FINAL R

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1. THE MEASURE OF TWO COMPLEMENTARY ANGLES ARE IN THE RATIO 1 : 5. WHAT ARE THE DEGREE MEASURES OF THE TWO ANGLES?

2

A. B. C. D.

0% 0%

43%

57%

7-1

A. and B. and C. and D. and

3

Cross multiply

Add x

Divide by 6

Answers are 15 and 90 15 = 75

2. THE POLYGONS ARE SIMILAR, BUT NOT NECESSARILY DRAWN TO SCALE. FIND THE VALUE OF X.

4A. B. C. D.

0% 0%

13%

88%

7-1

A

B

D

C

J

K

M

L

84 55

x

A.220B.27.5C.110D.15.8

5

Cross multiply

Divide by 8

Answer is 27.5

3. ARE THE TWO TRIANGLES SIMILAR? HOW DO YOU KNOW?

6A. B. C. D.

0%

38%

50%

13%7-3

° M

º

G

J

H

K

39

39

A.noB.Yes, by

SSSC.Yes, by AAD.Yes, by

SAS

7

Angles at M are vertical angles so

This makes the two triangles similar by AA

4. FIND THE GEOMETRIC MEAN OF THE PAIR OF NUMBERS. 242 AND 8

8A. B. C. D.

63%

0%

13%

25%7-4

A.44B.49C.1872D.54

9

Cross multiply

Take the square root of both sides

Answer is 44

5. WHAT IS THE VALUE OF X, GIVEN THAT ?

10A. B. C. D.

63%

0%

25%

13%7-5

B

A

C

P Q

7

35 40

xA.8B.10C.11D.16

11

Cross multiply

Divide by 35

Answer is 8

6. FIND THE LENGTH OF THE MISSING SIDE. THE TRIANGLE IS NOT DRAWN TO SCALE.

12A. B. C. D.

63%

13%

25%

0%

8-1

17

15

A. B. 64C. 4D.

13

Substitute

Simplify

Subtract 225 from both sides

Take the square root of both sides

Side length is 8.

7. FIND THE LENGTH OF THE LEG. IF YOUR ANSWER IS NOT AN INTEGER, LEAVE IT IN SIMPLEST RADICAL FORM.

14A. B. C. D.

13%

63%

25%

0%

8-2

45°

24

Not drawn to scale

A. B. C. D.

15

The legs of a 45-45-90 triangle are the same.

The hypotenuse is leg *

Divide 24 by

Simplify =

The answer is

8. FIND THE VALUE OF THE VARIABLE(S). IF YOUR ANSWER IS NOT AN INTEGER, LEAVE IT IN SIMPLEST RADICAL FORM.

16

A. B. C. D.

88%

0%

13%

0%

8-2

5 x

60°

10Not drawn to scale

A. B. C. D.2

17

The long leg of a 30-60-90 triangle is the short leg *.

Multiply 5 by

The answer is

9. FIND THE MISSING VALUE TO THE NEAREST HUNDREDTH.

18A. B. C. D.

0% 0%

50%50%

8-3

cos =25

A.23.58o

B.66.42o

C.21.8o

D.63.21o

To find degrees you use the inverse function:

Cos-1() = 66.42182152

The answer is 66.42o

19

10. FIND THE VALUE OF X. ROUND THE LENGTH TO THE NEAREST TENTH.

20A. B. C. D.

13%

25%

38%

25%

8-4

A.42.7 mB.6.5 mC.14.8 mD.6 m

16 mx

Not drawn to scale

21

Use trigonometry to find the missing side.

Set of trig function

Variable is in the top so we multiply by the trig function

Simplify

The answer is 6 m.

11. IN THE DIAGRAM, FIGURE RQTS IS THE IMAGE OF FIGURE DEFC AFTER A RIGID MOTION. NAME THE IMAGE OF ∠F.

22A. B. C. D.

13%

63%

13%13%

9-1

C

D

F

E

T

S

R

S

R

Q

A. ∠TB. ∠RC. ∠QD.∠S

The image of ∠F is ∠S.

23

C

D

F

E

T

S

R

S

R

Q

12. FIND THE IMAGE OF C UNDER THE TRANSLATION DESCRIBED BY THE TRANSLATION RULE .

24A. B. C. D.

