Geometry Test 4 Review

Multiple Choice

Consider the following table with information about all of the students taking Statistics at Happy High School.

Find P( Full-time | Male)

• 7/3

• 3/10

• 3/7

• 4/7

Multiple Choice

Mary is a good student. The probability that she studies and passes her test is 3/5. If the probability that she studies is 8/9. What is the probability that she passes given that she studies? 

• 27/40
• 1.48
• .008
• .0593

Multiple Choice

What is the probability that someone plays basketball?

• .50

• .68

• .52

• .46

Fill in the Blank

How many have a laptop and no car?

Multiple Choice

The image represents which of the following?

• intersection, "and"
• union, "or"
• intersection, "or"
• union, "and"

Multiple Choice

The image represents which of the following?

• intersection, "and"
• intersection, "or"
• union, "and"
• union, "or"

Multiple Choice

The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?

• {-4, -3, -2, -1, 0, 1, 2, 3}
• {-3, -2, -1, 1, 2, 3}
• {-4, -3, -2, -1, 1, 2, 3, 4}
• {-4, -3, -2, -1, 1, 2, 3}

Multiple Choice

Which is the correct set notation for 
A U B?

• {12, 14, 15, 18, 21}
• {10, 11, 12, 14, 15, 18, 21}
• {10, 11, 13, 16, 17, 19, 20}
• {12, 14, 15, 18}

Multiple Choice

Given P(A) = .8 and P( B| A) = .3, find P( A and B).

• 2.6

• .12

• .24

• .38

Multiple Choice

45% total of the children in a school have a dog, 30% total have a cat, and 18% have a dog and cat. What is the probability that a person owns a cat given they own a dog??

• 60%

• 40%

• 24%

• 1.7%

Multiple Choice

Let A and B be independent events. If P(A) = 0.5 and P(B) = 0.26, what is P(A and B)

• 0.52

• 0.13

• 0.24

• More information is needed to determine this value.

Multiple Choice

Given that P(A) = 0.54 and P(B) = 0.21 and P(A and B) = 0.15, determine if the events A and B are independent.

• Yes. (0.54)(0.21) does not equal 0.15 which means the events A and B are independent.

• Yes, P(A and B) is not zero so the events must be independent.

• No. P(A and B) = 0.15 which is not zero so the events are not independent.

• No. (0.54)(0.21) = (0.1134) which does not equal the stated value of P(A and B) which means A and B are not independent.

Multiple Choice

Lucy has the spinner pictured and spins it twice in a row. What is the probability that she lands on blue first and then on green?

• 1 / 16
• 1 ⁄ 6
• 1 ⁄ 8
• 3 ⁄ 4

Multiple Choice

If you spin two times, what is the probability of landing on green both times?

• $$\frac{1}{6}+\frac{1}{6}$$

• $$\frac{1}{6}\times\frac{1}{6}$$

• $$\frac{1}{6}\times\frac{2}{6}$$

• $$\frac{1}{3}\times\frac{1}{3}$$

Multiple Choice

What is the probability of rolling a 6 then landing on heads?

• $$\frac{1}{12}$$

• $$\frac{1}{2}$$

• $$\frac{1}{6}$$

• $$\frac{2}{12}$$

Multiple Choice

Gregg has 12 cards. Half are black, and half are red. He picks two cards out of the deck without replacement. What is the probability that both cards are red?

• 1/6

• 5/22

• 1/2

• 1/144

Multiple Choice

A basket contains 5 purple pencils and 9 brown pencils. If two pencils are picked at random one after the other without replacement, then what is the probability that both the pencils are purple?

• 9/182
• 5/182
• 2/91
• 10/91

Multiple Choice

Permutation, combination, or neither?
The batting order for seven players on a 12 person team.

• combination
• permutation
• neither

Multiple Choice

Which of the following is an example of combination?

• Form a passcode with 4 digits
• Students line up in a queue to assembly
• Choose 4 students in a class committee
• Choose the chairperson, secretary and treasurer in a club

Multiple Choice

What does ₁₀P₅ mean?

