[PDF] ACT MATH PREP - GEOMETRY - SCHOOLinSITES

2539_66eaa9ca72c634a82936647c852ed1c2c.pdf NAME______________________________________ DATE______________________________ CLASS_____

ACT MATH PREP - GEOMETRY

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1. A cube has a volume of 27

3in . What is the length of each of its edges? A. 3 B. 6 C. 9 D. 27 E. 81

2. A triangle has an area of 24 square inches

and a height of 8 inches. What could be the length of its base? A. 3 B. 4 C. 6 D. 12 E. 48

3. Cylinder A and cylinder B have a height of 3

inches, but cylinder B has a diameter four inches greater than that of cylinder A. If the diameter of cylinder B is 12 inches, how much greater is the volume of cylinder B than cylinder A ? A. 4 B. 12 C. 20 D. 60
E. 240

4. In right triangle ABC below,

8AC and 10BC . What is the length AB ? A. 6 B. 82
C. 45
D. 2 41 E. 4 41

5. In the figure below, X and Z lie on the circle

Y, which has a radius of 6. If the angle XYZ

is 60
, what is the area of sector XYZ ? A. 2 B. 3 C. 6 D. 9 E. 36
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ACT MATH PREP - GEOMETRY

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6. A square has a side length of 6 inches. What

is the length of its diagonal? A. 26
B. 62
C. 63
D. 6 E. 12

7. What is the slope of the linear equation

3 2 4 0 ? xy

A. 3 2 B. 3 2 C. 2 3 D. 2 3 E. 3

8. What is the distance between the points

2,3 and 4, 5 on the standard ,xy coordinate plane? A. 10 B. 10 C. 100
D. 106
E. 2 17

9. The area of the trapezoid below is 36 square

inches, the altitude is 4 inches, and the length of one base is 8 inches. What is the length, b, of the other base, in inches? A. 10 B. 12 C. 16 D. 26 E. 32

10. The picture shown below has a uniform

frame-width of 3 4 inches. What is the approximate area, in square inches, of the viewable portion of the picture? A. 49.00 B. 50.50 C. 564.25 D. 601.56 E. 640.00 NAME______________________________________ DATE______________________________ CLASS_____

ACT MATH PREP - GEOMETRY

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11. Two sides of a triangle measure 5 inches and

6 inches, respectively. Which of the

following could be the length of the third side? A. 10 B. 11 C. 12 D. 13 E. 14

12. A circle in the standard

,xy coordinate plane is tangent to the x-axis at 5 and tangent to the y-axis at 5. Which of the following is an equation of the circle? A. 225xy
B.

2225xy

C. 

225 5 5 xy

D. 225 5 25 xy E. 225 5 25 xy

13. If the volume of a cube is 8, what is the

shortest distance from the center of the cube to the base of the cube? A. 1 B. 2 C. 4 D. 2 E. 22

14. What is the area, in square units, of the

parallelogram shown below? A. 150 B. 240 C. 260 D. 300 E. 325

15. In the figure below,

ABC is a right triangle with legs that measure x and 2x inches, respectively. What is the length, in inches, of the hypotenuse? A. 3 B. 5 C. x D. 3x E. 5x NAME______________________________________ DATE______________________________ CLASS_____

ACT MATH PREP - GEOMETRY

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16. A rectangular patio is 12 feet longer than it

is wide. Its area is 160 square feet. How long, in feet, is it? A. 8 B. 10 C. 16 D. 20 E. 28

17. The ratio of the radii of two circles is 4:9.

What is the ratio of their circumferences?

A. 2:3 B. 4:6 C. 4:9 D. 8:18 E. 16:81

18. In

ABC , AB BC and the measure of A is 42
. What is the measure of C ? A. 21
B. 42
C. 48
D. 84
E. 138

19. In the figure below, LMNO is a trapezoid, P

lies on LO, and angle measures are as marked. What is the measure of angle MON? A. 40
B. 45
C. 50
D. 90
E. 95

20. For what value of n would the following

system of equations have an infinite number of solutions?

4 5 16

20 25 2

 xy x y n A. 8 B. 10 C. 32 D. 40 E. 80 NAME______________________________________ DATE______________________________ CLASS_____

ACT MATH PREP - GEOMETRY

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21. The length of arc OP of a circle is equal to

1 9 of the circumference of the circle. The length of the arc is 6 inches. What is the radius, in inches, of the circle? A. 9 B. 27 C. 54 D. 108 E. Not enough information

22. In an isosceles right triangle, the hypotenuse

is 10. What is the length of one (1) of the sides? A. 5 B. 10 C. 20 D. 52
E. 10 2

23. On the standard

,xy coordinate plane, point A is located at 3, 2 . Point M, the midpoint of AB, is located at 1,1 . What are the coordinates of point B ? A. 1, 1 B. 7, 5 C. 3,4 D. 2, 1 E. 5,4

24. In rhombus RHOM shown below, one side

measures 10 inches. If 16OR , what is the length of diagonal HM, in inches? A. 6 B. 12 C. 22 D. 24 E. 26

25. In the pentagon, shown below, one interior

angle measures 50
. What is the total measure of the other 4 interior angles? A. 130
B. 310
C. 490
D. 590
E. 670
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ACT MATH PREP - GEOMETRY

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26. Which of the following lines has the greatest

slope? A.

5102yx

B. 31yx
C.

2 8 5yx

D.

3 6 4yx

E.

5 20 xy

27. In the standard

,xy coordinate plane, what is the slope of the line joining the points 3,1 and 6, 2 ? A. 1 9 B. 3 C. 1 3 D. 1 3 E. 3

28. The ratio of the side lengths for a triangle is

exactly 5:10:12. In a second triangle similar to the first, the shortest side is 8 inches long.

To the nearest tenth of an inch, what is the

length of the longest side of the second triangle? A. 6.3 B. 7.5 C. 16.0 D. 19.2 E. Cannot be determined

29. What is the perimeter of the figure shown

below? A. 19 B. 28 C. 38 D. 90 E. Cannot be determined

30. A chord 16 inches long is 6 inches from the

center of a circle, as shown below. What is the radius of the circle, to the nearest tenth of an inch? A. 10 B. 11 C. 14 D. 24 E. 48 NAME______________________________________ DATE______________________________ CLASS_____

ACT MATH PREP - GEOMETRY

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Solutions.

1. The correct answer is A.

The formula for the volume of a cube is

3Vs where s is the length of each edge or side. Since 27V
, we have 327s
and the only value for s that satisfies this is 3s .

2. The correct answer is C.

The formula for the area of a triangle is

1 2A bh , where b is the base, and h is the height. We have 124 82