PreCalculus
Summer Review Packet
These problems represent a review of both Geometry and Algebra skills that you will need
for the first semester of this course You are expected to have a full understanding of this
material prior to the start of this course. If you wait until the week before school starts to
complete this packet, you may not have enough time to access additional resources if you
need them. You will be given another packet at the end of the first semester to review for
the work that will be done second semester.
Complete the packet on loose leaf paper (make sure to show all work to arrive at the
answer) and bring it with you (already stapled) on the first day of class. All graphs must
be done on graph paper. Answers are included at the end of the packet for you to use to
check your work.
Because this is review material, we will answer any questions the first few days of
class and will then move in to the new material for the course.
If you are having difficulty on a section of these problems, refer to the following resources:
 Your Algebra I/II notebook
 Your Geometry notebook
 Khanacademy.com
2016 – 2017
1
Definitions:
Write the letter of the word that best matches each definition.
Word Bank:
A. acute angle
D. obtuse angle
G. straight angle
1.
2.
3.
4.
5.
6.
______
______
______
______
______
______
B. angle
E. ray
H. supplementary angles
C. complementary angles
F. right angle
I. vertex
The joining of two rays at a common endpoint.
The common endpoint which joins two rays.
All points extending from a single point in a single direction.
An angle measuring 180
An angle measuring 90
An angle greater than 0 but less than 90
7. ______
An angle greater than 90 but less than 180
8. ______
9. ______
Two angles that sum to 90
Two angles that sum to 180
Radicals: Simplify completely.
10. 3 98
3
5
13. 5 80
11.
18
2
14. 20  2
12.
16.
15. 8 2  3 6
3 2
5 3
17.
10
3 30
Similar Triangles: Two triangles are similar if corresponding angles are congruent. If two triangles are
similar, corresponding sides are proportional.
Similar triangles are shown. Find the values of x and y.
18.
8
x
12
26
2016 – 2017
6
y
19.
3
12
10
8
x
y
2
Pythagorean Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the
squares of the legs (If C in  ABC is a right angle, then a 2  b 2  c 2 )
Find the value of x.
20.
21.
15
5
9
22.
23.
12
x
Special Right Triangles (45-45-90):
A 45  45  90 triangle is an isosceles right triangle with congruent legs. If the length of a leg is a, then
the length of the hypotenuse is a 2 .
a
a
Given the length of the legs, find the length of the hypotenuse of each 45  45  90 triangle.
24. 3 2
25. 5 6
Given the length of the hypotenuse, find the length of the legs of each 45  45  90 triangle.
26. 10
2016 – 2017
27. 4 3
3
Special Right Triangles (30-60-90):
In a 30  60  90 triangle, the shorter leg is opposite the 30 angle and the longer leg is opposite the 60
angle. If the shorter leg has a length a, then the hypotenuse has length 2a and the longer leg has the
length a 3 .
2a
a
Using the side given, find the other two sides of each 30  60  90 triangle.
29. Hypotenuse: 12
28. Short leg: 8 3
30. Long leg:
31. Hypotenuse: 4 2
6
SOHCAHTOA:
opposite
hypotenuse
adjacent
cos  
hypotenuse
opposite
tan  
adjacent
opposite
sin  
adjacent
Express sin, cos, and tan of  as ratios for each triangle.
9
40
4
15
sin  
32. cos  
tan  
2016 – 2017
sin  
33. cos  
tan  
sin  
34. cos  
tan  
6
sin  
35. cos  
tan  
4
Find the values of x and y to the nearest tenth. Make sure your calculator is in degree mode.
x
36.
37.
38.
39.
x
34
25
Find n to the nearest degree. Make sure your calculator is in degree mode.
40.
41.
31
42.
43.
9.5
60
Applications of Right Triangle Trigonometry:
Angle of elevation: If a person on the ground looks up to the top of a building, the angle formed between
the line of sight and the horizontal
Angle of depression: If a person standing on the top of a building looks down at an object on the ground,
the angle formed between the line of sight and the horizontal
44. From a point 80 meters from the base of a tower, the angle of elevation to the top of the tower is
28 . How tall is the tower?
45. The angle of depression from the top of a tower to a boulder on the ground is 38 . If the tower is
25 meters high, how far from the base of the tower is the boulder?
2016 – 2017
5
Unit Conversions: Perform the following conversions. Round answers to two decimal places if
necessary. Make sure to show your unit analysis!
