Algebra 2
Name_____________________________
Summer Assignment
Period_________Date______________
Ocean Township High School Mathematics Department
These are important topics from Algebra 1 that you must be comfortable doing before you can be successful in Algebra 2. This packet is to be completed in full and turned in on the first day of class. It will be graded and counted as your first quiz grade.
If you find that you need some assistance, please feel free to Google or YouTube the concepts. Within the directions of each problem, you will see key words that you should be using in your research.
Show all work that is required to be performed in order to solve the problem!
Partial credit will be awarded for every correct step given even though the final answer might be incorrect. Points will be deducted if your work is messy and illegible.
All answers must be exact and simplified unless the problem asks for an approximation!
1) Evaluate the expression.
5xy 6 y if x 3 & y 4
2) Evaluate the expression.
3x 2 2 xy if x 3 & y 4
3) Evaluate the expression.
x 3 y y x if x 6 & y 2
4) Evaluate the expression.
xy xx y if x 6 & y 2
5) Combine the like terms.
11x 5 y 7 y 4 x
6) Combine the like terms.
13x 2 7 x 8x 2 x
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7) Combine the like terms.
7 xy x 2 y 9 x 2 y 4 xy
8) Combine the like terms.
8x 2 12 x 3 3x 2 5x 3
9) Solve the linear equation.
2 x 9 25
10) Solve the linear equation.
11 20 3x
11) Solve the linear equation.
x
7 11
3
12) Solve the linear equation.
2 x 6 x 24
13) Solve the linear equation.
x 4 x 6 30
14) Solve the linear equation.
2x 4 11
15) Solve the linear equation.
53 x 25
16) Solve the linear equation.
2 x 32 x 4 0
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17) Solve the linear equation.
6x 2 33x 2 21
18) Solve the linear equation.
5x 33x 1 8x 45
19) Solve the linear equation.
6 x 4 x 20
20) Solve the linear equation.
11x 9 x 14
21) Solve the linear equation.
7 4 x 10 x 19
22) Solve the linear equation.
2 x 8 14 10 x
23) Solve the linear equation.
3x 2 5x 10
24) Solve the linear equation.
123 x 52 x 8
25) Solve the linear equation.
3x 14 5x 2 5x
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26) Solve the linear equation.
8x 5 2 x 11 7 x x
27) Solve the linear equation.
3x 4 23x 1 4 x
28) Solve the linear equation.
4x 8 6 x 3x x 8
29) Solve the inequality & graph the solution set.
3x 2 10
30) Solve the inequality & graph the solution set.
6 x 4 40
31) Solve the inequality & graph the solution set.
23 x 8
32) Solve the inequality & graph the solution set.
4x 2 20
33) Solve the inequality & graph the solution set.
2 x 9 25
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34) Solve the inequality & graph the solution set.
2x 5 16
35) Solve the inequality & graph the solution set.
3x 7 6 x 20
36) Solve the absolute value equation.
x 7 11
37) Solve the absolute value equation.
x3 9
38) Solve the absolute value equation.
2 x 1 31
39) Solve the absolute value equation.
3 x 4 2 20
40) Solve the absolute value equation.
x 2 6 19
41) Solve the absolute value inequality & graph the solution set.
x 7 11
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42) Solve the absolute value inequality & graph the solution set.
x3 9
43) Solve the absolute value inequality & graph the solution set.
x 3 13
44) Solve the absolute value inequality & graph the solution set.
2 x 1 31
45) Solve the absolute value inequality & graph the solution set.
x 2 6 19
46) Solve the absolute value inequality & graph the solution set.
3 x 4 2 20
47) Graph the linear equation (slope-intercept form).
y 3x 4
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48) Graph the linear equation (slope-intercept form).
3 y x 1
2
49) Graph the linear equation (slope-intercept form).
y 2 x
50) Graph the linear inequality (slope-intercept form).
1 y x2
3
51) Graph the linear inequality (slope-intercept form).
y x3
52) Graph the linear equation.
y4
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53) Graph the linear equation.
x 2
54) Graph the linear equation (standard form).
6x 2 y 8
55) Graph the linear equation (standard form).
3x 6 y 12
56) Write the equation in slope-intercept form and standard form for the line that is graphed.
Slope-intercept form_________________________
Standard form_________________________
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57) Write the equation in slope-intercept form and standard form for the line that is graphed.
Slope-intercept form_________________________
Standard form_________________________
58) Write the equation in slope-intercept form and standard form for the line that is graphed.
Slope-intercept form_________________________
Standard form_________________________
59) Determine the slope of the line that goes through the points.
5,6 & 2,15
60) Determine the slope of the line that goes through the points.
11,7 & 4,3
61) Determine the slope of the line that goes through the points.
5,6 & 2,6
62) Determine the slope of the line that goes through the points.
11,7 & 11,3
63) Find the equation for a line with the given properties.
Slope 0 & containing the point 5,6
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64) Find the slope-intercept equation for a line with the given properties.
