Accelerated Geometry/Algebra 2 Final Exam Review 2015...Name: _ ID: A 4 13. Graph the system of inequalities showing the feasible region to represent the number of first visits

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

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Accelerated Geometry/Algebra 2 Final Exam Review 2015

Multiple Choice

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

Solve the following system of equations by graphing.

____ 1. y = 11x − 6

y = − 6x + 11

a. (–1, 5) c. (5, 1)

b. (1, 7) d. (1, 5)

____ 2. 2y + 8x = 58

y − 5x = 11

a. (2, 21) c. (4, 20)

b. (21, 2) d. (1, 21)

Graph each system of equations and describe it as consistent and independent, consistent and dependent,

inconsistent, or none of these.

____ 3. 9x − 8y = 15

27x − 24y = 3

a. consistent and independent c. consistent and dependent

b. inconsistent d. none of these

____ 4. 5x − 8y = 6

6x − 6y = 6

a. inconsistent c. consistent and dependent

b. consistent and independent d. none of these

Solve each system of equations by using substitution.

____ 5. 8x + 7y = 18

3x – 5y = 22

a. (–2, 4) c. (4, –2)

b. (3, –2) d. (4, 0)

____ 6. 3r + 3s = 93r −6s =18a. (4, –0.5) c. (4, –1)

b. (5.5, 3) d. (2, –1)

Solve each system of equations by using elimination.

____ 7. 3p + 9q = 6

5p − 5q = 30

a. (6, –1) c. (5, 0.5)

b. (3.75, 2) d. (5, –1)

Name: ________________________ ID: A

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____ 8. 6a + 6b = 126a − 5b = 12a. (1, 0) c. (3, –0.5)

b. (2, 0) d. (2, 0.25)

Solve the system of inequalities by graphing.

____ 9. x > 2

y > 8

a. c.

b. d.

Name: ________________________ ID: A

3

____ 10. y > x – 6

y|| || ≤ 6

a. c.

b. d.

Find the coordinates of the vertices of the figure formed by each system of inequalities.

____ 11. y + x ≥ −9

y ≥ x − 7

2y + x ≤ 16

a. (–1, –8), (–30, 23), (–34, 25)

b. (–1, 8), (10, 3), (34, 25)

c. (–1, 25), (–34, 3), (10, –8)

d. (–1, –8), (10, 3), (–34, 25)

____ 12. y ≥ −2

2x + y ≤ 2

y ≤ 2x + 6

a. (2, –2), (–4, –2), (–1, 4)

b. (2, 4), (–1, –2), (–4, –2)

c. (2, –2), (4, 2), (1, –4)

d. (2, –2), (4, –2), (0, –8)

Name: ________________________ ID: A

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____ 13. Graph the system of inequalities showing the feasible region to represent the number of first visits and the

number of follow-ups that can be performed.

a. c.

b. d.

Solve the given system of equations.

____ 14. –3a = 36

10a + 3c = 9

2b + 5c = 23

a. a = –12, b = –96, c = 43 c. a = 12, b = –96, c = 43

b. a = –12, b = 43, c = –96 d. a = 43, b = –12, c = –96

____ 15. 11a + 2c = 10

–2a = 32

8b + 10c = 18

a. a = –16, b = –114, c = 93 c. a = –16, b = 93, c = –114

b. a = 16, b = –114, c = 93 d. a = 93, b = –16, c = –114

Name: ________________________ ID: A

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____ 16. Consider the quadratic function f x( ) = −2x2

+ 2x + 2. Find the y-intercept and the equation of the axis of

symmetry.

a. The y-intercept is –2.

The equation of the axis of symmetry is x = −1

2.

b. The y-intercept is 1

2.

The equation of the axis of symmetry is x = 2.

c. The y-intercept is + 2.

The equation of the axis of symmetry is x = 1

2.

d. The y-intercept is −1

2.

The equation of the axis of symmetry is x = –2.

Name: ________________________ ID: A

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____ 17. Graph the quadratic function f(x) = −2x2

+ 2x + 2.

a. c.

b. d.

Determine whether the given function has a maximum or a minimum value. Then, find the maximum or

minimum value of the function.

____ 18. f(x) = x2

− 2x + 2

a. The function has a maximum value. The maximum value of the function is 1.

b. The function has a maximum value. The maximum value of the function is 5.

c. The function has a minimum value. The minimum value of the function is 1.

d. The function has a minimum value. The minimum value of the function is 5.

Name: ________________________ ID: A

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____ 19. f(x) = −x2

+ 2x + 7

a. The function has a minimum value. The minimum value of the function is 8.

b. The function has a minimum value. The minimum value of the function is 4.

c. The function has a maximum value. The maximum value of the function is 4.

d. The function has a maximum value. The maximum value of the function is 8.

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which

the roots are located.

____ 20. x2

+ 5x + 4 = 0

a.

The solution set is 1, 4{ }.

c.

The solution set is −2.5, − 2.25{ }.

b.

The solution set is −4, − 1{ }.

d.


Name: ________________________ ID: A

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____ 21. −x2

+ 4x = 0

a.


c.

The solution set is −4, 0{ }.

b.

The solution set is −4 0{ }.

d.


Name: ________________________ ID: A

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____ 22. x2

+ 4x + 2 = 0

a.

One solution is between 3 and 4, while

the other solution is between 0 and 1.

c.

One solution is between –3 and 0, while

the other solution is between –4 and –1.

b.

One solution is between –3 and –1, while

the other solution is between 0 and –4.

d.



Name: ________________________ ID: A

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____ 23. −2x2

+ 3x + 4 = 0

a.

One solution is between 2 and –1, while


c.



b.

One solution is between 2 and 0, while


d.

One solution is between 0 and –1, while


Name: ________________________ ID: A

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Write a quadratic equation with the given roots. Write the equation in the form ax2

+ bx + c = 0, where a, b,

and c are integers.

____ 24. –5 and 2

a. x2

− 7x + 10 = 0 c. x2

− 3x + 10 = 0

b. x2

+ 7x + 10 = 0 d. x2

+ 3x − 10 = 0

____ 25. −5

4 and 8

a. 4x2

− 27x − 40 = 0 c. x2

− 27x − 40 = 0

b. 4x2

+ 27x + 40 = 0 d. x2

− 27x + 40 = 0

Solve the equation by factoring.

____ 26. x2

+ 3x − 28 = 0

a. −4, 7{ } c. 4, 7{ }b. −7, 4{ } d. −4, − 7{ }

____ 27. 2x2

+ 3x − 14 = 0

a. {–4, −7

2} c. {–4, 7}

b. {−7

2, 2} d. {2, 7}

Simplify.

____ 28. 196

a. 14 c. 196

b. 14 d. 3 14

____ 29. 245

64

a.7 5

8c.

5

8

b.49

8d.

7 7

8

____ 30. (2i)(−3i)(4i)

a. −24 c. 24i

b. −24i d. 24

____ 31. i7

a. −i c. i

b. 1 d. −1

____ 32. 11 + i( ) + 3 − 15i( )a. 14 − 14i c. 12 − 12i

b. − 4 + 4i d. 14 + 16i

Name: ________________________ ID: A

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____ 33. 11 − 12i( ) + 21 − 8i( )a. 9 + 19i c. 32 − 4i

b. 32 − 20i d. 29i − i

____ 34. 8 + 10i( )(5 − 8i)

a. 40 − 14i + 80 c. 40 − 14i − 80i2

b. 120 − 14i d. 88 + 50i

____ 35. −4 + 4i( )(−3 − 3i)

a. 16 + 12i c. 24 + 0i

b. 12 + 0i − 12i2

d. 12 + 0i + 12

____ 36. 3

6 + 7i

a.18

85+

21

85i c.

18

13+

21

13i

b.6

85−

7

85i d.

18

85−

21

85i

____ 37. 6 − 3i

8 − 11i

a.81

185+

42

185i c.

6

185−

3

185i

b.15

57+

42

57i d.

81

185−

42

185i

Solve the equation by using the Square Root Property.

____ 38. 16x2

− 48x + 36 = 49

a. {3

2} c. {−

13

4,

1

4}

b. {3

2, 7} d. {−

1

4,

13

4}

____ 39. 100x2

− 80x + 16 = 9

a. {1

10,

7

10} c. {

2

5}

b. {−7

10, −

1

10} d. {

2

5, 3}

Solve the equation by completing the square.

____ 40. x2

+ 2x − 3 = 0

a. −3, 1{ } c. −6, 1{ }b. −6, 2{ } d. −1, 3{ }

____ 41. 2x2

+ 2x = 0

a. −2, 0{ } c. 0{ }b. 0, 1{ } d. −1, 0{ }

Name: ________________________ ID: A

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Find the exact solution of the following quadratic equation by using the Quadratic Formula.

____ 42. x2

− 8x = 20

a. −10, 2{ } c. −4, 20{ }b. 20, 28{ } d. −2, 10{ }

____ 43. −x2

+ 3x + 7 = 0

a.3 − 37

−2,

3 + 37

−2

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔ

¸

˝

˛


c.−3 − −19

−2,

−3 + −19

−2

Ï

Ì

Ó


¸

˝

˛


b.−3 − 12

−2,

−3 + 12

−2

Ï

Ì

Ó


¸

˝

˛


d.−3 − 37

−2,

−3 + 37

−2

Ï

Ì

Ó


¸

˝

˛


Find the value of the discriminant. Then describe the number and type of roots for the equation.

____ 44. −x2

− 14x + 2 = 0

a. The discriminant is 196. Because the discriminant is greater than 0 and is a perfect

square, the two roots are real and rational.

b. The discriminant is –204. Because the discriminant is less than 0, the two roots are

complex.

c. The discriminant is 204. Because the discriminant is greater than 0 and is not a perfect

square, the two roots are real and irrational.

d. The discriminant is –188. Because the discriminant is less than 0, the two roots are

complex.

____ 45. x2

+ x + 7 = 0

a. The discriminant is –29.

Because the discriminant is less than 0, the two roots are complex.

b. The discriminant is 1.

Because the discriminant is greater than 0 and is a perfect square, the two roots are real

and rational.

c. The discriminant is –27.

Because the discriminant is less than 0, the two roots are complex.

d. The discriminant is 27.

Because the discriminant is greater than 0 and is a perfect square, the two roots are real

and rational.

Name: ________________________ ID: A

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Write the following quadratic function in vertex form. Then, identify the axis of symmetry.

____ 46. y = −3x2

+ 48x

a. The vertex form of the function is y = 3 x + 8( )2

+ 192.

The equation of the axis of symmetry is x = −192.

b. The vertex form of the function is y = x + 192( )2

+ 8.

The equation of the axis of symmetry is x = −8.

c. The vertex form of the function is y = −3 x − 8( )2

+ 192.


d. The vertex form of the function is y = −3 x + 8( )2

+ 192.


Name: ________________________ ID: A

15

Graph the quadratic inequality.

