Free Printable ACT Math Pre-Test

1.

What is the value of 7²-2[3+2(5-1)]?

a)

9

b)

940

c)

27

d)

-8

e)

-9

2.

What is the solution set of 2x-5=7-4x?

a)

{1}

b)

{2}

c)

{1/2}

d)

{-2}

e)

{-1/3}

3.

What percent of 24 is 18?

a)

75%

b)

150%

c)

25%

d)

33 1/3%

e)

133 1/3%

4.

How many curtains can be made from 20 meters of cloth if each curtain requires 2 1/2 meters?

a)

50

b)

20

c)

12

d)

8

e)

4

5.

What is the simplified form of

2x-{3x-2[x-(1-x)]}?

a)

3x-2

b)

-x-2

c)

-4x-1

d)

-x+2

e)

3x-2x²

6.

Which of the following numbers is NOT a prime?

a)

43

b)

51

c)

73

d)

97

e)

101

7.

If x=-2 and y=3, then -x-xy²=?

a)

16

b)

-34

c)

-38

d)

20

e)

144

8.

Which of the following is NOT a quadratic equation in one variable?

a)

3x²+5=5x+7

b)

x(2x+5)=8

c)

3²+5x=4²+2x

d)

x²=16

e)

(2x-3)²=5

9.

What is the simplified form of the expression (3x-1)²?

a)

9x²-1

b)

9x²-6x+1

c)

9x²+1

d)

9x²+6x+1

e)

9x+1

10.

If 2 less than five times a certain number is 1 more than twice the same number, which equation can be used to find the number?

a)

5(x-2)=2(x+1)

b)

5x+1=2x-2

c)

2-5x=1+2x

d)

5x-2=2x+1

e)

5(x-2)=2x+1

11.

The diameter of a circle is one side of a triangle, and the vertex is on the circle. What kind of triangle is formed?

a)

Isosceles

b)

Right

c)

Acute

d)

Scalene

e)

Equilateral

12.

In the rectangular coordinate system, the point associated with the ordered pair (-4,0) is located in which quadrant?

a)

I

b)

II

c)

III

d)

IV

e)

None of these

13.

Which of the following ordered pairs satisfies the equation

3x-2y=5?

a)

(-1,-1)

b)

(1,1)

c)

(1,-1)

d)

(-1,1)

e)

(5,-5)

14.

What is the sum of the fractions 5/12 and 7/18?

a)

3/5

b)

29/36

c)

1/35

d)

1/18

e)

2/5

15.

What is the value of log₃27?

a)

3

b)

9

c)

1/3

d)

1/9

e)

24

16.

Which is the largest of the following numbers?

a)

3.1415926

b)

22/7

c)

3.14

d)

3.1416

e)

All these numbers are equal.

17.

If Joan's English assignment is to read 80 pages, and she has read 4/5 of her assignment, how many pages does she have left to read?

a)

16

b)

20

c)

32

d)

48

e)

64

18.

What is the solution set of the following system of equations?

2x+y=-1

3x-2y=-19

a)

{(2,-5)}

b)

{(-3,5)}

c)

{(-7,-1)}

d)

There is no solution.

e)

There are infinitely many solutions.

19.

What is the set of prime factors of 6,440?

a)

{2, 5, 161}

b)

{2, 7, 23}

c)

{2, 5, 7, 23}

d)

{2, 5, 7}

e)

{2, 3,220}

20.

13 1/4 - 7 5/8 =?

a)

5 5/8

b)

5 7/8

c)

6 3/8

d)

6 1/2

e)

5

21.

What is the value of 16^-3/4?

a)

This is undefined.

b)

8

c)

1/8

d)

-8

e)

-1/8

22.

The trigonometric function sin(215^o) is equal to which of the following?

a)

sin(35^o)

b)

-cos(35^o)

c)

-cos(55^o)

d)

-sin(55^o)

e)

sin(55^o)

23.

In how many orders can 6 different books be placed on a shelf?

a)

1

b)

6

c)

12

d)

36

e)

720

24.

What is the value of -2^-2?

a)

4

b)

-4

c)

1/4

d)

-1/4

e)

None of these.

25.

What is the slope of the line whose equation is

2x-5y=7?

a)

-2

b)

-5

c)

5/2

d)

2/5

e)

2

26.

The length of each side of the pentagon shown below is 17 millimeters. What is the perimeter of the pentagon in millimeters?

a)

A. 22

b)

B. 44

c)

C. 68

d)

D. 85

e)

E. 102

27.

