Given that$\sqrt{2 x}-9=1, x=?$A. -32 B. 20 C. 25 D. 32 E. 50 Lily A. Numerade Educator ### Problem 20 Which of the following is a factored form of the expression$7 x^{2}+10 x-8 ?$F.$(x-1)(7 x+8)$G.$(x-4)(7 x+2)$H.$(x-8)(7 x-1)$J.$(x+2)(7 x-4)$K.$(x+4)(7 x-2)$ Lily A. Numerade Educator ### Problem 21 Which of the following is equivalent to$\sqrt{8} ?$A.$\frac{1}{8^{4}}$B.1 C.$\sqrt{2}$D.$8^{\frac{1}{4}}$E.$4^{8}$ Lily A. Numerade Educator ### Problem 22 If$x, y,$and$z$are positive integers such that$x^{y}=a$and$z^{y}=b,$then$a b=?$F.$x z y$G.$x z^{2} y$H.$(x z) y$J.$(x z)^{2 y}$K.$(x z)^{\frac{y}{2}}$ Lily A. Numerade Educator ### Problem 23 The mean age of the 5 people in the room is 30 years. One of the 5 people, whose age is 50 years, leaves the room. What is the mean age of the 4 people remaining in the room? A. 14 B. 20 C. 25 D. 30 E. 35 Lily A. Numerade Educator ### Problem 24 When 5 consecutive odd integers that are each greater than 34 are added, what is the smallest possible sum? F. 195 G. 185 H. 152 J. 147 K. 144 Lily A. Numerade Educator ### Problem 25 The probability that Event$X$will occur is$0.3 .$The probability that Event$Y$will occur is$0.6 .$Given that Events$X$and$Y$are mutually exclusive, what is the probability that Event$X$or Event$Y\$ will occur?
A. 0.18
B. 0.2
C. 0.3
D. 0.4
E. 0.9 Lily A.