Integrated Mathematics 2
Name___________________________________ ID: 1
FINAL PRACTICE (PART 1)
Date________________ Period____
ANGLE PAIR RELATIONSHIPS.
Solve for x.
1)
2)
15x + 10 80°
22x + 5
23x
3)
4)
15x 8x − 4
28x − 1
27x + 1
5)
67x − 2
25x − 2
Find the measure of the angle indicated in bold.
6)
7)
16x − 3
6x + 7
4x + 6
12x + 14
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8)
9)
8x + 5
14x − 1
11x − 1
6x − 6
10)
19x − 5 17x + 5
PARALLEL LINES AND TRANSVERSALS
Solve for x.
11)
12)
10x + 10
84°
7x + 7
11x + 4
13)
14)
26x − 4
14 + 6x
100°
100°
15)
10x
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Find the measure of the angle indicated in bold.
16)
17)
16x − 5
18x
19x − 5
14x + 5
18)
19)
13x + 5
x + 73
23x − 5
x + 113
20)
37x − 1 36x + 2
TRIANGLE CONGRUENCE
State if the two triangles are congruent. If they are, state how you know.
21)
22)
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23)
24)
25)
State what additional information is required in order to know that the triangles are congruent
for the reason given.
26) ASA
27) HL
C
A
B
D
F
A
U
B
C
E
W
28) ASA
29) ASA
B
D
M
F
C
K
U
L
H
S
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30) AAS
R
H
I
G
TRIANGLE SIMILARITY
Find the missing length. The triangles in each pair are similar.
31)
32)
M
42
L
U
70
N
?
30
T
T
6
S
?
B
34)
98
E
D
C
24
48
?
J
?
G
J
V
56
U
8
33)
F
C
40
L
L
132
K
35
K
35)
169
M
V
?
N
U
26
14
20
91
L
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Solve for x. The triangles in each pair are similar.
36)
37)
D
V
672
E
F
1092
989
D
R
W
9x − 215
338
J
S
U
1058
18x − 128
K
460
L
38)
39)
L
U
49
23x + 11
E
210
M
T
414
D
46
K
15x − 54
533
U
V
C
390
T
40)
R
18 + x
76
B
C
S
475
R
375
T
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PROBABILITY
Find the probability.
41) A box of chocolates contains eight milk
chocolates and five dark chocolates. You
randomly pick a chocolate and eat it.
Then you randomly pick another piece.
Both pieces are milk chocolate.
42) A bag contains eight red marbles and six
blue marbles. Another bag contains seven
green marbles and six yellow marbles.
You randomly pick one marble from each
bag. One marble is blue and one marble is
yellow.
43) Your sock drawer has six white socks, four
brown socks, and four black socks. You
randomly pick two socks and get a
matching pair of black socks.
44) There are four nickels and six dimes in
your pocket. You randomly pick a coin
out of your pocket and then return it to
your pocket. Then you randomly pick
another coin. Both times the coin is a
nickel.
45) A basket contains six apples and seven
peaches. You randomly select a piece of
fruit and then return it to the basket. Then
you randomly select another piece of fruit.
The first piece of fruit is an apple and the
second piece is a peach.
46) A cooler contains ten bottles of sports
drink: three lemon-lime flavored, four
orange flavored, and three fruit-punch
flavored. You randomly grab a bottle for
your coach, a bottle for your friend, and a
bottle for yourself. Your coach gets a
lemon-lime, your friend gets an orange,
and you get a fruit-punch.
47) You roll a fair six-sided die three times.
The die shows an even number every time.
48) A basket contains five apples and four
peaches. Three times, you randomly
select a piece of fruit, return it to the
basket, and then mix the fruit. All three
times, the fruit is an apple.
49) There are three nickels, three dimes, and
four quarters in your pocket. You
randomly pick three coins and place them
on a counter. The first two coins are a
dimes, and the third is a quarter.