0%

13%

38%

50%

9-1

A

B

C

D

E

4 8–4–8 x

4

8

–4

–8

y

A.BB.EC.AD.D

𝑇 ⟨ 4 ,5 ⟩ (𝐶 )

25

A

B

C

D

E

4 8–4–8 x

4

8

–4

–8

y1.

A.BMove C four units to the right.

Then move five units up.

New point is E(-3, -7)

13. FIND THE AREA. THE FIGURE IS NOT DRAWN TO SCALE.

26A. B. C. D.

50%

38%

13%

0%

10-1

36 in.

33 in.40 in.

A.1188 in2

B.69 in2

C.138 in2

D.1440 in2

To find area of a parallelogram:

Base x Height

(36)(33) = 1188

The answer is 1188 in2

27

36 in.

33 in.40 in.

14. FIND THE AREA. THE FIGURE IS NOT DRAWN TO SCALE.

28A. B. C. D.

25%

0%

75%

0%

10-1

2 cm

4.4 cm

A.4.4 cm2

B.6.4 cm2

C.8.8 cm2

D.17.6 cm2

To find area of a triangle:

(Base x Height)

(2)(4.4) = 4.4

The answer is 4.4 cm2

29

2 cm

4.4 cm

15. FIND THE AREA OF THE TRAPEZOID. LEAVE YOUR ANSWER IN SIMPLEST RADICAL FORM.

30A. B. C. D.

25% 25%

50%

0%

10-2

5 cm

9 cm

2 cm

45°

Not drawn to scale

A.31.5 cm2

B.7 cm2

C.81 cm2

D.94.5 cm2

To find area of a trapezoid:

(Sum of Bases)(Height)

(5 + 2 + 5 + 9)(9) = 94.5

The answer is 94.5 cm2

31

5 cm

9 cm

2 cm

45°

Not drawn to scale

16. WHAT IS THE AREA OF THE KITE?

32A. B. C. D.

13% 13%

25%

50%

10-2

2 2

126

ft ft

ftft A.11 ft2

B.72 ft2

C.36 ft2

D.44 ft2

To find area of a kite:

(diagonal 1)(diagonal 2)

(4)(18) = 36

The answer is 36 ft2

33

2 2

126

ft ft

ftft

17. FIND THE AREA OF A REGULAR HEXAGON WITH AN APOTHEM 17.3 MILES LONG AND A SIDE 20 MILES LONG. ROUND YOUR ANSWER TO THE NEAREST TENTH. 

34A. B. C. D.

0%

43%

14%

43%

10-3

A.173.2 mi2

B.2078.5 mi2

C.692.8 mi2

D.1038 mi2

To find area of a polygon:

(apothem)(perimeter)

(17.3)(120) = 1038

The answer is 1038 mi2

35

20 miles

17.3 miles

18. THE WIDTHS OF TWO SIMILAR RECTANGLES ARE 21 FT AND 18 FT. WHAT IS THE RATIO OF THE PERIMETERS? OF THE AREAS?

36

A. B. C. D.

57%

14%

29%

0%

10-4

A.8 : 7 and 64 : 49B.8 : 7 and 49 : 36C.7 : 6 and 64 : 49D.7 : 6 and 49 : 36

Ratio of perimeters is a : b:

Which reduces to:

Ratio of areas is a2 : b2:

Which simplifies to:

37

21 feet18 feet

19. FIND THE SIMILARITY RATIO AND THE RATIO OF PERIMETERS FOR TWO REGULAR PENTAGONS WITH AREAS OF AND .

38A. B. C. D.

43%

0%

14%

43%

10-4

A.4 : 7 ; 4 : 7B.16 : 49 ; 4 : 7C.16 : 49; 16 : 49 D.4 : 7; 16 : 49

Ratio of areas is a2 : b2:

Taking the square root gives you a : b:

Ratio of perimeters is also a : b:

39

𝟏𝟔𝒄𝒎𝟐

𝟒𝟗𝒄𝒎𝟐

20. FIND THE MEASURE OF .THE FIGURE IS NOT DRAWN TO SCALE.

40A. B. C. D.

0%

57%

14%

29%

10-6

B

A

D50°

O

C

35°

E

27°103°

A.188B.182C.162D.172

41

B

A

D50°

O

C

35°

E

27°103°

21. FIND THE CIRCUMFERENCE. LEAVE YOUR ANSWER IN TERMS OF .

42A. B. C. D.

