Free Printable Savvas Algebra 2

1.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

2.

Identify the 'a' value: y = 16x² -8x -24

a)

16

b)

8

c)

-8

d)

-24

3.

Identify the 'b' value: y = 16x² -8x -24

a)

16

b)

-8

c)

8

d)

-24

4.

Identify the 'b' value: y = 16x² -8x -24

a)

16

b)

-8

c)

8

d)

-24

5.

Identify the 'c' value: y = 16x² -8x -24

a)

16

b)

-8

c)

24

d)

-24

6.

Solve the equation by factoring:
x²-6x+8=0

a)

2, 4

b)

-2, -4

c)

-2, 4

d)

2, -4

7.

Solve the equation by the quadratic formula:

5x² - 35x + 60 = 0

a)

3, -4

b)

-3, 4

c)

3, 4

d)

-3, -4

8.

Solve by using the quadratic formula:
15x²+22x=-8

a)

-2/3, 4/5

b)

2/3, -4/5

c)

2/3, 4/5

d)

-2/3, -4/5

9.

Use the quadratic formula to find the solutions for
y = 3x³ + 8x - 1

a)

0.1167 and -2.7833

b)

.7 and -16.7

c)

.35 and -8.35

d)

0.2358 and -1.236

10.

Use the quadratic formula to find the solutions for
y = 2x² - 9x + 5

a)

-8.14 and 6.14

b)

-4.07 and 3.07

c)

-2.035 and 1.535

d)

ZERO solutions

11.

Use the quadratic formula to find the solutions for
y = -x² - 5x + 12

a)

-4.9 and -0.1

b)

-8.54 and 8.54

c)

-0.45 and 3.55

d)

-6.77 and 1.77

12.

Identify a, b, and c in: x²−6x+14

a)

3,5,9

b)

1,-6,14

c)

1,-6,-14

d)

1,6,14

13.

Solve 3x² - 11x + 10

a)

1.7 or 2

b)

1 or 2

c)

1.5 or 2

d)

-1.7 or 2

14.

Solve 8x² - 6x + 1 = 0

a)

No Solution

b)

0 or 1

c)

-0.5 or -0.25

d)

0.25 or 0.5

15.

find x for
2x²-8x-24=0

a)

x= 6, -2

b)

x= 2, -6

c)

x= 4, 2

d)

x= 2, 6

16.

find x for
x²+2x-8=0

a)

x= -4, 2

b)

x= -4, -2

c)

x= 4, 2

d)

x= -2, 4

17.

Factor
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

18.

Factor Completely:
x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

19.

Factor x²-6x+8

a)

(x-4)(x-2)

b)

(x+4)(x+2)

c)

(x-4)(x+2)

d)

(x+4)(x-2)

20.

a)

A

b)

B

c)

C

d)

D

21.

5x+4=^-6

a)

2

b)

-2

c)

10

d)

15

22.

-4x+1=21

a)

x=120

b)

x=5

c)

x=30

d)

x=-5

23.

Solve each equation for the following variable.
1. x - 4 = 12

a)

x = 8

b)

x = 16

c)

x = -8

d)

x = 3

24.

2. 2x + 6 = 14

a)

x = 4

b)

x = 10

c)

x = -4

d)

x = 3

25.

Solve for x:
-30 - 5x = 120

a)

x = 18

b)

x = -18

c)

x = 30

d)

x = -30

26.

What is the RANGE of this graph?

a)

-7<x<5

b)

-7≤x<5

c)

-3<x<1

d)

-3≤x<1

27.

a)

[-3, 2)

b)

(-4, 2]

c)

(-5, 2]

d)

[-4, 2]

28.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: (2,0)

b)

maximum: (2,5)

c)

minimum: (5,0)

d)

maximum: (5,0)

29.

Solve: 2^3x = 15

a)

2.3

b)

-2.3

c)

1.3

d)

-1.3

30.

log (x - 1) - log (x - 2) = log 5

a)

7

b)

4/9

c)

9/4

d)

1/7

31.

Solve:
log₄x² - log₄(x-1) = 1

a)

4

b)

3

c)

2

d)

1

32.

Solve.

a)

A

b)

B

c)

C

d)

D

33.

