Download Algebra 2 IB Summer Math Assignment ANSWER KEY

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!
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Order of Operations
Date________________ Period____
Evaluate each expression.
1) (30 − 3) ÷ 3
2) (21 − 5) ÷ 8
9
3) 1 + 7
2
2
4) 5 × 4 − 8
50
12
5) 8 + 6 × 9
6) 3 + 17 × 5
62
88
7) 7 + 12 × 11
8) 15 + 40 ÷ 20
139
9) 20 + 16 − 15
17
10) 19 − 15 − 3
21
11) 9 × (3 + 3) ÷ 6
1
12) (9 + 18 − 3) ÷ 8
9
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3
1
-1-
Worksheet by Kuta Software LLC
13) 9 + 6 ÷ (8 − 2)
14) 4(4 ÷ 2 + 4)
10
24
15) 6 + (5 + 8) × 4
16) 6 × 6 − (7 + 5)
58
24
17) (9 × 2) ÷ (2 + 1)
18) 2 − (4 + 3 − 6)
6
1
19) 7 × 7 − (8 − 2)
20) 9 − 7 − 6 ÷ 6
43
1
21) (4 − 1 + 8 ÷ 8) × 5
22) (10 × 2) ÷ (1 + 1)
20
10
24) 8 − 1 − (18 − 2) ÷ 8
23) 7 × 9 − 7 − 3 × 5
41
5
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2
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1
Name___________________________________
Properties of Exponents
Date________________ Period____
Simplify. Your answer should contain only positive exponents.
1) 2m 2 ⋅ 2m 3
2) m 4 ⋅ 2m −3
4m 5
2m
3) 4r
−3
⋅ 2r 2
4) 4n 4 ⋅ 2n −3
8n
8
r
5) 2k 4 ⋅ 4k
6) 2x 3 y −3 ⋅ 2x −1 y 3
8k 5
4x 2
7) 2 y 2 ⋅ 3x
8) 4v 3 ⋅ vu 2
6 y2x
9) 4a 3 b 2 ⋅ 3a −4 b −3
4v 4 u 2
10) x 2 y −4 ⋅ x 3 y 2
x5
y2
12
ab
11) ( x
2 0
)
12) (2x
1
13) (4r 0 )
)
1
16x 8
4
2
14) (4a 3 )
16a 6
256
15) (3k 4 )
2 −4
4
16) (4xy)
81k 16
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−1
1
4xy
3-1-
Worksheet by Kuta Software LLC
4 −1
17) (2b
2 −1 2
)
18) ( x y
x4
y2
1
2b 4
4 −3 −1
19) (2 x y
20) (3m)
)
y3
2x4
21)
r
22)
3
3n
4
24)
3n 3
4
m
4
2m 4
1
2
3m −4
26)
m3
4 x 0 y −2 z 3
27)
4x
2h 3 k 3
3 j4
4m 4 n 3 p 3
2 2
3 x 2 y −3 z 4
2h 3 j −3 k 4
28)
3 jk
z3
y2x
3m n p
2 x 4 y −4 z −3
2x2
3 yz 7
3
m7
29)
−1
1
4x5
n
25)
x
4x
1
2r
23)
−2
1
9m 2
2
2r
)
30)
4
3 x 3 y −1 z −1
−4 0 0
x y z
4m 2 n
3p
3x7
yz
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
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4
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1
Name___________________________________
More Properties of Exponents
Date________________ Period____
Simplify. Your answer should contain only positive exponents.
1) ( x −2 x −3 )
4
2) ( x 4 )
1
x 20
3) (n
3 3
)
⋅ 2n
2
4) (2v) ⋅ 2v
−1
2x2 y4 ⋅ 4x2 y4 ⋅ 3x
6)
−3 2
3 3
x y ⋅x
2 y3 ⋅ 3x y3
2 4
3x y
8x8y6
2 y2
x
3
2 2
8)
4x2
x4 y3
4
9)
2
8v 4
3x y
7)
⋅ 2x4
2
x8
2n 8
5)
−3
2 x −1 ⋅ 4 y x 2
3 xy
8
x
10)
(2 x 0) 2
2m
−4
(2m −4 ) 3
m8
4
x
4
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3x y
5
-1-
Worksheet by Kuta Software LLC
11)
(2m 2) −1
m
12)
2
−3 −3 0
)
4 3
−3
16) (2 x 0 y 2 )
x3
4 y5
2k 3 ⋅ k 2
( x −3 ) 4 x 4
18)
k −3
2k 8
21)
−3
1
8b 2 a 8
)
−1
⋅ 2 yx3
2 x −3
1
2x5
(2 x) −4
x
2 0
x4y3
15) ba 4 ⋅ (2ba 4 )
19)
( x −1 ) 3
14) x y ⋅ (2 y
1
17)
3
2x6
1
2m 4
13) (a b
2x
20)
⋅x
(2 x 3z 2) 3
3 4 2
−4 3
x y z ⋅x z
1
16 x 4
8 x 10 z
y4
(2 pm −1 q 0) −4 ⋅ 2m −1 p 3
(2h j 2k −2 ⋅ h 4 j −1 k 4) 0
22)
2 pq 2
2h −3 j −4 k −2
h3j 4k2
2
m3
16 p 2 q 2
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
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6
-2-
Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 1
Name___________________________________
Graphing Lines
Date________________ Period____
Sketch the graph of each line.
1)  x y
2)  x y