What is the coordinate of point P shown on the real number line below?

a)

F. -3 $\frac{3}{4}$

b)

G. -3 $\frac{1}{4}$

c)

H. -2undefined

d)

J. -2undefined

e)

K. -2

28.

If 4 + $\frac{x}{6}=6,\ then\ x=?$

a)

A. 12

b)

B. 16

c)

C. 32

d)

D. 40

e)

E. 60

29.

Which of the following is a general expression for the perimeter of the right triangle below, in miles?

a)

F. x+y+z

b)

G. 2(x+y)

c)

H. $\frac{x}{2}$ $\frac{y}{2}$

d)

J. $\frac{xy}{2}$

e)

K. xy

30.

Julia earned $5.20 per hour for 3 $\frac{1}{2}$ hours and Suki earned $4.80 per hour for 5 $\frac{1}{4}$ hours. Who earned more money and how much more?

a)

A. Julia earned $7.00 more.

b)

B. Julia earned $17.00 more.

c)

C. Suki earned $7.00 more.

d)

D. Suki earned $17.00 more.

e)

E. They each earned the same amount of money

31.

Tomas bought a new book on sale. It regularly cost $17.95, but was on sale for 20% off. How much did the book cost Tomas?

a)

F. $3.59

b)

G. $14.36

c)

H. 15.95

d)

J. $17.59

e)

K. $17.75

32.

Kane bought a bag of taffy at the candy store. He got 10 vanilla for his mom, 15 chocolate for his dad, 6 licorice for his sister, and 22 peppermint for himself. On the way home, Kane’s sister grabbed a piece out of the sack without looking. What are the chances that she pulled out a licorice piece?

a)

$A.\ \frac{1}{6}$

b)

B. $\frac{6}{6}$

c)

C. $\frac{6}{47}$

d)

D. $\frac{6}{53}$

e)

E. $\frac{47}{53}$

33.

Carmen was excited about the possibility of earning the “Mayfield Math Award.” In order to do this she must have anaverage score of at least 92 on her first 5 tests. If her first 4 scores were 96, 90, 89, and 97, what is the lowest possible score Carmen could have on the 5th test and still earn the award?

a)

F. 88

b)

G. 89

c)

H. 90

d)

J. 91

e)

K. 92

34.

The sum of the measures of the 3 angles in a triangle is 180°. If the measure of one angle in a triangle is 40°, which of the following could NOT be the measure of another angle in the triangle?

a)

A. 1 $\degree$

b)

B. 40 $\degree$

c)

C.90 $\degree$

d)

D. 99 $\frac{1}{2}\degree$

e)

E. 141 $\degree$

35.

In the teacher’s equation, the variable x represents the number of:

a)

F.

b)

G.

c)

H.

d)

J.

e)

K.

36.

What is the slope of the line determined by the equation 3x+y =4

a)

A. -3

b)

$\frac{1}{3}$

c)

C. $\frac{3}{4}$

d)

D. 1

e)

E. 3

37.

For all a and b, 6a ² b ³ – 3a ² b is equivalent to which of the following expressions?

a)

F.

b)

G.

c)

H.

d)

J.

e)

K.

38.

A certain school’s enrollment increased 5% this year over last year’s enrollment. If the school now has 1,260 students enrolled, how many students were enrolled last year?

a)

A. 1020

b)

B. 1197

c)

C.1200

d)

D.1255

e)

E. 1323

39.

In $\Delta$ PQR below, ∠PQR is a right angle; PQ is 3 units long; and QR is 5 units long. How many units long is PR ?

a)

F. 2

b)

G. 2 $\sqrt{2}$

c)

H. 4

d)

J. $\sqrt{34}$

e)

K.

40.

Paco wants to redecorate his room. On one wall he wants to put up new wallpaper. The wall is a 13-by-11-foot rectangle and has a door which takes up a 7-by-3-foot rectangular area. After the area of the door is subtracted, how many square feet of wall remain to be covered?

a)

A. 28

b)

B. 48

c)

C. 122

d)

D. 143

e)

E. 288

41.

A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?

a)

$44.44

b)

$109.08

c)

$118.80

d)

$408.04

e)

$444.40

42.

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

e)

50

43.

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

a)

-7

b)

-1/5

c)

1

d)

1/5

e)

7

44.

What is the greatest common factor of 42, 126, and 210 ?

a)

2

b)

6

c)

14

d)

21

e)

42

45.

Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?

a)

16

b)

17.5

c)

20.5

d)

22

e)

35

46.