____ 47. y > x2

− 3x + 5

a. c.

b. d.

Name: ________________________ ID: A

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____ 48. y < 2x2

− 6x + 10

a. c.

b. d.

____ 49. Find the geometric mean between each pair of numbers.

28 and 7

a. 35 c. 14

b. 196 d. 17.5

____ 50. Find the geometric mean between each pair of numbers.

256 and 841

a. 22.5 c. 464

b. 3 5 d. 4 29

Name: ________________________ ID: A

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____ 51. Find the measure of the BD.

a. 2 30 c. 23

b. 11.5 d. 120

____ 52. Find x.

a. 22 c. 1144

b. 2 286 d. 1594

Determine whether ∆QRS is a right triangle for the given vertices. Explain.

____ 53. Q(–6, –2), R(2, –5), S(–3, 6)

a. no; QR = 73 , QS = 73 , RS = 146 ; QR2 + QS2 ≠ RS2

b. yes; QR = 73 , QS = 73 , RS = 146 ; QR2 + QS2 = RS2

c. yes; QR = 73 , QS = 73 , RS = 146 ; RS2 + QS2 = RQ2

d. no; QR = 73 , QS = 73 , RS = 146 ; RS2 + QS2 ≠ RQ2

____ 54. Q(18, 13), R(17, –3), S(–18, 12)

a. no; QR = 257 , QS = 1297 , RS = 5 58 ; QR2 + QS2 ≠ RS2

b. yes; QR = 257 , QS = 1297 , RS = 5 58 ; RS2 + QS2 = RQ2

c. yes; QR = 257 , QS = 1297 , RS = 5 58 ; QR2 + QS2 ≠ RS2

d. no; QR = 257 , QS = 1297 , RS = 5 58 ; RS2 + QS2 = RQ2

Name: ________________________ ID: A

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____ 55. The length of a diagonal of a square is 24 2 millimeters. Find the perimeter of the square.

a. 576 millimeters c. 96 millimeters

b. 96 2 millimeters d. 1152 millimeters

____ 56. Find x and y.

a. x = 45°, y = 13.1 c. x = 30°, y = 13.1 2

b. x = 30°, y = 13.1 d. x = 45°, y = 13.1 2


a. x = 24 3, y = 24 c. x = 24, y = 24 3

b. x = 12 3, y = 12 d. x = 12, y = 12 3


a. x = 1.5 3, y = 1.5 c. x = 3, y = 3 3

b. x = 3 3, y = 3 d. x = 1.5, y = 1.5 3

____ 59. Find the measure of the angle to the nearest tenth of a degree.

cos Y = 0.5135a. 30.9 c. 0.5135

b. 59.1 d. 27.2

Name: ________________________ ID: A

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____ 60. Use the figure to find the trigonometric ratio below. Express the answer as a decimal rounded to the nearest

ten-thousandth.

cos B

AC = 5 5 , CB = 5 , AD = 11, CD = 2, DB = 1

a. 2.2361 c. 0.4472

b. 0.9839 d. 0.8944

____ 61. Lynn is standing at horizontal ground level with the base of the Sears Tower in Chicago. The angle formed

by the ground and the line segment from her position to the top of the building is 15.7°. The height of the

Sears Tower is 1450 feet. Find her distance from the Sears Tower to the nearest foot.

a. 408 ft c. 5159 ft

b. 7 ft d. 5358 ft

____ 62. Dolores is standing on a horizontal ground level with the base of the Statue of Liberty in New York City. The

angle formed by the ground and the line segment from her position to the top of the statue is 26.3°. The

height of the Statue of Liberty is approximately 93 meters. Find her distance from the Statue of Liberty to the

nearest meter.

a. 188 m c. 104 m

b. 0.005 m d. 210 m

____ 63. A rocket ship is two miles above sea level when it begins to climb at a constant angle of 3.5° for the next 40

ground miles. About how far above sea level is the rocket ship after its climb?

a. 2.4 mi c. 653.9 mi

b. 4.4 mi d. 655.9 mi

____ 64. A hot air balloon is one mile above sea level when it begins to climb at a constant angle of 4° for the next 50

ground miles. About how far above sea level is the hot air balloon after its climb?

a. 2.5 mi c. 4.5 mi

b. 3.5 mi d. 716.03 mi

A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°.

____ 65. How far off the ground is the raised end of the drawbridge in its initial setting?

a. 5.23 yd c. 685.80 yd

b. 59.77 yd d. 688.42 yd

____ 66. During one stage of the drawbridge’s motion, the raised end is 15 yards above the ground. What is the incline

of the drawbridge to the nearest hundredth?

a. 0.004° c. 14.48°

b. 14.04° d. 75.52°

____ 67. A hiker stops to rest and sees a deer in the distance. If the hiker is 48 yards lower than the deer and the angle

of elevation from the hiker to the deer is 15°, find the distance from the hiker to the deer.

a. 18.21 yd c. 179.14 yd

b. 49.69 yd d. 185.46 yd

Name: ________________________ ID: A

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____ 68. A water slide is 400 yards long with a vertical drop of 36.3 yards. Find the angle of depression of the slide.

a. 5.2° c. 436.3°

b. 84.8° d. 363.7°

____ 69. A tubing run is 150 yards long with a vertical drop of 21.6 yards. Find the angle of depression of the run.

a. 8.2° c. 81.7°

b. 8.3° d. 81.8°

Find each measure using the given measures of ∆KLM . Round measures to the nearest tenth.

____ 70. If m∠L = 48.4, m∠K = 24.5, and l = 37.9, find k.

a. 15.7 c. 28.3

b. 21.0 d. 68.3

____ 71. If m∠L = 47.1, k = 59.6, and l = 52.2, find m∠K.

a. 45.8 c. 56.7

b. 0.8 d. 43.6

____ 72. A playground is situated on a triangular plot of land. Two sides of the plot are 175 feet long and they meet at

an angle of 70°. For safety reasons, a fence is to be placed along the perimeter of the property. How much

fencing material is needed?

a. 110 ft c. 375.8 ft

b. 200.8 ft d. 550.8 ft

____ 73. In ∆ABC, given the following measures, find the measure of the missing side to the nearest tenth..

a = 14.2, c = 13.9, m∠B = 27.7

a. b = 6.7 c. b = 14.5

b. b = 394 d. b = 45.3

____ 74. In ∆DEF, given the lengths of the sides, find the measure of the stated angle to the nearest degree.

d = 5.4, e = 10.5, f = 10.8; m∠F

a. 0.20 c. –2.3

b. 102 d. 78

____ 75. Zack, Rachel, and Maddie are unraveling a huge ball of yarn to see how long it is. As they move away from

each other, they form a triangle. The distance from Zack to Rachel is 3 meters. The distance from Rachel to

Maddie is 2.5 meters. The distance from Maddie to Zack is 4 meters. Find the measures of the three angles in

the triangle.

a. m∠Z = 38.6, m∠R = 92.9, m∠M = 48.5

b. m∠Z = 48.5, m∠R = 38.6, m∠M = 92.9

c. m∠Z = 92.9, m∠R = 48.5, m∠M = 38.6

d. m∠Z = 60, m∠R = 60, m∠M = 60

____ 76. Tomas, Ling, and Daniel are experimenting with a giant rubber band. They each hold the rubber band to

create a triangle. The distance from Tomas to Ling is 24 inches. The distance from Ling to Daniel is 36

inches. The distance from Daniel to Tomas is 20 inches. Find the measures of the three angles in the triangle.

a. m∠L = 31.6, m∠T = 109.5, m∠D = 38.9

b. m∠L = 38.9, m∠T = 31.6, m∠D = 109.5

c. m∠L = 109.5, m∠T = 38.9, m∠D = 31.6

d. m∠L = 60, m∠T = 60, m∠D = 60

Name: ________________________ ID: A

21

____ 77. Tiffany, Lori, and Mika are practicing for an egg-toss contest. The distance from Tiffany to Lori is 17 inches.

The distance from Lori to Mika is 32 inches. The distance from Mika to Tiffany is 28 inches. Find the

measures of the three angles in the triangle.

a. m∠L = 60.9, m∠T = 87, m∠M = 32.1

b. m∠L = 32.1, m∠T = 60.9, m∠M = 87

c. m∠L = 87, m∠T = 32.1, m∠M = 60.9

d. m∠L = 60, m∠T = 60, m∠M = 60

____ 78. Taina, Luther, and Della are tapping a balloon to each other in the air, trying to keep it from touching the

ground. The distance from Taina to Luther is 22 inches. The distance from Luther to Della is 40 inches. The

distance from Della to Taina is 34 inches. Find the measures of the three angles in the triangle.

a. m∠L = 58.1, m∠T = 88.5, m∠D = 33.4

b. m∠L = 33.4, m∠T = 58.1, m∠D = 88.5

c. m∠L = 88.5, m∠T = 33.4, m∠D = 58.1

d. m∠L = 60, m∠T = 60, m∠D = 60

____ 79. Luna created a trash can in the shape of a triangular prism. The sides of the triangle are 1.6 feet, 2.3 feet, and

1.2 feet. Find the measures of the angles of the triangle to the nearest tenth.

a. 109.6, 41.0, 29.4 c. 101.8, 37.1, 41.1

b. 19.6, 49.1, 60.6 d. 60, 60, 60

____ 80. Hoshi is working on an art project in the shape of a triangular prism. The sides of the triangle are 2.4 feet,

1.5 feet, and 1.3 feet. Find the measures of the angles of the triangle to the nearest tenth.

a. 117.8, 33.6, 28.6 c. 25.0, 39.8, 115.2

b. 27.8, 56.4, 95.8 d. 60, 60, 60

The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest

hundredth if necessary.

____ 81. r = 13.1 km, d = ? , C = ?

a. d = 26.2 km, C = 82.31 km c. d = 6.55 km, C = 82.31 km

b. d = 26.2 km, C = 41.15 km d. d = 6.55 km, C = 41.15 km

____ 82. d = 22.3 km, r = ? , C = ?

a. r = 44.6 km, C = 35.03 km c. r = 11.15 km, C = 70.06 km

b. r = 11.15 km, C = 35.03 km d. r = 44.6 km, C = 70.06 km

____ 83. Find the exact circumference of the circle.

a. 7π cm c. 10π cm

b. 5π cm d. 4π cm

Name: ________________________ ID: A

22

____ 84. Find the exact circumference of the circle.

a. 12π 2 mm c. 12π mm

b. 24π 2 mm d. 6π 2 mm

Use the diagram to find the measure of the given angle.

____ 85. m∠BAC

a. 140 c. 130

b. 120 d. 150

____ 86. m∠BAF

a. 50 c. 130

b. 60 d. 40

____ 87. m∠EAD

a. 180 c. 60

b. 90 d. 30

____ 88. m∠FAE

a. 50 c. 60

b. 40 d. 30

Name: ________________________ ID: A

23

____ 89. m∠CAE

a. 170 c. 150

b. 160 d. 140

____ 90. m∠DAF

a. 110 c. 130

b. 120 d. 140

Use the diagram to find the measure of the given angle.

