Free Printable act 2

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?

a)

$\frac{1}{9}$

b)

$\frac{1}{15}$

c)

$\frac{6}{15}$

d)

$\frac{7}{15}$

e)

$\frac{8}{15}$

2.

Which of the following expressions is equivalent to $-4x^3-12x^3+9x^2$

a)

$x^8$

b)

$-7x^8$

c)

$-8x^3+9x^2$

d)

$-16x^3+9x^2$

e)

$-16x^6+9x^2$

3.

When $x=2,\ \ 10+3\left(12\div\left(3x\right)\right)$

a)

$12$

b)

$16$

c)

$26$

d)

$34$

e)

$104$

4.

$\left|6-4\right|-\left|3-8\right|=$

a)

$-7$

b)

$-3$

c)

$3$

d)

$7$

e)

$21$

5.

The expression $\left(4c-3d\right)\left(3c+d\right)$ is equivalent to:

a)

$12c^2-13cd-3d^2$

b)

$12c^2-13cd+3d^2$

c)

$12c^2-5cd-3d^2$

d)

$12c^2-5cd+3d^2$

e)

$12c^2-3d^2$

6.

Of the 180 students in a college course, $\frac{1}{4}$ of the students earned an A for the course, $\frac{1}{3}$ 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?

a)

$75$

b)

$90$

c)

$105$

d)

$120$

e)

$135$

7.

The number of fish $f$ , in Skipper’s Pond at the beginning of each year can be modeled by the equation $f\left(x\right)=3\left(2^x\right)$ , where $x$ represents the number of years after the beginning of the year $2000$ . For example, $x=0$ represents the beginning of the year $2000$ , $x=1$ represents the beginning of the year 2001, and so forth. According to the model, how many fish were in Skipper’s Pond at the beginning of the year 2006 ?

a)

$96$

b)

$192$

c)

$384$

d)

$1,458$

e)

$46,656$

8.

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. ?

a)

58

b)

68

c)

81

d)

94

e)

102

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 $\frac{3}{5}$

a)

11

b)

16

c)

20

d)

24

e)

32

10.

At his job, the first 40 hours of each week that Thomas works is regular time, and any additional time that he works is overtime. Thomas gets paid $15 per hour during regular time. During overtime Thomas gets paid 1.5 times as much as he gets paid during regular time. Thomas works 46 hours in 1 week and gets $117 in deductions taken out of his pay for this week. After the deductions are taken out, how much of Thomas’s pay for this week remains?

a)

$492

b)

$573

c)

$609

d)

$618

e)

$735

11.

What is $3\%$ of $4.14\cdot10^4$ ?

a)

1,242

b)

1,380

c)

12,420

d)

13,800

e)

124,200

12.

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?

a)

5

b)

50

c)

105

d)

210

e)

525

13.

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?

a)

81.0

b)

92.0

c)

94.0

d)

94.4

e)

96.6

14.

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?

a)

2.5

b)

5

c)

10

d)

12.5

e)

15

15.

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?

a)

Line

b)

Square

c)

Pentagon

d)

Parallelogram

e)

Scalene triangle

16.

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.)

a)

3

b)

6

c)

15

d)

120

e)

216

17.

Which of the following expressions is equal to (sin 60°)(cos 30°) + (cos 60°)(sin 30°) ?

a)

cos(60° − 30°)

b)

cos(60° + 30°)

c)

sin(60° − 30°)

d)

sin(60° + 30°)

e)

sin $\left(\frac{60\degree+30\degree}{2}\right)$

18.

There are (a) questions on Mathematics part of the ACT Test.

19.

The Mathematics portion of the ACT is limited to (a) minutes.

20.

If ax + b = c - x, what is the expression representing x?

a)

$x=\frac{c-b}{a}$

b)

$x=\frac{c+b}{a}$

c)

$x=\frac{c-b}{2a}$

d)

$x=\frac{c-b}{a+1}$

21.

(2x)²(3x³)=

a)

6x⁵

b)

12x⁶

c)

12x⁵

d)

6x⁶

22.

(3 + 4i) (3 - 4i) =

a)

7

b)

9 - 16i

c)

25

d)

9 + 16i

23.

If f(a) = 3 for f(x) = 2x² - 5x, what are the values of a?

a)

a = 3 and a = -1/2

b)

a = -3 and a = -1/2

c)

a = -3 and a = 1/2

d)

a = 3 only

24.

Two parallel lines are intersected by a transversal. What is the sum of the measure of angles D and E ?

a)

105

b)

210

c)

75

d)

150

25.

