PENNCREST HIGH SCHOOL
SUMMER REVIEW PACKET
For students in entering ALGEBRA 2 (Levels 1 and 2)
Name: __________________________________________________________
Assigning Teacher:

Mr. Beatty

Mr. Ikeler

Mr. Graham

Mrs. Miller

Ms. Cristaldi

Mrs. Price

Mr. Ritter

Other: _____________________________________
1.
This packet is to be handed in to your Algebra 2 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 Algebra 2 ( levels I and II)
Operations with Integers:
Evaluate each expression.
1.
8 + 2 – 7 __________
2.
23 – 8 – 2 ___________
3.
4 ∙ 2 – 5 _________
4.
9 ÷ 3 + 7 ___________
5.
2 + 7 ÷ 2 – 7 ________
6.
5 + 4 – 9 ÷ 3 _____
7.
48 ÷ 4 ÷ 3 _________
8.
7 ∙ (3 + 4) ___________
9.
(4 + 8) ÷ (3 – 1)___
Solve equations in one variable:
Solve each and check. SHOW all work!!
10.
4x + 9x = 39
11.
2n + 7n – 4n = 15
12.
8y – 2y + 4 = 22
13.
2n – 7n = 25
14.
-3x – 7x + 4 = 34
15.
- 4 = 2y – 6y
16.
3(x – 4) = 15
17.
4(5 – x) = 4
18.
2y + 4(y + 5) = -16
2
19.
3y = 2y + 14
20.
7x = 2x – 20
21.
r + 7 = 3r
22.
-3y = 4y + 35
23.
4n + 3 = 2n – 5
24.
-3y – 9 = 2y + 3
25.
8x + 5 = -3x – 17
26.
6 – 9n = 4 – n
27.
5y – 7 = -5y + 8
28.
–6 + 2x = 9 – 3x
29.
9 – 2n = 14 – 2n
30.
n + 4n = 2n – 15
31.
–3(2x – 3) = 20 – 4x
32.
1
 6x  9  7  2x
3
Exponents.
Simplify each expression.
33.
x( x) = __________
34.
n5  n7 = __________
35.
  x   x  = _____
36.
y 3  y 4   y 5  = _______
37.
x 4  x9 = __________
38.
 y  y 2  y 5  = ____
3
2
5
39.
 3x   7 x 2  = _________
40.
 4 y  7 y  = _________
41.
y  5 y 2  2 y 3  = __
42.
x 
43.
n 
= ____________
44.
x
45.
 x y
= _________
46.
 2x 
= ____________
47.
 4x y 
48.
n5
= ___________
n2
49.
x3
= ______________
x3
50.
x2 y5
= __________
xy 2
51.
x4 y6
= __________
xy
52.
25 x3 y 2
= __________
5 xy
53.
18m8 n5
= ________
3m6 n3
54.
4 x 2 y 5
= __________
2 xy 3
55.
81x 4 y 5 z 7
= ___________
9 x 2 yz 2
56.
20 x9 y 4 z 3
= _____
5 x7 y 2 z
2 4
2
= __________
4
3
9 8
3
2
3
3
= _________
2 3
= _______
Multiplying Binomials:
Find each product. (Hint: use FOIL.)
57.
(x + 2)(x + 5) = ______________
58.
(y + 4)(y – 3) = _________________
59.
(n – 5)(n – 3) = ______________
60.
(x + 3)(2x + 4) = _______________
61.
(4y – 2)(3y – 7) = ______________
62.
(5n + 3)(2n + 3) = ______________
63.
(8x – 4)(2x + 5) = ______________
64.
(9y + 7)(3y – 4) = ______________
65.
(x – 4)2 = _________________
66.
(y + 8)2 = _________________
67.
(x – 1)2 = _________________
68.
(y +2)2 = _________________
69.
(2n – 2)2 = _________________
70.
(5y + 4)2 = _________________
4
Factoring:
Factor each completely.
71.
x 2  4 x  4 = _______________
72.
25m 2  30m  9 = _______________
73.
x 2  12 x  36 = _______________
74.
16 y 2  8 y  1 = _______________
75.
9 x 2  42 x  49 = _______________
76.
81n 2  90n  25 = _______________
77.
x 2  5 x  6 = _______________
78.
x 2  3 x  4 = _______________
79.
y 2  4 y  21 = _______________
80.
n 2  3n  18 = _______________
81.
x 2  6 x  7 = _______________
82.
y 2  5 y  36 = _______________
83.
m2  12m  32 = _______________
84.
x 2  x  30 = _______________
85.
x 2  3 x  4 = _______________
86.
n 2  3n  18 = _______________
87.
2 x 2  15 x  7 = _______________
88.
3 y 2  13 y  10 = _______________
89.
7 x 2  11x  4 = _______________
90.
4m 2  3m  27 = _______________
91.
2 y 2  17 y  21 = _______________
92.
4 x 2  8 x  3 = _______________
93.
10 x 2  21x  10 = _______________
94.
14 y 2  33 y  5 = _______________
95.
6n 2  25n  14 = _______________
96.
4 x 2  18 x  10 = _______________
97.
4n 2  18n  10 = _______________
98.
4 y 2  4 = ___________________
5
Radicals:
Simplify each radical expression. Make sure there are no radicals left in the denominators. If
so, rationalize the denominator.
99.
12  3 = __________
100.
5  5 = _________
101.
6  8 = ________
102.
14  7 = ___________
103.
7  5 = _________
104.
5  10 = _______
105.
6
10
106.
3
5
107.
3 2
3
108.
4 2
12
109.
5
8
110.
5
3x
111.
3 2 4 2 2 2
112.
7 8 7 3 7
113.
114.
12  4 3
115.
117.
2 5  3 20
118.
20  45  5
120.
5 10  3
121.
7 8  12


