Download Spring Review 2017 - Blue Valley Schools

Cumulative Review
(7, 8, 9, 10, 11, 12)
Honors Geometry
Name _______________________ Hr ___
Disclaimer: This review is a small sampling of what could be on the final. (answers will be posted) For more review do the chapter
reviews at the end of each chapter, all of the answers are in the section titled “selected answer” of your textbook. Also, the
online textbook has great “checkpoint quizzes” and tutorials. The link to the book, username and password can be found on
my homepage.
You may make notecards for the final-one per chapterBe sure to know vocabulary and the “big” concepts from first semester.
Chapter 7
1)
If
h
2

, Complete the following statements:
k 15
a) 2k  ?
2)
b)
15
?
2
c)
h
15
?
d)
h k
?
k
d)
x 2
x

x 1 x  6
Solve the following proportions:
a)
6
7

2x  4 4 x  7
3)
MNP ~ XYZ
b)
x 2 x 2

x 1 x  4
2x  5 8x  5

6
9
Find x.
M
x+4
P
c)
80
Y
4x-5
Z
N
32
X
4)
Are the following triangles similar? If so, why?
a)
b)
c)
15
9
12
6
4
20
5)
10
6
6
4
Find the Geometric Mean between the following numbers:
a) 6 & 10
b) 8 & 14
c)
10 &
40
d)
45 &
5
6)
Find x.
a)
b)
X+2
X-2
14
X+4
X-1
7)
10
x+2
2x+1
Find x, y and z.
a)
b)
5
z
6
y
10
x-7
4
x
8)
The altitude divides the hypotenuse of a right triangle into parts 10in and 8in. What is the height of the triangle?
9)
Find the value for the each measurement
a)
TRS ~ TQP
TS = ______
QP = ________
b) EB = ________ ES = ________
Radicals
Simplify the following in simple radical form:
a) 4 54
b) 5 8 2 10
c)
e) 3 180
f) 6 14 3 21
g)
20  2 45
12 5
6
d) 10 27  2 75
h)
15 14
21
Chapter 8
1)
Find the missing length from each triangle.
a)
2)
b)
The numbers represent the lengths of the sides of a triangle. Classify each triangle as acute, obtuse or right.
a) 2, 5, 6
b) 13, 21, 24
c) 18, 24, 30
3)
A 20 ft ladder reaches a window 18 ft high. How far is the foot of the ladder from the base of the building?
How far must the foot of the ladder be moved to lower the top of the ladder by 2 ft?
4)
a)
Find the value of x and y.
5)
Each side of a rhombus is 12 in. long. Two of the sides form a 60° angle. Find the length of the longest
diagnonal. Round your answer to the nearest inch.
6)
Mike is standing 50 feet from a flagpole. The angle of elevation to look up at the top of the pole is 25°. If
Mike’s eye level is 6 feet from the ground, find the height of the flagpole to the nearest foot.
7)
The length of a ramp is 40 ft. If the ramp has a vertical rise of 3 ft, what is the angle of elevation?
b)
c)
8) From the top of a 100-foot cliff at the shore, the angle of depression to a ship on the water is 32o. About how far
is the ship from the shore?
9)
Find the area of a regular dodecagon if it has a radius of 12 cm.
10) Find the area of this triangle:
10 in
122°
15 in
11) Solve for each variable in the following triangles:
a)
a
b)
87
15
11
b
a
a
c
16
c
58
c)
c
b
12. Describe each vector as an ordered pair.
Give the coordinates to the nearest tenths.
105
15
b
25
13. Find the magnitude and direction of each vector.
Round your answers to the nearest tenth.
Chapter 10
1)
Find the area of the trapezoid:
30
12√2
45°
2)
A parallelogram has sides 12 cm and 20 cm. The
height corresponding to the 20 cm is 8 cm.
What is the height corresponding to the 12 cm?
3)
The perimeter of a rhombus is 260 ft. If one diagonal has a length of 50 ft, what is the area of the rhombus?
4)
Two similar polygons have areas of 100 ft2 and 196 ft2. If the smaller polygon has a side length of 10 ft, what is
the length of the corresponding side on the larger polygon?
5)
Find the area of the segment.
Leave your answer in terms of  .
6)
Find the length of the radius if A = 10  mm2
50
r
21
120
7. Find each shaded area. Round to the nearest tenth.
45o
8. Find the length of
Leave in terms of 
CDE
Chapter 11
1)
Find the surface area and volume of the following:
a)
b)
c)
d)
e)
2)
The volume of a sphere is 121500  in3. What is the surface area?
3)
The height of a cone is 4 times the length of the radius. If the volume is 288  in3, what is the length of the
radius?
4)
A stone is placed in a graduated cylinder with a diameter of 7 cm. If the water level rises 3.6 cm, what is the
volume of the stone?
5)
A sphere with a radius of 1.5 in was found at an archeology dig site. If the mass of the sphere is 272.85 g, find
the density of the metal.
6)
The surface areas of two similar cones are 96  cm2 and 216  cm 2. If the volume of the larger cone is
324  cm3, what is the volume of the smaller cone?
7)
Find the surface area and volume for this composite figure: (cone with a cylinder)
Chapter 12 – Circles
1. Use 3.14 for .
a. radius = 6, diameter= ? and circumference = ?
b. diameter = 16.2, radius = ? and circumference = ?
c.
circumference = 32.8, diameter = ? and radius = ?
2. Refer to the figure at the right.
3. Refer to the figure at the right:
AB and CB are tangents
a. m FG
b. mFEG
F
a. mA
c. m EH
d. mEFH
e. mFGE
b. BC
c. mB
4. Refer to the figure at the right.
a. mS
5. Refer to the figure at the right.
a. mBAE
b. m TPR
b. mABD
c. mACB
d. m EDA
6. Find the value of the variables in each of the following circles.
a.
b.
d.
c.
e.
9. What is the equation of a circle that has:
a. radius = 5, center = (0,3)
b. radius = 2 3 , center = (-2,6)
10. What are the coordinates of the center and length of the radius of a circle whose equation is:
a. (x  2)2  (y  1)2  36
b. (x  8)2  y 2  20
11. Write the standard equation of a circle given the endpoints of the diameter (-2,3) and (6,-7).
9-Transformations
1. find a single translation that has the same effect as each composition of translations
a. (x, y) -> (x + 4, y - 8) followed by (x, y) -> (x + 9, y - 5)
b. (x, y) -> (x + 1, y + 5) followed by (x, y) -> (x - 1, y - 7)
2. PNQ has vertices P(2, 5), N(-3, -1), and Q(4, 0)
a. Determine the image of PNQ under the translation (x, y) -> (x - 5, y - 2)
b. Determine the image of PNQ reflected across the y-axis.
c. Determine the image of PNQ reflected across line x = -3.
3. Regular Octagon EIGHTSUP is divided into eight congruent triangles. Find the image of each point or segment for
the given rotation.
a. 45o rotation of G about Z
b. 225o rotation of U about Z
c. 270o rotation of EI about Z
d. 360o rotation of ST about Z
4. Tell what types of symmetry each figure have. Sketch the lines of symmetry. If it has rotational symmetry, state
the angle of rotation.
a.
b.
c.
5. A dilation has center (0,0). Find the image of each point for the scale factor given.
a.
D(8,-16);
1
4
b. L(3,6); 3