Algebra 2

Name___________________________________ ID: 1

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Summer Homework Packet Date________________ Simplify each expression. (Hint: Use distributive property.) 1) - 4 ( 7b - 8 ) - 8 ( b + 2 ) 2) 3 ( a - 3 ) - 8 ( 9 - 9a )

3) 4 ( 2 - 9n ) + 3 ( 1 - 3n )

4) - ( r - 4 ) + 5 ( - 3 - 8r )

5) 9 ( 4 - 4n ) + 8 ( 5n - 1 )

6) 8 ( - 8a + 8 ) - ( 1 - 8a )

7) - 6b -

( )

7 5 b+1 2 2

8)

(

Period____

)

5 9 19 v+1 + 2 10 9

Worksheet by Kuta Software LLC ©P V2i0\1k5Y LKEuGtaaS ASKosfltYwwaBraew xLDLTC^.F ` gAGlhlU jreiugFhctysY KrxeNsLeTrYv\eHdN.F J yMYavdqe] QwaiotPhg HIwnmf[iNnoivtnea [AllYgBeVbtrkaf T1r.

Name: ___________________________ Date:__________________Pd._____ Exponent Rules Review Worksheet Product Rule: When multiplying monomials that have the same base, add the exponents. xm × xn = xm+ n Example 1: x × x3 × x 4 = x1+ 3+ 4 = x8 2 3 4 2 3 4 5 5 Example 2: 2 x y − 3x y = 2 ×( − 3) × x × x × y × y = − 6 x y

(

)(

)

Power Rule: When raising monomials to powers, multiply the exponents.

(x )

m n

= x m×n

Example 3: (x2y3)4 = x2 • 4 y3 • 4 = x8y12 Example 4: (2x3yz 2)3 = 23 x3 • 3 y3 z2 • 3 = 8x9y3z6 Quotient Rule: When dividing monomials that have the same base, subtract the exponents. xm = xm− n xn x3 56 Example 5: − 2 = x 3− ( − 2) = x 5 Example 6: 2 = 56 − 2 = 54 x 5 3 5 3 5 36m n 36 m n Example 7: = × × 4 = − 4m 2 n 4 − 9mn −9 m n Simplify each of the following. Copy the problem. Work on your own paper. 1) a × a 2 × a 3

2)

6) (2x2y3)2

7) (5x2y4)3

x3 11) x

18c 3 12) − 3c 2

(2a2b)(4ab2)

3)

(6x2)(-3x5)

8) (6x4y6)3

13)

9a 3b5 − 3ab 2

4) b3 ×b 4 ×b7 ×b

5) (3x3)(3x4)(-3x2)

9) (4x3y3)3

10) (7xy)2

− 48c 2 d 4 14) − 8cd

22 y 6 z 8 15) 2 yz − 7

Algebra 2

Name___________________________________ ID: 1

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Summer Homework Packet

Date________________ Period____

Simplify. Your answer should contain only positive exponents. (Hint: Use 1)

n

-2

0

-3

2)

(2n - 1 ) - 4

2

3)

× 2n

n × 2n

-3

×n

(n 2 ) 2

4)

p p

laws of exponents)

4

(2 p 3 ) 3

( ) x × 2x 2x

-1

-4

Find the discriminant of each quadratic equation then state the number and type of solutions. (Hint: The discriminant is the b^2 -4ac part of the quadratic formula.) 5) - 2b 2 - 8b - 8 = 0

6) 4 x 2 - 8 x + 4 = 0

7) - k 2 - 2k - 1 = 0

8) - 3v 2 - 5v - 3 = - 5

Worksheet by Kuta Software LLC

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9) - 4a 2 + 3a - 5 = 2

10) - m 2 + 3m - 3 = 2

11) 9n 2 + 7 = - 4n

12) - 8 x 2 + 4 x = 8

13) 3v 2 + 6v = - 3

14) 6 x 2 - 5 = - 5 - 8 x

15) 6n 2 + 4n + 4 = - 6

16) - 7n 2 - 1 = - 3n

Solve each equation. (Hint: For Absolute 17)

3 p = 15

Value equations, if |x| = 2, x = 2 or -2.) 18)

8+k =1

Worksheet by Kuta Software LLC

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19)

x - 8 = 13

21)

-

10 100 a = 9 27

20)

33 396 n = 7 49

22)

9 9 x = 32 64

Use the information provided to write the vertex form equation of each parabola. (Hint: Complete the square.) 23) y = x 2 + 20 x + 106