4^(x-2)= 64^(x+1)

a)

-2/5

b)

-5/2

c)

7/2

d)

2/7

34.

2^x+6=32

a)

x=-1

b)

x=11

c)

x=1

d)

x=-11

35.

Solve the exponential equation:

a)

-11/4

b)

6

c)

9/4

d)

8

36.

Simplify the following logarithmic function:
log₂2⁸=

a)

8

b)

2

c)

1

d)

16

37.

Rewrite as a single log:
4 log g - 2 log h

a)

log (4g/2h)

b)

log (g⁴/h²)

c)

log (g⁴ - h²)

d)

log (2gh)

38.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

39.

Expand.

a)

A

b)

B

c)

C

d)

D

40.

Expand.

a)

A

b)

B

c)

C

d)

D

41.

Condense logarithm

a)

15log₈u+ 3log₈v

b)

15log₈u- 3log₈v

c)

log₈(u¹⁵/v³)

d)

log₈u¹⁵v³

42.

Condense logarithm

a)

log₈(x⁶)/log₈(y³)

b)

log₈(x⁶/y³)

c)

log₈(x/y³)

d)

log₈(x⁶y³)

43.

Expand

a)

log₃9 - log₃x + log₃y

b)

log₃9 + log₃x + log₃y

c)

2 - log₃x + log₃y

d)

2 - log₃x - log₃y

44.

Expand

a)

2log₃6 + 2log₃x

b)

2log₃6 + log₃x

c)

4 + 2log₃x

d)

4 + log₃x

45.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

46.

Are the following inverses of each other?

a)

True

b)

False

47.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = √(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) =√(x+5)

d)

f^-1(x) = x² - 5

48.

Was the inverse function found correctly?

a)

no,

b)

yes

49.

Identify the Transformations.

a)

Vertical stretch by 2 and down 4

b)

Horizontal compression by ½ and down 4

c)

Vertical stretch by 2 and up 4

d)

Horizontal compression by ½ and right 4

50.

Solve the cube root equation

a)

344

b)

21

c)

-344

d)

-21

51.

Solve the cube root equation

a)

-984

b)

984

c)

26

d)

-26

52.

Solve the cube root equation

a)

78

b)

-228

c)

228

d)

-78

53.

Solve the cube root equation

a)

900

b)

990

c)

0

d)

90

54.

Solve the cube root equation

a)

27

b)

20

c)

3

d)

30

55.

Solve the cube root equation

a)

-125

b)

125

c)

25

d)

-25

56.

simplify

a)

a

b)

b

c)

c

d)

d

57.

simplify.

a)

a

b)

b

c)

c

d)

d

58.

simplify.

a)

a

b)

b

c)

c

d)

d

59.

simplify.

a)

a

b)

b

c)

c

d)

d

60.

simplify.

a)

a

b)

b

c)

c

d)

d

61.

simplify.

a)

a

b)

b

c)

c

d)

d

62.

simplify.

a)

a

b)

b

c)

c

d)

d

63.

simplify.

a)

a

b)

b

c)

c

d)

d

64.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

65.

Simplify.

a)

A

b)

B

c)

C

d)

D

66.

Simplify.

a)

A

b)

B

c)

C

d)

D

67.

Factor

k²- 7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

68.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

69.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

70.

Factor
81m² - 1

a)

not factorable

b)

(m-9)(m+9)

c)

9m(9m-1)

d)

(9m-1)(9m+1)

71.

12x + 9

a)

3(4x + 3)

b)

x(12+9)

c)

3(4x - 3)

d)

not factorable

72.

Factor Completely:
x⁴-9x²Hint: Factor GCF first.

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

73.

Simplify (x² + 3x - 10) / (x² - 1x - 2)

a)

(x - 5) / (x - 1)

b)

(x + 5) / (x + 1)

c)

(x - 2) / (x - 3)

d)

(x + 2) / (x + 3)

74.

Simplify (4x - 20) / (4x - 4)

a)

(x - 5) / (x - 1)

b)

(x + 5) / (x + 1)

c)

(x - 2) / (x - 3)

d)

(x + 2) / (x + 3)

75.