If a jogger runs 3.5 miles in 21 minutes, what is the jogger's average speed in miles per hour?

a)

10.5 mph

b)

1.225 mph

c)

10 mph

d)

6.5 mph

26.

What is the value of x $4^{x-1}=8^{\frac{x}{2}}$

a)

2/3

b)

4/3

c)

4

d)

no solution

27.

If a circle with its center at (2, -3) is tangent to the y-axis, what is the diameter of the circle?

a)

2

b)

3

c)

6

d)

4

28.

Find the perimeter if x = 15 ft and y = 10 ft.

a)

50 ft

b)

25 ft

c)

60 ft

d)

150 ft

29.

Find the area if a = 13 in, b = 9 in and c = 16 in.

a)

38 in²

b)

117 in²

c)

468 in²

d)

58.5 in²

30.

What is the algebraic expression for "the sum of n and 9"?

a)

n - 9

b)

n + 9

c)

n/9

d)

9n

31.

What is the sum?
-7 + 5

a)

-2

b)

12

c)

-12

d)

2

32.

Simplify
(1/3)(21m + 27)

a)

63m + 9

b)

7m + 9

c)

7m + 81

d)

7m + 27

33.

Find the number of degrees in the third angle of the triangle

a)

155

b)

112

c)

74

d)

68

34.

Find the measure of ∠ACD.

a)

130

b)

115

c)

65

d)

50

35.

(5n-8)(5n+8)

a)

25n²-64

b)

10n²

c)

5n²+16

d)

16

36.

Find the sum.
(5x²-3x + 4) + (6x -3x²- 3)

a)

3x² + 2x + 1

b)

2x² + 3x +1

c)

2x² + 5x - 7

d)

3x²+ 4x⁵ -7x

37.

a)

15

b)

25

c)

35

d)

65

e)

80

38.

What is the slope of line HM?

a)

$-\frac{3}{2}$

b)

-1

c)

$-\frac{2}{3}$

d)

$\frac{2}{3}$

e)

$\frac{3}{2}$

39.

If the area of rectangle ABCD is 1 square unit, which of the following expressions represents the area of the shaded region?

a)

$\frac{1}{8}\cdot\frac{1}{6}$

b)

$\frac{1}{8}\cdot\frac{5}{6}$

c)

$\frac{1}{8}\cdot\frac{7}{8}$

d)

$\frac{7}{8}\cdot\frac{1}{6}$

e)

$\frac{7}{8}\cdot\frac{5}{6}$

40.

What is the area of a triangle whose base is 10 in and height is 5 in?

a)

50 in²

b)

30 in²

c)

15 in²

d)

25 in²

41.

What is the scientific notation of 6700000?

a)

6.7 x 10⁵

b)

67 x 10⁶

c)

6.7 x 10⁶

d)

67 x 10⁵

42.

|-5| + |2| =

a)

-7

b)

3

c)

-3

d)

7

43.

^{There are 45 boys and 54 girls in your school's senior class. What is the ratio of boys to girls?}

a)

1:5

b)

1:6

c)

5:6

d)

5:11

44.

What is the value of the expression (y-x)³ when x =5 and y = 1?

a)

-64

b)

64

c)

-4

d)

16

45.

In a certain school district, exactly 30% of the students come from families that have only one child. If there are 7,340 students in the district, how many do not come from families with only one child?

a)

514

b)

2,202

c)

5,138

d)

7,120

46.

What is the slope intercept form of the equation: 3y + 2x = 24?

a)

y = -⅔x + 8

b)

y = -3/2x + 12

c)

m = 2b + 24

d)

y = 2x + 24

47.

When x = 3 and y = 5, by how much does the value of 3x² – 2y exceed the value of 2x²– 3y ?

a)

14

b)

4

c)

20

d)

16

e)

50

48.

What is 4% of 1,100?

a)

4

b)

4.4

c)

40

d)

44

e)

440

49.

A person 2 meters tall casts a shadow 3 meters long. At the same time a telephone pole casts a shadow 12 meters long. How many meters tall is the pole?

a)

4

b)

6

c)

8

d)

11

e)

16

50.

In a spice shop, cayenne pepper is sold for 50 cents per ounce for the first ounce, and 35 cents per ounce for any ounce after the first ounce. How many ounces of cayenne pepper can be bought for $2.95?

a)

7

b)

8

c)

9

d)

10

e)

11

51.

The two squares in the figure shown above have the same dimensions. The center of square A is a vertex of square B, and the center of square B is a vertex of square A. What is the area of the shaded region, in square centimeters?

a)

3

b)

9

c)

12

d)

36

e)

72

52.

