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Algebra 2 IB
Summer Math Assignment
ANSWER KEY
Use Khan Academy as a resource for help. There are videos explaining the objectives in this packet that you are required to know. www.khanacademy.org
Remember, there will be a test on these Algebra 1 objectives at the beginning of the school year!
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Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Order of Operations
Evaluate each expression.
1)
(
30 −
3) ÷ 3
9
2)
(
21 −
5) ÷ 8
2
3)
1 +
72
50
4)
5 × 4 −
8
12
5)
8 +
6 × 9
62
6)
3 +
17 × 5
88
7)
7 +
12 × 11
139
8)
15 +
40 ÷ 20
17
9)
20 + 16 −
15
21
10)
19 −
15 −
3
1
11)
9 ×
(
3 + 3) ÷ 6
9
12)
(
9 +
18 −
3) ÷ 8
3
-1-
1
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13)
9 +
6 ÷ (
8 −
2)
10
14)
4(
4 ÷ 2 + 4)
24
15)
6 +
(
5 + 8) × 4
58
16)
6 × 6 −
(
7 + 5)
24
17)
(
9 × 2) ÷ (
2 + 1)
6
18)
2 −
(
4 + 3 −
6)
1
19)
7 × 7 −
(
8 −
2)
43
20)
9 −
7 −
6 ÷ 6
1
21)
(
4 −
1 +
8 ÷ 8) × 5
20
22)
(
10 × 2) ÷ (
1 + 1)
10
23)
7 × 9 −
7 −
3 × 5
41
24)
8 −
1 −
(
18 −
2) ÷ 8
5
-2-
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
2
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Properties of Exponents
Simplify. Your answer should contain only positive exponents.
1) 2m2 ⋅ 2m
3
4m5
2) m4 ⋅ 2m
−3
2m
3) 4r−3
⋅ 2r2
8
r
4) 4n4 ⋅ 2n
−3
8n
5) 2k4 ⋅ 4k
8k5
6) 2x3y
−3 ⋅ 2x
−1y
3
4x2
7) 2y2 ⋅ 3x
6y2x
8) 4v3 ⋅ vu
2
4v4u2
9) 4a3b
2 ⋅ 3a
−4b
−3
12
ab
10) x2y
−4 ⋅ x
3y
2
x5
y2
11) (x2)0
1
12) (2x2)−4
1
16x8
13) (4r0)4
256
14) (4a3)2
16a6
15) (3k4)4
81k16
16) (4xy)−1
1
4xy
-1-3
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17)
(
2
b4)−1
1
2
b4
18)
(
x2
y−1)2
x4
y2
19)
(
2
x4
y−3)−1
y3
2
x4
20)
(3
m)−2
1
9
m2
21)
r2
2
r3
1
2
r
22)
x−1
4
x4
1
4
x5
23)
3
n4
3
n3
n
24)
m4
2
m4
1
2
25)
3
m−4
m3
3
m7
26)
2
x4
y−4
z−3
3
x2
y−3
z4
2
x2
3
yz7
27)
4
x0
y−2
z3
4
x
z3
y2x
28)
2
h3
j−3
k4
3
jk
2
h3k3
3
j4
29)
4
m4
n3
p3
3
m2
n2
p4
4
m2n
3
p
30)
3
x3
y−1
z−1
x−4
y0
z0
3
x7
yz
-2-
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________More Properties of Exponents
Simplify. Your answer should contain only positive exponents.
1)
(
x−2
x−3)4
1
x20
2)
(
x4)−3
⋅
2
x4
2
x8
3)
(
n3)3
⋅
2
n−1
2
n8
4)
(2
v)2 ⋅
2
v2
8
v4
5)
2
x2
y4 ⋅
4
x2
y4 ⋅ 3
x
3
x−3
y2
8
x8y6
6)
2
y3 ⋅
3
x
y3
3
x2
y4
2
y2
x
7)
x3
y3 ⋅
x3
4
x2
x4y3
4
8)
3
x2
y2
2
x−1
⋅
4
y
x2
3
xy
8
9)
x
(
2
x0)2
x
4
10)
2
m−4
(
2
m−4)3
m8
4
-1-
5
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11)
(
2
m2)−1
m2
1
2
m4
12)
2
x3
(
x−1)3
2
x6
13)
(
a−3
b−3)0
1
14)
x4
y3 ⋅
(
2
y2)0
x4y3
15)
b
a4 ⋅
(
2
b
a4)−3
1
8
b2a8
16)
(
2
x0
y2)−3
⋅
2
y
x3
x3
4
y5
17)
2
k3 ⋅
k2
k−3
2
k8
18)
(
x−3)4
x4
2
x−3
1
2
x5
19)
(2
x)−4
x−1
⋅
x
1
16
x4
20)
(
2
x3
z2)3
x3
y4
z2 ⋅
x−4
z3
8
x10z
y4
21)
(
2
p
m−1
q0)−4
⋅
2
m−1
p3
2
p
q2
m3
16
p2q2
22)
(
2
h
j2
k−2
⋅
h4
j−1
k4)0
2
h−3
j−4
k−2
h3j 4k2
2
-2-
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
6
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Graphing Lines
Sketch the graph of each line.