• Permutations with 5 choices and 10 positions
• Permutations with 10 choices and 5 positions
• Permutations with 5 numbers and 10 operations
• Permutations with 5 hot dogs and 10 drinks

Multiple Choice

Six friends are going to play a ball game. Each team has 3 players. How many different team combinations are possible?

• 120

• 6

• 18

• 20

Multiple Choice

How many ways can a club select a president, vice president, and a secretary from a group of 5 people?

• 12

• 60

• 15

• 125

Multiple Choice

There are approximately 17,620 people per square mile in New York City. If New York City is 468 square miles, approximately how many people live in New York City?

• 17,620
• 8,246,160
• 37
• .027

Multiple Choice

There are approximately 690 grizzly bears in Yellowstone National Park giving them a population density of about .1987 grizzlies per square mile. What is the area of the park to the nearest whole number?

• 731 mi²

• 137 mi²

• 3473 mi²

• 4337 mi²

Multiple Choice

A bar of copper has a mass of 216g and a volume of 24 cm3. What is the density of copper?

• 9g/cm3

• 5184g/cm3

• .11g/cm3

• 322mL

Multiple Choice

How many distinct permutations can be formed using the letters of the word TENNESSEE?

• 3780

• 362,880

• 9

• I can't think of another way you could miss this problem so this isn't the correct answer.

Multiple Choice

What does the r in the standard equation stand for?

• r is the distance of the circle

• r is the radius of the circle

• r is the x coordinate of the center of the circle

• r is the y coordinate of the center of the circle

Multiple Choice

What does (h,k) standard for in the standard circle equation?

• (h,k) is the center of the circle

• (h,k) is a point on the circle.

• (h,k) is a point that we guess and find

• (h,k) is the distance of the circle

Multiple Choice

What is the standard equation of a circle?

• (x-k)² + (y-h)² = r²

• (x+h)² + (y+k)² = r²

• (x-h)² + (y-k)² = r²

• (k-x)² + (h-y)² = r²

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

• (3,2)
• (-3, -2)
• (-2, -3)
• (2, 3)

Multiple Choice

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

• 4
• 2
• 3
• 16

Multiple Choice

What is the equation of a circle with a radius of $$4\sqrt[]{2}$$ and a center in the origin?

• x² + y² = $$4\sqrt[]{2}$$

• x² - y² = 32

• x² + y² = 32

• x² - y² = $$4\sqrt[]{2}$$

Multiple Choice

What is the equation of a circle with radius 4 and center (0, 8)?

• x² + (y-8)² = 16
• (x-8)² + y² = 4
• x² + (y-8)² = 4
• x² + (y+8)² = 16

Multiple Choice

Determine the equation of the circle in standard form: x² + y² + 6x - 12y + 20 = 0

• (x-3)² + (y+6)² = 25
• (x+3)² + (y-6)² = 25
• (x-3)² + (y+6)² = 45
• (x+3)² + (y-6)² = 5

Multiple Choice

What is the length L called?

• circumference

• tangent

• arc

• sector

Multiple Choice

What is the green area called?

• sector

• segment

• arc

• section

Multiple Choice

What is the ϴ called?

• sector

• segment

• arc

• central angle

Multiple Choice

Calculate the length of the bold arc.

• 49.7 ft

• 15.8 ft

• 24.9 ft

• 3.14 ft

Multiple Choice

Calculate the area of the sector.

• 9.2 sq. in.

• 10.5 sq. in.

• 31.4 sq. in.

• 38.2 sq. in.

Multiple Choice

Calculate the area of the sector.

• 52.3 in²

• 18,864 in²

• 60 in2

• 10.47 in

Multiple Choice

Given that m∠AOB = 13π/18 radians and the radius is 8 cm, what is the length of arc AB?

• 13π/8 cm

• 52π/9 cm

• π/9 cm

• 9π/52

Multiple Choice

• 9
• 4
• 5
• 36

Multiple Choice

• 1
• 2
• 3
• 4

Multiple Choice

Find the length of the missing segment.

• 12

• 34

• 169

• 13

Open Ended

If two lines are perpendicular, they form a ____ degree angle.

Multiple Choice

Find the measure of the indicated angle.

• 60°

• 120°

• 30°

• 90°

Multiple Choice

Find the measure of the indicated angle.

