Free Printable Final Review: Algebra 2

1.

a)

10

b)

-10

c)

10i

d)

-10i

2.

a)

5i

b)

-5i

c)

5+i

d)

-5

3.

Solve
3x² - 5 = -446

a)

±√-147

b)

7i√3

c)

±7i√3

d)

-7√3

4.

What does i² equal?

a)

-1

b)

√-1

c)

1

d)

-√1

5.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

6.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

7.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

8.

What is this?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

9.

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

10.

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

a)

16

b)

8

c)

-8

d)

-24

11.

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

a)

16

b)

-8

c)

8

d)

-24

12.

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

a)

16

b)

-8

c)

24

d)

-24

13.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

14.

Solve 2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

15.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

16.

Solve
2x² + 17x + 21 = 0

a)

x= ^-21/₂, -17

b)

x= ²/₃, 16

c)

x=-7, ^-3/₂

d)

x=15, -³/₇

17.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

18.

Solve the System Graphically.

$y=-\left(x-2\right)^2+4$

$y=-5$

a)

(-1,-5)

b)

(5,-5)

c)

(-1,-5) and (5,-5)

d)

(-5,5)

19.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

20.

What are the solutions to the graphed system?

a)

(0,-2) and (3,1)

b)

(-2,0) and (2,0)

c)

(0,-2) and (3,1)

d)

(2,2) and (1,0)

21.

(3x + 4y - 3z) - (2x - 6y + 7z)

a)

x + 10y - 10z

b)

-x +10y - 10z

c)

x -10y - 10z

d)

-x -10y - 10z

22.

Which of the following are examples of like terms?

a)

2 and 2x

b)

y³and x³

c)

y and x

d)

-3x and 3x

23.

Add the polynomials.
(2x + 5y) + (3x - 2y)

a)

3x + 5y

b)

5x + 3y

c)

5x + 7y

d)

7xy + 1xy

24.

Add the polynomials.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

25.

What is the standard form of the polynomial,
9x² + 5x + 27 + 2x³

a)

27 + 5x + 9x² + 2x³

b)

9x² + 5x + 2x³ + 27

c)

9x² + 5x + 27 + 2x³

d)

2x³ + 9x² + 5x + 27

26.

Find the sum.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

27.

Add: (3x² + 2x + 1) + (2x² - 4x - 5) + (3x - 1)

a)

5x² + 6x - 7

b)

8x²- 3x - 5

c)

5x²+ x - 5

d)

6x² + 8x + 5

28.

Simplify the expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

29.

Determine the product of (3c)(10c)

a)

13c²

b)

30c

c)

30c²

d)

13c

30.

Simplify the expression
7u²v⁵ (9uv³)

a)

16u²v⁸

b)

63u³v¹⁵

c)

63uv⁸

d)

63u³v⁸

31.

Determine the simplified form of the expression 5(3x + 2)

a)

3x + 10

b)

15x + 10

c)

15x - 10

d)

3x - 10

32.

Expand 3a(5a² + 8a + 2) using the distributive property.

a)

15a³ + 24a² + 6a

b)

10a³ + 24a + 6

c)

8a³ + 11a² + 6a

d)

15a² + 24a + 6

33.

Dividex⁴ + x³ +2x² +x -1 by (x+1)

a)

x² + 2x -1

b)

x³ + 2x-1

c)

x² - 2x + 1

d)

x³ - 2x + 1

34.

Multiply (3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

35.

Multiply: (r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

36.

Multiply (n - 5)(n - 1)

a)

n² - 5n + 5

b)

n² - 6n + 5

c)

n²+ 5

d)

n² + 6n + 5

37.

Multiply 7x²y³ (2x⁴y⁵+6xy³)

a)

14x⁸y¹⁵+42x²y⁹

b)

9x⁶y⁸+13x³y⁶

c)

14x⁶y⁸+42x³y⁶

d)

14x⁶y⁸+42x²y⁶

38.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

39.

The degree of the polynomial determines the max number of roots.

a)

True

b)

False

40.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

41.

f(x) = 2x³ - 3x² + 4x -10

What is the degree of f(x)?

a)

3

b)

2

c)

1

d)

0

42.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

43.

What does it mean to be a factor of a number?

a)

Divides evenly with a remainder of zero.

b)

Divides unevenly with a remainder of 1.

44.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

45.

Find the zeros of the polynomial.

a)

A

b)

B

c)

C

d)

D

46.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

47.

Which transformation transforms the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a vertical translation 4 units up

b)

a vertical translation 4 units down

c)

a horizontal translation 4 units to the left

d)

a horizontal translation 4 units to the right

48.

How did we transform from y=x²toy = -3x²

a)

reflection in x-axis and vertical shift down

b)

reflection x-axis and vertical stretch

c)

horizontal stretch

d)

reflection x-axis and vertical compression

49.

If the blue graph is
f(x) = x²the red must be...

a)

g(x) = (x + 3)²

b)

g(x) = (x - 3)²

c)

g(x) = x²+ 3

d)

g(x) = x²- 2

50.

