Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Analytic Geometry Final Exam Study Guide

Multiple Choice

Identify the choice that best completes the statement or answers the question.

1. Given: BD bisects ∠ABC, AB ≅ BC

Prove: AD ≅ CD

Proof:

Statements Reasons

1. AB ≅ BC 1. Given

2. BD ≅ BD 2. Reflexive Prop. of ≅

3. BD bisects ∠ABC 3. Given

4. ? 4. Def. of bisector

5. ∆ABD ≅ ∆CBD 5. SAS Congruence Postulate

6. AD ≅ CD6. Corresponding Parts of

Congruent Triangles are Congruent

The missing step in the proof is .

a. ∠BAD ≅ ∠BCD c. ∠ABD ≅ ∠CBD

b. ∠BDA ≅ ∠BDC d. ∠ABC ≅ ∠CBA

2. Compared to the graph of f(x) = x2, the graph of

g(x) = 2x2

− 5 is _______.

a. narrower and translated down

b. narrower and translated up

c. wider and translated down

d. wider and translated up

3. Given:∠B ≅ ∠E and ∠C ≅ ∠F. What other piece

of information is needed to show ∆ABC ≅ ∆DEF

by ASA Congruence Postulate?

a. EF ≅ FE

b. BC ≅ EF

c. ∠A ≅ ∠D

d. ∠B = ∠F

Name: ________________________ ID: A

2

4. Each letter of the alphabet is written on a card

using a red ink pen and placed in a container. Each

letter of the alphabet is also written on a card using

a black ink pen and placed in the same container.

A single card is drawn at random from the

container. What is the probability that the card has

a letter written in black ink, the letter B, the letter

A, or the letter D?

a.1

2

b.29

52

c.15

26

d.8

13

5. Find the values of x and y.

a. x = 84°, y = 96°

b. x = 84°, y = 64°

c. x = 12°, y = 96°

d. x = 12°, y = 84°

6. The graph of a circle has its center at (2,3) with a

radius of 10 units. Which point does NOT lie on

the circle?

a. (-4, -5)

b. (8, 11)

c. (-2, 6)

d. (-4, 11)

7. Angles A and B are complementary angles in a

right triangle. The value of tan(A) is 3

4. What is

the value of sin(A)?

a.3

5

b.5

3

c.4

3

d.5

4

8. Given m∠NOP = m∠NPO; NO = 2n + 4;

NP = 8n − 3; OP = 9; find NO.

a. NO = 3

b. NO = 19

3

c. NO = 7

6

d. NO = 22

9. What is the volume of a cylinder with a radius of 5

in. and a height of 9

2 in.?

a.225

2π in.

3

b.45

4π in.

3

c.27

8π in.

3

d.9

4π in.

3

10. In the diagram, a student has placed a mirror on

level ground, then stands so the top of a nearby tree

can be seen in the mirror.

What is the height of the tree?

a. 24 m

b. 35 m

c. 41 m

d. 59 m

Name: ________________________ ID: A

3

11. Mr. Pascal surveyed 240 men and 285 women

about their vehicles. Of those surveyed, 155 men

and 70 women said they own a red vehicle. If a

person is chosen at random from those surveyed,

what is the probability of choosing a woman or a

person that does own a red vehicle?

a.88

105

b.74

105

c.71

105

d.14

57

12. Completely factor 4m4

− 324.

a. 4m2

+ 36Ê

Ë

ÁÁÁÁÁˆ

¯

˜̃˜̃̃ m

2− 9

Ê

Ë

ÁÁÁÁÁˆ

¯

˜̃˜̃̃

b. 4 m2

+ 9Ê

Ë

ÁÁÁÁÁˆ

¯

˜̃˜̃̃ m + 3( ) m − 3( )

c. 4 m + 3( )2 m + 3( ) m − 3( )d. cannot be factored

13. Find the value of the variables in the parallelogram.

a. x = 52°, y = 10.5°, z = 159°

b. x = 21°, y = 55°, z = 104°

c. x = 55°, y = 21°, z = 104°

d. x = 10.5°, y = 52°, z = 159°

14. Complete the steps of this proof.

Given: parallelogram WXYZ

Prove: ∆XYZ ≅ ZWX

Statements Reasons

1. parallelogram WXYZ 1. Given

2. WZ || XY ; WX || YZ 2. Definition of parallelogram

3. ∠WZX ≅ ∠YXZ;

∠WXZ ≅ ∠YZX

3. ?

4. ZX ≅ ZX 4. Reflexive Property

5. ∆XYZ ≅ ∆ZWX 5. ASA Postulate

a. Consecutive Interior Anlges Theorem c. Vertical Angles Theorem

b. Alternate Interior Angles Theorem d. Alternate Exterior Angles Theorem

Name: ________________________ ID: A

4

15. In the circle shown, BC is a diameter and

mAB = 120°.