____ 91. ∠PRS

a. 95° c. 50°

b. 20° d. 85°

____ 92. ∠QRT

a. 95° c. 50°

b. 20° d. 85°

____ 93. ∠PRQ

a. 85° c. 50°

b. 20° d. 95°

____ 94. ∠SRT

a. 85° c. 50°

b. 20° d. 95°

Name: ________________________ ID: A

24

____ 95. In ñO, EC and AB are diameters, and ∠BOD ≅ ∠DOE ≅ ∠EOF ≅ ∠FOA.

Find m arc BC.

a. 270 c. 225

b. 90 d. 315

____ 96. In ñF, ∠CFD ≅ ∠DFE, m∠BFA = 7x, m∠AFE = 5x + 12, and BE and AC are diameters.

Find m arc DC.

a. 56 c. 50

b. 46 d. 49

Name: ________________________ ID: A

25

____ 97. In ñA, AC ≅ AF and AE = 10.

Find mEG.

a. 14 c. 10

b. 12 d. 16

____ 98. In ñU , TS = 15, UQ = US. Find mPR.

a. 28 c. 15

b. 30 d. 39

Name: ________________________ ID: A

26

____ 99.

If m∠BDC = 35, m arc AB = 100, and m arc CD = 100, find m∠1.

a. 45 c. 35

b. 70 d. 90

____ 100.

If m∠1 = 2x + 2, m∠2 = 9x, find m∠1.

a. 72 c. 75

b. 19 d. 18

Name: ________________________ ID: A

27

____ 101. In ñD, AB ≅ CB and m arc CE = 50. Find m∠BCE.

a. 85 c. 117

b. 108 d. 110

____ 102. Quadrilateral ABCD is inscribed in ñZ such that AB Ä DC and m∠BZC = 84. Find m∠DCA.

a. 48 c. 46

b. 44 d. 42

____ 103. Find x. Assume that segments that appear tangent are tangent.

a. 9 c. 12

b. 7 d. 17

Name: ________________________ ID: A

28


a. 7 c. 14

b. 6 d. 5


a. 7 c. 9

b. 5 d. 3


a. 11 c. 13

b. 29 d. 16

Name: ________________________ ID: A

29

Find the measure of the numbered angle.

____ 107.

a. 230 c. 130

b. 115 d. 125

____ 108.

a. 55 c. 75

b. 65 d. 60

Name: ________________________ ID: A

30

____ 109.

a. 62.5 c. 112.5

b. 105 d. 115

____ 110.

a. 60 c. 80

b. 70 d. 65

____ 111.

a. 115 c. 120

b. 125 d. 130

Name: ________________________ ID: A

31

____ 112.

a. 81 c. 94

b. 90 d. 102

____ 113.

a. 92 c. 94

b. 95 d. 90

____ 114.

a. 90 c. 220

b. 180 d. 110

Name: ________________________ ID: A

32

____ 115.

a. 100 c. 90

b. 180 d. 95

____ 116.

a. 70 c. 80

b. 75 d. 85

Name: ________________________ ID: A

33

Find x. Assume that any segment that appears to be tangent is tangent.

____ 117.

a. 15 c. 25

b. 35 d. 45

____ 118.

a. 50 c. 60

b. 40 d. 70

Name: ________________________ ID: A

34

____ 119.

a. 10 c. 12

b. 5 d. 15

____ 120.

a. 65 c. 68

b. 66 d. 62

____ 121.

a. 15 c. 20

b. 30 d. 10

Name: ________________________ ID: A

35

____ 122.

a. 12 c. 8

b. 14 d. 10

____ 123.

a. 22 c. 18

b. 9 d. 11

____ 124.

a. 15 c. 25

b. 20 d. 30

Name: ________________________ ID: A

36

____ 125.

a. 47 c. 44

b. 48 d. 43

____ 126.

a. 35 c. 25

b. 20 d. 30

Name: ________________________ ID: A

37

Find x. Round to the nearest tenth if necessary.

____ 127.

a. 5 c. 3

b. 6 d. 4

____ 128.

a. 2 c. 3

b. 1 d. 4

Name: ________________________ ID: A

38

____ 129.

a. 7 c. 9

b. 8 d. 10

____ 130.

a. 2 c. 2.5

b. 3 d. 3.5

____ 131.

a. 2 c. 3.2

b. 2.4 d. 3.5

Name: ________________________ ID: A

39

____ 132.

a. 10.5 c. 3.2

b. 2.4 d. 3.5

____ 133.

a. 4.2 c. 3.2

b. 3.8 d. 3.7

____ 134.

a. 4 c. 6

b. 5.5 d. 5

Name: ________________________ ID: A

40

____ 135.

a. 6 c. 7

b. 6.5 d. 7.2

____ 136.

a. 6 c. 4

b. 5 d. 3

Name: ________________________ ID: A

41

Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.

____ 137.

a. 5 c. 3.5

b. 2.8 d. 4

____ 138.

a. 9 c. 3

b. 2 d. 8

Name: ________________________ ID: A

42

____ 139.

a. 7.2 c. 1.7

b. 4 d. 3

____ 140.

a. 2.3 c. 2.8

b. 0.9 d. 3.4

____ 141.

a. 8.7 c. 5

b. 7 d. 10

Name: ________________________ ID: A

43

____ 142.

a. 8 c. 3

b. 10 d. 4

____ 143.

a. 3 c. 2

b. 7 d. 4

____ 144.

a. 4 c. 6

b. 5 d. 7

Name: ________________________ ID: A

44

____ 145.

a. 3.3 c. 3.1

b. 2.5 d. 4.5

____ 146.

a. 8.5 c. 9.3

b. 9.0 d. 9.6

____ 147. Write an equation for a circle with center at (–6, 10) and diameter 6.

a. (x + 6)2

+ (y − 10)2

= 9 c. (x − 6)2

+ (y + 10)2

= 9

b. (x + 6)2

+ (y − 10)2

= 36 d. (x − 6)2

+ (y + 10)2

= 36

____ 148. Write an equation for a circle with a diameter that has endpoints at (–10, 1) and (–8, 5). Round to the nearest

tenth if necessary.

a. (x − 9)2

+ (y + 3)2

= 20 c. (x + 9)2

+ (y − 3)2

= 5

b. (x − 9)2

+ (y + 3)2

= 5 d. (x + 9)2

+ (y − 3)2

= 20

Name: ________________________ ID: A

45

Graph the equation.

____ 149. x2

+ y2

= 16

a. c.

b. d.

Name: ________________________ ID: A

46

____ 150. (x + 1)2

+ (y + 3)2

= 16

a. c.

b. d.

ID: A

1

Accelerated Geometry/Algebra 2 Final Exam Review 2015

Answer Section

MULTIPLE CHOICE

1. ANS: D

Graph the equations and find their point of intersection.

Feedback

A What is the x-coordinate of the intersection?

B Did you graph both equations correctly?

C Write the coordinates of the intersection carefully.

D Correct!

PTS: 1 DIF: Average REF: Lesson 3-1

OBJ: 3-1.1 Solve systems of linear equations by graphing. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2

STA: 4.3.12 B.2 TOP: Solve systems of linear equations by graphing.

KEY: System of Linear Equations | Graphs

2. ANS: A

Graph the equations and find their point of intersection.

Feedback

A Correct!

B Did you plot the graphs correctly?

C Did you read the intersection of the graphs correctly?

D What is the x-coordinate of the intersection?


OBJ: 3-1.1 Solve systems of linear equations by graphing. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2

STA: 4.3.12 B.2 TOP: Solve systems of linear equations by graphing.

KEY: System of Linear Equations | Graphs

3. ANS: B

Graph the equations and check the number of solutions.

Feedback

A Did you check the number of solutions?

B Correct!

C Are the y-intercepts equal?

D Did you find the slope of each line?


OBJ: 3-1.2 Determine whether a system of linear equations is consistent and independent, consistent and

dependent, or inconsistent.

TOP: Determine whether a system of linear equations is consistent and independent, consistent and


KEY: System of Linear Equations | Consistent System | Inconsistent System

ID: A

2

4. ANS: B

Graph the equations and check the number of solutions.

Feedback

A Are the slopes equal?

B Correct!

C Are the y-intercepts equal?

D Did you plot the graphs correctly?


OBJ: 3-1.2 Determine whether a system of linear equations is consistent and independent, consistent and


TOP: Determine whether a system of linear equations is consistent and independent, consistent and


KEY: System of Linear Equations | Consistent System | Inconsistent System

5. ANS: C

By using the method of substitution, solve one equation for one variable in terms of the other variable. Then,

substitute this expression for the variable in the other equation.

Feedback

A Did you calculate the values correctly?

B Recalculate the value of x.

C Correct!

D Recalculate the value of y.


OBJ: 3-2.1 Solve systems of linear equations by using substitution.

NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 TOP: Solve systems of linear equations by using substitution.

KEY: System of Linear Equations | Substitution

6. ANS: C

By using the method of substitution, solve one equation for one variable in terms of the other variable. Then,

substitute this expression for the variable in the other equation.

Feedback

A Recalculate the value of s.

B Did you calculate correctly?

C Correct!

D Recalculate the value of r.


OBJ: 3-2.1 Solve systems of linear equations by using substitution.

NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 TOP: Solve systems of linear equations by using substitution.

KEY: System of Linear Equations | Substitution

ID: A

3

7. ANS: D

Use the method of elimination to obtain the required answer.

Feedback

A Recalculate the value of p.

B Did you calculate the values correctly?

C Recalculate the value of q.

D Correct!


OBJ: 3-2.2 Solve systems of linear equations by using elimination.

NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 TOP: Solve systems of linear equations by using elimination.

KEY: System of Linear Equations | Elimination

8. ANS: B

Use the method of elimination to obtain the required answer.

Feedback

A Recalculate the value of a.

B Correct!

C Did you calculate the values correctly?

D Recalculate the value of b.


OBJ: 3-2.2 Solve systems of linear equations by using elimination.

NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 TOP: Solve systems of linear equations by using elimination.

KEY: System of Linear Equations | Elimination

9. ANS: C

Both the inequalities should be plotted and the region common to both should be shaded.

Feedback

A You have plotted the first inequality incorrectly.

B You have plotted the second inequality incorrectly.

C Correct!

D You have plotted the inequalities incorrectly.


OBJ: 3-3.1 Solve systems of inequalities by graphing. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2

TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities | Graphs

ID: A

4

10. ANS: D

Plot the first inequality. Then, plot the positive and negative values of y and shade the common region.

Feedback

A What is the y-intercept of the first related equation?

B Did you plot the second equation correctly?

C Did you plot all the equations?

