PENNCREST HIGH SCHOOL
SUMMER REVIEW PACKET
For students in entering PRE-CALCULUS (All Levels)
Name: __________________________________________________________
Assigning Teacher:

Ms. Cristaldi

Ms. Sweeney

Mrs. Price

Ms. Matlock

Other: _____________________________________
1.
This packet is to be handed in to your Pre-Calculus teacher on the first day of the school
year.
All work must be shown in the packet OR on separate paper attached to the packet.
Completion of this packet is worth one-half of a major test grade and will be counted in
your first marking period grade.
2.
3.
1
Summer Review Packet for Students Entering Pre-Calculus (all levels)
Radicals:
Simplify each of the following.
1.
32
2.
(2 x )8
3.
5.
11
9
6.
60  105
7.
3

64
4.
5 6

5 2

8.
Complex Numbers:
Simplify.
9.
49
12.
 3  4i 
2
10. 6 12
11. 6(2  8i)  3(5  7i)
13. (6  4i)(6  4i)
14.
2
1  6i
5i
49m2 n8
3
2 5
Geometry:
Find the value of x.
15.
16.
9
17.
x
x
x
12
5
x
8
5
12
18. A square has perimeter 12 cm. Find the length of the diagonal.
A
A
19. If DE = 24, Find:
20. If BD = 16, Find:
45
30
AE = _______
D
EB = _______
45 45
AB = _______
60
30
E
D
45
AD = ________
45 C
45
B
60
DC = ________
E
30
B
C
AC = ________
AB = _______
AD = ________
BD = ________
DC = _______
CE = _______
BC = ________
AC = _______
EB = ________
CB = _______
DE = ________
3
Radical Equations:
Solve each equation. Be sure to check for extraneous solutions.
21. 4 x  x 3  6
23.
9u  4  7u  20
22.
x 8 5  0
24.
k 9  k  3
Equations of Lines:
25. State the slope and y-intercept of the linear equation: 5x – 4y = 8.
26. Find the x-intercept and y-intercept of the equation: 2x – y = 5
27. Write the equation in standard form: y = 7x – 5
Write the equation of the line in slope-intercept form with the following conditions:
28. slope = -5 and passes through the point (-3, -8)
29. passes through the points (4, 3) and (7, -2)
30. x-intercept = 3 and y-intercept = 2
4
Graphing:
Graph each function, inequality, and / or system.
2 x  y  4
32. 
x  y  2
31. 3 x  4 y  12
6
6
4
4
2
2
-5
5
-5
5
-2
-2
-4
-4
-6
-6
34. y  2  x  1
33. y  4 x  2
6
6
4
4
2
2
-5
5
-5
5
-2
-2
-4
-4
-6
-6
35. y  x  1
36. y  2 x  1
6
6
4
4
2
2
-5
5
-5
5
-2
-2
-4
-4
-6
-6
5
Systems of Equations:
Solve each system of equations. Use any method.
2 x  y  4
37. 
3x  2 y  1
2 x  y  4
38. 
3 x  y  14
2w  5 z  13
39. 
6w  3z  10
Exponents:
Express each of the following in simplest form. Answers should not have any negative
exponents.
40. 5a
0
3c
41. 1
c
2ef 1
42.
e 1
(n3 p 1 )2
43.
(np)2
45. (a 3 ) 2
46. (b3c 4 )5
47. 4m(3a 2 m)
Simplify.
44. 3m 2  2m
6
Polynomials:
Simplify.
48. 3x3  9  7 x 2  x3
49. 7m  6  (2m  5)
Multiply.
50. (3a + 1)(a – 2)
51. (s + 3)(s – 3)
52. (c – 5)2
53. (5x + 7y)(5x – 7y)
Factor completely. If the polynomial is prime, state so.
54. x 2  5 x  4
55. a 2  a  6
56. z 2  4 z  12
57. 6  5e  e 2
58. n 2  3n  4
59. 60  5h  5h 2
60. 2k 2  2k  60
61. 10b 4  15b 2
62. 9c 2  30c  25
63. 9n 2  4
64. 27 z 3  8
65. 2mn  2mt  2sn  2st
7
Polynomials Continued:
Solve each equation.
66. x 2  4 x  12  0
67. x 2  25  10 x
68. x 2  14 x  19  0
Find the value of the discriminant, describe the nature of the roots, then solve each quadratic.
Use EXACT values.
69. x 2  9 x  14  0
70. 5 x 2  2 x  4  0
Divide each polynomial.
71.
c3  3c 2  18c  16
c 2  3c  2
72.
x4  2x2  x  2
x2
Evaluate each function for the given value.
73. f ( x)  x 2  6 x  2
f (3)  ________
74. g ( x)  6 x  7
g ( x  h)  ________
8
75. f ( x)  3x 2  4
5 f ( x  2)  ________
Composition and Inverses of Functions:
Suppose f ( x)  2 x, g ( x)  3x  2, and h( x)  x 2  4 . Find the following:
76. f  g (2)  ________
77. f  g ( x)  ________
78. f  h(3)  ________
79. g  f ( x)  ________
Find the inverse, f -1(x) , if possible.
81. f ( x) 
80. f ( x)  5 x  2
1
1
x
2
3
Solving Polynomial Equations:
82.
Use Descartes’ Rule of Signs to determine the most possible positive, negative, and imaginary
roots. x3  2 x 2  5 x  5  0
P
N
i
83.
List all the possible rational roots for the function: f ( x)  x3  5x 2  2 x  12
p
:
q
84.
Find ALL of the zeros for the function: f ( x)  x3  3x 2  6 x  8
9
Rational Algebraic Expressions:
Simplify.
85.
5z3  z 2  z
3z
86.
m 2  25
m 2  5m
87.
10r 5 3s

