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Math - Practice ACT (25-26)

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MATHEMATICS TEST

50 Minutes—45 Questions

DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test.

You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator. Note: Unless otherwise stated, all of the following should be assumed.

1. Illustrative figures are not necessarily drawn to scale.

2. Geometric figures lie in a plane.

3. The word “line” indicates a straight line.

4. The word “average” indicates the arithmetic mean.

MATHEMATICS TEST

50 Minutes—45 Questions

DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test.

You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator. Note: Unless otherwise stated, all of the following should be assumed.

1. Illustrative figures are not necessarily drawn to scale.

2. Geometric figures lie in a plane.

3. The word “line” indicates a straight line.

4. The word “average” indicates the arithmetic mean.

Pitanje 1
1.

Cameron took 4 tests, and his scores were as follows: $100$, $60$, $80$, and $30$. Cameron took another test that was scored x. The mean score of the 5 tests he took is $72$. What is the value of x?

Pitanje 2
2.

In the Venn diagram below, circles S, C, and P represent farms raising sheep, cows, and pigs, respectively. How many of the 47 farms represented in the diagram do not raise cows?

Pitanje 3
3.

Marco designs a spinner wheel that has exactly 4 sections: red, blue, green, and yellow. He wants the spinner wheel to have a 25% chance of landing on each section. He spins the wheel 500 times.

The results of the spins are shown in this table.

Spinner wheel section

Number of times the spinner lands in each section

Red

80

Blue

165

Green

130

Yellow

125

Based on the results in this table, one of the following changes would be the best fix. Which one?

Pitanje 4
4.

In ΔABC, ∠A and ∠C are congruent, and the measure of ∠B is 143.6°. What is the measure of ∠A?

Pitanje 5
5.

x² - x - 30?

Pitanje 6
6.

Which of the following matrices is equal to $5 \begin{bmatrix} -4 & 2 \\ 0 & -5 \end{bmatrix}$

Pitanje 7
7.

Lavonne purchased some tickets and snack vouchers for an upcoming event and gave them to the members of her work group. Each member of her work group received the same number of tickets and the same number of snack vouchers. The total number of tickets she gave to her group was 30, and the total number of snack vouchers was 75. Which of the following could be the number of members in Lavonne’s work group?

Pitanje 8
8.

The initial speed, in miles per hour, of a certain car that skids to a stop can be estimated by multiplying the length of the skid, in feet, by 35 and then taking the square root of the product. According to this method, what is the estimated initial speed, in miles per hour, of the car when it makes a 108-foot skid?

Pitanje 9
9.

If $6y = 5x - 1$, then $x = ?$

Pitanje 10
10.

A boat is traveling at a speed of 30 miles per hour. What is the boat’s speed in feet per second?

(Note: $1$ mile = $5,280$ feet)

Pitanje 11
11.

An object is launched vertically at 30 meters per second from a 55-meter-tall platform. The height, h(t) meters, of the object t seconds after launch is modeled by h(t) = -4.9t^2 + 30t + 55. What will be the height, in meters, of the object 3 seconds after launch?

Pitanje 12
12.

The whole numbers $1$ through $30$ were each written on separate pieces of paper. Those $30$ pieces of paper were put into a jar. One piece of paper will be randomly drawn from this jar. What is the probability that this piece of paper will have a prime number written on it?

Pitanje 13
13.

For an angle with measure \alpha in a right triangle, \sin \alpha = \frac{5}{13} and \tan \alpha = \frac{5}{12}. What is the value of \cos \alpha?

Pitanje 14
14.

Which of the following values, if any, is the y-value of the solution set to the system of equations below? 2x - y = 7 -4x + 2y = 2

Pitanje 15
15.

Which of the following expressions is equivalent to $(y+7)^{3}$?

Pitanje 16
16.

The sum of 3 positive integers is 180, and the ratio of the integers is 5:3:2. What is the value of the smallest of the integers?

Pitanje 17
17.

Which of the following expressions is equivalent to $(x^{2}-y^{2})-(6x^{2}+4xy-y^{2})$?

Pitanje 18
18.

Given i = \sqrt{-1}, what is $\sqrt{9}+ \sqrt{-16}$?

Pitanje 19
19.

The first 5 terms of an arithmetic sequence are 7, 21, 35, 49, and 63. Let t_n represent the $n$th term of the sequence. What is the value of t_{25}?

Pitanje 20
20.

At a certain time of day, a flagpole casts a 9.0-foot-long shadow and a nearby 4.0-foot-tall fence post casts a 2.4-foot-long shadow. Given that both the flagpole and the fence post are vertical and on level ground, what is the height, in feet, of the flagpole?

Pitanje 21
21.

In rectangle ABCD shown, segments $\overline{BE}$ and $\overline{CE}$ partition the rectangle into $3$ triangles. Given DE = $7$centimeters, BE = $26$centimeters, and CE = $25$ centimeters, what is the length, in centimeters, of $\overline{BC}$?

Pitanje 22
22.

In a particular cleaning solution, the ratio of concentrated solution to water is 3:40. How many cups of concentrated solution should be added to 5 gallons of water to make the cleaning solution in the given ratio?

(Note: 4 cups = 1 quart; 4 quarts = 1 gallon)

Pitanje 23
23.

