-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
1/17
Algebra 2ID: 1
Name___________________________________
Period____Date________________Semester Review Packet
Find the value that completes the square and then rewrite as a perfect square.
1) x2 40x + __
A) 81; (x 9)2
B) 144; (x 12)2
C) 400; (x 20)2
D) 100; (x 10)2
2) y2 + 24y + __
A) 4; (y + 2)2
B) 144; (y + 12)2
C) 576; (y + 12)2
D) 144; (y + 12)2
3) m2 2m + __
A) 1; (m 1)2
B) 169; (m + 13)2
C) 4; (m 1)2
D) 1; (m 1)2
4) x2 + 10x + __
A) 36; (x + 6)2
B) 1; (x + 1)2
C) 256; (x + 16)2
D) 25; (x + 5)2
Find the discriminant of each quadratic equation then state the number and type of solutions.
5) x2 6x + 9 = 0
A) 0; one real solution
B) 72; two real solutions
C) 0; two real solutions
D) 0; two imaginary solutions
6) 4p2 8p + 4 = 0
A) 0; two real solutions
B) 0; one real solution
C) 144; two real solutions
D) 128; two real solutions
7) 3n2 + 6n 3 = 0
A) 72; two real solutions
B) 0; one real solution
C)81
; two real solutionsD) 0; two real solutions
8) 6m2 + 3m + 3 = 0
A) 63; one real solution
B) 63; two real solutions
C)63
; two imaginary solutionsD) 260; two imaginary solutions
Solve each equation.
9) 42 = 7(1 + p)
A) {5}
B) {11}C) { All real numbers. }
D) {16}
10) 3(4 + 3x) = 21
A) {2} B) {1}
C) {3} D) {6}
11) 55 = 5(7 + 4n)
A) {9} B) No solution.C) {1} D) {11}
12) 6(b + 7) = 24
A) {3}B) {3}C) { All real numbers. }
D) No solution.
Solve each equation by factoring.
13) x2 + 16 = 10x
A) {3, 8} B) {2, 8}
C) {6, 8} D) {2, 8}
14) r2 = 12r 35
A) {5, 4} B) {5, 6}
C) {5, 7} D) {5, 7}
-1-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
2/17
15) n2 13n = 40
A) {8, 8} B) {5, 8}
C) {3, 4} D) {5, 8}
16) a2 8 = 7a
A) {1, 6} B) {7, 0}
C) {1, 8} D) {8, 2}
Solve each equation with the quadratic formula.
17) x2 4 = 0
A) {5, 2} B) {2, 2}
C) {2, 5} D) {1, 1}
18) v2 + 12v 28 = 0
A) {14, 2}
B) {2, 14}
C) {11, 6}D) {6 + 43 , 6 43}
19) 4x2 64 = 0
A) {4, 4}
B) {8, 8}
C) {3 + 114, 3 114}D) {5, 7}
20) n2 5n 6 = 0
A) {3, 2}
B) {1, 6}
C) {5 + 312
,5 31
2}
D) {6, 1}
21) 4k2 + 6k 3 = 0
A) {2 77
, 2 7
7}
B) {3 + 214
,3 21
4}
C) { 305
, 30
5}
D) {2, 2}
22) 5p2 + 2p 13 = 0
A) {1 + 665
,1 66
5}
B) {7 + 372
,7 37
2}
C) {1 + 14, 1 14}
D) {7 + 612
,7 61
2}
23) 5n2 + 5n 9 = 0
A) {5 + 612 ,5 61
2 }B) {5 + 205
10,
5 205
10}
C) {5 + 7010
,5 70
10}
D) {5 + 612
,5 61
2}
24) 2x2 + 4x 11 = 0
A) {1 + 54 ,1 5
4 }B) {3 + 141
6,
3 141
6}
C) {1 + 54
,1 5
4}
D) {2 + 262
,2 26
2}
25) 2r2 + 2 = 0
A) {2 + i 62 ,2 i 6
2 }B) {i 22 ,
i 2
2 }C) { 2
2,
2
2}
D) {i, i}
26) 8m2 = 6
A) {2 + 22
,2 2
2}
B) {i 32 , i 3
2 }C) {1 + i, 1 i}
D) {4 + 2 2, 4 2 2}
-2-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
3/17
27) 6x2 = 2x 8
A) {2 + i 65 ,2 i 6
5 }B) {1, 43}C) {5 + i 1510 ,
5 i 15
10 }D) {1 + i 476 , 1 i 476 }
28) 2n2 = 2n 4
A) {2i 33 , 2i 3
3 }B) {1 + i 72 ,
1 i 7
2 }C) {2 + 2i 67 ,
2 2i 6
7 }D) {1 + i 72 , 1 i 72 }
Simplify. Your answer should contain only positive exponents.