Simplify (x²- 7x + 10) / (x²- 8x + 15)

a)

(x - 5) / (x - 1)

b)

(x + 5) / (x + 1)

c)

(x - 2) / (x - 3)

d)

(x + 2) / (x + 3)

76.

Solve the cube root equation

a)

36

b)

-216

c)

216

d)

-36

77.

Solve the cube root equation

a)

-984

b)

984

c)

26

d)

-26

78.

The graph of a function is shown. What are the domain and range of this function?

a)

Domain: (-∞, ∞)
Range: (-∞, ∞)

b)

Domain: [-7, ∞)
Range: (-∞, ∞)

c)

Domain: (-∞, ∞)
Range: (-∞, 3]

d)

Domain: [-7, ∞)
Range: (-∞, 3]

79.

The graph of a function is shown. What are the domain and range of this function?

a)

Domain: (-∞, ∞)
Range: (-∞, 2]

b)

Domain: [2, ∞)
Range: (-∞, ∞)

c)

Domain: (-∞, ∞)
Range: (-∞, ∞)

d)

Domain: (-∞, 2]
Range: [2, ∞)

80.

What is the minimum or maximum point of y = (x - 2)³ - 6?

a)

Minimum: -6

b)

Minimum: -2

c)

Maximum: 64

d)

None--it goes on forever

81.

What is the domain of the function?
*Hint: Domain is the set of all x-values included in the function.

a)

x≥3

b)

x≤3

c)

All real numbers

d)

-1≤x≤5

82.

When is this graph increasing? Hint: As x-values increase, where are the y-values increasing?

a)

x>2

b)

x<2

c)

y>2

d)

y<2

83.

What is the range of the function?
*Hint: Range is all of the y-values included in the function.

a)

y≤3

b)

y≥3

c)

All real numbers

d)

x≥3

84.

What is the range?

a)

y≥-3

b)

y≥-1

c)

All real numbers

d)

y≤-1

85.

Find the vertical asymptote(s) (if any) of the graph of the function.
3x / (x² - 9)

a)

x=3

b)

x=0

c)

None

d)

X=3, x=-3

86.

Find the vertical asymptote(s) (if any) of the graph of the function.
3x / (x² - 9)

a)

x=3

b)

x=0

c)

None

d)

X=3, x=-3

87.

State the vertical asymptote:
(x-2)
______
(x+5).

a)

x = -2/5

b)

x = -5/2

c)

x = -5

d)

x = 2

88.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

89.

Find the vertical asymptote(s).

a)

None

b)

x = 0

c)

x= 4

d)

x = -4, 4

90.

Where is the vertical asymptote?

a)

x=3

b)

DNE

c)

x=8

d)

y=3

91.

What is the horizontal asymptote?

a)

y = 2

b)

y = -2

c)

x = 2

d)

y = 0

92.

Find the horizontal asymptote.
4x-16
_________
x²-16

a)

y=2

b)

y=1

c)

y=0

d)

none

93.

What are the asymptotes?

a)

x=-3, y=1

b)

x=3, y =1

c)

x=-3, y =-1

d)

x=3 y=-1

94.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

95.

What are the asymptotes

a)

x=1, x= 2, y =1, y= 2

b)

x= 1, x=-1, y = 1

c)

x=1 y =1

d)

x=-1, y =1, y =-1

96.

Solve log(x) + log(x+3) = 1

a)

5

b)

-2

c)

-5

d)

2

97.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

98.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

99.

Expand

a)

A

b)

B

c)

C

d)

D

100.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

101.

a)

A

b)

B

c)

C

d)

D

102.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2 ; -4 is extraneous

d)

1 ; -3 is extraneous

103.

Solve for x:
5 e^6x+3= 0.1

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

104.

Solve 5e^{3x - 2} + 15 = 35

a)

1.13

b)

1.29

c)

1.10

d)

0.87

105.

Solve log₅(4x-7)=log₅(x+5).

a)

x=4

b)

x=-4

c)

x=3

d)

x=-2

106.

Solve

a)

A

b)

B

c)

C

d)

D

Savvas Algebra 2

Total questions: 106

Worksheet time: 5hrs 48mins

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