50) There are five nickels and five dimes in
your pocket. Three times, you randomly
pick a coin out of your pocket, return it to
your pocket, and then mix-up the change
in your pocket. The first time, the coin is
a nickel. The second time, it's a dime.
The third time, it's a nickel.
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SPECIAL RIGHT TRIANGLES
Find the missing side lengths. Leave your answers as radicals in simplest form.
51)
52)
u
y
v
45°
x
45°
7
53)
2
54)
x
8
45°
2
55)
y
45°
v
u
56)
u
v
281
30°
45°
7 2
v
57)
u
58)
y
128 3
3
30°
y
59)
x
60°
19
x
60)
y
60°
x
x
592
220 3
60°
y
TRIGONOMETRY
Find the missing side. Round to the nearest tenth.
61)
62)
20 71°
x
x
37°
15
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63)
64)
x
64°
x
12
69°
16
65)
20
x
57°
Find the measure of the indicated angle to the nearest degree.
66)
67)
68
50
32
14
?
48
?
60
68)
69)
95
74
57
?
70
76
?
24
70)
74
24
?
70
AREA OF REGULAR POLYGONS
Find the area of each regular polygon. Round your answer to the nearest tenth if necessary.
71)
72)
8.2
10
8.7
11.3
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73)
74)
15
8
8.3
14.4
75)
14
19.2
ARC LENGTH AND SECTOR AREA
Find the area of each regular polygon. Leave your answer in simplest form.
76)
77)
16 3
3
10 3
3
78)
79)
32 3
3
4 3
80)
28
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Find the length of each arc.
81)
82)
45° 16 cm
14 yd
83)
150°
84)
19 cm
19 in
240°
300°
85)
135°
14 mi
Find the area of each sector.
86)
87)
90°
8 in
19 yd
135°
88)
89)
11 yd
9 km 45°
75°
90)
90°
14 in
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Answers to FINAL PRACTICE (PART 1) (ID: 1)
1) 6
5) 2
9) 120°
13) 4
17) 90°
21) SSS
25) HL
29) ML ≅ SL
32) 42
36) 47
40) 42
44)
48)
52)
56)
59)
62)
66)
70)
74)
78)
82)
86)
90)
2) 5
3) 2
4) 8
6) 125°
7) 46°
8) 111°
10) 90°
11) 11
12) 6
14) 11
15) 9
16) 75°
18) 110°
19) 70°
20) 110°
22) ASA
23) Not congruent
24) SSS
26) C ≅ U
27) BC ≅ EF
28) B ≅ F
30) GHI ≅ RHI or HIG ≅ HIR
31) 56
33) 112
34) 66
35) 130
37) 31
38) 12
39) 33
14
18
6
41)
≈ 0.359
42)
≈ 0.198
43)
≈ 0.066
39
91
91
2
42
1
1
= 0.4
45)
≈ 0.249
46)
= 0.05
47) = 0.125
5
169
20
8
125
1
1
51) u = 7 2, v = 7
≈ 0.171
49)
≈ 0.033
50) = 0.125
729
30
8
55) u = 7, v = 7
x = 2 2, y = 2
53) x = 2, y = 2
54) u = 8 2, v = 8
u = 562, v = 281 3
64 3
58) x = 38, y = 19 3
57) x = 64, y =
3
61) 61.4
60) x = 440, y = 220
x = 296 3, y = 296
9.0
63) 27.4
64) 17.1
65) 13.0
28°
67) 16°
68) 71°
69) 37°
19°
71) 261
72) 417
73) 232.4
756
75) 1209.6
76) 25 3
77) 64 3
81) 4π cm
72 3
79) 512 3
80) 588 3
35π
76π
95π
21π
yd
83)
cm
84)
in
85)
mi
3
3
3
2
24π in²
361π
81π
605π
87)
yd²
88)
km²
89)
yd²
4
8
24
49π in²
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