     
y

















 x
     
















 x





 x





 x
4)  x y
3) y

     
y

















 x
     
y











6)  x y
5) x

     
y
y

















 x
     











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7
-1-
Worksheet by Kuta Software LLC

8)  x y
7) x y

     
y

















 x
     









y

















 x
     




 x





 x





 x
y











11) x y
12) x y

     

10) y

     


9) x y
y
y

















 x
     











y
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
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8
-2-
Worksheet by Kuta Software LLC

Kuta Software - Infinite Pre-Algebra
Name___________________________________
Graphing Lines in Slope-Intercept Form
Date________________ Period____
Sketch the graph of each line.
2) y x

1) y x




y








     

     
y






 x






 x





 x





 x











4) y x

3) y x

y









     
y







 x

     











5) y x
6) y

     
y

















 x
     











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y
9
-1-
Worksheet by Kuta Software LLC


7) y x

8) x



y








     

     
y






 x






 x





 x





 x










10) y x
9) y

     
y

















 x
     











12) y x

y








y


     


11) y x
y






 x

     











Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
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Answers to Graphing Linear Equations Using a Table of Values (ID: 1)
1)
2)
−6
−4
3)
6
6
6
4
4
4
2
2
2
−2 0
−2
2
4
6
−6
−4
−2 0
−2
2
4
6
−6
−4
−4
−6
−6
−6
5)
−4
6
6
4
4
4
2
2
2
−2 0
−2
2
4
6
−6
−4
−2 0
−2
2
4
6
−6
−4
−6
−6
−6
6
6
6
4
4
4
2
2
2
−2 0
−2
2
4
6
−6
−4
−2 0
−2
2
4
6
−6
−4
−2 0
−2
−4
−4
−4
−6
−6
−6
6
6
4
4
4
2
2
2
2
4
6
6
2
4
6
2
4
6
12)
6
−2 0
−2
4
9)
11)
−4
−2 0
−2
−4
10)
−6
−4
−4
8)
−4
2
6)
6
7)
−6
−2 0
−2
−4
4)
−6
−4
−6
−4
−2 0
−2
2
4
6
−6
−4
−2 0
−2
−4
−4
−4
−6
−6
−6
2
4
6
11
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-3-
Worksheet by Kuta Software LLC
Name :
Score :
Teacher :
Date :
Solving Systems of Equations by Substitution
1 ) 5x - 4y = -23
6 ) y = - 4_9 x - 3
-5x + 9y = 8
y = - 7_5 x - 3
(-7,-3)
(0,-3)
2 ) y = 1_2 x + 3
7 ) -5x + 9y = -12
y=5
3x + 2y = 22
(4,5)
(6,2)
3 ) 8x + 3y = -9
8 ) y = - 3x - 3
6x = -18
y = -3
(-3,5)
(0,-3)
4 ) y = - 2_5 x - 4
9 ) -3x - y = -24
y = 9_5 x + 7
y = 3x
(-5,-2)
(4,12)
5 ) y = - 3x - 15
10 ) y = x - 8
y = 1_4 x - 2
y = -4
(-4,-3)
(4,-4)
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Solving Systems of Equations by Elimination
1 ) y = 5_3 x - 1
6 ) 2x + y = -3
y = -6
-3x + 2y = -8
(-3,-6)
(2,-7)
(2/7, -25/7)
2) x + y = 7
7 ) y = 5_2 x - 4
x-y=3
y=-x+3
(5,2)
(2,1)
3 ) 4x + 6y = -6
8 ) y = 7_2 x - 5
6y = 18
y = -5
(-6,3)
(0,-5)
4 ) y = - 6x - 3
9 ) 9x - 2y = 19
y=-x+2
7x = 21
(-1,3)
(3,4)
5 ) y = - 2_5 x - 4
10 ) -3x + 2y = -5
y = 9_5 x + 7
3x = 21
(-5,-2)
(7,8)
Math-Aids.Com
Name :
Score :
Teacher :
Date
:
Solving Systems of Equations
Using
Any Method
Solving
Systems
ofofEquations
AnyMethod
Method
Solving
Systems
Equations Using
Using Any
1 ) y = 2x - 15
6 ) -x + 5y = -16
y = 5x
-3x + 7y = -8
(-5,-25)
(-9,-5)
2 ) 5x + 2y = 21
7 ) x - 2y = 15
-x - y = -9
2x + 3y = 2
(1,8)
(7,-4)
3 ) y = 7_2 x - 5
8 ) y = - 2x + 2
y = -5
y = 1_3 x - 5
(0,-5)
(3,-4)
4 ) y = 1_2 x + 3
9 ) y = 3_5 x - 5
y=5
y = - 1_3 x + 7
(4,5)
(90/7,
(6,5) 19/7)
5 ) 3x + 23y = -4
10 ) y = - 1_4 x + 6
5x = 20
y=4
(4,
-16/23)
(4,-8)
(8,4)
Math-Aids.Com
Factoring Trinomials (a = 1)
ANSWER KEY
Factor each completely.
1) b b 
2) n − n 
(b )(b )
3) m  m − 
(n − )(n − )
4) n n − 
(m − )(m )
5) n − n 
(n − )(n )
6) b b 
(b )
(n − )(n − )
7) m m − 
8) x  − x 
(m )(m − )
9) k  − k 
Not factorable
10) a a 
(a )(a )
(k − )(k − )
11) n − n − 
12) n − n 
(n )(n − )
(n − )(n − )
-1-
Worksheet by Kuta Software LLC
13) b − b 
14) n n 
(n )(n )
(b − )(b − )
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 )
21)  p   p − 
(v − )(v − )
22) v  − v − 
( p − )( p )
23) x  − x 
(v )(v − )
24) v  − v 
(x − )(x − )
25) p   p − 
(v − )(v − )
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 − 
(r
( p 
)(r − )
3) x  x  − x − 
(x
2)  p  −  p  p − 
)( p − )
4) v  − v  v − 
(v
− )(x )
)(v − )
5) n n − n − 
6) k  − k  k − 
(n − )(n )
(k )(k − )
7) v  v  v 
(v
8) n n − n − 
(n − )(n )
)(v )
9) n − n n − 
10) v  v  − v − 
(n )(n − )
11) v  − v  − v 
(v
(v
12) x  − x  x − 
(x
− )(v − )
13)  p   p −  p − 
( p 
− )(v )
)(x − )
14) r  − r  − r 
− )( p )
(r
-1-
− )(r − )
Worksheet by Kuta Software LLC
15) xw xk  −  yw −  yk

