Chapters 1-5 Review
Name _______________________________
1. Solve for the unknown value in each. Only use the Law of Sine or Cosine for non-right triangles.
a.
b.
x
c.
73
16
x
12
x
37
43
18
5
x = ________________
x = ________________
20
d.

e.
x = ________________
f.
7
35
14
12
73


θ = ________________
g.
28
12
θ = ________________
h.
x
θ = ________________
8
i.
37
19
11
51
11
x
x
9
x = ________________
x = ________________
x = ________________
2. Use special right triangles to solve for the missing values. Leave answers in exact values.
a.
y
b.
12
30
16
45
x
x
y
x = _____________ y = _____________
x = _____________ y = _____________
3. a. Connor is standing 125 feet from a large oak tree. To see the top of the tree, he gazes up
at an angle of 37°. If his eyes are 5.2 feet above the ground, how tall is the tree?
b. A 20-foot ladder is leaning against the side of a house. The bottom of the ladder is about 8 feet
from the wall. Find the angle the ladder forms with the ground.
4. Calculate the expected value of these spinner games.
a.
b.
10
-3
-5
5
3
5. The two spinners shown below are spun. If the letters match you win, otherwise you lose.
What is the probability that you win the game?
Construct an area model and include the appropriate probability for each box.
A
B
B
C
C
A
6. A bag contains the figures shown to the right. If you
reach in and pull out a shape at random, what is the
probability that you pull out:
a. A figure with at least one right angle?
b. A figure with an acute angle?
c. A shape with at least one pair of parallel sides?
d. A triangle?
7. Scabbers the rat is trying to find food in the maze shown below and he is equally likely to take any path
when coming to an intersection. If the food is stored in area A, what is the probability that Scabbers
finds food? Show organized work to support your answer.
B
A
8. Determine whether the triangle pairs below are similar. Create a flowchart for each pair to justify
your conclusions. NOTE: Figures may not be drawn to scale.
a.
B
10
R
8
b.
Z
K
C
100
9
10
12
J
8
A
Y
100
P
15
M
7
11
X
L
9. The following figures are similar, solve for the variable.
a. Δ𝐴𝐵𝐶 ~ΔPQR
b.
R
A
x
D
6
10
15
G
9
8
C
B
C
H
𝐴𝐵𝐶𝐷 ~KGHJ
A
8
Q
2x + 3
4
5
B
20
J
K
P
10. A triangle has sides of 7 and 20. Find the maximum and minimum length of the third side.
Write your answer as an inequality.
11. Find the area of the bolded parallelogram, trapezoid, and triangle below. Include proper units.
13in
a.
b.
10in
c.
16cm
15cm
12cm
8in
22cm
16ft
12ft
13ft
9cm
6in
5ft
12. For each diagram, name the relationship between the angles and calculate the value of x.
a.
6x – 24
2x + 12
b.
2x + 17
c.
3x
x + 20
3x – 4
d.
e.
7x - 6
5x + 11
4x + 15
4x – 15
3x + 20
f.
x - 15
2x
10ft
13. Perform each indicated transformations independent of each other. Properly label the image.
15
y
14
13
a. Reflect
12
ABC across line m
11
10
9
8
7
C
6
5
b. Rotate ABC clockwise 90
about the origin
4
3
2
A
B
1
–15 –14 –13 –12 –11 –10 –9
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
10
11
12
13
–2
–3
–4
14
x
c. Dilate ABC by a zoom factor of 2
from the origin.
–5
–6
–7
–8
–9
–10
–11
–12
–13
–14
–15
14. (12 pts) Create a Venn Diagram and answer the following questions below for the following situation.
A survey of faculty and students at the Boston University film school revealed the following:
51 admire Moe
49 admire Larry
60 admire Curly
34 admire Moe and Larry
32 admire Larry and Curly
36 admire Moe and Curly
24 admire all three of the Stooges
1 admires none of the Three Stooges
a) How many people were surveyed?
b) How many admire Curly, but not Larry nor Moe?
c) How many admire exactly two of the Stooges?
d) How many admire exactly one of the Stooges?