Free Printable Algebra II Final exam review

1.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

2.

Which function is graphed?

a)

f(x) = -|2x - 3| + 5

b)

f(x) = -|x + 5| - 3

c)

f(x) = -|2x + 6| + 5

d)

f(x) = -2|x + 5| - 3

3.

Find $\left(f-g\right)\left(x\right)$ if $f\left(x\right)=\ x^2+8x$ and $g\left(x\right)=\ 3x+5$

a)

$-x^2-5x+5$

b)

$x^2+5x+5$

c)

$x^2+5x-5$

d)

$x^2+11x+5$

4.

What is true about the graph?

a)

The range is [-3,3]

b)

The domain is [-3,2)

c)

The domain is (-3,2)

d)

The domain is (-3,3]

5.

What is the domain of the function?

a)

(-1,1)

b)

[-1,1]

c)

(-2,2)

d)

[-2,2]

6.

Evaluate the expression for the given value of the variable(s). $-4x+3y^2;\ x=-2,\ y=2$

a)

0

b)

20

c)

-20

d)

4

7.

Evaluate the expression for the given value of the variable(s). $\sqrt{x^3+y^2};\ x=2,\ y=-1$

a)

3

b)

9

c)

-3

d)

$\sqrt{3}$

8.

Evaluate the expression for the given value of the variable(s). $\left|3b^2+2\right|-\left|5-b\right|-2b^3;\ b=2$

a)

1

b)

-1

c)

-5

d)

5

9.

Combine like terms and simplify. $-5\left(-2a+6\right)+7a$

a)

$21a$

b)

$17a-30$

c)

$-3a-30$

d)

$17a+30$

e)

$17a+6$

10.

Combine like terms and simplify. $-\left(x+y\right)^2-2x^2+3y^2-6xy$

a)

$-3x^2-2y^2-8xy$

b)

$-3x^2-2y^2+8xy$

c)

$-3x^2+2y^2-6xy$

d)

$-3x^2+2y^2-8xy$

e)

$x^2+4y^2-6xy$

11.

Solve the following equation :

2x-5=6-20x

a)

$x=-2$

b)

$x=\frac{1}{2}$

c)

$x=2$

d)

$x=-\frac{1}{2}$

12.

$2x-2=3\left(x-1\right)-5\left(6-2x\right)$ Solve the ab equation

a)

$x=\frac{31}{11}$

b)

$x=-\frac{31}{11}$

c)

$x=\frac{11}{31}$

d)

$x=-\frac{11}{31}$

13.

Use an algebraic equation to solve the problem

A rectangle is twice as long as wide. The perimeter of the rectangle is 50 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary.

a)

5 cm by 10 cm

b)

15 cm by 30 cm

c)

25 cm by 50 cm

d)

2 cm by 4 cm

14.

Is the following statement ALWAYS, SOMETIMES, or NEVER true?
$-3\left(2x-7\right)+4x+4=8x-2\left(5x-8\right)+9$

a)

ALWAYS

b)

NEVER

c)

SOMETIMES

d)

No valid answer

15.

Is the following statement ALWAYS, SOMETIMES, or NEVER true? $3x+3\left(x+3\right)=5\left(x-6\right)+x$

a)

ALWAYS

b)

SOMETIMES

c)

NEVER

d)

No valid answer

16.

Is the following statement ALWAYS, SOMETIMES, or NEVER true? $-1[7x+6-7(x+1)]=-4x-6$

a)

ALWAYS

b)

NEVER

c)

SOMETIMES

d)

No vilid answer

17.

Solve and graph the inequality $3t–12≤–9$

a)

b)

c)

d)

18.

Solve and graph the inequality. $c–10+3c<2$

a)

b)

c)

d)

19.

Which graph represents the solution to the
inequality below? $\frac{5-\left(9-5x\right)}{-2}<-5$

a)

b)

c)

d)

20.

Solve the inequality. Graph the solution set. $2+2k\le8$

a)

b)

c)

d)

21.

Solve the equation or formula for the indicated variable. $S=5r^2t$ for $t$

a)

b)

c)

d)

22.

Solve the equation or formula for the indicated variable. $T=\frac{4U}{E}$ for $U$

a)

b)

c)

d)

23.

What inequality represents the sentence?

"14 fewer than a number is at least –8"

a)

$x+14\le-8$

b)

$x-14\ge-8$

c)

$14-x\ge-8$

d)

$x-14<-8$

24.

What inequality represents the sentence?