D Correct!


OBJ: 3-3.1 Solve systems of inequalities by graphing. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2

TOP: Solve systems of inequalities by graphing. KEY: System of Inequalities | Graphs

11. ANS: D

Solve the system of inequalities by graphing the inequalities on the same coordinate plane. The solution set is

represented by the intersection of the graphs.

Feedback

A Did you plot the inequalities correctly?

B Did you check the sign of the coordinates?

C You have interchanged the coordinates.

D Correct!

PTS: 1 DIF: Advanced REF: Lesson 3-3

OBJ: 3-3.2 Determine the coordinates of the vertices of a region formed by the graph of a system of

inequalities. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2

TOP: Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities.

KEY: System of Inequalities | Graphs

12. ANS: A

Solve the system of inequalities by graphing the inequalities on the same coordinate plane. The solution set is

represented by the intersection of the graphs.

Feedback

A Correct!

B You have interchanged the coordinates.

C Did you check the sign of the coordinates?

D Did you plot the inequalities correctly?


OBJ: 3-3.2 Determine the coordinates of the vertices of a region formed by the graph of a system of

inequalities. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2

TOP: Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities.

KEY: System of Inequalities | Graphs

ID: A

5

13. ANS: A

Write the system of inequalities and then plot the graph.

Feedback

A Correct!

B Did you check the values of the inequalities?

C Did you use the correct sign in plotting the inequalities?

D Did you check the intercept of the inequalities?


OBJ: 3-4.2 Solve real-world problems using linear programming.

NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2

TOP: Solve real-world problems using linear programming.

KEY: Linear Programming | Real-World Problems

14. ANS: A

Solve three equations simultaneously.

Feedback

A Correct!

B Check whether the values of the variables have been interchanged.

C Only two of the values are correct.

D The values of a, b, and c are interchanged.


OBJ: 3-5.1 Solve systems of linear equations in three variables.

NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2

TOP: Solve systems of linear equations in three variables.

KEY: System of Equations | Three Variables

15. ANS: A

Solve three equations simultaneously.

Feedback

A Correct!

B Only two of the values are correct.

C Check whether the values of the variables have been interchanged.

D The values of a, b, and c are interchanged.


OBJ: 3-5.1 Solve systems of linear equations in three variables.

NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2

TOP: Solve systems of linear equations in three variables.

KEY: System of Equations | Three Variables

ID: A

6

16. ANS: C

For the quadratic equation ax2

+ bx + c, the y-intercept is c and the equation of axis of

symmetry is x =−b

2a.

Feedback

A Did you check the signs?

B Did you interchange the y-intercept and the x-coordinate of the vertex?

C Correct!

D Did you use the correct formulas for the y-intercept and the x-coordinate of the vertex?

PTS: 1 DIF: Average REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.

NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 TOP: Graph quadratic functions.

KEY: Quadratic Functions | Graph Quadratic Functions

17. ANS: B

First, choose integer values for x. Then evaluate the function for each x value. Graph the resulting coordinate

pairs and connect the points with a smooth curve.

Feedback

A Graph ordered pairs that satisfy the function.

B Correct!

C Did you plot the graph correctly?

D When the coefficient of x2 is less than 0, the graphs opens down.

PTS: 1 DIF: Advanced REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.

NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 TOP: Graph quadratic functions.

KEY: Quadratic Functions | Graph Quadratic Functions

18. ANS: C

The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the

function.

Feedback

A The coefficient of x2 is greater than zero.

B The graph of this function opens up.

C Correct!

D What is the value of the y-coordinate of the vertex?


OBJ: 5-1.2 Find and interpret the maximum and minimum values of a quadratic function.

NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3

TOP: Find and interpret the maximum and minimum values of a quadratic function.

KEY: Maximum Values | Minimum Values | Quadratic Functions

ID: A

7

19. ANS: D

The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the

function.

Feedback

A The graph of the function opens down.

B The coefficient of x2 is less than zero.

C What is the value of the y-coordinate of the vertex?

D Correct!


OBJ: 5-1.2 Find and interpret the maximum and minimum values of a quadratic function.

NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3

TOP: Find and interpret the maximum and minimum values of a quadratic function.

KEY: Maximum Values | Minimum Values | Quadratic Functions

20. ANS: B

The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic

equation because f(x) = 0 at those points.

Feedback

A What are the x-intercepts of the graph?

B Correct!

C Find the zeros of the function, not the vertex.

D The zeros of the function are the solutions of the related equation.


OBJ: 5-2.1 Solve quadratic equations by graphing. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2

STA: 4.3.12 B.3 TOP: Solve quadratic equations by graphing.

KEY: Quadratic Equations | Solve Quadratic Equations

21. ANS: A

The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic

equation because f(x) = 0 at those points.

Feedback

A Correct!

B The zeros of the function are the solutions of the related equation.

C What are the x-intercepts of the graph?

D Find the zeros of the function, not the vertex.


OBJ: 5-2.1 Solve quadratic equations by graphing. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2

STA: 4.3.12 B.3 TOP: Solve quadratic equations by graphing.


ID: A

8

22. ANS: D

When exact roots cannot be found by graphing, you can estimate solutions by stating the consecutive integers

between which the roots are located.

Feedback

A Is the coefficient of x2 less than zero?

B Did you graph the function correctly?

C When the coefficient of x2 is greater than 0, the graph opens up.

D Correct!


OBJ: 5-2.2 Estimate solutions of quadratic equations by graphing.

NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2 STA: 4.3.12 B.2

TOP: Estimate solutions of quadratic equations by graphing.


23. ANS: D

When exact roots cannot be found by graphing, you can estimate solutions by stating the consecutive integers

between which the roots are located.

Feedback

A Did you graph the function correctly?

B When the coefficient of x2 is less than 0, the graph opens down.

C Is the coefficient of x2 greater than 0?

D Correct!


OBJ: 5-2.2 Estimate solutions of quadratic equations by graphing.


TOP: Estimate solutions of quadratic equations by graphing.


24. ANS: D

A quadratic equation with roots p and q can be written as (x − p)(x − q) = 0, which can be further simplified.

Feedback

A Did you verify the answer by substituting the values?

B Did you calculate the coefficients correctly?

C Did you check the signs of the coefficients?

D Correct!


OBJ: 5-3.1 Write quadratic equations in intercept form. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2

TOP: Write quadratic equations in intercept form.

KEY: Quadratic Equations | Roots of Quadratic Equations

ID: A

9

25. ANS: A

A quadratic equation with roots p and q can be written as (x − p)(x − q) = 0, which can be further simplified.

Feedback

A Correct!

B Did you check the signs of the coefficients?

C Did you calculate the coefficients correctly?

D Did you verify the answer by substituting the values?


OBJ: 5-3.1 Write quadratic equations in intercept form. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2

TOP: Write quadratic equations in intercept form.

KEY: Quadratic Equations | Roots of Quadratic Equations

26. ANS: B

For any real numbers a and b, if ab = 0, then either a = 0, b − 0, or both a and b are equal to zero.

Feedback

A Did you use the Zero Product Property correctly?

B Correct!

C Did you verify the answer by substituting the values?

D Did you factor the binomial correctly?


OBJ: 5-3.2 Solve quadratic equations by factoring. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2

STA: 4.3.12 D.2 TOP: Solve quadratic equations by factoring.

KEY: Quadratic Equations | Solve Quadratic Equations | Factoring

27. ANS: B

For any real numbers a and b, if ab = 0, then either a = 0, b = 0, or both a and b are equal to zero.

Feedback

A Did you use the Zero Product Property correctly?

B Correct!

C Did you factor the binomial correctly?



OBJ: 5-3.2 Solve quadratic equations by factoring. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2

STA: 4.3.12 D.2 TOP: Solve quadratic equations by factoring.

KEY: Quadratic Equations | Solve Quadratic Equations | Factoring

ID: A

10

28. ANS: A

For any numbers a, b, and c, abc = a ⋅ b ⋅ c . Also, −1 = i2

= i.

Feedback

A Correct!

B Check for the radical sign.

C Take the square root of the number.

D Check your calculation.

PTS: 1 DIF: Basic REF: Lesson 5-4 OBJ: 5-4.1 Find square roots.

NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2 TOP: Find square roots.

KEY: Square Roots

29. ANS: A

a

b=

a

b

Feedback

A Correct!

B Check the numerator.

C Check the square root of the numerator.

D Check your calculation.

PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.1 Find square roots.

NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2 TOP: Find square roots.

KEY: Square Roots

30. ANS: C

Multiply the real numbers and imaginary numbers separately.

Feedback

A Check your calculation.

B Check the sign.

C Correct!

D Multiply the imaginary numbers again.


OBJ: 5-4.2 Perform operations with pure imaginary numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform operations with pure imaginary numbers. KEY: Imaginary Numbers

ID: A

11

31. ANS: A

Multiply the real numbers and imaginary numbers separately.

Feedback

A Check your calculation.

B Check the sign.

C Correct!

D Compute again.


OBJ: 5-4.2 Perform operations with pure imaginary numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform operations with pure imaginary numbers. KEY: Imaginary Numbers

32. ANS: A

Combine the real and imaginary parts of the complex numbers to add them.

Feedback

A Correct!

B Combine the real parts and then combine the imaginary parts.

C Add the real and imaginary parts of the two numbers separately.

D Did you combine the similar terms correctly?


OBJ: 5-4.3 Perform addition and subtraction operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform addition and subtraction operations with complex numbers.

KEY: Complex Numbers | Add Complex Numbers | Subtract Complex Numbers

33. ANS: B

Combine the real and imaginary parts of the complex numbers to add them.

Feedback

A Combine the real parts and then combine the imaginary parts.

B Correct!

C Combine the similar terms correctly.

D Add the real and imaginary parts of the two numbers separately.


OBJ: 5-4.3 Perform addition and subtraction operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform addition and subtraction operations with complex numbers.

KEY: Complex Numbers | Add Complex Numbers | Subtract Complex Numbers

ID: A

12

34. ANS: B

Use the FOIL method to multiply the complex numbers and use the formula i2

= −1. Combine the real parts

and then the imaginary parts of the two numbers.

Feedback

A Did you combine the real parts?

B Correct!

C Use the value of i2.

D Did you use the FOIL method to find the product?


OBJ: 5-4.4 Perform multiplication operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform multiplication operations with complex numbers.

KEY: Complex Numbers | Multiply Complex Numbers

35. ANS: C

Use the FOIL method to multiply the complex numbers and use the formula i2

= −1. Combine the real parts

and then the imaginary parts of the two numbers.

Feedback

A Use the FOIL method to find the product.

B Use the value of i2.

C Correct!

D Combine the real parts.


OBJ: 5-4.4 Perform multiplication operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform multiplication operations with complex numbers.

KEY: Complex Numbers | Multiply Complex Numbers

36. ANS: D

Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL

method and the difference of squares to simplify the given expression.