In the figure, ray EF was constructed starting from rays ED and EG. By using a compass D and G were marked equidistant from E on rays ED and EG. The compass was then used to locate a point F, distinct from E, so that F is equidistant from D and G. For all constructions defined by the above steps, the measures of ∠DEF and ∠GEF:

a)

are equal.

b)

are NOT equal

c)

sum to 30°.

d)

sum to 45°.

47.

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 = (1/2)w + 3

b)

l = 2w + 3

c)

l = 2w - 3

d)

l = w - 3

48.

A typical high school student consumes 67.5 pounds of sugar per year. As part of a new nutrition plan, each member of a track team plans to lower the sugar he or she consumes by at least 20% for the coming year. Assuming each track member had consumed sugar at the level of a typical high school student and will adhere to this plan for the coming year, what is the maximum number of pounds of sugar to be consumed by each track team member in the coming year?

a)

14

b)

44

c)

48

d)

54

49.

If xy = 144, x + y = 30, and x > y, what is the value of x – y ?

a)

4

b)

6

c)

18

d)

24

50.

Which of the following is the sine of angle A in the right triangle below?

a)

5\13

b)

5\12

c)

12\13

d)

12\5

51.

Ding’s Diner advertised this daily lunch special: “Choose 1 item from each column—only $4.95!” Thus, each daily lunch special consists of a salad, a soup, a sandwich, and a drink.

a)

4

b)

14

c)

30

d)

120

52.

The volume, V, of the right circular cone with radius r and height h, shown below, can be found using the formula V = (1/3)r2h. A cone-shaped paper cup has a volume of 142 cubic centimeters and a height of 8.5 centimeters. What is the radius, to the nearest centimeter, of the paper cup?

a)

2

b)

4

c)

8

d)

12

53.

A boat departs Port Isabelle, Texas, traveling to an oil rig. The oil rig is located 9 miles east and 12 miles north of the boat’s departure point. About how many miles is the oil rig from the departure point?

a)

3

b)

15

c)

21

d)

225

54.

In the figure below, ∠ ABC ≅ ∠ DFE, ∠ BAC ≅ ∠ FDE, D and F are on AB, AD ≅ FB, and distances in centimeters are as shown. What is the length of AD, in centimeters?

a)

5

b)

4

c)

3

d)

2

55.

A DVD player with a list price of $100 is marked down 30%. If John gets an employee discount of 20% off the sale price, how much does John pay for the DVD player ?

a)

$86.00

b)

$77.60

c)

$56.00

d)

$50.00

56.

What is 7% of $4.58\ \times\ 10^6$ ?

a)

3,206,000

b)

320,600

c)

763.33

d)

76.33

57.

The Carousel Clothes Shop is advertising a sale featuring 30% off the marked price on any item. Which of the following gives the sale price, in dollars, of an item with a marked price of p dollars?

a)

0.3p

b)

p - 30p

c)

p - 0.3

d)

p - 0.3p

58.

Brian bought a pair of jeans for 2/3 of the original price of $48 and a belt for 40% of its original price of $12.50. Ignoring sales tax, what is the total amount for these purchases?

a)

$21.00

b)

$27.00

c)

$37.00

d)

$39.50

59.

Which of the following is NOT equivalent to to 80% of n?

a)

0.80n

b)

8(0.10n)

c)

$\frac{4n}{5}$

d)

$\frac{8n}{100}$

60.

What is 4% of $7.34\ \times10^4$ ?

a)

29,360

b)

2,936

c)

1,835

d)

183.5

61.

What is 5% of 50?

a)

0.5

b)

2.5

c)

10

d)

25

62.

Jennifer's best long jump distance increased by 10% from 1990 to 1991 and by 20% from 1991 to 1992. By what percent did her best long jump distance increase from 1990 to 1992?

a)

32%

b)

30%

c)

20%

d)

15%

63.

Suppose that replacing an old electric water heater with a new, energy-efficient electric water heater will reduce a home's average monthly electric bill by 20%. If the old electric water heater in a home with a current average monthly electric bill of $110 is replaced by a new energy-efficient one, what will be the home's new average monthly electric bill?

a)

$22.00

b)

$88.00

c)

$90.00

d)

$109.80

64.

While watching TV from 7:00 pm to 8:00 pm, you count 20 commercials, each 30 seconds long. To the nearest percent, what percent of the hour is taken up by commercials?

a)

6%

b)

10%

c)

17%

d)

50%

65.

Mr. Jones earns a total of $320 each week at his job in Shaba's Supermarket. If 18% of his pay is withheld for taxes, insurance, and other deductions, what is his take-home pay each week?

a)

$57.60

b)

$262.40

c)

$300.50

d)

$338.00

66.