"The product of a number and 12 is no more than 15."

a)

$12n<15$

b)

$12n>15$

c)

$12\ge15$

d)

$12\le15$

25.

Solve the inequality. Graph the solution set.
$2r–9\ge–6$

a)

b)

c)

d)

26.

Solve the inequality. Graph the solution set. $26+6b\ge2(3b+4)$

a)

b)

c)

d)

27.

Solve the problem by writing an inequality.

"A club decides to sell T-shirts for $15 as a fund-raiser. It costs $20 plus $9 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $150."

a)

$15x-(9x+20)\ge150\ ;\ x\ge28.33$

b)

$15x-9x+20\ge150\ ;\ x\ge20$

c)

$\left(8x+20\right)-15x\ge150\ ;\ x\ge20$

d)

$15x-9\left(x+20\right)\ge150\ ;\ x\ge20$

28.

If the perimeter of a rectangular picture frame must be less than 200 in., and the width is 36 in., what must the height h of the frame be?

a)

$h<64$ in.

b)

$h>128$ in.

c)

$h>64$ in.

d)

$h<128$ in.

29.

Is the inequality sometimes, always, or never true? $-2(2x+9)>-4x+9$

a)

ALWAYS

b)

SUMTIMES

c)

NEVER

d)

No valid answer

30.

Is the inequality sometimes, always, or never true? $2(10x-5)-9x\le11x+13$

a)

ALWAYS

b)

SOMETIME

c)

NEVER

d)

No valid answer

31.

Solve the compound inequality. Write your solution in interval notation. $4x–5<–17\ \$ or $5x+6>31$

a)

b)

c)

d)

32.

Solve the compound inequality. Write your solution in interval notation. $-2\le2x-4<4$

a)

b)

c)

d)

33.

Solve the absolute value equation. Graph the solution. $|x-3|=1$

a)

b)

c)

d)

34.

Solve the absolute value equation. Graph the solution. $2|4x-5|-2=-4$

a)

b)

c)

d)

35.

$|4x+1|=-3$ Solve the absolute value equation. Graph the solution.

a)

b)

c)

d)

36.

Solve the absolute value equation. Graph the solution. $4|3x+5|+2=10$

a)

b)

c)

d)

37.

Solve the inequality. Graph the solution. $|2x+3|\ge19$

a)

b)

c)

d)

38.

Solve the inequality. Graph the solution. $|2x+10|\le26$

a)

b)

c)

d)

39.

Solve the inequality. Graph the solution. $|4x+8|>28$

a)

b)

c)

d)

40.

Factor

a)

A

b)

B

c)

C

d)

D

41.

a)

A

b)

B

c)

C

d)

D

42.

Factor

a)

A

b)

B

c)

C

d)

D

43.

a)

A

b)

B

c)

C

d)

D

44.

Factor

a)

A

b)

B

c)

C

d)

D

45.

a)

A

b)

B

c)

C

d)

D

46.

Multiply

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

Solve the system

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

a)

$\left(1,3\right)$

b)

$\left(1,-3\right)$

c)

$\left(-1,-3\right)$

d)

$\left(-1,3\right)$

49.

If g(x) = 6x + 4 and
f(x) = 2x - 7
Find f(x) * g(x)

a)

8x - 3

b)

4x + 11

c)

12x² - 28

d)

12x² - 34x - 28

50.

What is the equation of this line?

a)

y = 2x +2

b)

y = 2x -2

c)

y = -x + 2

d)

Cannot be Determined

51.

find the slope

a)

3/2

b)

-3/2

c)

(-0,-3)

d)

none of the above

52.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

53.

What is the equation of this line in standard form?

a)

y = 4x + 3

b)

4x - y = 3

c)

4x - y = -3

d)

x - 4y = -3

54.

What is 15x + y = 34 written in slope-intercept form?

a)

y = 15x + 34

b)

y = -15x + 34

c)

y = 15x - 34

d)

y = -15x - 34

55.

What is 4x - 3y = 12 written in slope-intercept form?

a)

y = (4/3)x - 12

b)

y = (4/3)x + 4

c)

y = (4/3)x - 4

d)

y = -(4/3)x - 4

56.

What is the equation of this line in slope-intercept form?

a)

y = 4x + 3

b)

y = -4x + 3

c)

y = (1/4)x + 3

d)

y = (-1/4)x + 3

57.

Write in standard form.
y = -3x + 5

a)

y = -3x + 5

b)

3x + y = 5

c)

3x - y = 5

d)

-3x + y = -5

58.

f(x) = 5x² + 2

a)

Stretch of 5
Up 2

b)

Shrink of 5
Up 2

c)

Stretch of 5
Down 2

d)

Shrink of 5
Down 2

59.