What is the measure of ∠ABC?

a. 15°

b. 30°

c. 60°

d. 120°

16.

A student stands 80 feet in front of the school.

The distance to the top of the flagpole from

where the student is standing is 220 feet. What

is the approximate angle of elevation to the top

of the flagpole?

a. 21°

b. 62°

c. 20°

d. 69°

17. The spokes of a bicycle wheel form 10 congruent

central angles. The diameter of the circle formed

by the outer edge of the wheel is 23 inches.

What is the length, to the nearest 0.1 inch, of the

outer edge of the wheel between two consecutive

spokes?

a. 1.8 inches

b. 5.7 inches

c. 7.2 inches

d. 10.3 inches

18. Right triangle PQR has sides of length 6 units, 8

units, and 10 units. The triangle is dilated by a

scale factor of 4 about point Q. What is the area of

P ′Q ′R′?

a. 96 square units

b. 193 square units

c. 384 square units

d. 768 square units

19. Completely factor 3x4

− 15x3

− 18x2

.

a. x2

3x2

+ 2Ê

Ë

ÁÁÁÁÁˆ

¯

˜̃˜̃̃ 1x − 9( )

b. 3 x2

+ 1Ê

Ë

ÁÁÁÁÁˆ

¯

˜̃˜̃̃ x

2− 6

Ê

Ë

ÁÁÁÁÁˆ

¯

˜̃˜̃̃

c. 3x2

x + 1( ) x − 6( )d. cannot be factored

20. A random survey was conducted to gather information about age and employment status. This table shows the

data that were collected.

Employment Survey Results

Employment Status Age less than 18 Age greater than 18

Has Job 587 20

Does Not Have Job 92 245

Find P(Has job | Age greater than 18).

a. 0.73 c. 0.97

b. 0.86 d. 0.08

Name: ________________________ ID: A

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21. Solve. x2

− 10x + 29 = 0

a. −5 + 4i, −5 − 4i c. 5 + 4i, 5 − 4i

b. −5 + 2i, −5 − 2i d. 5 + 2i, 5 − 2i

22. Circle Y is shown.

What is the area of the shaded part of the circle?

a.57

4π cm2 c.

405

8π cm2

b.135

8π cm2 d.

513

8π cm2

23. Proving the vertical angle theorem.

Given: ∠1 and ∠2 are vertical angles

Prove: m∠1 = m∠2

Proof:

Statements Reasons

1. ∠1 and ∠2 are vertical angles given

2. m∠1 + m∠3 = 180°

m∠2 + m∠3 = 180°linear pair property

3.

4. m∠1 = m∠2 subtraction property

Which of the following statements and reasons completes the proof?

a. m∠1 + m∠3 = m∠2 + m∠3 by the

substitution property.

c. m∠3 = m∠3 by the reflexive

property.

b. m∠1 + m∠4 = 180° and m∠2 + m∠4

= 180° by the linear pair property.

d. m∠1 + m∠2 = 360° by the addition

property.

Name: ________________________ ID: A

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24. Which of the following is equivalent to 4x

3

4?

a. 12x43

b. 64x34

c. 256x43

d. 256x34

25.

Amy is standing 50 meters from the base of the

Washington Monument in Washington, DC.

She estimates that the angle of elevation to the

top of the building is 60°. One of her friends is

at the top of the building. What is the distance

between Amy and her friend? (Assume the

monument meets the ground at a right angle.)

a. 58 meters

b. 87 meters

c. 25 meters

d. 100 meters

26. In the diagram, JG Ä QR.

What is the value of x?

a. 11

b. 6

c. 5

d. 3

27. Which equation can be used to find the

horizontal length, r, of the illuminated area?

a. cos 40° = r

12ft

b. cos 40° = 12ft

r

c. tan 40° = r

12ft

d. sin 40° = r

12ft

Name: ________________________ ID: A

7

28. In Mr. Fibonacci’s class, there are 16 boys and 12

girls. On Monday, 5 boys and 4 girls were wearing

white shirts. What is the difference between the

probability of a student chosen from Mr.

Fibonacci’s class being a girl and the probability of

a student chosen from Mr. Fibonacci’s class being

a girl wearing a white shirt?

a.1

7

b.2

7

c.1

3

d.3

4

29. If X = 7 inches, Y = 24 inches, and Z = 25

inches, what is the cosine of A?

a.25

7

b.24

25

c.25

24

d.7

25

30. Simplify the expression 243x155

a. 3x10

b. 9x3

c. 3x3

d. 9x10

31. This Venn Diagram shows the names of students in

Mr. Euclid’s class that own bicycles and

skateboards.

