Free Printable Geometry ACT Review

1.

In the figure, lines BE and CF intersect at point A. Points G and D are in the interiors of angles $\angle BAF$ and $\angle CAE,$ respectively. Some angle measures are given. What is the measure of $\angle BAG\ ?$

a)

$56\degree$

b)

$60\degree$

c)

$84\degree$

d)

$90\degree$

e)

$96\degree$

2.

In the figure, parallel line l and m are intersected by transversal n, forming the numbered angles. Which of the following congruence statements is NOT necessarily true?

a)

$\angle1\cong\angle5$

b)

$\angle2\cong\angle8$

c)

$\angle3\cong\angle5$

d)

$\angle4\cong\angle7$

e)

$\angle6\cong\angle8$

3.

The blood types of 150 people are determined for a study. The results show that 62 people have Type O blood, 67 have Type A blood, 15 have Type B blood, and the others have Type AB blood. If 1 person from this study is randomly selected, what is the probability that this person has either Type O or Type AB blood?

a)

$\frac{1}{3}$

b)

$\frac{11}{25}$

c)

$\frac{14}{25}$

d)

$\frac{31}{75}$

e)

$\frac{34}{75}$

4.

The chart below shows the possible combinations of numbers that can land faceup when 2 numbered cubes are rolled at the same time. Each combination are equally likely. What is the probability of rolling the numbered cubes so that the sum of the numbers that land faceup is 8 or greater?

a)

$\frac{5}{12}$

b)

$\frac{5}{18}$

c)

$\frac{5}{36}$

d)

$\frac{13}{18}$

e)

$0$

5.

In the standard (x, y) coordinate plane, the line with equation $y+1=\frac{3}{4}\left(2x+8\right)$ has a slope of:

a)

$\frac{3}{4}$

b)

$\frac{3}{2}$

c)

$2$

d)

$5$

e)

$8$

6.

A parallelogram has a perimeter of 88 inches, and 1 of its sides measures 18 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

a)

18, 18, 34

b)

18, 17, 17

c)

18, 26, 26

d)

18, 35, 35

e)

Cannot Be Determined

7.

Thomas wants to tile a rectangular floor with square tiles that measure 12 inches on a side. The floor measures 10 feet 6 inches long by 8 feet 6 inches wide. If he is able to cut the tiles without waste, what is the minimum number of times Thomas needs to completely cover the floor?

a)

80

b)

90

c)

98

d)

99

e)

100

8.

In the standard (x, y) coordinate plane below, $\Delta ABC$ is bounded by $\overline{AB}\ ,\ \overline{AC\ },$ and the y-axis. Which of the following values is closest to the area, in square coordinate units, of $\Delta ABC\ ?$

a)

15.8

b)

31.6

c)

35.0

d)

70.0

e)

79.1

9.

In right triangle $\Delta JKL,$ the right angle is at K, the length of $\overline{JK}$ is 10 cm, and $\sin L=\frac{5}{11}.$ What is the value of $\cos J\ ?$

a)

$\frac{5}{11}$

b)

$\frac{6}{11}$

c)

$\frac{5}{\sqrt[]{96}}$

d)

$\frac{6}{\sqrt[]{96}}$

e)

$\frac{5}{\sqrt[]{146}}$

10.

Jermaine will build a metal wall sculpture that is composed of 3 circles of different sizes, shown at the left. The smallest circle will have a diameter of 8 inches, and the diameters of the 3 circles will be in a ratio of 1:2:4. To reinforce the sculpture, Jermaine will place a straight metal bar from the center of the smallest circle, through the center of the middle circle, to the center of the largest circle. What will be the length, in inches, of the bar?

a)

28

b)

36

c)

56

d)

64

e)

72

11.

Juan will flip a fair 2-sided coin and spin a wheel. The coin has 1 heads side and 1 tails side. The wheel has an equal chance of stopping on any one of its 4 sections: red, blue, yellow, and green. What is the probability that the coin lands tails side up and the wheel stops on the green section?

a)

$\frac{1}{8}$

b)

$\frac{1}{6}$

c)

$\frac{1}{3}$

d)

$\frac{1}{2}$

e)

$\frac{3}{4}$

12.

In the circle shown below, C is the center, $\overline{AB}$ is a diameter, and $\overline{CD}$ is a radius of length 10 inches that is perpendicular to $\overline{AB}$ . Which of the following values is closest to the area, in square inches, of the shaded region (combined area of the semicircle and $\Delta BCD$ )?

a)

150

b)

186

c)

207

d)

236

e)

264

13.

A pyramid has a square base with a side length of 6 feet. The volume of the pyramid is 144 cubic feet. What is the height, in feet, of the pyramid? (Note: The volume of a pyramid with base area B and height h is $\frac{1}{3}Bh$ .)

a)

8

b)

12

c)

24

d)

48

e)

72

14.

A spin of a certain spinner has 5 possible outcomes. The table shows the probability of spinning each of the 5 out comes. The probability of spinning Outcome 4 is a and the probability of spinning Outcome 5 is 2a. What is the value of a?

a)

0.06

b)

0.09

c)

0.12

d)

0.18

e)

0.33

15.

The quadrants of the standard (x, y) coordinate plane are shown. The vertices of $\Delta ABC$ are A(-3, 3), B(-3, 1), and C(-1, 1). The triangle is translated by $x'=x+5$ and $y'=y-2.$ The image of (x, y) on $\Delta ABC$ is (x', y') on $\Delta A'B'C'.$ The vertices of $\Delta A'B'C'$ lie in which of the quadrant(s)?

a)

Quadrant I only

b)

Quadrant II only

c)

Quadrant II only

d)

Quadrants I and IV only

e)

Quadrants II and III only

16.

