Free Printable Algebra 2 3rd Quarter Review

1.

$i^2=$

a)

$i$

b)

$-1$

c)

$-i$

d)

$1$

2.

$\sqrt{-1}=$

a)

$i$

b)

$-1$

c)

$-i$

d)

$1$

3.

$\sqrt{-64}$

a)

$8i$

b)

$-8$

c)

$8$

d)

$\pm8i$

4.

Solve: $x^2+36=0$

a)

$\pm6$

b)

$-6$

c)

$6i$

d)

$\pm6i$

5.

$\left(3-i\right)-\left(2+4i\right)=$

a)

$10+10i$

b)

$1-5i$

c)

$6-4i^2$

d)

$10$

6.

$\left(3-i\right)\left(2+4i\right)=$

a)

$10+10i$

b)

$1-5i$

c)

$6-4i^2$

d)

$10$

7.

$\sqrt{-12}$

a)

$2i\sqrt{3}$

b)

$4i\sqrt{3}$

c)

$-2\sqrt{3}$

d)

$-4i\sqrt{3}$

8.

$\sqrt{-18}$

a)

$3i\sqrt{2}$

b)

$9i\sqrt{2}$

c)

$-3\sqrt{2}$

d)

$-9i\sqrt{2}$

9.

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

a)

4

b)

2

c)

8

d)

20

10.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

11.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

12.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

13.

Complete the Square
x² + 10x + ____

a)

x² + 10x - 100

b)

x² + 10x + 100

c)

x² + 10x - 25

d)

x² + 10x + 25

14.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

15.

Solve by completing the square.
$x^2-8x-20=0$

a)

$x=\left\{-2,\ 10\right\}$

b)

$x=\left\{-10,\ 2\right\}$

c)

$x=\left\{-20,\ -8\right\}$

d)

$x=\left\{8,\ 20\right\}$

16.

Solve by completing the square.
$x^2-12x+20=0$

a)

$x=\left\{2,\ 10\right\}$

b)

$x=\left\{-10,\ -2\right\}$

c)

$x=\left\{-12,\ 20\right\}$

d)

$x=\left\{12,\ 20\right\}$

17.

Solve by completing the square.
$x^2-6x-27=0$

a)

$x=\left\{-9,\ -3\right\}$

b)

$x=\left\{-3,\ 9\right\}$

c)

$x=\left\{-9,\ 3\right\}$

d)

$x=\left\{3,\ 9\right\}$

18.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

19.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

20.

Factor 4x² - 81

a)

(4x - 9)(x + 9)

b)

(2x - 9)(2x + 9)

c)

(2x - 9)(2x - 9)

d)

(4x - 1)(x + 81)

21.

Factor

k^2+7k+10

.

a)

$(k+2)(k-5)$

b)

$(k+2)(k+5)$

c)

$(k+10)(k+4)$

d)

$(k-2)(k-5)$

22.

Factor $k^2-2k-24$

a)

$(k-4)(k+6)$

b)

$(k+4)(k+6)$

c)

$(k+6)(k-1)$

d)

$(k+4)(k-6)$

23.

Does the quadratic have a maximum or minimum vertex, and does the parabola open up or down?

a)

max/ opens down

b)

min/ opens up

c)

max/ opens up

d)

min/ opens down

24.

What is the vertex for
f(x)=4(x-2)² + 3

a)

(-2, 3)

b)

(2,-3)

c)

(4,3)

d)

(2,3)

25.

What is the axis of symmetry for
f(x)=4(x-2)² + 3

a)

4

b)

2

c)

x = -2

d)

x = 2

26.

Which of the following equations matches vertex form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

27.

What piece of information does h identify in the following equation?
y=a(x-h)²+k

a)

y value of the vertex

b)

Axis of Symmetry

c)

Direction (facing up or down)

d)

x-intercept

28.

Explain the translation:

y = (x + 9)² + 5

a)

translated left 9, up 5

b)

translated left 9, down 5

c)

translated right 9, up 5

d)

translated right 9, down 5

29.

Explain the translation:

y = (x - 5)² - 1

a)

translated right 5, up 1

b)

translated left 5, down 1

c)

translated right 5, down 1

d)

translated left 5, up 1

30.

If the blue graph is
f(x) = x²
then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

31.