Ticket sales for this year's annual concert at County Stadium were $350,000. The promoter is predicting that next year's ticket sales, in dollars, will be 60% greater than this year's. How many dollars in ticket sales is the promoter predicting for next year?

a)

$350,060

b)

$410,000

c)

$560,000

d)

$950,000

67.

An advertisement for tires says, "Buy 3 tires at the regular price and get the fourth tire free!" This offer is equivalent to what discount off the regular price of all 4 tires?

a)

1/4 %

b)

1/3 %

c)

25%

d)

40%

68.

Adina plays in a bowling league. Her bowling scores for last week are listed below. What is the median of Adina's bowling scores for last week?

142, 186, 201, 191, 116, 201, 175

a)

180 1/2

b)

186

c)

191

d)

201

69.

An organization promoting good nutritional habits collected data on fat calories in foods from 9 fast food restaurants. The values represent the number of fat calories in a small order of french fries from each restaurant.

160, 106, 104, 113, 160, 103, 161, 89, 96

What is the median number of fat calories in a small order of fries at these restaurants?

a)

106

b)

108

c)

125

d)

128

70.

What is the mean of the list of numbers below?

62, 100, 93, 62, 72, 78, 50, 85, 62, 36

a)

62

b)

67

c)

70

d)

75

71.

The vector i represents 1 mile per hour east, and the vector j represents 1 mile per hour north. Maria is jogging south at 12 miles per hour. One of the following vectors represents Maria's velocity in miles per hour. Which one?

a)

-12i

b)

-12j

c)

12i

d)

12j

e)

12i + 12j

72.

a)

F

b)

G

c)

H

d)

J

e)

K

73.

Aurelio is purchasing carpet tiles to cover an area of his living room floor that is $8\ \frac{1}{3}$ 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?

a)

5

b)

11

c)

21

d)

30

e)

84

74.

In the standard (x, y) coordinate plane, a circle with its center at (8, 5) and a radius of 9 coordinate units has which of the following equations?

a)

$\left(x\ -\ 8\right)^2+\left(y\ -\ 5\right)^2\ =\ 81$

b)

$\left(x\ -\ 8\right)^2+\ \left(y\ -\ 5\right)^2=\ 9\$

c)

$\left(x\ +\ 8\right)^2+\ \left(y+5\right)^2=81$

d)

$\left(x+8\right)^2+\left(y+5\right)^2=9$

e)

$\left(x+5\right)^2+\left(y+8\right)^2=81$

75.

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?

a)

$1,537,500

b)

$1,556,750

c)

$1,568,250

d)

$2,500,000

e)

$2,550,000

76.

What percent of the volunteers actually carry Yq77?

a)

57.5%

b)

60.0%

c)

60.5%

d)

61.5%

e)

62.5%

77.

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

a)

10

b)

25

c)

35

d)

385

e)

400

78.

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?

a)

0.017

b)

0.026

c)

0.035

d)

0.041

e)

0.063

79.

a)

A

b)

B

c)

C

d)

D

e)

E

80.

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)

Paraellelogram

e)

Scalene Triangle

81.

The equation $24x^2+2x\ =\ 15$ has 2 solutions. What is the greater of the 2 solutions.

a)

$\frac{3}{4}$

b)

$\frac{4}{3}$

c)

$\frac{5}{6}$

d)

$\frac{7}{6}$

e)

$\frac{11}{15}$

82.

Which of the following expressions is equal to $\left(\sin60\degree\right)\left(\cos30\degree\right)+\left(\cos60\degree\right)\left(\sin30\degree\right)$ ?

a)

$\cos\left(60\degree-30\degree\right)$

b)

$\left(\cos60\degree+30\degree\right)$

c)

$\sin\left(60\degree-30\degree\right)$

d)

$\sin\left(60\degree+30\degree\right)$

e)

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

83.

What is the area, in square units, of a circle that has a circumference $12\pi$ units long?

a)

$6\pi$

b)

$12\pi$

c)

$24\pi$

d)

$36\pi$

e)

$144\pi$

84.

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

85.

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

a)

$\frac{1}{x\ -\ y}$

b)

$\frac{x\ +\ y}{x\ -\ y\ }$

c)

$\frac{x+y}{2x}$

d)

$\frac{x^2+y^2}{x^2-y^2}$

e)

$x^2+y^2$

ACT Math Pre-Test

Total questions: 85

Worksheet time: 3hrs 45mins

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