Let $f(t) = 7e^{3t} + 1$. Which of the following numbers is closest to the value of $f(5)$?

Pitanje 24
24.

Which of the following expresses 40° in radians?

Pitanje 25
25.

Let the function $f$ be defined as $f(x) = -9x^{2}$. In the standard $(x,y)$ coordinate plane, the graph of $y = f(x)$ undergoes a transformation such that the result is the graph of $y = f(x) - 4$. Under this transformation, the graph of $y = f(x)$ is:

Pitanje 26
26.

For all positive values of $a$, $b$, $c$, and $d$, when $\frac{1}{2} ab^{2} + c = d$, which of the following expressions is equal to $b$?

Pitanje 27
27.

On a trip, $2$ sisters counted $1,430$ vehicles. They divided the vehicles into categories: cars, trucks, and other. They noted the color of each as white, black, red, or other, as shown in the table. What is the probability that a randomly selected truck is black?

White

Black

Red

Other

Total

Car

118

62

97

197

474

Truck

100

31

116

232

479

Other

86

85

94

212

477

Total

304

178

307

641

1,430

Pitanje 28
28.

A regular hexagon is inscribed in a circle with a diameter of $18$ inches, as shown. What is the perimeter, in inches, of the hexagon?

Pitanje 29
29.

Tanya earns $$34,000$ in her 1st year at a job. She is given a raise of the same dollar amount each year, resulting in her earning $$38,080$ in the 4th year at the job. What is the total of Tanya’s earnings during her 4 years at the job?

Pitanje 30
30.

In the standard $(x,y)$ coordinate plane, how many points are both $5$ coordinate units from the origin and also $2$ coordinate units from the line $y=0$?

Pitanje 31
31.

In \triangle ABC, if the measure of \angle A is less than the measure of \angle B, and the measure of \angle B is less than the measure of \angle C, what is the correct ordering of the side lengths, from least to greatest?

Pitanje 32
32.

Lajuan sells exactly 4 kinds of pies in his bakery: apple, pecan, coconut cream, and peach. Of the pies he sold on Thursday, \frac{1}{4} were apple, \frac{1}{2} were pecan, 24 were coconut cream, and 8 were peach. How many total pies did Lajuan sell on Thursday?

Pitanje 33
33.

In a certain quadrilateral, 2 opposite angles each measure (3x + 5)^\circ. The other 2 opposite angles each measure (x + 3)^\circ. What is the value of $x$?

Pitanje 34
34.

The first 4 terms of a sequence are shown in the table. The sequence is defined by a_1 = 2 and a_n = a_{n-1} + (n - 1)^2 for n \geq 2. What is the sixth term, a_6, of this sequence?

$a_1$

$a_2$

$a_3$

$a_4$

2

3

7

16

Pitanje 35
35.

On the real number line, how many integers are between -\frac{65}{6} and \frac{75}{2}?

Pitanje 36
36.

During a particular experiment, 2 events, A and B, can each occur. Events A and B are mutually exclusive during this experiment. Which of the following probabilities is 0?

Pitanje 37
37.

The polynomial function defined by $p(x) = x^{3} + x^{2} - 8x - 12$ has $(x - 3)$ as one of its linear factors. What are all and only the zeros of $p$?

Pitanje 38
38.

Jonathan rode his bike every day for 18 days. The table shows each of the distances he rode. The table also shows the number of days he rode each of those distances.

Distance (in miles)

Number of days

1

2

3

4

4

3

5

6

7

3

What is the median daily distance, in miles, that Jonathan rode his bike for the 18 days?

Pitanje 39
39.

A tourism organization randomly selected 100 tourists finishing their summer visit to Spain. The organization asked them how many cities they had toured in the country. The table shows the results. Based on these data, for the population of tourists that visited Spain during the summer, what is the best estimate of the mean number of cities toured?

Number of cities

1

2

3

Number of tourists

10

40

50

Pitanje 40
40.

Given the equation $\sqrt[4]{x}=y$, where y is a real number, what must be true of x? $x$ is:

Pitanje 41
41.

Given that 1 \leq m \leq 4, 4 \leq n \leq 6, and 8 \leq p \leq 10, what is the greatest possible value for \left(\frac{m}{n}\right)\left(\frac{1}{p}\right)?

Pitanje 42
42.

Which of the following datasets has the largest standard deviation?

1
Pitanje 43
43.

Michael has a cylindrical fish tank, shown, that has an inside diameter of 18 inches. When he put colored gravel in his fish tank, the water level of the tank rose 2 inches. What is the volume of the gravel in cubic inches?

IES

$x$

$f(x)$

$g(x)$

$h(x)$

1

2

4

3

2

1

5

1

3

4

2

5

4

5

3

4

5

3

1

2

1
Pitanje 44
44.

The table gives values of f(x), g(x), and h(x) for all positive integers x \leq 5. Given h(f(a)g(a)) = 1 where a is a positive integer less than or equal to 5, what is the value of a?

F
Pitanje 45
45.

Each time Coin C is tossed, it lands faceup or facedown. The probability of landing faceup is 3 times the probability of landing facedown. In a certain game, the player wins $1.00 when Coin C lands faceup and the player wins $2.00 when Coin C lands facedown. To the nearest cent, what is the expected value of each toss of Coin C in this game?