If x = 3y + 4 then 3x – y =

a)

9y - 4

b)

9y - 12

c)

6y + 12

d)

6y + 8

e)

8y + 12

53.

The budget for a department is reduced by 25 percent, and then that amount is reduced by a further 25 percent, what percent of the original budget is the final budget?

a)

42.5 %

b)

50 %

c)

56.25 %

d)

66 %

e)

75 %

54.

Reggie goes to the music store and spends $5.00 on guitar strings. He spends three times that amount on a music book, and half the amount he spent on the music book on a box of premium guitar picks. How much did Reggie spend at the music store?

a)

$21.75

b)

$27.50

c)

$28.25

d)

$31.50

e)

$33.00

55.

If 537¹⁰² were calculated, it would have 279 digits. What would the digit farthest to the right be (the ones digit)?

a)

1

b)

3

c)

4

d)

7

e)

9

56.

If q is 15 less than t, then the sum of four times t and two times q is equivalent to which of the following?

a)

2t - 15

b)

4t - 30

c)

2t - 30

d)

6t - 30

e)

6t - 60

57.

Sophie will be n years old 2 years from now. How old was she 5 years ago?

a)

n - 3

b)

n - 5

c)

n - 7

d)

n + 3

e)

n + 7

58.

The average of 6 numbers is 48. What is the 6th number if the first 5

numbers are 34, 43, 52, 58, and 56?

a)

43

b)

45

c)

46

d)

49

e)

50

59.

A sandbox in the shape of a right rectangular prism has a length of

24 inches and a width of 18 inches. The volume of sand in the sandbox

is 5,184 cubic inches. To the nearest inch, what is the depth of sand in

the sandbox?

a)

6

b)

12

c)

36

d)

42

e)

72

60.

At Nifty Thrift Shop, Ben paid less than $20 for his purchase of n shirts and n pairs of pants. Each shirt cost s dollars, and each pair of pants cost p dollars. Which of the following expressions represents the amount of money, in dollars, that Ben should have received back after he paid for his clothes with $20?

(Note: There is no tax on purchases at Nifty Thrift Shop.)

a)

$n\left(p+s\right)$

b)

$nps$

c)

$20-nps$

d)

$20-n\left(p-s\right)$

e)

$20-n\left(p+s\right)$

61.

$\left|4\left(3\right)+5\left(-7\right)\right|=?$

a)

-23

b)

23

c)

35

d)

39

e)

47

62.

A circle with radius r inches is shown in the figure below; 4 non-overlapping squares, each with side s inches, are removed from the circle. The shaded region is the area of the circle remaining after the 4 squares were removed.

What is the area, in square inches, of the shaded region?

a)

$\pi r^2-4s^2$

b)

$\pi r^2-2s^2$

c)

$\pi r^2-s^2$

d)

$\pi r^2$

e)

$4s^2$

63.

In the figure below, lines q and r are parallel, line s is a transversal, and 3 angle measures are given in degrees. What is the value of b - a ?

a)

-20

b)

40

c)

70

d)

90

e)

110

64.

Which of the following graphs shows the solution set for the

inequality $2y-1\le9?$

a)

b)

c)

d)

e)

65.

Given the function $m\left(n\right)=2n^3+4$ , what is m(-2)?

a)

20

b)

10

c)

-4

d)

-12

e)

-16

66.

A semi-circle with center X is shown below. Points A, X, and D lie on the diameter. The measure of ∠AXC is 110°, the measure of ∠BXD is 90°, and the measure of ∠AXD is 180°. What is the measure of∠BXC?

a)

40

b)

35

c)

30

d)

20

e)

15

67.

The table below shows the number of cups of chopped onion, carrot, and celery required to make 600 ounces of each of 3 types of soup sold at Soup-a-Palooza Restaurant. Let x represent the price of 1 cup of chopped onion, y the price of 1 cup of chopped carrot, and z the price of 1 cup of chopped celery. All prices are in dollars.

How many cups of chopped onion are required to make 320 ounces of

vegetable soup?

a)

1.6

b)

1.8

c)

2.1

d)

2.6

e)

2.9

68.

What is the value of the expression (y-x)³ when x =5 and y = 1?

a)

-64

b)

64

c)

-4

d)

16

69.

What is the smallest positive integer that is divisible by 3, divisible by 5, and divisible by 6 (with no remainders)?

a)

15

b)

30

c)

60

d)

90

70.

In a certain school district, exactly 30% of the students come from families that have only one child. If there are 7,340 students in the district, how many do not come from families with only one child?

a)

514

b)

2,202

c)

5,138

d)

7,120

71.