Example: Convert 2 days into seconds 2 days 
Conversions
1 hour = 3600 seconds
1 meter = 3.28 feet
1 kg = 2.2 lbs
24 hours 60 min 60sec


 172,800sec
1day 1hour 1min
1 mile = 5280 feet
1 km = 0.62 miles
1 lb = 0.45 kg
1 yard = 3 feet
1 foot = 12 inches
1 inch = 2.54 cm = 25.4 mm
46. 565,900 seconds into days
47. 17 years into minutes
48. 43 miles into feet
49. 165 pounds into kilograms
50. 100 yards into meters
51. 22,647 inches into miles
52. 1100 feet per second into miles per hour
53. 53 yards per hour into inches per week
54. 721 lbs per week into kg per second
55. 88 inches per second into miles per day
Function Transformations:
Describe the transformations for each function. (vertical shift, horizontal shift, reflection, vertical stretch,
vertical compression) with respect to its parent function. Identify the domain and range for each
function. Parent functions are y  x ; y  x 2 ; y  x . Graph each function (all graphs are to be done on
graph paper). You should check your graphs using your calculator.
56. y  x  4  3
58. y  2 x
60. y   x  3  6
62. y  2 x 2
2
64. y  x  5  2
1
x
66. y  
2
2016 – 2017
57. y  x  5  1
1
x
3
2
61. y   x  8   2
59. y  
1 2
x
2
65. y  x  3  1
63. y 
67. y  4 x
6
Inverses: Find the inverse of each function.
68. y  4 x  1
1
70. y  x  11
2
69. y  6 x  3
3
71. y   x  7
4
Factoring: Factor the following expressions completely.
72. n 2  8n
74. 4 x3  38 x 2  90 x
76. 4 x 2  12 x  9
78. 8k 3  8k 2  3k  3
Solve: Use the most efficient method possible.
80. 4n 2  9  157
82. 4r 2  25
84. 6a 2  8  28
2016 – 2017
73.
75.
77.
79.
b 2  14b  40
14a 2  2a  12
16m2  1
m4  m2  12
81. 3 x 2  28  5 x
83. 25b 2  60b  36
85. 10v 2  6v  8
7
PreCalculus Summer Review Packet – Answers
1. B
5. F
9. H
2. I
6. A
10. 21 2
14. 2 10
13. 20 5
3
9
20. 12
24. 6
17.
28. 24,16 3
sin   8 17
32. cos   15 17
tan   8 15
36. x  9.2
40.
44.
48.
52.
n9
 42.5 m
227, 040 ft
750 mi/hr

56. shift right 4, up
3
D :all  R: y  3
60. shift left 3, up 6
D :all  R: y  6
64. shift right 5,
down 2
D : x  5 R: y  2
x 1
68. f 1 
4
72. n  n  8 
76.
 2 x  3
2
80.  37
84.  6
2016 – 2017
3. E
7. D
15
5
15. 48 3
11.
18. x  10.4, y  9
19. x  6.4, y  2.5
21. 5 2
25. 10 3
22. 1
29. 6, 6 3
sin   40 41
33. cos   9 41
tan   40 9
37. x  26.8 y  20.9
41. n  52
45.  32 m
49. 75kg
53. 18,144in/wk
57. shift left 5, down
1
D :all  R: y  1
61. shift right 8,
down 2
D :all  R: y  2
65. shift left 3, up 1
D : x  3 R: y  1
3 x
6
73.  b  10  b  4 
69. f 1 
77.  4m  1 4m  1
7
81.  , 4
3
3  i 71
85.
10
26. 5 2
30. 2, 2 2
sin   1 2
4. G
8. C
12. 9 2
16.
6
5
23. 4 3
27. 2 6
31. 2 2, 2 6
sin   2 2
34. cos   3 2
35. cos   2 2
42. n  65
46.  6.55days
50.  91.46 m
43. n  47
47. 8,985, 200 min
51.  0.36 miles
55. 120 mi/day
tan   3 3
38. x  70.5 y  25.7
54.  5.42 x104 kg/sec
58. vertical stretch
D :all  R: y  0
62. vertical
stretch/refl.
D :all  R: y  0
66. vertical comp/refl.
D : x  0 R: y  0
70. f 1  2 x  22
74. 2 x  2 x  9  x  5 
78.
 8k
82. 
5
2
2
 3  k  1
tan   1
39. x  18.8
59. vertical
comp/refl.
D :all  R: y  0
63. vertical comp
D :all  R: y  0
67. vertical stretch
D : x  0 R: y  0
28  4 x
3
75. 2  7a  6  a  1
71. f 1 
79.  m  2  m  2   m
83.
6
5
8
2
3
