17-18 cp geometry final exam review
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1
17-18 CP Geometry – Final Exam REVIEW
Identify the scale factor of each dilation.
1. 2.
Dilate the following given each scale factor. Be sure to label the images properly.
3. Scale factor of
1
4 4. Scale factor of 2
2
Chapter 7 – Similarity
1. Solve the proportions:
a) 2𝑥−1
4=
1
3 b)
𝑥−3
5=
𝑥+5
7
2. Solve: 6
2 8
x
x
A. 5 B. 6 C. 12 D. 14
3. Given ABC DEF . Find the value of x.
Justify your answer.
Are the following triangles similar? If so, justify your answer, and write a similarity statement.
4. a)
3
b)
5. List the ways you can prove two triangles similar.
6. EKN is similar to OHT . If 49m K and 73Tm , find Em .
7. The triangles are similar. Find the missing side(s) in each figure.
a)
b)
M
P Q
6
15
N
R S
12
28
4
c) d)
e) f)
For #8-9, refer to the figure at the right.
In the figure, l || m || n.
8. Complete the proportion ?
EF BC
DE
A. AB B. AC C. DE D. EF
9. If AB = 8, BC = 14, and DF = 33, find EF.
A. 20 B. 21 C. 22 D. 25
5
Chapter 8 – Right Triangles (Geo Mean, Pythagorean, Special Right, and Trig)
.
6
11) Find the length of the hypotenuse.
12) Write as a simplified radical.
a) 2
√3 b)
12
√2 c)
20
√5
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
13) 14)
15) 16)
17) 18)
7
19) Find the area of the trapezoid. Leave your answer in simplest radical form.
*Hint: find the height first!
Write an equation involving sine, cosine, or tangent that can be used to find x. Then, solve the equation.
Round answers to TWO decimal places.
20) 21) 22)
23) 24) 25)
26) If the 5
tan( )12
A what is the cos( )?A
21
x5
54 x
1033
5.2
x
17
x
41 x
5
8 x
8
5
8
27) Mrs. Laird is flying a kite and lets out 100 feet of string. Her kite is 52 feet high. What is the angle of
elevation of the kite?
28) A 17 foot ladder is leaning against a house. The angle of elevation of the ladder is 22°. How far up the
side of the house does the ladder reach?
29) A 15 foot tree casts a shadow that is 8.5 feet in length. What is the angle of elevation of the sun?
Convert each radian measure to degrees:
30) 10𝜋
2 31)
7𝜋
5 32)
11𝜋
3
Convert each degree measure to radians:
33) 200 34) 180 35) 700
9
Chapter 9 - Circles
1. Find the circumference and area of the circle:
a) b)
Circumference Exact _____________ Circumference Exact ____________________
Circumference Rounded to tenth ___________ Circumference Rounded to tenth ___________
Area Exact _____________ Area Exact ____________________
Area Rounded to tenth ___________ Area Rounded to tenth ___________
2. If the circumference of a circle is 51in what is the radius? Round your answer to the nearest tenth.
3. If the area of a circle is 2100 cm , then what is the radius?
Find the area of the shaded region in each circle below, using 3.14 for π. Round to the nearest tenth.
4. 5. 6.
7.
3in
707 in
155
4 in
60
22in
60
10
For #8-9, refer to the figure at the right.
In the figure, AC is a diameter of Circle R.
8. ABC is a
A. major arc B. semicircle C. minor arc D. central arc
9. Find m BD .
A. 105 B. 125 C. 140 D. 155
Find the length of AB in each circle using the pi button on your calculator. Round to the nearest tenth.
10. 11.
Find the length of ABC in each circle using 3.14 for π. Round to the nearest tenth.
12.
8 in
120 80
5 in
12in
120
11
Assume that the lines that appear to be tangent are tangent. Find the value of x.
13. 14.
15. Find the measure of the central angle formed by:
a) Frogs
b) Dogs
Each polygon is circumscribed about the circle. Find the perimeter of each polygon.
16. 17.
x
52
5
x
9cm 12cm
8cm7cm
15in
18in
13in
6in
4in
8
12
Find the value of x. If necessary, round to TWO decimal places.
18. 19. 20.
Find the value of each variable. If necessary, round to TWO decimal places. Justify your answer.
21. 22. 23.
For 21-23, write the standard equation of each circle.
24. C(2, -7); r = 7 25. C(-10, -5); passes through the point (-5, 5)
26. 27. C(-2, -3); passes through the point (4, 5)
15
12x x
9924
x
6.6
2.13
5
97
x
58
23
x
y
x
y
w
67
86
162
13
28. Identify the center and radius of the following and graph:
a) 2 2( 5) ( 9) 72x y b) 𝑥2 + (𝑦 − 3)2 = 25
center: ________________ center: _______________
radius: ________________ radius: _______________
Chapter 10 – Area and Surface Area
Find the area of each triangle to the nearest whole number.
1. 54. 2.
3. A kite has diagonals 9.2 ft and 8 ft. What is the area of the kite?
14
4. Find the area of the following figures:
a) b)
c) d)
e) f)
5. Find the area of each composite figure:
a) b)
8in
5
9
7
15 c) Find the area of the shaded region. Round to the nearest tenth if necessary.
Find the lateral area and surface area of each. Use 3.14 for pi. Round to the nearest hundredth.
6. LA = N/A_________
SA = _____________
7.
LA = _____________
SA = _____________
8.
LA = _____________
SA = _____________
16
9.
LA = _____________
SA = _____________
10.
LA = _____________
SA = _____________
11.
LA = _____________
SA = _____________
12. Find the surface area of the sphere with a diameter of 16 cm, in terms of π.
13. Find the lateral area of the following:
17
Chapter 11- Volume
Find the volume of each solid. Use 3.14 for pi. Round to the nearest tenth, if necessary.
1. 2.
3. 4.
5.
Find the volume of the following spheres. Give each answer rounded to the nearest cubic unit.
6. 7.
18
8. The volume of a cylindrical container is 80 cubic inches. If the height of the cylinder is 5 inches, what is
the length of the radius?
__________________
9. Your family is hosting a fun basketball tournament at your house for their 4th of July picnic.
A) The basketball you ordered has a diameter of 9.5 inches. What is its volume? ____________
B) To ensure that you have enough for the day, you order a box of basketballs. ____________
The box is a rectangular prism with length 29 inches, width/depth of 20 inches,
and height 20 inches. What is the volume of the box?
C) If the box contains 6 basketballs, what is the amount of leftover ____________
space/air inside the box?