In the equation f(x)=1/2(x+9)²-1, what happens to the parabola?

a)

Reflect, horizontal compress by 1/2, left 9, down 1

b)

Vertical compress by 1/2, left 9, down 1

c)

Horizontal Compress by 1/2, right 9, down 1

d)

Vertical Stretch by 1/2, left 9, down 1

51.

In the equation f(x)=5(x+3)²-10 what does the 5 do?

a)

Vertical stretch by 5

b)

Horizontal compress by 5

c)

Reflect

d)

Move up 5

52.

$f\left(x\right)=x^2-2x+3$
Write a function that indicates a vertical stretch by 3.

a)

$f\left(x\right)=-3x^2+6x-9$

b)

$f\left(x\right)=3x^2-6x+9$

c)

$f\left(x\right)=9x^2-18x+27$

53.

Describe the transformation:

f\left(x\right)-1

a)

Up 1

b)

Down 1

c)

Right 1

d)

Left 1

54.

Describe the transformation:

\frac{1}{2}f\left(x\right)

a)

Vertical Compression by 1/2

b)

Vertical Stretch by 2

c)

Up 1/2

d)

Right 1/2

55.

Describe the transformation:

f\left(x+2\right)

a)

Up 2

b)

Down 2

c)

Right 2

d)

Left 2

56.

Describe the transformation:

f\left(5x\right)

a)

Horizontal Compression by 1/5

b)

Horizontal Stretch by 5

c)

Left 5

d)

Up 5

57.

Describe the transformation:

-f\left(x\right)

a)

Reflection across the x-axis

b)

Reflection across the y-axis

c)

Down 1

d)

Left 1

58.

Identify the parent function:

f\left(x\right)=2\left|x-2\right|+5

a)

$f\left(x\right)=\left|x\right|$

b)

$f\left(x\right)=x^2$

c)

$f\left(x\right)=\sqrt{x}$

59.

Describe the transformation:

f\left(x\right)=3\left|x-2\right|+5

a)

Vertical stretch by 3, Left 2, Up 5

b)

Vertical stretch by 3, Right 2, Up 5

c)

Vertical compression by 3, Right 2, Up 5

d)

Vertical stretch by 3, Down 2, Right 5

60.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

61.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

62.

solve for c

a)

7

b)

9

c)

4

d)

13

63.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

64.

a)

27/36

b)

27/45

c)

45/36

d)

45/27

65.

a)

18/30

b)

24/30

c)

18/24

d)

24/18

66.

Give the Ratio for TAN X

a)

Adj/Opp

b)

Opp/Adj

c)

Adj/Hyp

d)

Opp/Hyp

67.

a)

A

b)

B

c)

C

d)

D

68.

a)

A

b)

B

c)

C

d)

D

69.

What is the correct equation to solve for x?

a)

tan (45) = x/13

b)

cos (45) = x/13

c)

sin (45) = 13/x

d)

sin (45) = x/13

70.

Cos X

a)

⁸/₁₅

b)

¹⁷/₁₅

c)

¹⁵/₁₇

d)

⁸/₁₇

71.

Sin C

a)

²⁴/₃₀

b)

¹⁸/₃₀

c)

³⁰/₂₄

d)

³⁰/₁₈

72.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

73.

Which number is the EXPONENT?
4^{2 =}16

a)

4

b)

2

c)

16

74.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

75.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

76.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

77.

a)

1/96a¹⁰b⁸

b)

-4a^-10b^-2/24b⁶

c)

a^-10/6b⁸

d)

1/6a¹⁰b⁸

78.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

79.

Use the change of base formula and your calculator to approximate the log.

a)

A

b)

B

c)

C

d)

D

80.

Use the change of base formula and your calculator to approximate the log.

a)

A

b)

B

c)

C

d)

D

81.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

82.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

83.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

84.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

85.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

86.

Rewrite 10³ = 1000 in logarithmic form.

a)

log ₁₀₀₀ 3 = 10

b)

log ₃10 = 1000

c)

log 3 = 1000

d)

log 1000 = 3

87.

Evaluate: log ₂16 = x

a)

3

b)

2

c)

4

d)

5

88.

Simplify: e^ln7

a)

log_e7

b)

7

c)

ln7

d)

e⁷

89.

Solve for x.
log₅1 = x

a)

0

b)

-1

c)

2

d)

1

90.

Change to Logarithmic Form:
12² = 144

a)

log₂ 144 = 12

b)

log₁₂ 144 = 2

c)

log ₁₂ 2 = 144

d)

log ₂ 12 = 144

91.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

92.

a)

b)

c)

d)

93.

a)

b)

c)

d)

94.

a)

b)

c)

d)

95.

a)

b)

c)

d)

96.

a)

b)

c)

d)

97.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

98.

Factor and cancel out in order to simplify.

a)

9(x+10)

b)

x+10

c)

9

d)

x+9

99.

Simplify.

a)

A

b)

B

c)

C

d)

D

100.

simplify by factoring out and canceling out.

a)

a

b)

b

c)

c

d)

d

Final Review: Algebra 2

Total questions: 100

Worksheet time: 7hrs 55mins

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