Quiz about ACT Math Practice Test

Question 1

The numbers 1 through 15 were each written on individual pieces of paper, 1 number per piece. Then the 15 pieces of paper were put in a jar. One piece of paper will be drawn from the jar at random. What is the probability of drawing a piece of paper with a number less than 9 written on it?

Accepted Answer

8/15

Answer

1/9

Answer

1/15

Answer

6/15

Answer

7/15

Question 2

When x = 2, 10 + 3(12 + (3x)) = ?

Accepted Answer

16

Answer

12

Answer

26

Answer

34

Answer

104

Question 3

|6 - 4| - |3 - 8| = ?

Accepted Answer

-3

Answer

-7

Answer

3

Answer

7

Answer

21

Question 4

Of the 180 students in a college course, 1/4 of the students earned an A for the course, 1/3 of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?

Accepted Answer

75

Answer

90

Answer

105

Answer

120

Answer

135

Question 5

The number of fish, f, in Skipper's Pond at the beginning of each year can be modeled by the equation f(x) = 3(2^x), where x represents the number of years after the beginning of the year 2000. According to the model, how many fish were in Skipper's Pond at the beginning of the year 2006?

Accepted Answer

192

Answer

96

Answer

1,384

Answer

4,458

Answer

46,656

Question 6

Manish drove from Chicago to Baton Rouge. At 8:00 a.m., he was 510 km from Baton Rouge. At 1:00 p.m., he was 105 km from Baton Rouge. Which of the following values is closest to Manish's average speed, in kilometers per hour, from 8:00 a.m. to 1:00 p.m.?

Accepted Answer

81

Answer

58

Answer

68

Answer

94

Answer

102

Question 7

In the figure shown below, E and G lie on AC, D and F lie on AB, DE and FG are parallel to BC, and the given lengths are in feet. What is the length of AC, in feet?

Accepted Answer

42

Answer

13

Answer

26

Answer

29

Answer

48

Question 8

Katerina runs 15 miles in 2 1/2 hours. What is the average number of minutes it takes her to run 1 mile?

Accepted Answer

10

Answer

6

Answer

12 1/2

Answer

16 2/3

Answer

17 1/2

Question 9

A bag contains 8 red marbles, 9 yellow marbles, and 7 green marbles. How many additional red marbles must be added to the 24 marbles already in the bag so that the probability of randomly drawing a red marble is 3/5?

Accepted Answer

16

Answer

9

Answer

20

Answer

24

Answer

32

Question 10

In the standard (x,y) coordinate plane, the point (2,1) is the midpoint of CD. Point C has coordinates (6,8). What are the coordinates of point D?

Accepted Answer

(-2, -6)

Answer

(-2, -2)

Answer

(4, 9/2)

Answer

(10, 10)

Answer

(10, 15)

Question 11

At Sweet Stuff Fresh Produce the price of a bag of grapes depends on the total number of bags purchased at 1 time, as shown in the table below. In 2 trips to Sweet Stuff this week, Janelle purchased 3 bags of grapes on Monday and 4 bags of grapes on Wednesday. How much money would Janelle have saved if she had instead purchased 7 bags of grapes in 1 trip on Monday?

Accepted Answer

$2.00

Answer

$0.20

Answer

$1.00

Answer

$1.40

Answer

$2.50

Question 12

$$\left(\frac{27}{64}\right)^{-\frac{2}{3}}=?$$

Accepted Answer

16/9

Answer

-9/16

Answer

-9/32

Answer

9/16

Answer

32/9

Question 13

Loto begins at his back door and walks 8 yards east, 6 yards north, 12 yards east, and 5 yards north to the barn door. About how many yards less would he walk if he could walk directly from the back door to the barn door?

Accepted Answer

8

Answer

19

Answer

23

Answer

26

Answer

31

Question 14

In the figure below, A, B, C, and D lie on the circle centered at O. Which of the following does NOT appear in the figure?

Accepted Answer

Scalene triangle

Answer

Acute triangle

Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Right triangle

Question 15

What is the slope of a line, in the standard (x,y) coordinate plane, that is parallel to x + 5y = 9?

Accepted Answer

-1/5

Answer

-5

Answer

1/5

Answer

9/5

Answer

9

Question 16

Given y = -x/(x - 1) and x > 1, which of the following is a possible value of y?