24) y = - 3 x 2 - 36 x - 109

25) y = - 5 x 2 - 60 x - 185

26) y = - 7 x 2 - 42 x - 60

Worksheet by Kuta Software LLC

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Use the information provided to write the intercept form equation of each parabola. (Hint: Use Greatest Common Factor and then factor. EX: 27) y = - 8 x 2 - 16 x + 280

28) y = -

29) y = 2 x 2 - 2 x - 12

1 2 13 x + x - 21 2 2

30) y = x 2 + 11 x + 24

Identify the vertex, axis of symmetry, direction of opening, min/max value, and x-intercepts of each. Then sketch the graph. 31) y = x 2 + 10 x + 24

32) y = x 2 + 9 x + 18

y

-8

-6

-4

y

8

8

6

6

4

4

2

2

-2

2

4

6

8 x

-8

-6

-4

-2

2

-2

-2

-4

-4

-6

-6

-8

-8

4

6

8 x

Worksheet by Kuta Software LLC

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33) y = 2 x 2 - 20 x + 42

34) y =

y 8

1 2 5 14 x - x3 3 3 y

-8

-6

-4

6

8

4

6

2

4

-2

2

4

2

8 x

6

-2 -8

-6

-4

-2

2

-4

-2

-6

-4

-8

-6

4

6

8 x

-8

Simplify. (Hint: Simplify 35) - 3

18 -

12 + 3

37) 3

20 -

20 -

39) 3

12 -

54 + 2

the radicals and then combine like terms.)

2 +2

8 -3

27 - 3

3

2

3

36) - 3

12 - 3

5 +2

45 - 2

3

38) 3

54 + 3

6 +3

54 + 2

8

40) 3

20 - 3

3 +2

18 - 2

27

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Solve each equation with the quadratic formula. Leave answers in simplified radical form. (Hint:You need to make a quadratic expression equal to zero before using the quadratic formula .) 41) 6n 2 + 4n = 10

42) v 2 - 19 = 10v

43) 3 p 2 + 5 p = 2

44) 4 p 2 = - 3 p + 7

Sketch the graph of each lin ear equation. (Hint:You need to get the Y value by itself to determine the slope and the Y-Intercept.) 45) 5 x - 4 y = 20

46) 3 x + y = - 5 y

y

6

6

5

5

4

4

3

3

2

2

1

1

-6 -5 -4 -3 -2 -1

1

2

3

4

5

6 x

-6 -5 -4 -3 -2 -1

1

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

47) x-intercept = 4, y-intercept = 4

3

4

5

6 x

48) x-intercept = - 3, y-intercept = 3

y

y

6

6

5

5

4

4

3

3

2

2

1

1

-6 -5 -4 -3 -2 -1

2

1

2

3

4

5

6 x

-6 -5 -4 -3 -2 -1

1

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

2

3

4

5

6 x

-6

-6-

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49) y = 6 x - 4

50) y = 1 y

y

6

6

5

5

4

4

3

3

2

2

1

1

-6 -5 -4 -3 -2 -1

1

2

3

4

5

6 x

-6 -5 -4 -3 -2 -1

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

51) - 9 + 8 x - 3 y = 0

2

3

4

5

6 x

1

2

3

4

5

6 x

52) - 5 x - 3 y = 9

y

y

6

6

5

5

4

4

3

3

2

2

1

1

-6 -5 -4 -3 -2 -1

1

1

2

3

4

5

6 x

-6 -5 -4 -3 -2 -1

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

Solve each linear

system algebraically AND by graphing. (Hint: To solve algebraically, make both

linear equations equal to each other.)

3 x-2 4 1 y=- x+2 4

1 x+2 4 y= x-3

53) y =

54) y = -

y 5

y 5

4

4

3

3

2

2

1

1

-5

-4

-3

-2

-1

1

2

3

4

5 x

-1 -5

-4

-3

-2

-1

1

2

3

4

5 x

-1

-2

-2

-3

-3

-4

-4

-5

-5

Worksheet by Kuta Software LLC

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55) y = - 4 y = -3 x - 1

56) y = - x + 3 y = -x - 1 y

-5

-4

-3

-2

y

5

5

4

4

3

3

2

2

1

1

-1

1

2

3

4

5 x

-5

-4

-3

-2

-1

1

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

Solve each linear

2

3

4

5 x

system by graphing. (Hint: Get the Y value by itself before graphing.) 58) 2 y + x = - 8 -1 = y - x

1 y=0 2 -4 + 2 y = - x

57) x + 2 +

y 5

y 5

4

4

3

3

2

2

1

1

-5

-4

-3

-2

-1

1

2

3

4

5 x

-1 -5

-4

-3

-2

-1

1

2

3

4

5 x

-1

-2

-2

-3

-3

-4

-4

-5

-5

Worksheet by Kuta Software LLC

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