Quiz about Geometry ACT Review - Z08

Question 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 $$\angle BAG\ ?$$

Accepted Answer

$$84\degree$$

Answer

$$56\degree$$

Answer

$$60\degree$$

Answer

$$90\degree$$

Answer

$$96\degree$$

Question 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?

Accepted Answer

$$\angle4\cong\angle7$$

Answer

$$\angle1\cong\angle5$$

Answer

$$\angle2\cong\angle8$$

Answer

$$\angle3\cong\angle5$$

Answer

$$\angle6\cong\angle8$$

Question 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?

Accepted Answer

$$\frac{34}{75}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{11}{25}$$

Answer

$$\frac{14}{25}$$

Answer

$$\frac{31}{75}$$

Question 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?

Accepted Answer

$$\frac{5}{12}$$

Answer

$$\frac{5}{18}$$

Answer

$$\frac{5}{36}$$

Answer

$$\frac{13}{18}$$

Answer

$$0$$

Question 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:

Accepted Answer

$$\frac{3}{2}$$

Answer

$$\frac{3}{4}$$

Answer

$$2$$

Answer

$$5$$

Answer

$$8$$

Question 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?

Accepted Answer

18, 26, 26

Answer

18, 18, 34

Answer

18, 17, 17

Answer

18, 35, 35

Answer

Cannot Be Determined

Question 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?

Accepted Answer

90

Answer

80

Answer

98

Answer

99

Answer

100

Question 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 $$\Delta ABC\ ?$$

Accepted Answer

35.0

Answer

15.8

Answer

31.6

Answer

70.0

Answer

79.1

Question 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 $$\cos J\ ?$$

Accepted Answer

$$\frac{5}{11}$$

Answer

$$\frac{6}{11}$$

Answer

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

Answer

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

Answer

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

Question 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?

Accepted Answer

36

Answer

28

Answer

56

Answer

64

Answer

72

Question 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?

Accepted Answer

$$\frac{1}{8}$$

Answer

$$\frac{1}{6}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{1}{2}$$

Answer

$$\frac{3}{4}$$

Question 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 $$\Delta BCD$$ )?

Accepted Answer

207

Answer

150

Answer

186

Answer

236

Answer

264

Question 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 $$\frac{1}{3}Bh$$ .)

Accepted Answer

12

Answer

8

Answer

24

Answer

48

Answer

72

Question 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?

Accepted Answer

0.06

Answer

0.09

Answer

0.12

Answer

0.18

Answer

0.33

Question 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 $$x$$ and $$y$$ The image of (x, y) on $$\Delta ABC$$ is (x', y') on $$\Delta A$$ The vertices of $$\Delta A$$ lie in which of the quadrant(s)?

Accepted Answer

Quadrants I and IV only

Answer

Quadrant I only

Answer

Quadrant II only

Answer

Quadrant II only

Answer

Quadrants II and III only

Question 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)?

Accepted Answer

$$48\pi-96$$

Answer

$$12\pi-24$$

Answer

$$12\pi-48$$

Answer

$$48\pi-48$$

Answer

$$192\pi-96$$

Question 17

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

Accepted Answer

$$ an^{-1}\left(\frac{4}{3} ight)$$

Answer

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

Answer

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

Answer

$$ an^{-1}\left(\frac{3}{4} ight)$$

Answer

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

Question 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?

Accepted Answer

8

Answer

6

Answer

4

Answer

3

Answer

2

Question 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?

Accepted Answer

72

Answer

10

Answer

12

Answer

24

Answer

120

Question 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?

Accepted Answer

nonisosceles trapezoid

Answer

Parallelogram

Answer

Rhombus

Answer

Isosceles Trapezoid

Answer

Quadrilateral that is not a trapezoid

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