Accepted Answer

1.9

Answer

-1.9

Answer

-0.9

Answer

0.0

Answer

0.9

Question 17

The set of all positive integers that are divisible by both 15 and 35 is infinite. What is the least positive integer in this set?

Accepted Answer

105

Answer

5

Answer

50

Answer

210

Answer

525

Question 18

On the first 7 statistics tests of the semester, Jamal scored 61, 76, 79, 80, 80, 84, and 91. The mean, median, and mode of his scores were 79, 80, and 80, respectively. On the 8th statistics test, Jamal scored 90. How do the mean, median, and mode of all 8 of his scores compare to the mean, median, and mode of his first 7 scores?

Accepted Answer

Mean greater, Median equal, Mode equal

Answer

Mean greater, Median greater, Mode greater

Answer

Mean greater, Median equal, Mode greater

Answer

Mean greater, Median greater, Mode equal

Answer

Mean equal, Median greater, Mode greater

Question 19

The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 edge touching. What is the total number of white cubes that were used to build the prism?

Accepted Answer

105

Answer

45

Answer

102

Answer

140

Answer

210

Question 20

One side of square ABCD has a length of 12 meters. A certain rectangle whose area is equal to the area of ABCD has a width of 8 meters. What is the length, in meters, of the rectangle?

Accepted Answer

18

Answer

12

Answer

16

Answer

20

Answer

24

Question 21

The average of a list of 4 numbers is 92.0. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40, and the fourth number in the new list is 48. What is the average of this new list of numbers?

Accepted Answer

94.0

Answer

81.0

Answer

92.0

Answer

94.4

Answer

96.6

Question 22

Four identical glasses are shown below. One glass is empty, and the other 3 glasses are 4/5 full, 1/2 full, and 3/4 full of water, respectively. If the water were redistributed equally among the 4 glasses, what fractional part of each glass would be filled?

Accepted Answer

31/80

Answer

2/11

Answer

8/11

Answer

3/22

Answer

31/60

Question 23

Aurelio is purchasing carpet tiles to cover an area of his living room floor that is 8 1/3 feet wide by 10 feet long. Each carpet tile is a square 20 inches wide by 20 inches long. What is the minimum number of carpet tiles that Aurelio must purchase to cover this area of his living room floor?

Accepted Answer

30

Answer

5

Answer

11

Answer

21

Answer

84

Question 24

It cost $2,500 to administer each Yq test and $50 to administer each Sam77 test. What was the total cost to administer both tests to all the volunteers?

Accepted Answer

$2,550,000

Answer

$1,537,500

Answer

$1,566,750

Answer

$1,568,250

Answer

$2,500,000

Question 25

What percent of the volunteers actually carry Yq77?

Accepted Answer

61.5%

Answer

57.5%

Answer

60.0%

Answer

60.5%

Answer

62.5%

Question 26

For how many volunteers did the Sam77 test give an incorrect result?

Accepted Answer

35

Answer

10

Answer

25

Answer

385

Answer

400

Question 27

One of the volunteers whose Sam77 test result was positive will be chosen at random. To the nearest 0.001, what is the probability the chosen volunteer does NOT possess Yq77?

Accepted Answer

0.017

Answer

0.026

Answer

0.035

Answer

0.041

Answer

0.063

Question 28

Given matrices X = [-1 0] and Y = [-2 -1], which of the following matrices is XY?

Accepted Answer

[ 2]

Answer

[-4]

Answer

[-3]

Answer

[-2]

Answer

[ 3]

Question 29

Regardless of how the graph is oriented in the standard (x,y) coordinate plane, NO graph in one of the following categories has a vertical line of symmetry. Which one?

Accepted Answer

Scalene triangle

Answer

Line

Answer

Square

Answer

Pentagon

Answer

Parallelogram

Question 30

A barrel contains 25 liters of a solvent mixture that is 40% solvent and 60% water. Lee will add pure solvent to the barrel, without removing any of the mixture currently in the barrel, so that the new mixture will contain 50% solvent and 50% water. How many liters of pure solvent should Lee add to create this new mixture?