43%

14%14%

29%

10-6

5.7 cm

A. 11.4 cmB. 8.55 cmC. 2.85 cmD.5.7 cm

To find circumference of a circle:

()(radius) or ()(diameter)

()(5.7) = 5.7

The answer is 5.7 cm2

43

5.7 cm

22. FIND THE LENGTH OF . LEAVE YOUR ANSWER IN TERMS OF .

44A. B. C. D.

86%

0%0%

14%10-6

10 m

X

Y

P

A. 30 mB. 15 mC. 5 mD.900 m

To find the length of an arc:

The answer is 15 m.

45

10 m

X

Y

P

23. FIND THE AREA OF THE CIRCLE. LEAVE YOUR ANSWER IN TERMS OF . 

46A. B. C. D.

0% 0%0%0%

10-7

4.1 m

A. 4.2025 cm2B. 8.405 cm2C. 16.81 cm2D.11.2 cm2

90

To find area of a circle:

()(radius)2

()() 2 = 4.2025 The answer is 4.2025 cm2

47

4.1 m

A.None of these

24. THE AREA OF SECTOR AOB IS . FIND THE EXACT AREA OF THE SHADED REGION.

48A. B. C. D.

0% 0%0%0%

10-7

A

OB

9 ft

90

To find area of a segment of a circle:

The answer is ft2

49

A

OB

9 ft

25. FIND THE PROBABILITY THAT A POINT CHOSEN AT RANDOM FROM IS ON THE SEGMENT .

50A. B. C. D.

0% 0%0%0%

10-8

J

0

K L M N O P Q R S T

1 2 3 4 5 6 7 8 9 10

A. B. C. D.

90

51

J

0

K L M N O P Q R S T

1 2 3 4 5 6 7 8 9 10

To find probability:

The answer is

26. USE EULER’S FORMULA TO FIND THE MISSING NUMBER.

FACES: 25VERTICES: 17EDGES: ?

52A. B. C. D.

0% 0%0%0%

11-1

A.43B.40C.39D.41

90

53

Faces + Vertices = Edges + 2

F + V = E + 2

25 + 17 = E + 2 Plug in values

42= E + 2 Simplify

40= E Subtract 2 from both sides

The answer is

27. USE FORMULAS TO FIND THE LATERAL AREA AND SURFACE AREA OF THE GIVEN PRISM. ROUND YOUR ANSWER TO THE NEAREST WHOLE NUMBER.

54

A. B. C. D.

0% 0%0%0%

11-2

4 m4 m

13 m

Not drawn to scaleA. ; B. ; C. ; D. ;

90

55

LA = (perimeter of base)(height)

LA = (34)(4)

LA = 136

4 m4 m

13 m

Not drawn to scale

SA = LA + 2*B

SA = 136 + 2(13*4)

SA = 136 + 104 = 240

28. FIND THE SURFACE AREA OF THE CYLINDER IN TERMS OF .

56A. B. C. D.

0% 0%0%0%

11-2

9 cm

19 cm

Not drawn to scale

A. 504 cm2B. 333 cm2C. 382.5 cm2D.211.5 cm2

90

57

SA =

SA =

SA =

SA =

9 cm

19 cm

Not drawn to scale

29. FIND THE SURFACE AREA OF THE REGULAR PYRAMID SHOWN TO THE NEAREST WHOLE NUMBER.

58A. B. C. D.

0% 0%0%0%

11-3

A. B. C. D.

90

59

SA

SA =

SA =

SA =

SA =

30. FIND THE SURFACE AREA OF THE CONE TO THE NEAREST TENTH.

60A. B. C. D.

0% 0%0%0%

11-3

A. B. C. D.

90

61

SA

SA

SA

SA =

SA =

31. FIND THE VOLUME OF THE GIVEN PRISM. ROUND TO THE NEAREST TENTH IF NECESSARY. 

62A. B. C. D.

0% 0%0%0%

11-4

13.2 cm

6 cm

3.9 cm

Not drawn to scale

A. B. C. D.

90

63

Volume

V

V

V

13.2 cm

6 cm

3.9 cm

Not drawn to scale

32. FIND THE VOLUME OF THE CYLINDER IN TERMS OF .

64A. B. C. D.