What is the vertex for
f(x)=4(x-2)² + 3

a)

(-2, 3)

b)

(2,-3)

c)

(4,3)

d)

(2,3)

32.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

33.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

34.

Solve Using the Quadratic Formula
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

35.

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

a)

16

b)

-8

c)

24

d)

-24

36.

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

37.

Name "c" for the equation
4x² - 5x + 7 = 10

a)

7

b)

17

c)

-5

d)

-3

38.

a)

A

b)

B

c)

C

d)

D

39.

a)

A

b)

B

c)

C

d)

D

40.

a)

A

b)

B

c)

C

d)

D

41.

Use the quadratic formula to determine the solutions.

2x² + 2x - 12?

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

42.

Use the quadratic formula to determine the solutions.

2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

43.

The formula to determine how many solutions a quadratic equation is called the discriminant which is...

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

44.

What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

45.

If the discriminant is negative, you will have....

a)

two real solutions

b)

two irrational solutions

c)

no solution

d)

one solution

46.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

47.

Use the discriminant to determine the number of solutions the following quadratic equation has.

6x² − 2x − 3 = 0

a)

76 Two Solutions

b)

29 Two Solutions

c)

68 Two Solutions

d)

none of these

48.

What is the degree of the polynomial?

3y² + y⁴ + 4

a)

2

b)

3

c)

4

d)

5

49.

What is the degree of the polynomial:

3x² + 9x⁵ − 4 + 10x⁸ + 2x⁹

a)

8

b)

9

c)

5

d)

-4

50.

Describe the degree and leading coefficient for the polynomial shown.

a)

Lead Coefficient: Positive

Degree: Even

b)

Lead Coefficient: Positive

Degree: Odd

c)

Lead Coefficient: Negative

Degree: Even

d)

Lead Coefficient: Negative

Degree: Odd

51.

Describe the degree and leading coefficient for the polynomial shown.

a)

Lead Coefficient: Positive

Degree: Even

b)

Lead Coefficient: Positive

Degree: Odd

c)

Lead Coefficient: Negative

Degree: Even

d)

Lead Coefficient: Negative

Degree: Odd

52.

Describe the degree and leading coefficient for the polynomial shown.

a)

Lead Coefficient: Positive

Degree: Even

b)

Lead Coefficient: Positive

Degree: Odd

c)

Lead Coefficient: Negative

Degree: Even

d)

Lead Coefficient: Negative

Degree: Odd

53.

Describe the degree and leading coefficient for the polynomial shown.

a)

Lead Coefficient: Positive

Degree: Even

b)

Lead Coefficient: Positive

Degree: Odd

c)

Lead Coefficient: Negative

Degree: Even

d)

Lead Coefficient: Negative

Degree: Odd

54.

Describe the degree and leading coefficient for the polynomial shown.

a)

Lead Coefficient: Positive

Degree: Even

b)

Lead Coefficient: Positive

Degree: Odd

c)

Lead Coefficient: Negative

Degree: Even

d)

Lead Coefficient: Negative

Degree: Odd

55.

In the above graph complete the following end behavior: (f(x)=y)
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

56.

Which shows the polynomial $8x^2+16x+8$ completely factored?

a)

$\left(4x+4\right)^2$

b)

$\left(4x+4\right)\left(2x+2\right)$

c)

$8\left(x+1\right)^2$

d)

$8\left(x+1\right)\left(x-1\right)$

57.

Add the polynomial (-3x + 4) + (8x - 5)

a)

5x - 9

b)

5x - 1

c)

11x - 1

d)

11x - 9

e)

None of these

58.

Subtract the following polynomials:
(3x²-3x+2)-(x²-2x+1)

a)

2x²+x+1

b)

2x²-5x+3

c)

2x²-x+1

d)

4x²-5x+3

59.

Subtract the following polynomials:
(2x³+6x²+4x-2)-(x³+4x²-x)

a)

x³+2x²+5x-2

b)

x³+10x²+3x-2

c)

3x³+2x+4x-3

d)

3x³+10x²-3x-2

60.

(4x³-5x²+3x)+(-2x³-x²+6x)

a)

2x³-6x²-9x

b)

2x³+6x²+9x

c)

-2x³-6x²+9x

d)

2x³-6x²+9x

e)

None of these

61.