Accepted Answer

5

Answer

2.5

Answer

10

Answer

12.5

Answer

15

Question 31

For all $$x e\pm y,\ \frac{x}{x+y}+\frac{y}{x-y}=?$$

Accepted Answer

$$\frac{\left(x^2+y^2\right)}{\left(x^2-y^2\right)}$$

Answer

$$\frac{1}{\left(x-y\right)}$$

Answer

$$\frac{\left(x+y\right)}{\left(x-y\right)}$$

Answer

$$\frac{\left(x+y\right)}{2x}$$

Answer

$$x^2+y^2$$

Question 32

Mary, James, and Carlos sold 1/4-page advertisements for the school yearbook. Mary sold twice as many as Carlos did, and James sold 3 times as many as Mary did. What fraction of these advertisements did Carlos sell?

Accepted Answer

1/9

Answer

1/7

Answer

1/6

Answer

1/5

Answer

1/3

Question 33

In a window display at a flower shop, there are 3 spots for 1 plant each. To fill these 3 spots, Emily has 6 plants to select from, each of a different type. Selecting from the 6 plants, Emily can make how many possible display arrangements with 1 plant in each spot? (Note: The positions of the unselected plants do not matter.)

Accepted Answer

120

Answer

3

Answer

6

Answer

15

Answer

216

Question 34

Point M will remain fixed, and point Q will move to the right along the x-axis. As Q continues to move to the right, which of the following statements describes what will happen to the slope of MQ?

Accepted Answer

It will increase but never be positive.

Answer

It will decrease and eventually be negative.

Answer

It will decrease but never be negative.

Answer

It will stay the same.

Answer

It will increase and eventually be positive.

Question 35

One of the following values is equal to f(5a). Which one?

Accepted Answer

8b

Answer

3a

Answer

5a

Answer

5b

Answer

8a

Question 36

Twelve jurors are needed for an upcoming trial. The diagram below illustrates a part of the process of jury selection. The 12 jurors will be selected from a jury pool of about 60 people. The court records show a trend that only 40% of the people who are summoned for jury duty actually appear and that of the people who appear, 1/3 are excused. If this same trend continues, how many people should be summoned to have as close as possible to 60 people in the jury pool?

Accepted Answer

225

Answer

45

Answer

90

Answer

150

Answer

800

Question 37

What is the 275th digit after the decimal point in the repeating decimal $$0\overline{.6295}$$ ?

Accepted Answer

9

Answer

0

Answer

2

Answer

5

Answer

6

Question 38

Given that p is a positive number, n is a negative number, and |p| > |n|, which of the following expressions has the greatest value?

Accepted Answer

$$\left|\frac{p-n}{n}\right|$$

Answer

$$\left|\frac{p-n}{p}\right|$$

Answer

$$\left|\frac{p+n}{p-n}\right|$$

Answer

$$\left|\frac{p+n}{p}\right|$$

Answer

$$\left|\frac{p+n}{n}\right|$$

Question 39

If $$i=\sqrt[]{-1}$$ , then $$\frac{i+i^2+i^3}{i^3+i^4+i^5}$$ =?

Accepted Answer

-1

Answer

-3

Answer

(1/2)

Answer

1

Answer

3

Question 40

In one of the following graphs in the standard (x,y) coordinate plane, the solution set to the system of inequalities below is shown shaded. Which one?

Accepted Answer

K.

Answer

F.

Answer

G.

Answer

H.

Answer

J.

Question 41

Let a, b, c, and d be real numbers. Given that ac = 1, $$\frac{b+c}{d}$$ Is undefined, and abc = d, which of the following must be true?

Accepted Answer

b = 0

Answer

a = 0 or c = 0

Answer

a = 1 and c = 1

Answer

a = -c

Answer

b + c = 0

Question 42

A cosine function is shown in the standard (x,y) coordinate plane below. One of the following equations represents this function. Which one?

Accepted Answer

y = 3 cos(2x)

Answer

y = 2 cos(x/3)

Answer

y = 2 cos(3x)

Answer

y = 3 cos(x/3)

Answer

y = 3 cos(x/2)

Question 43

If a publisher charges $15 for the first copy of a book that is ordered and $12 for each additional copy, which of the following expressions represents the cost of y books?

Accepted Answer

12y + 3

Answer

12y + 15

Answer

15y - 3

Answer

15y + 3

Answer

15y + 12

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