1)
x
y
x
y
2)
x
y
x
y
3)
y
x
y
4)
x
y
x
y
5)
x
x
y
6)
x
y
x
y
-1-
7
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7)
x
y
x
y
8)
x
y
x
y
9)
x
y
x
y
10)
y
x
y
11)
x
y
x
y
12)
x
y
x
y
-2-
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
8
©Q j2U0X1E2q 8Kpubt4aU hSEo0f9tWwFaFrKeU YLNLFCa.J m FArlWlx TrXiwgzhItlsT LrMeDsweWrCvneLdu.Q o HMEaUdCe1 Tw4iotchr sI9nUfIiznNiAtNeC 2Purreu-3Aflog2eJb0rVaE.z Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Graphing Lines in Slope-Intercept Form
Sketch the graph of each line.
1)
y
x
x
y
2)
y
x
x
y
3)
y
x
x
y
4)
y
x
x
y
5)
y
x
x
y
6)
y
x
y
-1-9
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7)
y
x
x
y
8)
x
x
y
9)
y
x
y
10)
y
x
x
y
11)
y
x
x
y
12)
y
x
x
y
-2-
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
10
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Answers to Graphing Linear Equations Using a Table of Values (ID: 1)
1)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
2)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
3)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
4)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
5)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
6)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
7)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
8)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
9)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
10)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
11)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
12)
−6 −4 −2 0 2 4 6
−6
−4
−2
2
4
6
11
Name :Teacher : Date :
Score :
Math-Aids.Com
Solving Systems of Equations by SubstitutionSolving Systems of Equations by Substitution
1 ) 5x - 4y = -23
-5x + 9y = 8
(-7,-3)
2 ) y = 12_ x + 3
y = 5
(4,5)
3 ) 8x + 3y = -9
6x = -18
(-3,5)
4 ) y = - 25_ x - 4
y = 95_ x + 7
(-5,-2)
5 ) y = - 3x - 15
y = 14_ x - 2
(-4,-3)
6 ) y = - 49_ x - 3
y = - 75_ x - 3
(0,-3)
7 ) -5x + 9y = -12
3x + 2y = 22
(6,2)
8 ) y = - 3x - 3
y = -3
(0,-3)
9 ) -3x - y = -24
y = 3x
(4,12)
10 ) y = x - 8
y = -4
(4,-4)
Name :Teacher : Date :
Score :
Math-Aids.Com
Solving Systems of Equations by EliminationSolving Systems of Equations by Elimination
1 ) y = 53_ x - 1
y = -6
(-3,-6)
2 ) x + y = 7
x - y = 3
(5,2)
3 ) 4x + 6y = -6
6y = 18
(-6,3)
4 ) y = - 6x - 3
y = - x + 2
(-1,3)
5 ) y = - 25_ x - 4
y = 95_ x + 7
(-5,-2)
6 ) 2x + y = -3
-3x + 2y = -8
(2,-7)
7 ) y = 52_ x - 4
y = - x + 3
(2,1)
8 ) y = 72_ x - 5
y = -5
(0,-5)
9 ) 9x - 2y = 19
7x = 21
(3,4)
10 ) -3x + 2y = -5
3x = 21
(7,8)
(2/7, -25/7)
Name :Teacher : Date :
Score :
Math-Aids.Com
Solving Systems of Equations Using Any MethodSolving Systems of Equations Using Any Method
1 ) y = 2x - 15
y = 5x
(-5,-25)
2 ) 5x + 2y = 21
-x - y = -9
(1,8)
3 ) y = 72_ x - 5
y = -5
(0,-5)
4 ) y = 12_ x + 3
y = 5
(4,5)
5 ) 3x + 23y = -4
5x = 20
(4,-8)
6 ) -x + 5y = -16
-3x + 7y = -8
(-9,-5)
7 ) x - 2y = 15
2x + 3y = 2
(7,-4)
8 ) y = - 2x + 2
y = 13_ x - 5
(3,-4)
9 ) y = 35_ x - 5
y = - 13_ x + 7
(6,5)
10 ) y = - 14_ x + 6
y = 4
(8,4)
Solving Systems of Equations Using Any Method
Solving Systems of Equations Using Any Method
(4, -16/23)
(90/7, 19/7)
Factoring Trinomials (a = 1)
ANSWER KEY
Factor each completely.