Add the following polynomials

(x³-6x²+3)+(3x³+4x-1)

a)

4x³-2x²+2

b)

4x³-6x²+4x+2

c)

-2x³+2x+2

d)

4x³-2x²-2

e)

None of these

62.

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

a)

x-intercept

b)

zero

c)

root

d)

all of these.

63.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

64.

If a zero of a polynomial function has multiplicity 4 that means:

a)

The x intercept is at (4, 0)

b)

The graph will "bounce back" at that zero

c)

The graph will "pass through" at that zero

d)

Zeros cannot have multiplicity of 4

65.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

66.

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

a)

0

b)

-3

c)

9

d)

5

67.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

68.

Factor Completely: x⁴-9x²

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

69.

Factor Completely: 2k²-14k-60

a)

2(k-10)(k-3)

b)

Not Factorable

c)

(k-5)(k+9)

d)

2(k-10)(k+3)

70.

In the above graph, which root has a multiplicity of 2?

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

a)

-1

b)

-3

c)

-120

d)

4

71.

Simplify:
√45

a)

9√5

b)

3√5

c)

5√9

d)

3√15

72.

Simplify:
3√16

a)

12

b)

48

c)

√12

d)

3√4

73.

a² + b² = c^{2
a = 9 b = 40}

a)

c = 41

b)

c = 65

c)

c = 25

d)

c = 5

74.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

75.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

76.

What is the length of u and v in this 30-60-90 triangle?

a)

u = 8 v = 4√3

b)

u = 4√2 v = 8

c)

u = 16 v = 8

d)

u = 4√3 v = 8

77.

Considering the lengths of the sides of the triangle, what measure will < A have to be?

a)

30

b)

45

c)

60

d)

90

78.

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by √2

d)

Divide that leg by √2

79.

What is the length of y in this 45-45-90 triangle?

a)

8√2

b)

4√2

c)

4

d)

8

80.

Find the length of m.

a)

4

b)

6

c)

12

d)

2√3

81.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

82.

What is the formula used to solve for the hypotenuse?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

83.

What is the correct ratio you would use to solve for "w"?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

84.

Which is the correct ratio you would use to solve for "x"?

a)

sin 28 = x/14

b)

cos 28 = x/14

c)

tan 28 = x/14

d)

tan 28 = 14/x

85.

What is the acronym to help you remember the ratios to use in trigonometry?

a)

RIGHTANG

b)

SOHCAHTOA

c)

SHOCHATOA

d)

SAHCOHTOA

86.

Choose the correct ratio you could use to solve for "x".

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

87.

Find x rounded to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

88.

Which trig function would you use to solve this problem for "x"?

a)

Sine

b)

Cosine

c)

Tangent

d)

Pythagorean Theorem

89.

Find the measure of the missing angle to the nearest degree.

a)

49^o

b)

90^o

c)

41^o

d)

33^o

90.

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle to the nearest degree.

a)

49°

b)

57°

c)

45°

d)

54°

91.

Find the value of "x" rounded to the nearest hundredth.

a)

6.09

b)

18.77

c)

5.52

d)

7.68

92.

What is the side across from the right angle called?

a)

Leg

b)

Pythagoras

c)

Hypotenuse

d)

Altitude

93.

Which trig function would you use with this diagram?

a)

^Sin

b)

^Cos

c)

^Tan

d)

^Wha??

94.

What is the ratio for tangent?

a)

O/A

b)

A/O

c)

A/H

d)

O/H

95.

Find cosA

a)

30/16

b)

30/34

c)

30/15

d)

16/34

96.

What is the ratio for cosine?

a)

H/A

b)

O/A

c)

A/H

d)

A/O

97.

What is the ratio for sine?

a)

O/H

b)

H/A

c)

H/O

d)

O/A

98.

Find sinC

a)

21/35

b)

28/21

c)

35/28

d)

28/35

99.

What is the correct equation to solve for x ?

a)

tan (58) = x/11

b)

tan (58) = 11/x

c)

cos (58) = x/11

d)

sin (58) = x/11

100.

a)

A

b)

B

c)

C

d)

D

101.

a)

x = 105.26
y = 98.91

b)

x = 98.91
y = 105.26

c)

x = 47.19
y = 12.31

d)

x = 12.31
y = 47.31

Algebra 2 3rd Quarter Review

Total questions: 101

Worksheet time: 51mins

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