FINAL REVIEW GEOMETRY B QUESTIONS SIMILAR TO WHAT WILL BE ON THE FINAL EXAM.
-
Upload
edwina-mcgee -
Category
Documents
-
view
218 -
download
0
Transcript of FINAL REVIEW GEOMETRY B QUESTIONS SIMILAR TO WHAT WILL BE ON THE FINAL EXAM.
FINAL R
EVIEW
GEOMETR
Y
BQ
UE
ST
I ON
S S
I MI L
AR
TO
WH
AT
WI L
L B
E O
N T
HE
FI N
AL
EX
AM
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