Feedback

A Multiply the numerator with the conjugate of the denominator.

B Have you multiplied the constant in the numerator with its conjugate of the

denominator?

C Did you multiply the conjugates correctly in the denominator?

D Correct!


OBJ: 5-4.5 Perform division operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform division operations with complex numbers.

KEY: Complex Numbers | Divide Complex Numbers

ID: A

13

37. ANS: A

Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL

method and the difference of squares to simplify the given expression.

Feedback

A Correct!

B Did you multiply the conjugates correctly in the denominator?

C Multiply the numerator also with the conjugate of the denominator.

D Did you combine the similar terms correctly?


OBJ: 5-4.5 Perform division operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform division operations with complex numbers.

KEY: Complex Numbers | Divide Complex Numbers

38. ANS: D

For any real number n, if x2

= n, then x = ± n .

Feedback

A Did you use the Square Root Property correctly?

B Did you verify the answer by substituting the values?

C Did you factor the perfect square trinomial correctly?

D Correct!


OBJ: 5-5.1 Solve quadratic equations by using the Square Root Property.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: 4.3.12 D.2

TOP: Solve quadratic equations by using the Square Root Property.

KEY: Quadratic Equations | Solve Quadratic Equations | Square Root Property

39. ANS: A

For any real number n, if x2

= n, then x = ± n .

Feedback

A Correct!

B Did you factor the perfect square trinomial correctly?

C Did you use the Square Root Property correctly?



OBJ: 5-5.1 Solve quadratic equations by using the Square Root Property.


TOP: Solve quadratic equations by using the Square Root Property.

KEY: Quadratic Equations | Solve Quadratic Equations | Square Root Property

ID: A

14

40. ANS: A

To complete the square for any quadratic expression of the form x2

+ bx, find half of b, and square the result.

Then, add the result to x2

+ bx.

Feedback

A Correct!

B Did you make the quadratic expression a perfect square?

C Did you verify the answer by substituting the values?

D Did you check the signs of the roots?


OBJ: 5-5.2 Solve quadratic equations by completing the square.


TOP: Solve quadratic equations by completing the square.

KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square

41. ANS: D

To complete the square for any quadratic expression of the form x2

+ bx, find half of b, and square the result.

Then, add the result to x2

+ bx.

Feedback

A Did you make the quadratic expression a perfect square?

B Did you check the signs of the roots?

C Find both the solutions.

D Correct!


OBJ: 5-5.2 Solve quadratic equations by completing the square.


TOP: Solve quadratic equations by completing the square.

KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square

42. ANS: D

The solution of a quadratic equation of the form ax2

+ bx + c = 0, where a ≠ 0, is obtained by using the

formula x =−b ± b

2− 4ac

2a.

Feedback

A Did you check the signs of the solution?

B Did you use the correct formula?

C Did you substitute the values of a, b, and c correctly in the formula?

D Correct!


OBJ: 5-6.1 Solve quadratic equations by using the Quadratic Formula.


TOP: Solve quadratic equations by using the Quadratic Formula.

KEY: Quadratic Equations | Solve Quadratic Equations | Quadratic Formula

ID: A

15

43. ANS: D

The solution of a quadratic equation of the form ax2

+ bx + c = 0, where a ≠ 0, is obtained by using the

formula x =−b ± b

2− 4ac

2a.

Feedback

A Did you substitute the values of a, b, and c correctly in the formula?

B Did you evaluate the discriminant correctly?

C Did you use the correct formula?

D Correct!


OBJ: 5-6.1 Solve quadratic equations by using the Quadratic Formula.


TOP: Solve quadratic equations by using the Quadratic Formula.

KEY: Quadratic Equations | Solve Quadratic Equations | Quadratic Formula

44. ANS: C

If b2

− 4ac > 0 and b2

− 4ac is a perfect square, then the roots are rational.

If b2

− 4ac > 0 and b2

− 4ac is not a perfect square, then the roots are real and irrational.

Feedback

A Did you use the correct formula for the discriminant?

B Did you check the sign of the answer?

C Correct!

D Did you use the correct order of operations while evaluating the discriminant?

PTS: 1 DIF: Basic REF: Lesson 5-6

OBJ: 5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.


TOP: Use the discriminant to determine the number and types of roots of a quadratic equation.

KEY: Quadratic Equations | Roots of Quadratic Equations | Discriminates

45. ANS: C

If b2

− 4ac < 0, then the roots are complex.

Feedback

A Did you use the correct order of operations while evaluating the discriminant?

B Did you use the correct formula for the discriminant?

C Correct!

D Did you check the sign of the answer?


OBJ: 5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.


TOP: Use the discriminant to determine the number and types of roots of a quadratic equation.

KEY: Quadratic Equations | Roots of Quadratic Equations | Discriminates

ID: A

16

46. ANS: C

The vertex form of a quadratic function is y = a(x − h)2

+ k .

The equation of the axis of symmetry of a parabola is x = h.

Feedback

A Did you use the correct equation of the axis of symmetry?

B Did you check the x-coordinate of the vertex?

C Correct!

D Did you identify the coordinates of the vertex correctly?


OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k.


TOP: Analyze quadratic functions in the form y = a(x - h)^2 + k.

KEY: Quadratic Functions | Axis of Symmetry

47. ANS: A

Graph the related quadratic equation. Because the inequality symbol is >, the parabola should be dashed. Test

a point (x1 , y1) inside the parabola. If (x1 , y1) is the solution of the inequality, shade the region inside the

parabola. If (x1 , y1) is not a solution, shade the region outside the parabola.

Feedback

A Correct!

B What is the inequality symbol used in the equation?

C Did you test a point inside the parabola correctly?

D Did you shade correctly?


OBJ: 5-8.1 Graph quadratic inequalities in two variables. NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3

STA: 4.3.12 B.1 TOP: Graph quadratic inequalities in two variables.

KEY: Quadratic Inequalities | Graph Quadratic Inequalities

48. ANS: A

Graph the related quadratic equation. Since the inequality symbol is <, the parabola should be dashed. Test a

point (x1 , y1) inside the parabola. If (x1 , y1) is the solution of the inequality, shade the region inside the

parabola. If (x1 , y1) is not a solution, shade the region outside the parabola.

Feedback

A Correct!

B Did you test a point inside the parabola correctly?

C Did you shade correctly?

D What is the inequality symbol used in the equation?


OBJ: 5-8.1 Graph quadratic inequalities in two variables. NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3

STA: 4.3.12 B.1 TOP: Graph quadratic inequalities in two variables.

KEY: Quadratic Inequalities | Graph Quadratic Inequalities

ID: A

17

49. ANS: C

Find the product of the given numbers. Find the square root of the product.

Feedback

A How do you find the geometric mean?

B Remember to take the square root of the product.

C Correct!

D This is the arithmetic mean not geometric mean.


OBJ: 8-1.1 Find the geometric mean between two numbers. NAT: NCTM GM.1 | NCTM GM.1b

TOP: Find the geometric mean between two numbers. KEY: Geometric Mean

50. ANS: D

Find the product of the given numbers. Find the square root of the product.

Feedback

A This is the arithmetic mean not geometric mean.

B How do you find the geometric mean?

C Remember to take the square root of the product.

D Correct!


OBJ: 8-1.1 Find the geometric mean between two numbers. NAT: NCTM GM.1 | NCTM GM.1b

TOP: Find the geometric mean between two numbers. KEY: Geometric Mean

51. ANS: A

The altitude is the geometric mean between the measures of the two segments of the hypotenuse.

Feedback

A Correct!

B This is the arithmetic mean not geometric mean.

C How do you find the geometric mean?

D Remember to take the square root of the product.


OBJ: 8-1.2 Solve problems involving relationships between parts of a right triangle and the altitude

hypotenuse. NAT: NCTM GM.1 | NCTM GM.1b STA: 4.2.12 E.1

TOP: Solve problems involving relationships between parts of a right triangle and the altitude hypotenuse.

KEY: Triangles | Altitudes | Hypotenuse

ID: A

18

52. ANS: B

The sum of the squares of the two sides is equal to the square of the hypotenuse.

Feedback

A Remember to square the numbers.

B Correct!

C Remember to find the square root.

D Which side is the hypotenuse?


OBJ: 8-2.1 Use the Pythagorean Theorem. NAT: NCTM GM.1 | NCTM GM.1b

STA: 4.2.12 A.1 | 4.2.12 E.1 TOP: Use the Pythagorean Theorem.

KEY: Pythagorean Theorem

53. ANS: B

Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter

sides is equal to the square of the third side, the triangle is a right triangle.

Feedback

A What is the converse of the Pythagorean Theorem?

B Correct!

C Check the Pythagorean Theorem.

D Check the Pythagorean Theorem.


OBJ: 8-2.2 Use the converse of the Pythagorean Theorem. NAT: NCTM GM.1 | NCTM GM.1b

STA: 4.2.12 A.1 | 4.2.12 E.1 TOP: Use the converse of the Pythagorean Theorem.

KEY: Converse of Pythagorean Theorem

54. ANS: A

Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter

sides is equal to the square of the third side, the triangle is a right triangle.

Feedback

A Correct!

B Check the Pythagorean Theorem.

C What is the converse of the Pythagorean Theorem?

D Check the Pythagorean Theorem.


OBJ: 8-2.2 Use the converse of the Pythagorean Theorem. NAT: NCTM GM.1 | NCTM GM.1b

STA: 4.2.12 A.1 | 4.2.12 E.1 TOP: Use the converse of the Pythagorean Theorem.

KEY: Converse of Pythagorean Theorem

ID: A

19

55. ANS: C

To find the leg of a 45°-45°-90° triangle when the hypotenuse is given, divide the hypotenuse by 2 . To

find the perimeter of the square, find the sum of all the sides.

Feedback

A This is the area, not the perimeter of the square.

B Is the number given the length of a side or the diagonal?

C Correct!

D Before the perimeter can be found, first find the length of each side.


OBJ: 8-3.1 Use properties of 45º-45º-90º triangles. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 E.1 TOP: Use properties of 45º-45º-90º triangles.

KEY: Triangles | 45-45-90 Triangles

56. ANS: D

The length of the hypotenuse is equal to the length of a leg times 2 . The diagonal of a square bisects the

angle.

Feedback

A Multiply by the square root of two to find the length of the hypotenuse.

B Check the length of the hypotenuse and the size of the angle.

C The diagonal of a square bisects the angle.

D Correct!





57. ANS: D

The shorter leg is half the length of the hypotenuse. The longer leg is 3 times the length of the shorter leg.

Feedback

A How do you find the length of the side opposite the 60° angle?

B Switch the x and y values.

C How do you find the length of the side opposite the 30° angle?

D Correct!





ID: A

20

58. ANS: D

The shorter leg is half the length of the hypotenuse. The longer leg is 3 times the length of the shorter leg.