3 6  24

6
116.

3 3  4 3 9 3
32  5 2
119.
2 12  27  48
122.
9  7 9  7 
Slopes, Equations of Lines, and Graphing:
Find the slope of each line from its graph.
123.
Slope = _________
124.
Slope = __________
125.
Slope = _________
2
2
2
-2
-1
0
1
2
-2
-2
-1
0
1
2
-1
0
1
3
-2
-2
Find the slope of the line containing the given points. (Recall: slope = m =
y2  y1
)
x2  x1
126.
A(2, 3); B(4, 1) _____________
127.
E(-1, -5); F(4, 3) _________________
128.
H(-3, 4); I(7, -2) _____________
129.
L(-2, 3); M(-5, 3) ________________
Graph each linear equation.
130. y  3x  4
131. y  4  x
6
6
4
4
2
2
-5
-5
5
5
-2
-2
-4
-4
-6
-6
132.
x = -4
133.
6
y=3
6
4
4
2
2
-5
5
-5
5
-2
-2
-4
-4
-6
-6
7
1
134. y   x  2
2
135. 2 x  y  3
6
6
4
4
2
2
-5
5
-5
5
-2
-2
-4
-4
-6
-6
Graph each linear inequality.
136.
6
x > -2
y<3
y > 2x – 3
6
4
4
2
2
-5
138.
137.
5
-5
5
-2
-2
-4
-4
-6
-6
139.
6
3x – y < -3
6
4
4
2
2
-5
5
-5
5
-2
-2
-4
-4
-6
-6
8
Write the equation of the line in slope-intercept form (y = mx +b). Then find the slope and the yintercept.
140.
142.
2x + y = 7 _________________
141.
y – 4x = -3 _____________________
Slope: ___________
Slope: ________________
y-intercept: __________
y-intercept: ______________
3y + 9 = 0 ____________
143.
4y – 2 = 3x ______________
Slope: ___________
Slope: ________________
y-intercept: __________
y-intercept: ______________
Systems of Linear Equations:
Solve each system of equations. List your answer as a point (x, y).
144.
x  y  6

x  y  4
145.
 y  3x  7

 y  3x  5
146.
 x  5 y  14

3x  y  6
147.
5 x  2 y  11

3x  5 y  19
9