For any ellipse, the area is $\pi ab,$ where a and b are half the lengths of the major and minor axes, respectively. What is the area, in square feet, of the shaded region (the region outside of the rhombus and inside the ellipse)?

a)

$12\pi-24$

b)

$12\pi-48$

c)

$48\pi-48$

d)

$48\pi-96$

e)

$192\pi-96$

17.

Which of the following expressions gives the measure of $\angle EBC?$

a)

$\sin^{-1}\left(\frac{3}{5}\right)$

b)

$\sin^{-1}\left(\frac{3}{4}\right)$

c)

$\tan^{-1}\left(\frac{3}{4}\right)$

d)

$\tan^{-1}\left(\frac{4}{3}\right)$

e)

$\cos^{-1}\left(\frac{4}{5}\right)$

18.

A toddler has 2 sets of blocks. The blocks within each set are equal-sized cubes. The blocks within one set are smaller than the blocks within the other set. The edge length of each smaller black is 1/2 the edge length of each larger block. How many of the smaller blocks must be stacked together to create an arrangement with the same volume as 1 larger block?

a)

8

b)

6

c)

4

d)

3

e)

2

19.

How many seating arrangements are possible for 5 people to sit in the 5 seats of a car if 1 person sits in each seat and only 3 of the 5 people can sit in the driver's seat?

a)

10

b)

12

c)

24

d)

72

e)

120

20.

Quadrilateral ABCD in the standard (x, y) coordinate plane has these 4 vertices: A(0,6), B(-1, 1), C(3, 1), and D(3, 6). Which of the following categories most precisely describes this quadrilateral?

a)

Parallelogram

b)

Rhombus

c)

Isosceles Trapezoid

d)

Quadrilateral that is not a trapezoid

e)

nonisosceles trapezoid

21.

The sides of a right triangle are 3, 4, and 5. In a triangle, the smallest angle is across from the (a) side. . Using the smallest angle as a reference angle, (b) is the length of the opposite side, (c) is the length of the hypotenuse, so (d) is the length of the adjacent side. Using this information, the cosine of the smallest angle is (e)

Choose from the below words

shortest

3

5

4

4/5

longest

3/5

3/4

4/3

5/3

22.

Angle A and Angle B are complementary angles. $m\angle A\ =\ 2x+3$ and $m\angle B=3x+7$ . To find the value of x, you would (a) because complementary angles (b) . The value of x is

(c)

Choose from the below words

add the 2 expressions and set them = to 90

add up to 90

16

add up to 180

are equal to each other

add the 2 expressions and set them = to 180

set the 2 expressions equal to each other

34

2

-4

23.

Angle A and Angle B form a linear pair of angles, $m\angle A=4x-10$ and $m\angle B=6x+20$ . To find the value of x you would (a) because linear pairs of angles (b) . So the value of x is

(c) .

Choose from the below words

add the 2 expressions and set them equal to 180

add up to 180

17

add the 2 expressions and set them equal to 90

add up to 90

are equal to each other

set the expressions equal to each other

8

19

-15

24.

Match the correct symbol two what it represents:

The union of two sets. (a)

The intersection of two sets. (b)

"is perpendicular to" (c)

"is similar to" (d)

"is parallel to" (e)

Choose from the below words

$\cup$

$\cap$

$\perp$

$\sim$

$\parallel$

$\cong$

$\approx$

$\ne$

$=$

$\mu$

25.

Match the symbol to the expression:

"is congruent to" (a)

"is approximately equal to" (b)

"is similar to" (c)

"is not equal to" (d)

"is equal to" (e)

Choose from the below words

$\cong$

$\approx$

$\sim$

$\ne$

$=$

$\perp$

$\parallel$

$\mu$

$\cup$

$\cap$

26.

Circles & Spheres

A = (a) C = (b) V = (c) SA = (d)

Choose from the below words

$\pi r^2$

$2\pi r$

$\frac{4\pi r^3}{3}$

$4\pi r^2$

$2B+Ph$

$B+\frac{1}{2}Pl$

Bh

$\frac{Bh}{3}$

$Bh$

$\frac{bh}{2}$

27.

Pyramids & Cones

V = (a) SA = (b)

Choose from the below words

$\frac{Bh}{3}$

$B+\frac{1}{2}Pl$

$\pi r^2$

$2B+Ph$

$\frac{4\pi r^3}{3}$

$\frac{bh}{2}$

$4\pi r^2$

$Bh$

$2\pi r$

$bh$

28.

The formula used to find the Area of a Parallelogram is (a) and the formula to find the Volume of a Prism or Cylinder is (b) because "B" represents (c) and "b" represents (d) .

Choose from the below words

$bh$

$Bh$

Area of the Base

length of the base

$\pi r^2$

$2B+Ph$

$B+\frac{1}{2}Pl$

$\frac{4\pi r^3}{3}$

$Perimeter\ of\ the\ base$

29.

Prisms & Cylinders

V = (a) SA = (b)

Choose from the below words

$Bh$

$2B+Ph$

$\pi r^2$

$\frac{4\pi r^3}{3}$

$\frac{bh}{2}$

$4\pi r^2$

$2\pi r$

$bh$

$B+\frac{1}{2}Pl$

$\frac{Bh}{3}$

30.

A right isosceles triangle has (a) congruent sides and (b) .

Choose from the below words

3

2

at least 1 acute angle

1 obtuse angle

1 right angle

no

all acute angles

Geometry ACT Review - Z08

Total questions: 30

Worksheet time: 25mins

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