Feedback

A Switch the x and y values.

B How do you find the length of the side opposite the 60° angle?

C How do you find the length of the side opposite the 30° angle?

D Correct!





59. ANS: B

In trigonometry, you can find the measure of an angle by using the inverse of sine, cosine, or tangent.

Feedback

A Which trigonometric ratio should be used?

B Correct!

C This is the ratio not the angle.

D Which trigonometric ratio should be used?


OBJ: 8-4.1 Find trigonometric ratios using right triangles. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 E.1 TOP: Find trigonometric ratios using right triangles.

KEY: Trigonometric Ratios | Right Triangles

60. ANS: C

Determine the ratio associated with the given trigonometric term. Divide the numerator by the denominator.

Feedback

A Check the setup of the ratio.

B Which trigonometric ratio are you asked to find?

C Correct!

D Which trigonometric ratio are you asked to find?


OBJ: 8-4.1 Find trigonometric ratios using right triangles. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 E.1 TOP: Find trigonometric ratios using right triangles.

KEY: Trigonometric Ratios | Right Triangles

ID: A

21

61. ANS: C

Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the

numbers given. Solve for the answer.

Feedback

A Check the trigonometric ratio.

B Which trigonometric ratio should be used?

C Correct!



OBJ: 8-4.2 Solve problems using trigonometric ratios. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 E.1 TOP: Solve problems using trigonometric ratios.

KEY: Trigonometric Ratios | Solve Problems

62. ANS: A



Feedback

A Correct!

B Check the trigonometric ratio.

C Which trigonometric ratio should be used?






63. ANS: B



Feedback

A Remember to include the initial height of two miles.

B Correct!

C Which trigonometric ratio should be used?






ID: A

22

64. ANS: C



Feedback

A Do not subtract the initial height of the balloon.

B Remember to include the initial height of one mile.

C Correct!






65. ANS: A



Feedback

A Correct!

B Do not use the cosine ratio.

C What is the sine ratio?

D What is the sine ratio?


OBJ: 8-5.1 Solve problems involving angles of elevation. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 A.1 | 4.2.12 E.1 TOP: Solve problems involving angles of elevation.

KEY: Angle of Elevation

66. ANS: C



Feedback

A Did you use the inverse sine to solve.

B Do not use the tangent ratio.

C Correct!

D Do not use the cosine ratio.





ID: A

23

67. ANS: D



Feedback

A Do not use inverse sine to solve.


C Do not use the tangent ratio.

D Correct!





68. ANS: A



Feedback

A Correct!


C Do not add together the numbers given.

D Do not subtract the numbers given.


OBJ: 8-5.2 Solve problems involving angles of depression. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 A.1 | 4.2.12 E.1 TOP: Solve problems involving angles of depression.

KEY: Angle of Depression

69. ANS: B



Feedback

A Do not use the tangent ratio.

B Correct!

C Do not use the cosine ratio.

D Do not use the tangent ratio.


OBJ: 8-5.2 Solve problems involving angles of depression. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 A.1 | 4.2.12 E.1 TOP: Solve problems involving angles of depression.

KEY: Angle of Depression

ID: A

24

70. ANS: B

Substitute the given values into the Law of Sines. Cross multiply. Divide each side by sinL.

Feedback

A Remember to divide both sides by the sine of angle L.

B Correct!

C Check the setup of the proportion.

D Check the Law of Sines to determine the setup of the ratios.


OBJ: 8-6.1 Use the Law of Sines to solve triangles. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 E.1 | 4.5.12 E.1 TOP: Use the Law of Sines to solve triangles.

KEY: Law of Sines | Solve Triangles

71. ANS: C

Substitute the given values into the Law of Sines. Cross multiply. Divide each side by the length of side l.

Feedback

A Check the Law of Sines to determine the setup of the ratios.

B Remember to take the inverse of sine to solve for the angle.

C Correct!

D Remember to divide both sides by the length of side l.


OBJ: 8-6.1 Use the Law of Sines to solve triangles. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 E.1 | 4.5.12 E.1 TOP: Use the Law of Sines to solve triangles.

KEY: Law of Sines | Solve Triangles

72. ANS: D

Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the

missing side. Find the perimeter.

Feedback

A This is the sum of the other two angles of the triangle.

B This is the length of one side of the triangle.

C Remember to include all three sides.

D Correct!


OBJ: 8-6.2 Solve problems by using the Law of Sines. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 E.1 | 4.5.12 E.1 TOP: Solve problems by using the Law of Sines.

KEY: Law of Sines | Solve Problems

ID: A

25

73. ANS: A

Substitute the given values into the Law of Cosines. Simplify the equation. Find the square root of both sides.

Feedback

A Correct!

B Check the equation for the Law of Cosines.

C Should sine or cosine be used to solve the problem?

D Remember to find the square root of this number.


OBJ: 8-7.1 Use the Law of Cosines to solve triangles. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 E.1 | 4.5.12 E.1 TOP: Use the Law of Cosines to solve triangles.

KEY: Law of Cosines | Solve Triangles

74. ANS: D

Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated

angle by using inverse cosine.

Feedback

A Remember to find the inverse cosine.

B Do not subtract the angle from 180.

C Check the work for this equation.

D Correct!


OBJ: 8-7.1 Use the Law of Cosines to solve triangles. NAT: NCTM GM.1 | NCTM GM.1d

STA: 4.2.12 E.1 | 4.5.12 E.1 TOP: Use the Law of Cosines to solve triangles.

KEY: Law of Cosines | Solve Triangles

75. ANS: A



Feedback

A Correct!

B Which angle goes with each vertex?

C Which angle goes with each vertex?

D The triangle is not equilateral.


OBJ: 8-7.2 Solve problems by using the Law of Cosines.

NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 STA: 4.2.12 E.1 | 4.5.12 E.1

TOP: Solve problems by using the Law of Cosines. KEY: Law of Cosines | Solve Problems

ID: A

26

76. ANS: A



Feedback

A Correct!








77. ANS: A



Feedback

A Correct!








78. ANS: A



Feedback

A Correct!








ID: A

27

79. ANS: A



Feedback

A Correct!

B Use the cosine ratio not sine ratio to solve.

C Use the cosine ratio not the tangent ratio to solve.






80. ANS: A



Feedback

A Correct!

B Use the cosine ratio not sine ratio to solve.

C Use the cosine ratio not the tangent ratio to solve.






81. ANS: A

diameter = 2 × radius

Circumference = (2 × radius × π) or (diameter × π)

Feedback

A Correct!

B Check your circumference calculation.

C Check your diameter calculation.

D Check both your diameter and circumference calculations.


OBJ: 10-1.1 Identify and use parts of circles. NAT: NCTM ME.2

STA: 4.2.12 A.3 TOP: Identify and use parts of circles. KEY: Circles | Parts of Circles

ID: A

28

82. ANS: C

radius = diameter ÷ 2

Circumference = (2 × radius × π) or (diameter × π)

Feedback

A Check both your radius and circumference calculations.

B Check your circumference calculation.

C Correct!

D Check your radius calculation.


OBJ: 10-1.1 Identify and use parts of circles. NAT: NCTM ME.2

STA: 4.2.12 A.3 TOP: Identify and use parts of circles. KEY: Circles | Parts of Circles

83. ANS: B

The circumference formula is diameter × π. The diameter shown also happens to be the hypotenuse of the

right triangle inscribed in the circle, so it can be found by using the Pythagorean Theorem.

Feedback

A Use the Pythagorean Theorem.

B Correct!

C How did you find the diameter?

D Use the Pythagorean Theorem.


OBJ: 10-1.2 Solve problems involving the circumference of a circle.

NAT: NCTM GM.1 | NCTM GM.1a | NCTM ME.2 STA: 4.5.12 E.1

TOP: Solve problems involving the circumference of a circle. KEY: Circles | Circumference

84. ANS: A

The circumference formula is diameter × π. The diameter shown also happens to be the diagonal of a square,

so it can be found by multiplying the side of the square by 2 .

Feedback

A Correct!

B Check your diameter again.

C You need a 2 in your answer.

D You need to double your radius.


OBJ: 10-1.2 Solve problems involving the circumference of a circle.

NAT: NCTM GM.1 | NCTM GM.1a | NCTM ME.2 STA: 4.5.12 E.1

TOP: Solve problems involving the circumference of a circle. KEY: Circles | Circumference

ID: A

29

85. ANS: C

∠BAC forms a linear pair with ∠CAD, so their sum is 180.

Feedback

A Check your subtraction.

B How many degrees are in a linear pair?

C Correct!

D Check your subtraction.


OBJ: 10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.

TOP: Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.

KEY: Major Arcs | Minor Arcs | Semicircles | Central Angles

86. ANS: A

∠BAF is a vertical angle with ∠BAC, so they are congruent.

Feedback

A Correct!

B Remember vertical angles.

C How are vertical angles related?

D Remember vertical angles.





87. ANS: B

∠EAD is a right angle, so its measure is 90.

Feedback

A It's a right angle.

B Correct!

C It's a right angle.

D What is the measure of a right angle?





ID: A

30

88. ANS: B

∠FAE is complementary with ∠BAF.

Feedback

A Did you subtract carefully?

B Correct!

C With what angle is it complementary?

D What is the measure of angle BAE?





89. ANS: D

∠CAE is equal to the sum of ∠CAD and ∠EAD.

Feedback

A Add the two angles that make up this angle.

B Add the two angles that make up this angle.

C What is the measure of angle DAE?

D Correct!





90. ANS: C

∠DAF is equal to the sum of ∠DAE and ∠FAE..

Feedback

A Add the two angles that make up this angle.

B Add the two angles that make up this angle.

C Correct!

D What two angles did you add together?





ID: A

31

91. ANS: A

∠PRS and ∠QRT are vertical angles and are therefore congruent. So, set the two expressions equal and solve

for x.

Feedback

A Correct!

B That's the answer for x, you need the measure of ∠PRS .

C Did you use vertical angles?

D How are vertical angles related?





92. ANS: A

∠PRS and ∠QRT are vertical angles and are therefore congruent. So, set the two expressions equal and solve

for x.

Feedback

A Correct!

B That's the answer for x, you need the measure of ∠QRT.

C How are vertical angles related?

D Did you use vertical angles?





93. ANS: A

∠PRQ and ∠QRT are a linear pair and are therefore supplementary. First find m∠QRT. ∠PRS and ∠QRT

are vertical angles and are therefore congruent. So, set the two expressions equal and solve for x.

Feedback

A Correct!

B That's the answer for x, you need the measure of ∠PRQ.

C Check over your work.

D How many degrees are in a linear pair?





ID: A

32

94. ANS: A

∠SRT and ∠PRS are a linear pair and are therefore supplementary. First find m∠PRS . ∠PRS and ∠QRT are

vertical angles and are therefore congruent. So, set the two expressions equal and solve for x.

Feedback

A Correct!