16) mc md − n c − n
(x −  y)(w k  )
d (m − n
)(c d )
17) x  u x  v  yu 
18) ac  ak  bc  bk
yv (x  y)(u  v)
(a b)(c k )
19) bc − bd − xc xd
(b − x)(c − d )

20) mn − m  n − m
(m )(n − m)
21) xy − x ry − r
(x r)( y − )
22) xy x ry r
23) a z − a  c xz −
24) xy  − x −  y
(x r)( y )
xc (a x)(z − c)
25) xy − b  xb − by
(x − b)( y b)
27) xy x  y
(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
Kuta Software - Infinite Algebra 1
Name___________________________________
Factoring Special Cases
Date________________ Period____
Factor each completely.
1) 16n 2 − 9
2) 4m 2 − 25
(4n + 3)(4n − 3)
3) 16b 2 − 40b + 25
(2m + 5)(2m − 5)
4) 4 x 2 − 4 x + 1
(4b − 5) 2
5) 9 x 2 − 1
(2 x − 1) 2
6) n 2 − 25
(3 x + 1)(3 x − 1)
7) n 4 − 100
(n + 5)(n − 5)
8) a 4 − 9
(n 2 + 10)(n 2 − 10)
9) k 4 − 36
(a 2 + 3)(a 2 − 3)
10) n 4 − 49
(k 2 + 6)(k 2 − 6)
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(n 2 + 7)(n 2 − 7)
-1-
Worksheet by Kuta Software LLC
11) 98n 2 − 200
12) 3 + 6b + 3b 2
2(7n + 10)(7n − 10)
13) 400 − 36v 2
3(1 + b)
14) 100 x 2 + 180 x + 81
4(10 + 3v)(10 − 3v)
15) 10n 2 + 100n + 250
10(n + 5)
(10 x + 9) 2
16) 49n 2 − 56n + 16
2
17) 49 x 2 − 100
(7n − 4) 2
18) 1 − r 2
(7 x + 10)(7 x − 10)
19) 10 p 3 − 1960 p
(1 + r)(1 − r)
20) 343b 2 − 7b 4
10 p( p + 14)( p − 14)
21) 81v 4 − 900v 2
2
7b 2 (7 + b)(7 − b)
22) 200m 4 + 80m 3 + 8m 2
9v 2 (3v + 10)(3v − 10)
8m 2 (5m + 1) 2
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC