ACT Mathematics Practice Test 2

Gianna is converting a 12-foot-by-15-foot room in her house to a craft room. Gianna will install tile herself but will have CC Installations build and install the cabinets. The scale drawing shown below displays the location of the cabinets in the craft room (0.25 inch represents 2 feet). Cabinets will be installed along one of the 12-foot walls from floor to ceiling, and 4 cabinets that are each 3 feet tall x will be installed in the middle of the room. These are the only cabinets that will be installed, and each of them will be 2 feet wide and 2 feet deep. CC Installations has given Gianna an estimate of $2,150.00 for building and installing the cabinets. Gianna will install tile on the portion of the floor that will NOT be covered by cabinets. What is the area, in square feet, of the portion of the floor that will NOT be covered by cabinets?

72

90

140

156

164

Gianna is converting a 12-foot-by-15-foot room in her house to a craft room. Gianna will install tile herself but will have CC Installations build and install the cabinets. The scale drawing shown below displays the location of the cabinets in the craft room (0.25 inch represents 2 feet). Cabinets will be installed along one of the 12-foot walls from floor to ceiling, and 4 cabinets that are each 3 feet tall x will be installed in the middle of the room. These are the only cabinets that will be installed, and each of them will be 2 feet wide and 2 feet deep. CC Installations has given Gianna an estimate of $2,150.00 for building and installing the cabinets. CC Installations’ estimate consists of a $650.00 charge for labor, plus a fixed charge per cabinet. The labor charge and the charge per cabinet remain the same for any number of cabinets built and installed. CC Installations would give Gianna what estimate if the craft room were to have twice as many cabinets as Gianna is planning to have?

$2,800.00

$3,000.00

$3,450.00

$3,650.00

$4,300.00

Which of the following is the solution statement for the inequality shown? −5 < 1 − 3x < 10

−5 < x < 10

−3 < x

−3 < x < 2

−2 < x < 3

x < −3 or x > 2

What fraction lies exactly halfway between 2/3 and 3/4 ?

3/5

5/6

7/12

9/16

17/24

A container is 1/8 full of water. After 10 cups of water 8 are added, the container is 3/4 full. What is the volume of the container, in cups?

13 1/3

13 1/2

15

16

40

When ABCD is reflected over the y-axis to A′B′C′D′, what are the coordinates of D′ ?

(−12, 1)

(−12, −1)

( 12, −1)

( 1, 12)

( 1,−12)

As part of a probability experiment, Elliott is to answer 4 multiple-choice questions. For each question, there are 3 possible answers, only 1 of which is correct. If Elliott randomly and independently answers each question, what is the probability that he will answer the 4 questions correctly?

27/81

12/81

4/81

3/81

1/81

A dog eats 7 cans of food in 3 days. At this rate, how many cans of food does the dog eat in 3 + d days?

7/3 + d

1/5 + a/3

7/3 + 7/3d

7 + d/3

7 + 7d/3

The square below is divided into 3 rows of equal area. In the top row, the region labeled A has the same area as the region labeled B. In the middle row, the 3 regions have equal areas. In the bottom row, the 4 regions have equal areas. What fraction of the square’s area is in a region labeled A ?

1/9

3/9

6/9

13/12

13/36

What is the difference between the mean and the median of the set {3, 8, 10, 15} ?

0

1

4

9

12

Which of the following vertical lines cuts ABCD into 2 trapezoids with equal areas?

x = 2.5

x = 3.5

x = 4.5

x = 5.5

x = 6.5

You can find the volume of an irregularly shaped solid object by completely submerging it in water and calculating the volume of water the object displaces. You completely submerge a solid object in a rectangular tank that has a base 40 centimeters by 30 centimeters and is filled with water to a depth of 20 centimeters. The object sinks to the bottom, and the water level goes up 0.25 centimeters. What is the volume, in cubic centimeters, of the object?

300

240

200

150

75

Given f (x) = x − 1/x and g(x) = 1/x, what is f (g1)1/22 ?

-3

-3/2

-2/3

0

3/2

To make a 750-piece jigsaw puzzle more challenging, a puzzle company includes 5 extra pieces in the box along with the 750 pieces, and those 5 extra pieces do not fit anywhere in the puzzle. If you buy such a puzzle box, break the seal on the box, and immediately select 1 piece at random, what is the probability that it will be 1 of the extra pieces?

1/5

1/755

1/750

5/735

5/730

Which of the following is the graph of the region 1 < x + y < 2 in the standard (x,y) coordinate plane?

After completing the poll, Kelly wondered how many of the students polled had skied both cross-country and 4 6 x K. 4 6 x downhill. How many of the students polled indicated that they had skied both cross-country and downhill?

73

65

47

18

8

If x:y = 5:2 and y:z = 3:2, what is the ratio of x:z ?

3:1

3:5

5:3

8:4

15:4

Trapezoid ABCD is graphed in the standard (x,y) coordinate plane below. What is the slope of CD?

-3

-1

1

5/21

3/2

Where a dollar is the amount of the loan, r is the annual interest rate expressed as a decimal, and y years is the length of the loan. When a is multiplied by 2, what is the effect on p?

p is divided by 6

p is divided by 2

p does not change

p is multiplied by 2

p is multiplied by 4

Which of the following describes a true relationship between the functions f (x) = (x − 3)2 + 2 and g(x) = _1_ x + 1 graphed below in the standard (x,y) coordinate plane?

f (x) = g(x) for exactly 2 values of x

f (x) = g(x) for exactly 1 value of x

f (x) < g(x) for all x

f (x) > g(x) for all x

f (x) is the inverse of g(x)

Which of the following number line graphs shows the solution set to the inequality ⎪x − 5⎪ < −1 ?

The points E(6,4) and F(14,12) lie in the standard (x_,_y_) coordinate plane shown . Point D lies on EF between E and Fsuch that the length of EF is 4 times the length of DE . What are the coordinates of D ?

( 7, 5)

( 8, 6)

( 8, 8)

(10, 8)

(12,10)

Only tenth-, eleventh-, and twelfth-grade students attend Washington High School. The ratio of tenth graders to the school’s total student population is 86:255, and the ratio of eleventh graders to the school’s total student population is 18:51. If 1 student is chosen at random from the entire school, which grade is that student most likely to be in?

Tenth

Eleventh

Twelfth

All grades are equally likely

Cannot be determined from the given information

A formula for the surface area (A) of the rectangular solid shown below is A = 2lw + 2lh + 2wh where l represents length; w, width; and h, height. By doubling each of the dimensions (l, w, and h), the surface area will be multiplied by what factor?

2

4

6

8

12

Gianna is converting a 12-foot-by-15-foot room in her house to a craft room. Gianna will install tile herself but will have CC Installations build and install the cabinets. The scale drawing shown below displays the location of the cabinets in the craft room (0.25 inch represents 2 feet). Cabinets will be installed along one of the 12-foot walls from floor to ceiling, and 4 cabinets that are each 3 feet tall x will be installed in the middle of the room. These are the only cabinets that will be installed, and each of them will be 2 feet wide and 2 feet deep. CC Installations has given Gianna an estimate of $2,150.00 for building and installing the cabinets. A 15-foot wall is how many inches long in the scale drawing?

1.5

1.875

3

3.375

3.75