29) 3nm3
4n2
A) 12n3m3 B) 12m4n
C) m2n2 D) 9n4
30) 3x4y
2 x
2y
2
A) 6yx B) 9x7y8
C)3
x2D) 8x5y4
31) 4x3y
3 4y
2
A) 6x2y8 B)4x5
y
C) 16x3y5 D)1
x6y4
32) m 4nm4
A)3n6
mB) 4m6n3
C) 8m5n3 D) 4m5n
33) (y1)3
A) 27y6 B)64y3
x6
C)1
y
3D) 27x6y6
34) (2vu4)4
A)256u8
v12B) 16v4u16
C)1
v
9D)
u3v3
8
35)4vu
2
4u3
A)3v4
4B)
v
u5
C)u4
3v6D)
v3u2
4
36)4xy
3
4yx4
A)y5x3
4B)
3
2
C)3y3
xD)
y2
x3
37)ba
4
a
A)4
a5B)
b
a5
C)b6
2D) 2a2b4
38)3x
xy4
A)4y4
3x2B)
3
4
C) 3y4 D)4y6
x
-3-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
4/17
Factor each completely.
39) v3 8v2 20v
A) v(v + 2)(v 10)B) (v + 4)(v 5)C) v(v + 2)(v + 10)D) v(v + 10)(v 2)
40) 2a2 + 8a 10
A) Not factorable
B) 3(a 10)(a 8)C) 2(a + 5)(a + 1)D) 2(a + 5)(a 1)
41) 2r2 + 8r 90
A) 2(r 9)(r 5)B) 2(r+ 9)(r+ 5)C) 2(r+ 9)(r 5)D) 2(r+ 15)(r 3)
42) x2 17x + 72
A) (x 9)(x + 8)B) (x 9)(x 8)C) (x + 4)(x + 18)D) (x + 9)(x + 8)
43) 27m3 + 125
A) (3m + 5)(9m2 15m + 25)B) (3m + 5)(9m2 + 15m + 25)C) (3m 5)(9m2 + 15m + 25)
D) (3m + 5)3
44) 125x3 8
A) (5x 2)3
B) (5x 2)(25x2 + 10x + 4)C) (5x 2)(5x + 2)D) (5x + 2)(25x2 10x + 4)
45) 125m3 + 27
A) (5m + 3)(25m2 15m + 9)B) (5m + 3)(25m2 + 15m + 9)
C) (5m + 3)3
D) (5m 3)(25m2 + 15m + 9)
46) 3x3 81
A) 3(x 3)3
B) 3(x 3)(x + 3)C) 3(x + 3)(x2 3x + 9)D) 3(x 3)(x2 + 3x + 9)
Evaluate each function.
47) h(a) = a2 + a; Find h(4)
A) 56 B) 72
C) 42 D) 20
48) h(t) = t+ 1; Find h(10)
A) 10 B) 2
C) 9 D) 449) h(x) = 3x + 1; Find h(6)
A) 25 B) 17
C) 7 D) 22
50) f(n) = n2 + 2n; Find f(8)
A) 15 B) 35
C) 48 D) 1
Find the inverse of each function.
51) f(x) =5 3x
5
A) f1(x) = x + 2
B) f1(x) = x + 26
C) f1(x) =
5x + 5
3
D) f1(x) = 3x 4
52) f(n) =2 5n
2
A) f1(n) =
4n
3
B) f1(n) =
4
3n +
4
3
C) f1(n) = 2n + 8
D) f1(n) =
2n + 2
5
-4-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
5/17
53) g(x) = 3x 5
A) g1(x) =
3
2x
B) g1(x) = 2
3
5x
C) g1(x) = 1
2
3x
D) g1(x) =1
3x +
5
3
54) g(x) =8 + x
2
A) g1(x) =
3x 15
7
B) g1(x) = 5 +
4
5x
C) g1(x) = 2x 8
D) g1(x) = x + 154
Sketch the graph of each line.