Slope
3
& containing the point 8,16
4
65) Find the slope-intercept equation for a line with the given properties.
Containing the points 4,4 & 6,21
66) Find the slope-intercept equation for a line with the given properties. x int 3 & y int 8
67) Find the slope & y-intercept of the line.
y 4
Slope =
Y-intercept =
68) Find the slope & y-intercept of the line.
x5
Slope =
Y-intercept =
69) Find the slope-intercept equation for a line with the given properties.
Parallel to y 2 x 7 & containing the point 7,6
70) Find the slope of the line perpendicular to the line containing the points.
2,5
& 6,9
71) Find the slope-intercept equation for a line with the given properties.
Perpendicular to y 4 x & containing the point 8,9
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72) Find the equation for a line with the given properties.
Perpendicular to y 4 & containing the point
11,9
73) Simplify using properties of exponents.
4xy 3x y
7
5 2
74) Simplify using properties of exponents.
18 x 3 y 7
12 xy10
75) Simplify using properties of exponents.
3x y
5 3 4
76) Simplify using properties of exponents.
4xy 3x y
7 2
5 2
77) Simplify using properties of exponents.
8 x 3 y 7 z 5
12 x 1 y10 z 6
78) Subtract the polynomials.
4x
5
6 x 3 x 2 9 x 16 3x 4 5x3 7 x 2 x 12
79) Multiply the polynomials.
5 3x 4 5x 3 7 x 2 x 12
80) Multiply the polynomials.
2 x 4 x 5 6 x 3 x 2 9 x 16
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81) Multiply the polynomials.
x 42x 3
82) Multiply the polynomials.
3x 42 x 1
83) Factor the polynomial (greatest common factor).
30 x 18 y 12
84) Factor the polynomial (greatest common factor).
17 x 6 16 x 5 4 x 4
85) Factor the polynomial (greatest common factor).
12 x 2 16 xy 4 x 4
86) Factor the polynomial.
x 2 10 x 16
87) Factor the polynomial.
x 2 10 x 24
88) Factor the polynomial.
x 2 12 x 27
89) Factor the polynomial.
2 x 2 5x 12
90) Factor the polynomial.
3x 2 37 x 12
91) Factor the polynomial.
4 x 2 20 x 25
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92) Factor the polynomial.
x 2 49
93) Factor the polynomial.
9 x 2 100
94) Factor the polynomial.
2 x 2 14 x 24
95) Factor the polynomial.
3x 3 12 x
96) Solve the system of equations by graphing.
y 3x 4
1
y x3
2
97) Solve the system of equations by graphing.
x y 2
x 3 y 6
98) Solve the system of equations by using substitution or elimination.
y 5x 1
2 x y 2
99) Solve the system of equations by using substitution or elimination.
x y 5
x 2 y 3
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100) Solve the system of equations by using substitution or elimination.
x 12 7 y
3x 5 y 10
101) Solve the system of equations by using substitution or elimination.
x y 5
x y 11
102) Solve the system of equations by using substitution or elimination.
2 x 6 y 10
3x y 9
103) Solve the system of equations by using substitution or elimination.
4 x 3 y 2
3x 2 y 3
104) Simplify the radical.
28
105) Simplify the radical.
128
106) Multiply the radicals and simplify.
2 6
107) Multiply the radicals and simplify.
5 5
108) Multiply the radicals and simplify.
3 82 6
109) Multiply the radicals and simplify.
6 2 5 18
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110) Add the radicals.
3 2 5 2 2
111) Add the radicals.
4 7 5 3 6 3 8 7
112) Add the radicals.
12 75
113) Add the radicals.
3 8 5 18
114) Evaluate the function notation.
f x 2 x 7
Find f 5
115) Evaluate the function notation.
3 g x x 4
5
Find g 10
116) Evaluate the function notation.
h x 4 x 2 3x 11
Find h 3
117) Find the value of
x in the function notation equation. f x 2 x 7
Find x so that f x 5
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118) Find the value of
x in the function notation equation.
3
g x x 4
5
Find m so that g m 10
Use the graph of p x to answer the following questions.
119) Find p 9
120) Find p4
121) Find p8
122) Find x so that p( x) 5
123) Find x so that p( x) 4
124) Find x so that p( x) 1
125) Solve the problem using a system of equations.
A farmer has only chicken and pigs on his farm with a total of 48 heads and 130 legs.
How many chicken and pigs does he have?
126) Solve the problem using a system of equations.
At the “Strikes to Spare” bowling lanes, the management is trying to decide on a plan to attract large groups on Sundays. Plan A is a $25 charge for the group, then $1.50 per game per each member. Plan B is to lower the charge to $20 but raise the price per game to $1.60. How many games would need to be bowled to result in the same price? What is that price?
127) Solve the system of equations by using substitution or elimination.
x y 2 z 3
x 2 y z 5
2 x y z 8
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