0% 0%0%0%

11-4

A. B. C. D.

90

65

Volume

V

V

V

33. FIND THE VOLUME OF THE SQUARE PYRAMID SHOWN. ROUND TO THE NEAREST TENTH IF NECESSARY.

66A. B. C. D.

0% 0%0%0%

11-5

A. B. C. D.

90

67

Volume

V

V

V

34. FIND THE VOLUME OF THE SQUARE PYRAMID SHOWN. ROUND TO THE NEAREST TENTH IF NECESSARY.

68A. B. C. D.

0% 0%0%0%

11-5

A. B. C. D.

90

69

Volume

V

V

35. FIND THE VOLUME OF THE OBLIQUE CONE SHOWN IN TERMS OF .

70A. B. C. D.

0% 0%0%0%

11-5

A. B. C. D.

90

71

Volume

V

V

36. FIND THE SURFACE AREA OF THE SPHERE WITH THE GIVEN DIMENSION. LEAVE YOUR ANSWER IN TERMS OF .

DIAMETER OF 14 CM

72A. B. C. D.

0% 0%0%0%

11-6

A. B. C. D.

90

73

S

SA 14 cm

37. FIND THE VOLUME OF THE SPHERE SHOWN. GIVE EACH ANSWER ROUNDED TO THE NEAREST CUBIC UNIT.

74A. B. C. D.

0% 0%0%0%

11-6

9 mm

A. B. C. D.

90

9 mm

75

V

38. ASSUME THAT LINES THAT APPEAR TO BE TANGENT ARE TANGENT. O IS THE CENTER OF THE CIRCLE. FIND THE VALUE OF X. (FIGURES ARE NOT DRAWN TO SCALE.)

76A. B. C. D.

0% 0%0%0%

12-1

O   x°

A.45B.67.5C.315D.270

90

77

O   x°𝒎∠𝑶=𝟏𝟑𝟓

Tangent lines are perpendicular to the radius of the circle so the red angles are 90 degrees.

135 + 90 + 90 = 315360 315 = 45x = 45o

39. FIND THE VALUE OF X. IF NECESSARY, ROUND YOUR ANSWER TO THE NEAREST TENTH. O IS THE CENTER OF THE CIRCLE. THE FIGURE IS NOT DRAWN TO SCALE.

78

A. B. C. D.

0% 0%0%0%

12-2

O

12

9

x

A.12B.9C.15D.5

90

79

Rotate the radius around until it makes a right triangle.

O

12

9

x

40. FIND THE MEASURE OF ∠BAC IN CIRCLE O. (THE FIGURE IS NOT DRAWN TO SCALE.)

80A. B. C. D.

0% 0%0%0%

12-3

A

C

O

B

40º

A.50B.80C.20D.40

90

81

Inscribed angles are half their intercepted arcs measure.

A

C

O

B

40º

41. IS TANGENT TO CIRCLE O AT A. IF , WHAT IS YAC? (THE FIGURE IS NOT DRAWN TO SCALE.)

82A. B. C. D.

0% 0%0%0%

12-3

B

A

Y

O

C

A.132B.48C.78D.156

90

Measure of is half of its intercepted arc

= =

83

B

A

Y

O

C

24

42. AND . FIND . (THE FIGURE IS NOT DRAWN TO SCALE.)

84A. B. C. D.

0% 0%0%0%

12-4

D

A

E

C

B

A.33.5B.93.5C.86.5D.67

90

Measure of is half of the difference of its intercepted arcs

85

D

A

E

C

B

120 53

43. FIND THE VALUE OF X. IF NECESSARY, ROUND YOUR ANSWER TO THE NEAREST TENTH. THE FIGURES ARE NOT DRAWN TO SCALE. THE FIGURE CONSISTS OF A TANGENT AND A SECANT TO THE CIRCLE

86

A. B. C. D.

0% 0%0%0%

12-4

12

x5

A.9.2B.7.7C.14.

3D.85

90

87

12

x5 The formula is:

44. WRITE THE STANDARD EQUATION FOR THE CIRCLE.

CENTER (10, –6), R = 6

88A. B. C. D.

0% 0%0%0%

12-5

A. B. C. D.

90

89

The equation for a circle is :center (10, –6), r = 6