55) 5x 2y = 2
A)
6 4 2 0 2 4 6
6
4
2
2
4
6
B)
6 4 2 0 2 4 6
6
4
2
2
4
6
C)
6 4 2 0 2 4 6
6
4
2
2
4
6
D)
6 4 2 0 2 4 6
6
4
2
2
4
6
56) 5x + 4y = 12
A)
6 4 2 0 2 4 6
6
4
2
2
4
6
B)
6 4 2 0 2 4 6
6
4
2
2
4
6
C)
6 4 2 0 2 4 6
6
4
2
2
4
6
D)
6 4 2 0 2 4 6
6
4
2
2
4
6
-5-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
6/17
57) y = 1
A)
6 4 2 0 2 4 6
6
4
2
2
4
6
B)
6 4 2 0 2 4 6
6
4
2
2
4
6
C)
6 4 2 0 2 4 6
6
4
2
2
4
6
D)
6 4 2 0 2 4 6
6
4
2
2
4
6
58) y = 2
A)
6 4 2 0 2 4 6
6
4
2
2
4
6
B)
6 4 2 0 2 4 6
6
4
2
2
4
6
C)
6 4 2 0 2 4 6
6
4
2
2
4
6
D)
6 4 2 0 2 4 6
6
4
2
2
4
6
-6-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
7/17
Sketch the graph of each linear inequality.
59) x > 1
A)
6 4 2 0 2 4 6
6
4
2
2
4
6
B)
6 4 2 0 2 4 6
6
4
2
2
4
6
C)
6 4 2 0 2 4 6
6
4
2
2
4
6
D)
6 4 2 0 2 4 6
6
4
2
2
4
6
60) y > x 5
A)
6 4 2 0 2 4 6
6
4
2
2
4
6
B)
6 4 2 0 2 4 6
6
4
2
2
4
6
C)
6 4 2 0 2 4 6
6
4
2
2
4
6
D)
6 4 2 0 2 4 6
6
4
2
2
4
6
-7-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
8/17
61) y < 2x 1
A)
6 4 2 0 2 4 6
6
4
2
2
4
6
B)
6 4 2 0 2 4 6
6
4
2
2
4
6
C)
6 4 2 0 2 4 6
6
4
2
2
4
6
D)
6 4 2 0 2 4 6
6
4
2
2
4
6
62) y 1
5x 4
A)
6 4 2 0 2 4 6
6
4
2
2
4
6
B)
6 4 2 0 2 4 6
6
4
2
2
4
6
C)
6 4 2 0 2 4 6
6
4
2
2
4
6
D)
6 4 2 0 2 4 6
6
4
2
2
4
6
-8-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
9/17
Identify the vertex and axis of symmetry of each. Then sketch the graph.
63) y = x2 + 8x + 12
A)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 4)Axis of Sym.: x = 4
B)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 4)Axis of Sym.: x = 4
C)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 4)Axis of Sym.: x = 4
D)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 4)Axis of Sym.: x = 4
64) y = 2x2 + 16x 34
A)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 2)Axis of Sym.: x = 4
B)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 2)Axis of Sym.: x = 4
C)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (2, 4)Axis of Sym.: x = 2
D)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (3, 3)Axis of Sym.: x = 3
-9-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
10/17
65) y = (x + 2)2 6
A)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (2, 6)Axis of Sym.: x = 2
B)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (6, 2)Axis of Sym.: x = 6
C)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (2, 6)Axis of Sym.: x = 2
D)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (2, 6)Axis of Sym.: x = 2
66) y = 2(x + 4)2 4
A)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 4)Axis of Sym.: x = 4
B)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 4)Axis of Sym.: x = 4
C)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 4)Axis of Sym.: x = 4
D)
x
y
8 6 4 2 2 4 6 8
8
6
4
2
2
4
6
8 Vertex: (4, 4)Axis of Sym.: x = 4
-10-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
11/17
Sketch the graph of each function.
