Quiz about Geometry ACT Review - F07

Question 1

In the standard (x, y) coordinate plane, what is the slope of the line with the equation $$y-2=\frac{1}{2}\left(x+3\right)?$$

Accepted Answer

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

Answer

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

Answer

$$-2$$

Answer

$$1$$

Answer

$$3$$

Question 2

The parallelogram below has consecutive angles with measures $$x\degree\ and\ 28\degree.$$ What is the value of x?

Accepted Answer

152

Answer

112

Answer

118

Answer

124

Answer

146

Question 3

Two sides lengths of the right triangle shown are given in inches. How many inches long is the hypotenuse?

Accepted Answer

$$\sqrt[]{73}$$

Answer

$$\sqrt[]{22}$$

Answer

$$\sqrt[]{55}$$

Answer

11

Answer

73

Question 4

All the kindergarten students at Cannon Elementary School are in exactly 1 of 3 classes. The 1st class has 10 boys and 15 girls, the 2nd class has 9 boys and 17 girls, and the 3rd class has 11 boys and 12 girls. All the kindergarten students at Cannon Elementary School are gathered in the gym for an assembly where 1 kindergarten student is randomly selected to win a prize. What is the probability that the selected student will be a boy?

Accepted Answer

$$\frac{15}{37}$$

Answer

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

Answer

$$\frac{15}{22}$$

Answer

$$\frac{22}{37}$$

Answer

$$\frac{19}{51}$$

Question 5

A square and a rectangle have the same area. The length of the rectangle is 45 centimeters, and the width of the rectangle is 5 centimeters. What is the length, in centimeters, of a side of the square?

Accepted Answer

15

Answer

10

Answer

25

Answer

100

Answer

225

Question 6

Square ABEF and parallelogram ACDG are shown in the figure. Points E and F are on $$\overline{DG},$$ B is on $$\overline{AC},$$ and the lengths given are in inches. What is the ratio of the area of ABEF to the area of ACDG?

Accepted Answer

3:8

Answer

1:8

Answer

1:16

Answer

8:1

Answer

8:3

Question 7

A wheelchair ramp will be constructed for a public library. The ramp will extend 20 inches horizontally for every 1 inch of rise vertically. The rise of the ramp will be 30 inches. Which of the following values is closest to the length, in feet, the ramp will extend horizontally?

Accepted Answer

50

Answer

3

Answer

10

Answer

18

Answer

36

Question 8

In the standard (x, y) coordinate plane, A is located at (4, 9). What is the location of the image of A that results from reflecting A over the y-axis?

Accepted Answer

(-4, 9)

Answer

(-9, 4)

Answer

(-4, -9)

Answer

(4, -9)

Answer

(9, -4)

Question 9

Naomi is going to install baseboard around the perimeter of her room's rectangular floor, shown below. The floor has dimensions 15 feet by 20 feet. The 2 doorways in her room are each 3 feet wide and do not require baseboard. Assuming an average cost of $0.30 per linear foot requiring baseboard, how much will it cost Naomi to purchase baseboard for her room?

Accepted Answer

$19.20

Answer

$10.50

Answer

$21.00

Answer

$88.20

Answer

$90.00

Question 10

The probability that Event A will occur is $$\frac{1}{8}.$$ The probability that Event B will occur is $$\frac{1}{4}.$$ Given that Events A and B are mutually exclusive, what is the probability that Event A or Event B will occur?

Accepted Answer

$$\frac{3}{8}$$

Answer

$$\frac{1}{32}$$

Answer

$$\frac{1}{12}$$

Answer

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

Answer

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

Question 11

As shown in the figure, D is on side $$\overline{CE}$$ of rectangle ABCE such that the measure of $$\angle ADB\ is\ 90\degree.$$ Which of the following angles must be congruent to $$\angle1?$$

Accepted Answer

$$\angle3\ and\ \angle6$$

Answer

$$\angle2\ only$$

Answer

$$\angle4\ only$$

Answer

$$\angle5\ only$$

Answer

$$\angle2\ and\ \angle4$$

Question 12

The area of a circle is $$64\pi$$ square inches. What is the circumference, in inches, of the circles?

Accepted Answer

$$16\pi$$

Answer

$$8\pi$$

Answer

$$24\pi$$

Answer

$$32\pi$$

Answer

$$64\pi$$

Question 13

In the standard (x, y) coordinate plane, points A(2, 3), B(4, 0) and C(7, b) lie on the same line. What is b?

Accepted Answer

$$-\frac{9}{2}$$

Answer

$$-\frac{21}{2}$$

Answer

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

Answer

$$6$$

Answer

$$\frac{19}{3}$$

Question 14

A jar contains 2 green mints and 3 white mints. If Renee randomly takes 2 mints out of the jar to eat, what is the probability that both of these mints are green?

