Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 1 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. 4 & 3 6 5 y x if y xy 2) Evaluate the expression. 4 & 3 2 3 2 y x if xy x 3) Evaluate the expression. 2 & 6 3 y x if x y y x 4) Evaluate the expression. 2 & 6 y x if y x x xy 5) Combine the like terms. x y y x 4 7 5 11 6) Combine the like terms. x x x x 2 2 8 7 13
Transcript
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 1
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.
4&365 yxifyxy
2) Evaluate the expression.
4&323 2 yxifxyx
3) Evaluate the expression.
2&63 yxifxyyx
4) Evaluate the expression.
2&6 yxifyxxxy
5) Combine the like terms.
xyyx 47511
6) Combine the like terms.
xxxx 22 8713
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 2
7) Combine the like terms.
xyyxyxxy 497 22
8) Combine the like terms.
3232 53128 xxxx
9) Solve the linear equation.
2592 x
10) Solve the linear equation.
x32011
11) Solve the linear equation.
1173
x
12) Solve the linear equation.
2462 xx
13) Solve the linear equation.
3064 xx
14) Solve the linear equation.
1142 x
15) Solve the linear equation.
2535 x
16) Solve the linear equation.
04232 xx
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 3
17) Solve the linear equation.
2123326 xx
18) Solve the linear equation.
4581335 xxx
19) Solve the linear equation.
2046 xx
20) Solve the linear equation.
14911 xx
21) Solve the linear equation.
191047 xx
22) Solve the linear equation.
xx 101482
23) Solve the linear equation.
10523 xx
24) Solve the linear equation.
825312 xx
25) Solve the linear equation.
xxx 525143
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 4
26) Solve the linear equation.
xxxx 711258
27) Solve the linear equation.
xxx 413243
28) Solve the linear equation.
83684 xxxx
29) Solve the inequality & graph the solution set.
1023 x
30) Solve the inequality & graph the solution set.
4046 x
31) Solve the inequality & graph the solution set.
832 x
32) Solve the inequality & graph the solution set.
2024 x
33) Solve the inequality & graph the solution set.
2592 x
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 5
34) Solve the inequality & graph the solution set.
1652 x
35) Solve the inequality & graph the solution set.
20673 xx
36) Solve the absolute value equation.
117 x
37) Solve the absolute value equation.
93 x
38) Solve the absolute value equation.
3112 x
39) Solve the absolute value equation.
20243 x
40) Solve the absolute value equation.
1962 x
41) Solve the absolute value inequality & graph the solution set.
117 x
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 6
42) Solve the absolute value inequality & graph the solution set.
93 x
43) Solve the absolute value inequality & graph the solution set.
133 x
44) Solve the absolute value inequality & graph the solution set.
3112 x
45) Solve the absolute value inequality & graph the solution set.
1962 x
46) Solve the absolute value inequality & graph the solution set.
20243 x
47) Graph the linear equation (slope-intercept form).
43 xy
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 7
48) Graph the linear equation (slope-intercept form).
12
3 xy
49) Graph the linear equation (slope-intercept form).
xy 2
50) Graph the linear inequality (slope-intercept form).
23
1 xy
51) Graph the linear inequality (slope-intercept form).
3 xy
52) Graph the linear equation.
4y
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 8
53) Graph the linear equation.
2x
54) Graph the linear equation (standard form).
826 yx
55) Graph the linear equation (standard form).
1263 yx
56) Write the equation in slope-intercept form and standard form for the line that is graphed.
Slope-intercept form_________________________ Standard form_________________________
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 9
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.
15,2&6,5
60) Determine the slope of the line that goes through the points.
3,4&7,11
61) Determine the slope of the line that goes through the points.
6,2&6,5
62) Determine the slope of the line that goes through the points.
3,11&7,11
63) Find the equation for a line with the given properties.
0Slope & containing the point 6,5
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 10
64) Find the slope-intercept equation for a line with the given properties.
4
3Slope & containing the point 16,8
65) Find the slope-intercept equation for a line with the given properties.
Containing the points 21,6&4,4
66) Find the slope-intercept equation for a line with the given properties.
3int x & 8int y
67) Find the slope & y-intercept of the line.
4y
Slope = Y-intercept =
68) Find the slope & y-intercept of the line.
5x Slope = Y-intercept =
69) Find the slope-intercept equation for a line with the given properties.
Parallel to 72 xy & containing the point 6,7
70) Find the slope of the line perpendicular to the line containing the points.
9,6&5,2
71) Find the slope-intercept equation for a line with the given properties.
Perpendicular to xy 4 & containing the point 9,8
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 11
72) Find the equation for a line with the given properties.
Perpendicular to 4y & containing the point 9,11
73) Simplify using properties of exponents.
257 34 yxxy
74) Simplify using properties of exponents.
10
73
12
18
xy
yx
75) Simplify using properties of exponents.
4353 yx
76) Simplify using properties of exponents.
2527 34 yxxy
77) Simplify using properties of exponents.
6101
573
12
8
zyx
zyx
78) Subtract the polynomials.
1275316964 234235 xxxxxxxx
79) Multiply the polynomials.
127535 234 xxxx
80) Multiply the polynomials.
169642 235 xxxxx
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 12
81) Multiply the polynomials.
324 xx
82) Multiply the polynomials.
1243 xx
83) Factor the polynomial (greatest common factor).
121830 yx
84) Factor the polynomial (greatest common factor).
456 41617 xxx
85) Factor the polynomial (greatest common factor).
42 41612 xxyx
86) Factor the polynomial.
16102 xx
87) Factor the polynomial.
24102 xx
88) Factor the polynomial.
27122 xx
89) Factor the polynomial.
1252 2 xx
90) Factor the polynomial.
12373 2 xx
91) Factor the polynomial.
25204 2 xx
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 13
92) Factor the polynomial.
492 x
93) Factor the polynomial.
1009 2 x
94) Factor the polynomial.
24142 2 xx
95) Factor the polynomial.
xx 123 3
96) Solve the system of equations by graphing.
32
1
43
xy
xy
97) Solve the system of equations by graphing.
63
2
yx
yx
98) Solve the system of equations by using substitution or elimination.
22
15
yx
xy
99) Solve the system of equations by using substitution or elimination.
32
5
yx
yx
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 14
100) Solve the system of equations by using substitution or elimination.
1053
712
yx
yx
101) Solve the system of equations by using substitution or elimination.
11
5
yx
yx
102) Solve the system of equations by using substitution or elimination.
93
1062
yx
yx
103) Solve the system of equations by using substitution or elimination.
323
234
yx
yx
104) Simplify the radical.
28
105) Simplify the radical.
128
106) Multiply the radicals and simplify.
62
107) Multiply the radicals and simplify.
55
108) Multiply the radicals and simplify.
6283
109) Multiply the radicals and simplify.
18526
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 15
110) Add the radicals.
22523
111) Add the radicals.
78363574
112) Add the radicals.
7512
113) Add the radicals.
18583
114) Evaluate the function notation.
5
72
fFind
xxf
115) Evaluate the function notation.
10
45
3
gFind
xxg
116) Evaluate the function notation.
3
1134 2
hFind
xxxh
117) Find the value of x in the function notation equation.
5
72
xfthatsoxFind
xxf
Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 16
118) Find the value of x in the function notation equation.
10
45
3
mgthatsomFind
xxg
Use the graph of xp to answer the following questions.
119) 9pFind
120) 4pFind
121) 8pFind
122) 5)( xpthatsoxFind
123) 4)( xpthatsoxFind
124) 1)( xpthatsoxFind
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.