• 60°

• 120°

• 30°

• 90°

Multiple Choice

If arc VY = 132° and ∠ YUV = 41° , what is the measure of arc XV?

• 35°

• 40°

• 45°

• 50°

Multiple Choice

What is the correct conversion factor to use when converting from radians to degrees?

• $$\frac{\pi}{180}$$

• $$\frac{180}{\pi}$$

Multiple Choice

What is the correct conversion factor to use when converting from degrees to radians?

• $$\frac{\pi}{180}$$

• $$\frac{180}{\pi}$$

Multiple Choice

Convert 7π/ 6 radians into degrees

• 225

• 210

• 270

• 240

Multiple Choice

Convert 150⁰ to radians

• 5π/6
• 3π/4
• 7π/6
• 2π/3

Multiple Choice

Based on the unit circle, what is the value of sin?

• y

• x

• x/y

• y/x

Multiple Choice

Based on the unit circle, what is the value of tan?

• y/r
• x/r
• r/y
• y/x

Multiple Choice

Based on the unit circle, what is the value of cos?

• y

• x

• x/y

• y/x

Multiple Choice

sin $$\frac{\pi}{2}$$

• $$\frac{\sqrt[]{3}}{2}$$

• $$\frac{\sqrt[]{2}}{2}$$

• $$\frac{1}{2}$$

• 1

Multiple Choice

cos $$\frac{\pi}{4}$$

• $$\frac{\sqrt[]{3}}{2}$$

• $$\frac{\sqrt[]{2}}{2}$$

• $$\frac{1}{2}$$

• 1

Solving Right Triangles

Pythagorean Theorem​

• When a problem involves only sides, use Pythagorean Theorem

Trigonometry

• When a problem involves both sides and angles, use SOH-CAH-TOA

Multiple Choice

Solve for x. Round to the nearest tenth.

• 9.8
• 0.1
• 0.038
• 9.9

The Pythagorean Theorem

Multiple Choice

Solve for x.

• 24.20
• 4.92
• 290.4
• 29.75

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Find the missing side.

• 18

• 16

• 17

• 19

Multiple Choice

Find the missing side.

• 11

• 12

• 13

• 14

Multiple Choice

Find the length of x.

• 4.39
• 3.21
• 2.19
• 2.05
• 1.71

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest tenth.

• 9.4
• 55.2
• 20.15
• 19.4
• 37.6

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest degree.

• 32°
• 44°
• 61°
• 50°
• 46°

Multiple Choice

Sin(60°) = Cos( ?°)

• 10

• 20

• 30

• 40

Multiple Choice

Sin(20°) = ?

• sin(70)

• cos(70)

• cos(20)

• tan(20)

Multiple Choice

What does CPCTC stand for?

• Congruent parts of congruent triangles are congruent

• Corresponding parts of congruent triangles are congruent

• Corresponding parts of corresponding triangles are corresponding

Multiple Choice

Given 

$$\Delta ABC\ \cong\Delta DEF\$$  
$$\angle A\ \cong\ ?$$  

• $$\angle D$$  

• $$\angle E$$  

• $$\angle F$$  

• $$\angle C$$  

Multiple Choice

Given 

$$\Delta ABC\ \cong\Delta DEF\$$  
$$\overline{BC}\ \cong\ ?$$  

• $$\overline{DE}$$  

• $$\overline{EF}$$  

• $$\overline{DF}$$  

• $$\overline{FE}$$  

Multiple Choice

What is Reason F?

• SSS Congruence

• SAS Congruence

• ASA Congruence

• AAS Congruence

• HL Congruence

Multiple Choice

What is Reason C?

• SSS Congruence

• SAS Congruence

• ASA Congruence

• AAS Congruence

• HL Congruence

Multiple Choice

Find the missing length.

• 21
• 18
• 16
• 24

Multiple Choice

What is the measure of x?

• 12
• 15
• 6
• 9

Multiple Choice

Which proportion should you use to find x?

• 15 / x = 7 / 14

• x / 7 = 14 / 15

• 7 / x = 15 / 14

• x / 15 = 7 / 14

Multiple Choice

What is the Reason #3?