B That's the answer for x, you need the measure of ∠SRT.

C Did you use vertical angles?

D Did you use a linear pair?





95. ANS: B

Since the diameters EC and AB are perpendicular, they form right angles which measure 90. Additionally,

since ∠BOD ≅ ∠DOE ≅ ∠EOF ≅ ∠FOA, all of those angles are 1

290°( ) which is 45°. The measure of an arc

is equal to the measure of its central angle, so add any angles that are necessary to find the measure of the

given angle and its intercepted arc.

Feedback

A What are the measures of the four smaller angles?

B Correct!

C All large angles are 90° and small ones are 45°.

D All large angles are 90° and small ones are 45°.

PTS: 1 DIF: Average REF: Lesson 10-2 OBJ: 10-2.2 Find arc length.

NAT: NCTM GM.1 | NCTM GM.1b STA: 4.2.12 A.3 TOP: Find arc length.

KEY: Arcs | Arc Length

96. ANS: D

Since BE is a diameter, m∠BFA + m∠AFE = 180. Solve the equation, then substitute the value of x to find

m∠BFA. Since ∠BFA and ∠EFC are vertical angles, they are congruent. Additionally, use the fact that

m arc DC = m∠CFD =1

2m∠CFE =

1

2m∠BFA.

Feedback

A m∠BFA + m∠AFE = 180

B Did you make use of vertical angles?

C Did you solve for x?

D Correct!

PTS: 1 DIF: Average REF: Lesson 10-2 OBJ: 10-2.2 Find arc length.

NAT: NCTM GM.1 | NCTM GM.1b STA: 4.2.12 A.3 TOP: Find arc length.

KEY: Arcs | Arc Length

ID: A

33

97. ANS: B

Since AF, EF and AE form a right triangle, you can use the Pythagorean Theorem to find mEF. Since CF is

a segment that passes through the center of the circle and is perpendicular to chord EG, it also bisects EG.

That means mEG = 2 × mEF.

Feedback

A You need to double the length of EF.

B Correct!

C The hypotenuse is not the solution.

D Use the other leg of triangle AFE.


OBJ: 10-3.1 Recognize and use relationships between arcs and chords.

NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2 STA: 4.2.12 A.3

TOP: Recognize and use relationships between arcs and chords.

KEY: Arcs | Chords | Diameters

98. ANS: B

Since UQ and US are congruent and perpendicular to separate chords, the chords PR and TR must also be

congruent. Additionally, UQ and US bisect these chords, so TS = RS. So take the given measure of TS and

double it. That will be the measure of TR and also PR.

Feedback

A What is the relationship between PR and TS?

B Correct!

C Isn't PR longer than TS?

D What is the relationship between PR and TS?


OBJ: 10-3.1 Recognize and use relationships between arcs and chords.


TOP: Recognize and use relationships between arcs and chords.

KEY: Arcs | Chords | Diameters

ID: A

34

99. ANS: A

The measure of BC is 2 × m∠BDC. Since the full circle measures 360, then mAD is

360 – (mAB + mBC + mCD). Finally, since ∠1 is an inscribed angle for AD, its measure is 1

2mAD.

Feedback

A Correct!

B Focus on AD.

C Can you find the measure of AD?

D Inscribed angles are half the measure of the arc.


OBJ: 10-4.1 Find measures of inscribed angles.


TOP: Find measures of inscribed angles. KEY: Inscribed Angles | Measure of Inscribed Angles

100. ANS: D

m∠B = 90 since it is inscribed in a semicircle. Since the sum of the angles in any triangle is 180°,

m∠1 + m∠2 = 90. Substitute the given values for ∠1 and ∠2 into that equation. Then substitute the value

found for x into the expression for ∠1.

Feedback

A You are looking for ∠1.

B ∠1 + ∠2 = 90°.

C Did you find the value of x?

D Correct!


OBJ: 10-4.1 Find measures of inscribed angles.


TOP: Find measures of inscribed angles. KEY: Inscribed Angles | Measure of Inscribed Angles

101. ANS: D

m∠BCE = m∠BCA + m∠ACE, so begin by finding the measures of ∠BCA and ∠ACE. Since ∆ABC and

∆AEC are both inscribed in semicircles, they are right triangles (∠B and ∠E are right angles). Additionally,

since AB ≅ CB, ∆ABC is isosceles. That makes m∠BCA = 45. Now for ∠ACE. Since ∠CAE is an inscribed

angle, its measure is one-half its intercepted arc (arc CE). That makes ∠ACE = 90° − ∠CAE. Finally, add the

measures of the two angles to get the final answer.

Feedback

A How do you find the measure of and inscribed angle?

B ∆ABC is an isosceles right triangle; ∠ACE = 90° − ∠CAE.

C Did you subtract carefully when finding the measure of ∠CAE?

D Correct!


OBJ: 10-4.2 Find measures of angles of inscribed polygons. NAT: NCTM GM.1 | NCTM GM.1a

STA: 4.2.12 A.3 TOP: Find measures of angles of inscribed polygons.

KEY: Inscribed Polygons | Measure of Inscribed Angles

ID: A

35

102. ANS: D

First note that m arc BC = m∠BZC because a central angle of a circle is always congruent to its intercepted

arc. Secondly, m∠BAC is one-half m arc BC, as the measure of an inscribed angle is half the measure of its

intercepted arc. Since AB Ä DC, ∠DCA ≅ ∠BAC because alternate interior angles are congruent. So

m∠DCA = m∠BAC.

Feedback

A Look for alternate interior angles.

B Look for alternate interior angles.

C Did you find the measure of ∠BAC?.

D Correct!


OBJ: 10-4.2 Find measures of angles of inscribed polygons. NAT: NCTM GM.1 | NCTM GM.1a

STA: 4.2.12 A.3 TOP: Find measures of angles of inscribed polygons.

KEY: Inscribed Polygons | Measure of Inscribed Angles

103. ANS: C

The triangle shown is a right triangle since the tangent segment, CB, intersects a radius, AB, which always

results in a right angle. So to solve for x, use the Pythagorean Theorem.

Feedback

A Did you use the Pythagorean Theorem?

B Use the Pythagorean Theorem.

C Correct!

D Is the triangle a right triangle?

PTS: 1 DIF: Average REF: Lesson 10-5 OBJ: 10-5.1 Use properties of tangents.

NAT: NCTM GM.1 | NCTM GM.1a STA: 4.2.12 A.3 TOP: Use properties of tangents.

KEY: Tangents

104. ANS: B

The triangle shown is a right triangle since the tangent segment, FE, intersects a radius, DE, which always

results in a right angle. So to solve for x, use the Pythagorean Theorem. Note that mDE = x since they are

both radii of the same circle.

Feedback

A Use the Pythagorean Theorem and mDE = x.

B Correct!

C Is the triangle a right?

D Use the Pythagorean Theorem and mDE = x.

PTS: 1 DIF: Average REF: Lesson 10-5 OBJ: 10-5.1 Use properties of tangents.

NAT: NCTM GM.1 | NCTM GM.1a STA: 4.2.12 A.3 TOP: Use properties of tangents.

KEY: Tangents

ID: A

36

105. ANS: B

Recall that two tangents from the same external point are congruent. So, for example, mHN = mHJ and

mKJ = mKL. Those two equalities, plus the fact that mHK = mHJ + mJK allows us to make the equality

mHK = mHN + mKL. Substitute the appropriate values into that equation and solve for x.

Feedback

A Are two tangents to a circle from the same external point congruent?

B Correct!

C The mKJ = mKL and mHN = mHJ .

D The mKJ = mKL and mHN = mHJ .


OBJ: 10-5.2 Solve problems involving circumscribed polygons.


TOP: Solve problems involving circumscribed polygons. KEY: Circumscribed Polygons

106. ANS: A

Recall that two tangents from the same external point are congruent. So, for example, mPW = mPQ and

mRQ = mRS . Those two equalities, plus the fact that mPR = mPQ + mRQ, lead us to the equation

mPR = mPW + mRS . Substitute the appropriate values into this equation and solve for x.

Feedback

A Correct!

B Are two tangents to a circle from the same external point congruent?

C PW=PQ and RQ=RS.

D PW=PQ and RQ=RS.


OBJ: 10-5.2 Solve problems involving circumscribed polygons.


TOP: Solve problems involving circumscribed polygons. KEY: Circumscribed Polygons

107. ANS: B

When two secants intersect in the interior of a circle, then the measure of an angle formed by this intersection

is equal to one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Feedback

A Did you add the intercepted arcs?

B Correct!

C Add the intercepted arcs and divide by 2.

D Did you divide correctly?


OBJ: 10-6.1 Find measures of angles formed by lines intersecting on or inside a circle.


TOP: Find measures of angles formed by lines intersecting on or inside a circle.

KEY: Measure of Angles | Circles

ID: A

37

108. ANS: B


is equal to one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Feedback

A What is the relationship between the two angles formed when two secants intersect in

the interior of a circle?

B Correct!


D Be careful with division.






109. ANS: C


is equal to one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. In this

diagram, the measure of one of the intercepted arcs for ∠5 is not given, but it can be found since the sum of

all of the arcs must be 360. Subtracting the sum of the other 3 arcs from 360, leaves 110.

Feedback

A Did you use the correct arcs?

B Add the intercepted arcs and divide by 2.

C Correct!

D Did you find the measure of the unlabeled arc?






ID: A

38

110. ANS: A



diagram, the measures of the intercepted arcs for ∠3 are not given, but they must have a sum of 120° since

the arcs shown have a sum of 240 (360 – 240 = 120).

Feedback

A Correct!

B Did you use the correct arcs?


D Did you divide correctly?






111. ANS: B



diagram, the measures of the intercepted arcs for ∠6 are not given, but they have a sum of 250 since the arcs

shown have a sum of 110 (360 – 110 = 250).

Feedback

A Add the intercepted arcs and divide by 2.

B Correct!

C Did you divide correctly?

D How do you find the measures of the other two arcs?






ID: A

39

112. ANS: A



diagram the measures of the intercepted arcs for ∠4 are not given. However, the full circle measures 360°, so

3a° + 4a° +6a° +7a° = 360°. Solving this equation, a = 18. So the intercepted arcs for ∠4 are 54° and 108°.

Feedback

A Correct!

B What is the sum of the measures of the arcs intercepted by ∠4 and its vertical angle?


D Did you find the value of a?






113. ANS: D



diagram the measures of the intercepted arcs for ∠7 are not given. However, the full circle measures 360°, so

2x° + 2x° +4x° +4x° = 360°. Solving this equation, x = 30°. So the intercepted arcs for ∠7 are 60° and 120°.

Feedback

A What are the measures of the intercepted arcs of ∠7 and its vertical angle?

B Did you find the value of x?.


D Correct!






ID: A

40

114. ANS: D

When a secant intersects a tangent at the point of tangency, then the measure of the angle formed is one-half

the measure of the intercepted arc. In this diagram, the measure of the intercepted arc for ∠8 is 220.