1) b b 2) n
− n
(b )(b ) (n − )(n − )
3) m m − 4) n
n −
(m − )(m ) (n − )(n )
5) n − n 6) b
b
(n − )(n − ) (b )
7) m m − 8) x
− x
(m )(m − ) Not factorable
9) k − k 10) a
a
(k − )(k − ) (a )(a )
11) n − n − 12) n
− n
(n )(n − ) (n − )(n − )
-1- Worksheet by Kuta Software LLC
13) b − b 14) n
n
(b − )(b − ) (n )(n )
15) n n − 16) n
n
(n )(n − ) (n n )
17) k k 18) a
− a −
(k )(k ) (a − )(a )
19) p p 20) v
− v
( p )( p ) (v − )(v − )
21) p p − 22) v
− v −
( p − )( p ) (v )(v − )
23) x − x 24) v
− v
(x − )(x − ) (v − )(v − )
25) p p − 26) v
v
( p − )( p ) (v )(v )
-2- Worksheet by Kuta Software LLC
Factoring By Grouping
ANSWER KEY
Factor each completely.
1) r − r
r − 2) p
− p
p −
(r )(r − ) ( p )( p − )
3) x x
− x − 4) v
− v
v −
(x − )(x ) (v
)(v − )
5) n n
− n − 6) k
− k
k −
(n − )(n ) (k
)(k − )
7) v v
v 8) n
n
− n −
(v )(v ) (n
− )(n )
9) n − n
n − 10) v
v − v −
(n )(n − ) (v
− )(v )
11) v − v
− v 12) x
− x x −
(v − )(v − ) (x
)(x − )
13) p p
− p − 14) r − r − r
( p − )( p ) (r
− )(r − ) -1- Worksheet by Kuta Software LLC
15) xw xk − yw − yk
(x − y)(w k )
17) x u x
v yu
yv (x y)(u v)
19) bc − bd − xc xd
(b − x)(c − d ) 21) xy − x ry − r
(x r)( y − )
23) a z − a
c xz −
xc (a x)(z − c)
25) xy − b xb − by
(x − b)( y b) 27) xy x y
(x )( y )
16) mc md − n c − n
d (m − n )(c d )
18) ac ak
bc
bk
(a b)(c
k )
20) mn − m n − m
(m )(n − m)
22) xy x ry r
(x r)( y )
24) xy − x − y
(x − )( y − ) 26) mz − nc mc − nz
(m − n)(z c)
28) uv u u v
(u )(v u)
-2- Worksheet by Kuta Software LLC
©o j2A0s1Q2g kKeuLtra0 ESvoXfGtFw7air3ez fLvLrCe.O Z oAvl5ld er7iPgyhat8s2 brAeqseebrxvveydF.W B xMwaYdZeD Nwii0tIhw oIqnvfFiOnUigtqe8 FAOlxgGejbVrEaI S1u.B Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Factoring Special Cases
Factor each completely.
1)
16
n2 − 9
(
4
n + 3)(
4
n − 3)
2)
4
m2 − 25
(
2
m + 5)(
2
m − 5)
3)
16
b2 − 40
b + 25
(
4
b − 5)2
4)
4
x2 − 4
x + 1
(
2
x − 1)2
5)
9
x2 − 1
(
3
x + 1)(
3
x − 1)
6)
n2 − 25
(
n + 5)(
n − 5)
7)
n4 − 100
(
n2 + 10)(
n2 − 10)
8)
a4 − 9
(
a2 + 3)(
a2 − 3)
9)
k4 − 36
(
k2 + 6)(
k2 − 6)
10)
n4 − 49
(
n2 + 7)(
n2 − 7)
-1-
©g Z2J0z1s2d YKruBt3aP NSMoGfbtJwcaZrNee vLtL0CR.8 j 0AYlPlx Proi0gUhAtpsF pr1ebsFearTvPeedr.k Y dMuazd7e7 SwPiGtWh6 fIunVf1iSnCittyeA hAZl2gWekbGrMac m1B.f Worksheet by Kuta Software LLC
11)
98
n2 − 200
2(
7
n + 10)(
7
n − 10)
12)
3 + 6
b + 3
b2
3
(
1 +
b)2
13)
400 − 36
v2
4(
10 + 3
v)(
10 − 3
v)
14)
100
x2 + 180
x + 81
(
10
x + 9)2
15)
10
n2 + 100
n + 250
10
(
n + 5)2
16)
49
n2 − 56
n + 16
(
7
n − 4)2
17)
49
x2 − 100
(
7
x + 10)(
7
x − 10)
18)
1 −
r2
(
1 +
r)(
1 −
r)
19)
10
p3 − 1960
p
10
p(
p + 14)(
p − 14)
20)
343
b2 − 7
b4
7
b2(
7 +
b)(
7 −
b)
21)
81
v4 − 900
v2
9
v2(
3
v + 10)(
3
v − 10)
22)
200
m4 + 80
m3 + 8
m2
8
m2
(
5
m + 1)2
-2-
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com