67) y > 2x2 4x 5
A)
8 6 4 2 0 2
12
10
8
6
4
2
B)
8 6 4 2 0 2 4
14
12
10
8
6
4
2
C)
0 2 4 6 8 10
12
10
8
6
4
2
D)
7 6 5 4 3 2 1 0
1
2
3
4
5
6
7
8
68) y > 2x2 + 12x 17
A)
0 1 2 3 4 5 6 7 8 9 10
10
8
6
4
2
B)
10 0 10 20 30
50
40
30
20
10
C)
6 5 4 3 2 1 0 1
6
5
4
3
2
1
1
D)
4 2 0 2 4
8
6
4
2
2
-11-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
12/17
69) y 2x2 8x 6
A)
6 4 2 0 2 4 6 8
2
4
6
8
10
12
14
B)
1 0 1 2 3 4 5
3
2
1
1
2
3
C)
0 1 2 3 4 5 6 7 8 9 10
2
4
6
8
10
D)
6 4 2 0 2
6
4
2
2
70) y < x2 6x 13
A)
7 6 5 4 3 2 1 0 1
8
6
4
2
B)
2 0 2 4 6
2
4
6
8
10
C)
6 4 2 0 2 4
2
4
6
8
10
12
D)
6 5 4 3 2 1 0
1
2
3
4
5
6
7
Solve each system by graphing.
71) y = 2
3x + 4
y =4
3x 2
A) (1, 2) B) (3, 2)C) (2, 3) D) (3, 2)
72) y =7
4x + 3
y =1
4x 3
A) (4, 4) B) (5, 2)C) (5, 4) D) (5, 5)
-12-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
13/17
73) y = x 3
y = 2x + 3
A) (1, 2) B) (2, 1)C) (1, 4) D) (2, 1)
74) y =1
2x + 1
y =5
2x 3
A) (2, 2) B) (2, 2)C) (4, 4) D) (2, 2)
75) x + 4y = 8
5x + 4y = 8
A) (4, 3)B) Infinite number of solutions
C) No solution
D) (4, 3)
76) x y = 4
y = 2
A) (2, 2) B) (2, 4)C) (2, 4) D) (2, 2)
77) 2x + y = 3
x + 3y = 6
A) (3, 3) B) No solutionC) (3, 3) D) (3, 3)
78) x y = 2
6x y = 3
A) (1, 3)B) (1, 3)C) Infinite number of solutions
D) (1, 3)
-13-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
14/17
Sketch the solution to each system of inequalities.
79) y > x + 3
y > x 2
A)
4 2 0 2 4
4
2
2
4
B)
4 2 0 2 4
4
2
2
4
C)
4 2 0 2 4
4
2
2
4
D)
4 2 0 2 4
4
2
2
4
80) y 4
3x 1
y 1
3x + 2
A)
4 2 0 2 4
4
2
2
4
B)
4 2 0 2 4
4
2
2
4
C)
4 2 0 2 4
4
2
2
4
D)
4 2 0 2 4
4
2
2
4
-14-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
15/17
81) y 1
3x 2
y >2
3x + 1
A)
4 2 0 2 4
4
2
2
4
B)
4 2 0 2 4
4
2
2
4
C)
4 2 0 2 4
4
2
2
4
D)
4 2 0 2 4
4
2
2
4
82) y 1
3x + 1
y >4
3x 2
A)
4 2 0 2 4
4
2
2
4
B)
4 2 0 2 4
4
2
2
4
C)
4 2 0 2 4
4
2
2
4
D)
4 2 0 2 4
4
2
2
4
-15-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
16/17
Write the slope-intercept form of the equation of each line.
83)
5 4 3 2 1 0 1 2 3 4 5
4
2
2
4
A) y = 2
5x + 2
B) y =2
5x + 2
C) y =4
5x + 2
D) y=x
+ 2
84)
5 4 3 2 1 0 1 2 3 4 5
4
2
2
4
A) y =3
2x + 4
B) y = 3
2x + 4
C) y = 4x 3
2
D) y = 4x +3
2
85) 4x 7y = 3
A) y =5
7
x +3
7
B) y =4
7x +
3
7
C) y = 4
7x +
3
7
D) y =2
7x +
3
7
86) 7x 5y = 51
A) y =51
5
x +4
5
B) y = 51
5x +
4
5
C) y =7
5x
51
5
D) y =4
5x
51
5
Write the slope-intercept form of the equation of the line through the given point with the given slope.