Accepted Answer

$$\frac{1}{10}$$

Answer

$$\frac{3}{10}$$

Answer

$$\frac{1}{20}$$

Answer

$$\frac{9}{20}$$

Answer

$$\frac{3}{5}$$

Question 15

The diagram shows the location of Manuel's boat, which is on a lake and anchored to a stationary buoy at point B. On the shore, Manuel's house is at point H and his nearest neighbor's house is at point N, which is 150 meters from H. The measures of 2 angles are given. Which of the following expressions represents the straight-line distance, in meters, from B to N?

Accepted Answer

$$\frac{150\sin50\degree}{\sin70\degree}$$

Answer

$$\frac{150\sin50\degree}{\sin60\degree}$$

Answer

$$\frac{150\sin60\degree}{\sin50\degree}$$

Answer

$$\frac{150\sin60\degree}{\sin70\degree}$$

Answer

$$\frac{150\sin70\degree}{\sin50\degree}$$

Question 16

Packmore Box Company manufactures a standard rectangular box a feet by b feet by c feet. A customer ordered a new box with double the double the volume of the standard box. Which of the following expressions represents the volume, in cubic feet, of the new box?

Accepted Answer

$$2abc$$

Answer

$$8abc$$

Answer

$$a^2b^2c^2$$

Answer

$$2a+b+c$$

Answer

$$2a+2b+2c$$

Question 17

For her mathematics class, Ms. Wilkerson is preparing a probability experiment using only dried kidney beans, dried pinto beans, and an empty jar. First, she puts 4 kidney beans into the empty jar. How many pinto beans must be added to the jar in order to make the probability of drawing a kidney bean exactly $$\frac{1}{5}$$ when randomly drawing 1 bean from the jar?

Accepted Answer

16

Answer

20

Answer

5

Answer

4

Answer

1

Question 18

The center of the circle shown is at B, and the length of diameter $$\overline{AD}\ is\ 12\ cm.$$ The measure of arc DE is $$60\degree,$$ and the measure of arc AC is $$70\degree.$$ What is the measure of major arc ACE?

Accepted Answer

$$240\degree$$

Answer

$$130\degree$$

Answer

$$230\degree$$

Answer

$$250\degree$$

Answer

$$260\degree$$

Question 19

The center of the circle shown is at B, and the length of diameter $$\overline{AD}\ is\ 12\ cm.$$ The measure of arc DE is $$60\degree,$$ and the measure of arc AC is $$70\degree.$$ Triangle $$\Delta ACD$$ is a right triangle. Which of the following expressions represents the length, in centimeters, of
$$\overline{AC}\ ?$$

Accepted Answer

$$12\sin35\degree$$

Answer

$$6\sin35\degree$$

Answer

$$6\sin55\degree$$

Answer

$$6\sin70\degree$$

Answer

$$12\sin70\degree$$

Question 20

The center of the circle shown is at B, and the length of diameter $$\overline{AD}\ is\ 12\ cm.$$ The measure of arc DE is $$60\degree,$$ and the measure of arc AC is $$70\degree.$$ Triangle $$\Delta ACD$$ is a right triangle. If all points on the circle remain fixed in their current positions except E, which movers along the circle counterclockwise until it reaches A, the length of $$\overline{CE}$$ during this movement will:

Accepted Answer

increase, then decrease.

Answer

remain unchanged.

Answer

decrease, then increase.

Answer

decrease only.

Answer

increase only.

Question 21

Let a, b, and c be the respective side lengths, in feet, of a triangle. Given that a is 5 and b is 7, which of the following inequalities gives all and only the possible values of c?

Accepted Answer

$$2<c<12$$

Answer

$$c>2$$

Answer

$$c<12$$

Answer

$$0<c<12$$

Answer

$$5<c<7$$

Question 22

Carnell is paid a regular hourly wage of $13.50 per hour for working up to and including 40 hours in 1 week. For each additional hour he works in a week, Carnell is paid twice his regular hourly wage. Carnell worked 48 hours this week. What is his pay for this week? (Note: Amounts are before taxes and benefits are deducted.)

Accepted Answer

$756.00

Answer

$594.00

Answer

$648.00

Answer

$864.00

Answer

$1,296.00

Question 23

Sofia earned scores of 85, 86, 87, and 82 points on 4 math tests. What score must Sofia earn on the 5th math test for the average of the 5 tests to be exactly 3 points higher than the average of the first 4 tests?

Accepted Answer

100

Answer

70

Answer

82

Answer

85

Answer

88

Question 24

When Professor Soto began his trip to a mathematics conference, he noted that the 2 digits of the recorded temperature, in degrees Fahrenheit, had a sum of 8. Later, he noted that the 2 digits were reversed and that the temperature had warmed $$18\degree F.$$ What was the temperature, in degrees Fahrenheit, at the beginning of his trip?

Accepted Answer

$$35\degree F$$

Answer

$$17\degree F$$

Answer

$$26\degree F$$

Answer

$$53\degree F$$

Answer

$$62\degree F$$

Question 25

A quadrilateral that is NOT a parallelogram but has two pairs of congruent sides.

Accepted Answer

Kite

Answer

Trapezoid

Answer

Rectangle

Answer

Rhombus

Answer

Square

Geometry ACT Review - F07

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