• AA ~

• SAS ~

• SSS ~

• Not Similar Triangles

Multiple Choice

Complete each proportion.
AB / BM  =  ? / CD

• BC
• AC
• MD
• MC

Multiple Choice

What reason can be given for line 2?

• Corresponding Angles

• Reflexive Property

• Alternate Interior Angles

Multiple Choice

What reasons can be given to support line 2?

• Corresponding Angles

• Vertical Angles

• Alternate Interior Angles

Multiple Choice

Choose the correct scale factor:

• 2
• 3
• 1/3
• 1/2

Multiple Choice

Enlargement or reduction?  Find the scale factor!

• It's a reduction; the scale factor is 2.
• It's an enlargement; the scale factor is 2.
• It's an enlargement; the scale factor is 1/2.
• It's a reduction; the scale factor is 1/2.

Multiple Choice

What type of construction do you see?

• midpoint

• angle bisector

• perpendicular bisector

• altitude

Multiple Choice

The given diagram is what kind of construction?

• Perpendicular bisector

• Congruent angles

• Angle bisector

• Congruent line segments

Multiple Choice

The drawing shows a compass and straight edge construction of...what?

• the bisector of a given angle

• a perpendicular to a given line at a point on the line

• a perpendicular to a given line from a point NOT on the line

• an angle congruent to a given angle

Multiple Select

Cash constructed a segment bisector as shown. What is true about the segment bisector? Select all that apply.

• It is perpendicular to segment AB

• It divides segment AB into two congruent segments

• It is exactly the same length as segment AB

• It intersects segment AB at the midpoint

Multiple Choice

ABCD is a rectangle.  m∠BCE = 4x-23 and m∠DCE = 5+5x.  Find m∠BEC. 

• 25
• 12
• 130
• 32

Multiple Choice

If JM = x+17 and MK = 5x-23, find JL.

• 23

• 27

• 46

• 54

Multiple Choice

Solve for X

• 22
• 16
• 40
• 35

Multiple Choice

Translation, rotations, & reflections produce __________ Images

• Congruent
• Bigger
• Smaller
• Similar

Multiple Choice

Dilations produce __________ Images

• Congruent
• Bigger
• Smaller
• Similar

Multiple Choice

Write a rule for the translation.

•  (x -1, y  + 2)
•  (x -2, y  + 1)
•  (x +2, y  - 1)
• (x +1, y  -  2)

Multiple Choice

Identify the transformation.

• Reflection across y-axis
• 90 Rotation counter clockwise
• Translation 5 units left, 1 unit up.
• Translation 5 units right, 1 unit down

Multiple Choice

Which of the following describes the sequence of transformations shown?

• Reflection, then a rotation.

• Rotation, then a translation.

• Reflection across the x-axis, then a reflection across the y-axis.

• Translation, then a rotation.

Multiple Choice

Which sequence of transformations will map trapezoid A to its image A'?

• Reflection, then a translation

• Rotation, then a translation

• Reflection, then a rotation

• Rotation, then a dilation

Multiple Choice

If the red triangle is rotated 180 degrees, then reflected over the line y=2, what is the resulting image?

• Green Triangle

• Blue Triangle

• Orange Triangle

• Red Triangle

Multiple Choice

How do you find the area of a rectangle?

• Length + Length + Length + Length
• Length + Width
• Length x Width
• Width x Width

Multiple Choice

Which of the following is the correct set up for the Table method when multiply (x + 3) (2x - 4)   _{(click on the question to see the image in the background)}

• A
• B
• C
• D

Multiple Choice

What is the area for the given rectangle:

• 6x³ - 9x² + 10x - 15
• 6x² + 1x - 15
• 6x² + 4x + 4
• 6x³ + 1x² - 15x

Multiple Choice

Simplify:

-7(6 + x) - 8x

• -1 - 9x

• -42 - 15x

• -42 - 8x

• 36 - 8x

Multiple Choice

What is the radius of the cylinder?

• 40

• 20

• 10

Multiple Choice

Find the volume of the figure.

• 1,800 cm³
• 900 cm³
• 600 cm³
• 750 cm³

Multiple Choice

Given a sphere has a Volume 972π, what is the radius?

• 3

• 9

• 27

• 729