Let set A be the names of students who own

bicycles, and let set B be the names of students who

own skateboards. Find A ∪ B’.

a. {Joe, Mike, Linda, Rose}

b. {Ryan, Sarah, Mariko, Nina, Dion, Joe, Mike,

Linda, Rose, Brett, Juan, Tobi}

c. {Amy, Gabe, Abi}

d. {Ryan, Sarah, Mariko, Nina, Dion, Joe, Mike,

Linda, Rose, Amy, Gabe, Abi}

32. Find the volume of the oblique cylinder below

given the radius, 3 cm, and the slant height, 5 cm.

a. 75π cm2

b. 36π cm2

c. 45π cm2

d. 9 cm2

Name: ________________________ ID: A

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33. If ∆ABC ≅ ∆DEF, AB = 10 feet, m∠B = 27°, and

m∠F = 14°, which of the following statements is

false?

a. AC = DF

b. ∠C ≅ ∠F

c. m∠E = 139°

d. AB = DE

34. The following triangles are similar. What is the

measure of DE?

a.6

5

b.8

5

c.9

5

d. 2

35. The diagram below shows a part of a roof. The

highest part of the roof is called the apex.

How many feet above the base is the apex of the

roof?

a. 8

b. 9

c. 12

d. 20

36. One vertex of a polygon is A(−4,5). If the polygon

is dilated about the point (0, 2) with scale factor of

-2, what is the location of A′?

a. (-8, 8)

b. (-8, 10)

c. (8, -10)

d. (8, -4)

37. What is the x-coordinate of the vertex for the graph

of the equation y =2

3x

2− 6x + 4?

a.1

18

b.1

3

c. 3

d.9

2

38. What is the correct factorization of −5x2

+ 9x + 2?

a. −1 5x − 1( ) x + 2( )b. −1 5x + 1( ) x − 2( )c. −1 5x − 2( ) x + 1( )d. −1 5x + 2( ) x − 1( )

39. What is the result of (−1 + 5i) • (6 + 2i2)

a. −4 + 20i

b. 4 + 28i

c. −8 + 40i

d. −6 − 2i

40. Circle E is shown.

What is the length of CD ?

a.29

72π yd.

b.29

6π yd.

c.29

3π yd.

d.29

2π yd.

Name: ________________________ ID: A

9

41. The perimeter of a rectangle is the sum of

the side lengths: perimeter = 2l + 2w, where

l is the rectangle’s length and w is the

rectangle’s width.

What is the perimeter of the rectangle in

simplest form?a. 9x +1

b. 18x +2

c. 18x + 10

d. 18x + 6

42. If x

3

5= 8, what is the value of x?

a. x = 853

b. x = 835

c. x =1

853

d. x = 825

43. Simplify the following expression using

rational exponents.

x • x43

a. x

b. x

2

3

c. x

5

6

d. x

11

6

44. Refer to the figure below. Which of the following statements is true?

HLK is isosceles with base HK , ∠IHL and ∠JKL are right angles, IK ≅ JH

a. ∆HIL ≅ ∆KJL by HL c. ∆HKI ≅ ∆HJK by SAS

b. ∆HLK ≅ ∆JLK by SSS d. There are no congruent triangles.

Name: ________________________ ID: A

10

45. Refer to the figure shown. Which of the following statements is true?

a. ∆TUV ≅ ∆XWV by ASA c. ∆TUV ≅ ∆WXV by SAS

b. ∆TUV ≅ ∆VWX by SAS d. ∆TUV ≅ ∆WXV by SSS

46. Perform the indicated operation. Let f x( ) = x + 1 and g x( ) = x − 1.

f x( ) ⋅ g x( )

a. 2x2

− 1

b. 2x2

c. 2x2

+ 1

d. x2

− 1

47. A random survey was conducted about gender and hair color. This table records the data.

Hair Color

Brown Blonde Red

Male 548 876 82

Female 612 716 66

What is the probability that a randomly selected person has blonde hair, given that the person selected is female?

a. 0.51 c. 0.58

b. 0.55 d. 0.63

48. The area of a rectangle is the product of the side lengths: area = lw, where l is the rectangle’s

length and w is the rectangle’s width.

What is the area of the rectangle in simplest form?

a. 20x2

+ 7x − 6 c. 20x2

− 6

b. 20x2

− 7x − 6 d. 9x + 1

ID: A

1

Analytic Geometry Final Exam Study Guide

Answer Section

MULTIPLE CHOICE

1. C

2. A

3. B

4. B

5. D

6. C

7. A

8. B

9. A

10. A

11. A

12. A

13. B

14. B

15. B

16. D

17. C

18. C

19. C

20. D

21. D

22. D

23. A

24. D

25. D

26. B

27. A

28. B

29. D

30. C

31. D

32. B

33. C

34. C

35. C

36. D

37. D

38. B

39. A

ID: A

2

40. C

41. B

42. A

43. D

44. A

45. C

46. D

47. A

48. A