21s 2 5r 3
88.
a 2  5a  6 3a  12

a4
a2
89.
2x x

5 3
90.
ba ab

a 2b
ab 2
91.
2  a 2 3a  4

a 2  a 3a  3
1
2
93.
1
2
4
1
1
6
 2
m m
2 2

m m2
5
95.
92.
6d  9 6  13d  6d 2

5d  1 15d 2  7d  2
1
z
94.
z 1
1
1 1

x x2
96.
4 3
1  2
x x
2
10
Solving Rational Equations:
Solve each equation. Check your solutions.
97.
12 3 3
 
x 4 2
98.
x  10 4

x2  2 x
99.
5
x

1
x5 x5
Probability:
Find each value.
100. P(9, 4)  ______
101. P(7, 0)  ______
103. C (6,5)  C (4, 2)  ______
104.
102. C (10,8)  ______
P(10,3)
 ______
P(5,3)
105. A company manufactures bicycles in 8 different styles. Each style comes in 7 different
colors. How many different bicycles does the company make?
106. How many was can 6 children form a line to use the drinking fountain?
107. What is the probability that the numbers that result from tossing two dice have a sum of 2?
108. The probability that an event will occur is
2
. What are the ODDS that the event will occur?
7
109. There are 7 women and 4 men on a committee. If a 4-person subcommittee is selected at
random, what are the odds that it will consist of 3 men and 1 woman?
110. How many different ways can the letter of the word MINIMUM be arranged?
11
Statistics:
Given the following data set: 44, 31, 24, 36, 28, 42, 39, 36, 28, 36, 43, 44
111. Find the mean, median, and mode(s)
112. Draw a line plot for the data.
113. Draw a stem-and-leaf plot for the data.
114. Draw a box and whisker graph and identify the quartiles, range, and outliers.
115. Find the standard deviation for the data and draw and identify the values for + 1, + 2, and + 3
standard deviations from the mean.
116. Given the following set of data on attendance at North Stadium, make a scatter plot, find the
prediction equation (best fit line), and predict the attendance when the temperature is 64◦.
14
12
Temperature Attendance
10
25
30,000
41
43,000
55
52,000
60
60,000
20
25,000
8
6
4
2
I
12
5
10
15