87) through: (4, 4), slope = 2
A) y = 2x + 2 B) y = 4x + 2
C) y = 2x + 2 D) y = 2x + 4
88) through: (3, 4), slope = 0
A) x = 4 B) x = 1
C) y = 4 D) x = 4
Write the slope-intercept form of the equation of the line through the given points.
89) through: (0, 5) and (5, 5)
A) y = 2x + 5 B) y = 5x 2
C) y = 2x + 5 D) y = x 2
90) through: (0, 5) and (2, 0)
A) y =5
2x + 5
B) y = 5
2x + 5
C) y = 5x + 5
2
D) y = x +5
2
Write the slope-intercept form of the equation of the line described.
91) through: (5, 5), parallel to y = 1
5x 3
A) y = x 4 B) y = 1
5x 4
C) y =1
5x 4 D) y = 4x 4
92) through: (5, 4), parallel to y = 8
5x + 5
A) y = 8
5x 4 B) y = 4x
1
5
C) y = 1
5x 4 D) y = 4x
1
5
-16-
-
7/28/2019 Algebra 2 - Semester Review Packet No Answers
17/17
93) through: (4, 5), perp. to y = 1
2x + 5
A) y = 3x + 2 B) y = 3x + 2
C) y = 2x 3 D) y = 2x 3
94) through: (1, 4), perp. to y = x + 1
A) y = 2x 5 B) y = x 5
C) y = 5x + 1 D) y = x 5
Simplify each expression.
95) (1 + b4 + b2) + (7b4 7b2 + 7)
A) 3b4 7b2 + 8
B) 3b4 8b2 + 8
C) 3b4 6b2 + 8
D) 8b4 6b2 + 8
96) (7 + 2x3 4x2) (3x4 3x3 + x2)
A) 3x4 + 11x3 5x2 + 7
B) 3x4 + 11x3 + x2 + 3
C) 3x4 + 5x3 5x2 + 7
D) 3x4 + 11x3 5x2 + 3
97) Wilbur and Ndiba each improved their yards by planting rose bushes and ornamental grass. They
bought their supplies from the same store. Wilbur spent $78 on 3 rose bushes and 6 bunches of
ornamental grass. Ndiba spent $136 on 12 rose bushes and 2 bunches of ornamental grass. What is the
cost of one rose bush and the cost of one bunch of ornamental grass?
A) rose bush: $5, bunch of ornamental grass: $7 B) rose bush: $10, bunch of ornamental grass: $8
C) rose bush: $8, bunch of ornamental grass: $10 D) rose bush: $12, bunch of ornamental grass: $4
98) Lisa and Shayna each improved their yards by planting hostas and ivy. They bought their supplies from
the same store. Lisa spent $46 on 2 hostas and 4 pots of ivy. Shayna spent $78 on 4 hostas and 6 pots
of ivy. What is the cost of one hosta and the cost of one pot of ivy?
A) hosta: $5, pot of ivy: $10 B) hosta: $4, pot of ivy: $3
C) hosta: $7, pot of ivy: $9 D) hosta: $9, pot of ivy: $7
99) The water park is a popular field trip destination. This year the senior class at High School A and the
senior class at High School B both planned trips there. The senior class at High School A rented and
filled 8 vans and 7 buses with 251 students. High School B rented and filled 9 vans and 14 buses with
411 students. Each van and each bus carried the same number of students. How many students can a
van carry? How many students can a bus carry?
A) Van: 13, Bus: 21 B) Van: 18, Bus: 13C) Van: 21, Bus: 13 D) Van: 5, Bus: 10
100) Amy and Jennifer each improved their yards by planting daylilies and ornamental grass. They bought
their supplies from the same store. Amy spent $108 on 8 daylilies and 14 bunches of ornamental grass.
Jennifer spent $78 on 12 daylilies and 7 bunches of ornamental grass. What is the cost of one daylily
and the cost of one bunch of ornamental grass?
A) daylily: $6, bunch of ornamental grass: $3 B) daylily: $4, bunch of ornamental grass: $3
C) daylily: $3, bunch of ornamental grass: $6 D) daylily: $2, bunch of ornamental grass: $7