What is the slope intercept form of the equation: 3y + 2x = 24?

a)

y = -⅔x + 8

b)

y = -3/2x + 12

c)

m = 2b + 24

d)

y = 2x + 24

72.

What is the slope of the line perpendicular to the line 3x + 2y = 19?

a)

-3/2

b)

-2/3

c)

2/3

d)

3/2

73.

The volume of a cone is given by the formula: V = π/3 r² h, where r is the radius of the base of the cone and h is the height of the cone. What is the volume, in cubic centimeters, of a cone with a height of 8 cm and a base with a radius of 3 cm?

a)

72π

b)

48π

c)

24π

d)

12π

74.

Given m and n are parallel lines, t is a transversal crossing both m and n, and m∡8 = 100 degrees, what is the measure of ∡3?

a)

50 degrees

b)

80 degrees

c)

100 degrees

d)

120 degrees

75.

In the figure ∡B = 40°, and ∡W = 75°. What is the measure of ∡H?

a)

35 degrees

b)

65 degrees

c)

70 degrees

d)

75 degrees

76.

When x = 3 and y = 5, by how much does the value of 3x² – 2y exceed the value of 2x² – 3y ?

a)

4

b)

14

c)

16

d)

20

77.

What is the value of x when 2x + 3 = 3x – 4 ?

a)

-7

b)

-1/5

c)

1/5

d)

7

78.

The length, in inches, of a box is 3 inches less than twice its width, in inches. Which of the following gives the length, l inches, in terms of the width, w inches, of the box?

a)

l = 2w + 3

b)

l = w – 3

c)

l = 2w – 3

d)

l = w + 3

79.

What is the degree measure of the acute angle formed by the hands of a 12-hour clock that reads exactly 1 o’clock?

a)

30°

b)

15°

c)

45°

d)

60°

80.

What type of number is 5/8?

a)

Rational

b)

Irrational

c)

both

d)

neither

81.

A lunch menu has 3 types of sandwiches, 4 types of chips, and 5 types of drinks. How many ways can a person order a sandwich, chips and a drink?

a)

12

b)

25

c)

60

d)

120

82.

a)

F

b)

G

c)

H

d)

J

83.

a)

F

b)

G

c)

J

d)

K

84.

a)

A

b)

B

c)

D

d)

E

85.

a)

B

b)

C

c)

D

d)

E

86.

a)

G

b)

H

c)

J

d)

K

87.

a)

A

b)

B

c)

C

d)

E

88.

a)

F

b)

H

c)

J

d)

K

89.

a)

A

b)

B

c)

D

d)

E

90.

a)

F

b)

H

c)

J

d)

K

91.

a)

A

b)

C

c)

D

d)

E

92.

a)

A

b)

B

c)

C

d)

D

93.

a)

G

b)

H

c)

J

d)

K

94.

a)

G

b)

H

c)

J

d)

K

95.

a)

B

b)

C

c)

D

d)

E

96.

a)

G

b)

H

c)

J

d)

K

97.

a)

A

b)

B

c)

C

d)

D

98.

a)

F

b)

H

c)

J

d)

K

99.

a)

A

b)

B

c)

D

d)

E

100.

a)

B

b)

C

c)

D

d)

E

101.

a)

F

b)

G

c)

J

d)

K

102.

a)

F

b)

G

c)

H

d)

J

103.

a)

F

b)

H

c)

J

d)

K

104.

The ratio of boys to dirls at <ilwood School is 4 to 5. If there are a total of 27 children at the school, how many boys attend the Milwood school?

a)

4

b)

9

c)

12

d)

14

e)

17

105.

Linda computed the average of her six biology test scores by mistakenly adding the totals of five scores and dividing by five, giving her an average score of 88. When she realized her mistake, she recalculated to include the sixth test score of 82. What is the average of Linda's six biology tests?

a)

82

b)

85

c)

86

d)

87

e)

88

106.

In the process of milling grain, 3% of the original is lost due to spillage, and another 5% is lost due to mildew. If the mil starts out with 490 tons of grain, how much (in tons) remains to be sold after milling?

a)

425

b)

426

c)

420.5

d)

440

e)

450.8

107.

A rectangular box has a base measuring a by a meters and a height of b meters. Whic of the following represents the surface area of the box?

a)

6ab

b)

$a^2b$

c)

$a^2+2ab$

d)

$2a\left(a+2b\right)$

e)

$2\left(a^2+b^2\right)$

108.

In the word HAWKS, how many ways is it possible to rearrange the letters if none repeat and the letter W must go last?

a)

5

b)

15

c)

24

d)

120

e)

625

act 2

Total questions: 108

Worksheet time: 2hrs 33mins

Similar Resources on Wayground