Feedback

A How is the measure of the angle related to the measure of the intercepted arc?

B Find half the measure of the intercepted arc.

C Should you have divided by two?

D Correct!






115. ANS: C


the measure of the intercepted arc. In this diagram, the measure of the intercepted arc for ∠9 is 180 because

the chord is also a diameter of the circle.

Feedback

A Find half the measure of the intercepted arc.

B Should you have divided by two?

C Correct!

D Find half the measure of the intercepted arc.






116. ANS: A


the measure of the intercepted arc. In this diagram, the measure of the intercepted arc for ∠10 is 140 since

360 – 220 = 140.

Feedback

A Correct!

B Find half the measure of the intercepted arc.

C How are the measures of the angle and the intercepted arc related?

D Find half the measure of the intercepted arc.






ID: A

41

117. ANS: C

When two secants intersect in the exterior of a circle, then the measure of the angle formed is equal to

one-half the positive difference of the measures of the intercepted arcs.

Feedback


B Use subtraction, not addition.

C Correct!

D Did you subtract carefully?


OBJ: 10-6.2 Find measures of angles formed by lines intersecting outside the circle.


TOP: Find measures of angles formed by lines intersecting outside the circle.


118. ANS: B



Feedback


B Correct!

C Use subtraction, not addition.

D Did you find one-half of the positive difference?






119. ANS: D



Feedback

A What is the measure of the intercepted arc nearest the angle?

B Check your subtraction.

C Check your subtraction.

D Did you find the positive difference of the measures of the intercepted arcs?






ID: A

42

120. ANS: A



Feedback

A Correct!

B What is the measure of the other intercepted arc?


D Did you find the positive difference of the measures of the intercepted arcs?






121. ANS: A



Feedback

A Correct!

B Did you take one-half of the positive difference of the measures of the intercepted arcs?


D Did you subtract carefully?






122. ANS: D



Feedback

A How are the angle and the intercepted arcs related?


C Did you subtract carefully?

D Correct!






ID: A

43

123. ANS: A

When a secant and tangent intersect in the exterior of a circle, then the measure of the angle formed is equal

to one-half the positive difference of the measures of the intercepted arcs.

Feedback

A Correct!

B Did you subtract carefully?

C What is the relationship between the angle and the intercepted arcs?







124. ANS: C



Feedback

A What is the relationship between the angle and the intercepted arcs?


C Correct!







125. ANS: D



Feedback



C Were you careful with subtraction?

D Correct!






ID: A

44

126. ANS: C



Feedback


B Did you subtract carefully?

C Correct.







127. ANS: D

The products of the segments for each intersecting chord are equal.

Feedback

A Use multiplication, not addition.

B Multiply the segments and set them equal to each other.

C Multiply the segments and set them equal to each other.

D Correct!


OBJ: 10-7.1 Find measures of segments that intersect in the interior of a circle.


TOP: Find measures of segments that intersect in the interior of a circle.

KEY: Circles | Interior of Circles

128. ANS: A


Feedback

A Correct!

B Use multiplication, not addition.


D Multiply the segments and set them equal to each other.






ID: A

45

129. ANS: C


Feedback



C Correct!







130. ANS: B


Feedback


B Correct!








131. ANS: C


Feedback



C Correct!







ID: A

46

132. ANS: A


Feedback

A Correct!









133. ANS: B


Feedback

A Multiply the segments and set them equal to each other.

B Correct!








134. ANS: D


Feedback

A Did you factor correctly?


C Use multiplication, not addition.

D Correct!






ID: A

47

135. ANS: A


Feedback

A Correct!

B Use multiplication, not addition.








136. ANS: D


Feedback

A Multiply the segments and set them equal to each other.

B Did you factor correctly?

C Use multiplication, not addition.

D Correct!






137. ANS: D

When a secant segment and a tangent segment intersect in the exterior of a circle, set the product of each

external part of the secant segment and the entire secant segment equal to the square of the tangent segment.

Feedback

A Check your multiplication.

B You need to multiply, not add.

C Check the segments in your multiplication.

D Correct!


OBJ: 10-7.2 Find measures of segments that intersect in the exterior of a circle.

NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2 STA: 4.2.12 A.3

TOP: Find measures of segments that intersect in the exterior of a circle.

KEY: Circles | Exterior of Circles

ID: A

48

138. ANS: A



Feedback

A Correct!

B Check the segments in your multiplication.

C You need to multiply, not add.

D Check your multiplication.






139. ANS: B



Feedback

A Check the segments in your multiplication.

B Correct!








140. ANS: A



Feedback

A Correct!









ID: A

49

141. ANS: D



Feedback


B Check your multiplication.


D Correct!






142. ANS: A

When two secant segments intersect in the exterior of a circle, set an equality between the product of each

external segment and the entire segment.

Feedback

A Correct!


C Check the segments in your multiplication.

D You need to multiply, not add.






143. ANS: A



Feedback

A Correct!



D Check the segments in your multiplication.






ID: A

50

144. ANS: C



Feedback

A Check your multiplication.


C Correct!







145. ANS: D


external segment and the entire segment. .

Feedback


B You need to multiply, not add.

C Check your multiplication.

D Correct!






146. ANS: D



Feedback

A You need to multiply, not add.


C Check your multiplication.

D Correct!






ID: A

51

147. ANS: A

The equation of a circle is (x − h)2

+ (y − k)2

= r2 where (h, k) is the center and r is the radius. In this

problem, the center is given, but not the radius. The radius is one-half the diameter, so first divide the given

diameter by 2 to get the radius.

Feedback

A Correct!

B You need to square the radius, not the diameter.

C You need the opposite signs on your center coordinates.

D You need the opposite signs on your center coordinates and you need to square the

radius, not the diameter.


OBJ: 10-8.1 Write the equation of a circle. NAT: NCTM GM.2 | NCTM GM.2a

STA: 4.5.12 E.1 TOP: Write the equation of a circle. KEY: Circles | Equation of Circles

148. ANS: C

The equation of a circle is (x − h)2

+ (y − k)2

= r2 where (h, k) is the center and r is the radius. The center is

the midpoint of the endpoints of the diameter. Use the distance formula to find the diameter, which is the

distance between the endpoints. The radius is one-half the diameter, so the divide the diameter by 2 to get the

radius.

Feedback

A You need the opposite signs on your center coordinates and you need to square the

radius, not the diameter.

B You need the opposite signs on your center coordinates.

C Correct!

D You need to square the radius, not the diameter.


OBJ: 10-8.1 Write the equation of a circle. NAT: NCTM GM.2 | NCTM GM.2a

STA: 4.5.12 E.1 TOP: Write the equation of a circle. KEY: Circles | Equation of Circles

149. ANS: A

The graph of an equation of the form x2

+ y2

= r2 will be a circle centered at (0, 0) and with radius r.

Feedback

A Correct!

B Check your radius.

C Check your radius.

D Check your radius.


OBJ: 10-8.2 Graph a circle on the coordinate plane.

NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 STA: 4.5.12 E.1

TOP: Graph a circle on the coordinate plane.

KEY: Circles | Graph Circles | Coordinate Plane

ID: A

52

150. ANS: D

The graph of an equation of the form (x − h)2

+ (y − k)2

= r2 will be a circle centered at (h,k) and with radius

r.

Feedback

A Check the signs of your center coordinates.

B Reverse your center coordinates.

C Check the signs of your center coordinates and reverse the x and y coordinates.

D Correct!


OBJ: 10-8.2 Graph a circle on the coordinate plane.

NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3 STA: 4.5.12 E.1

TOP: Graph a circle on the coordinate plane.

KEY: Circles | Graph Circles | Coordinate Plane

ID: A Accelerated Geometry/Algebra 2 Final Exam Review 2015 [Answer Strip]

_____ 1.D

_____ 2.A

_____ 3.B

_____ 4.B

_____ 5.C

_____ 6.C

_____ 7.D

_____ 8.B

_____ 9.C

_____ 10.D

_____ 11.D

_____ 12.A

_____ 13.A

_____ 14.A

_____ 15.A

_____ 16.C


_____ 17.B

_____ 18.C

_____ 19.D

_____ 20.B

_____ 21.A _____ 22.D _____ 23.D


_____ 24.D

_____ 25.A

_____ 26.B

_____ 27.B

_____ 28.A

_____ 29.A

_____ 30.C

_____ 31.A

_____ 32.A

_____ 33.B

_____ 34.B

_____ 35.C

_____ 36.D

_____ 37.A

_____ 38.D

_____ 39.A

_____ 40.A

_____ 41.D

_____ 42.D

_____ 43.D

_____ 44.C

_____ 45.C

_____ 46.C _____ 47.A


_____ 48.A

_____ 49.C

_____ 50.D

_____ 51.A

_____ 52.B

_____ 53.B

_____ 54.A

_____ 55.C

_____ 56.D

_____ 57.D

_____ 58.D

_____ 59.B

_____ 60.C

_____ 61.C

_____ 62.A

_____ 63.B

_____ 64.C

_____ 65.A

_____ 66.C

_____ 67.D

_____ 68.A

_____ 69.B

_____ 70.B

_____ 71.C

_____ 72.D

_____ 73.A

_____ 74.D

_____ 75.A

_____ 76.A


_____ 77.A

_____ 78.A

_____ 79.A

_____ 80.A

_____ 81.A

_____ 82.C

_____ 83.B

_____ 84.A

_____ 85.C

_____ 86.A

_____ 87.B

_____ 88.B

_____ 89.D

_____ 90.C

_____ 91.A

_____ 92.A

_____ 93.A

_____ 94.A

_____ 95.B

_____ 96.D

_____ 97.B

_____ 98.B


_____ 99.A

_____100.D

_____101.D

_____102.D

_____103.C

_____104.B

_____105.B

_____106.A

_____107.B

_____108.B

_____109.C

_____110.A

_____111.B


_____112.A

_____113.D

_____114.D

_____115.C

_____116.A

_____117.C

_____118.B

_____119.D

_____120.A

_____121.A

_____122.D

_____123.A

_____124.C


_____125.D

_____126.C

_____127.D

_____128.A

_____129.C

_____130.B

_____131.C

_____132.A

_____133.B

_____134.D

_____135.A

_____136.D


_____137.D

_____138.A

_____139.B

_____140.A

_____141.D

_____142.A

_____143.A

_____144.C

_____145.D

_____146.D

_____147.A

_____148.C

_____149.A


_____150.D

Documents

Accelerated Geometry/Algebra 2 Final Exam Review 2015...Name: _____ ID: A 4 ____ 13. Graph the system of inequalities showing the feasible region to represent the number of first visits

Accelerated Geometry/Algebra 2 Final Exam Review 2015...Name: _ ID: A 4 13. Graph the system of inequalities showing the feasible region to represent the number of first visits