.
If the blue is f(x)=x^2,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

60.

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

61.

What are the following transformations?
- f(x+2)

a)

reflection over the y axis and 2 units to the right

b)

reflection over the x axis and 2 units right

c)

reflection over the y axis and 2 units left

d)

reflection over the x axis and 2 units left

62.

What are the following transformations:
f(-x) - 4

a)

reflection over the x axis and 4 units right

b)

reflection over the x axis and 4 units down

c)

reflection over the y axis and 4 units right

d)

reflection over the y axis and 4 units down

63.

Which of the following transformations are present?
-2f(x - 1) + 2

a)

Shift 1 unit down

b)

Shift 1 unit up

c)

Shift 1 unit left

d)

Shift 1 unit right

64.

Which equation describes the transformation of shifting f(x)=x³ four units down?

a)

x³+ 4

b)

x³- 4

c)

(x - 4)³

d)

(x + 4)³

65.

Which equation describes the transformation of shifting f(x)=x³ seven units up?

a)

x³+7

b)

x³-7

c)

(x-7)³

d)

(x+7)³

66.

What are the transformations of this functions compared to the parent function y = √(x)?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

67.

a)

f(x)=3∣x−2∣−2

b)

f(x)=1/3∣x+2∣−2

c)

f(x)=3∣x+2∣−2

d)

f(x) = 1/3∣x−2∣+2

68.

What is the equation of this graph?

a)

f(x) = (x + 2)² - 3

b)

f(x) = (x - 2)² - 3

c)

f(x) = |x + 2| - 3

d)

f(x) = |x - 2| - 3

69.

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

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

70.

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

a)

Vertical Compression by a factor of 2

b)

Vertical Stretch by a factor of 2

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

71.

Which transformation will occur if f(x) = x² is replaced with 1/2⋅f(x)?

a)

Vertical Compression by a factor of 1/2

b)

Vertical Stretch by a factor of 1/2

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

72.

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

a)

Translation left 2 units

b)

Narrower

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

73.

Find the equation of the transformed graph

a)

$y=x^2+3$

b)

$y=\left(x+3\right)^2$

c)

$y=\ x^2-3$

d)

$y=\left(x-3\right)^2$

74.

a)

$y=\ \left|x\right|\ -\ 1$

b)

$y=\ -\ \left|x\right|\$

c)

$y=\ \left|x\right|\$

d)

$y=\ \left|x-1\right|$

75.

Which quadratic function is represented by the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

76.

What is the best method do you use?

y = 6x − 11

−2x − 3y = −7

a)

Graphing

b)

Substitution because a variable is defined

c)

Elimination because both equations are in standard form.

77.

Solve for x and y
5x + 3y = 7
y = 4

a)

(4,1)

b)

(4,-1)

c)

(1,4)

d)

(-1,4)

78.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

79.

Solve the system of equations.
y = 4x+1
3x + 2y = 13

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

∅

80.

Solve the system given:
3x - y = 7
2x + y = 3

a)

(-1,2)

b)

(5,4)

c)

(4,5)

d)

(2,-1)

81.

Solve the system:

y= 3x -13

2x +4y =4

a)

(5,2)

b)

(4, -1)

c)

(-4, -1)

d)

(5, -2)

e)

(-4, 1)

82.

Solve the system:

x+ 3y = 9

2x+ y = −2

a)

(3,2)

b)

(-2, 2)

c)

(3, -4)

d)

(-3, 4)

e)

(0.5, -3)

83.

Solve the system:

y=5x−5

y= −4x+22

a)

(1, 2)

b)

(3, 10)

c)

(-1, 2)

d)

(-3, 10)

84.

Where is the vertex?

a)

$\left(0,\ -3\right)$

b)

$\left(1,\ -4\right)$

c)

$\left(-1,\ 0\right)$

d)

$\left(3,\ 0\right)$

e)

$\left(1,\ 0\right)$

85.

Which are x-intercepts? Check all that apply.

a)

$\left(0,\ -3\right)$

b)

$\left(1,\ -4\right)$

c)

$\left(-1,\ 0\right)$

d)

$\left(3,\ 0\right)$

e)

$\left(1,\ 0\right)$

86.

Does the graph have a maximum or a minimum?

a)

Maximum

b)

Minimum

c)

Both

d)

Neither

87.

Does the graph have a maximum or a minimum?

a)

Maximum

b)

Minimum

c)

Both

d)

Neither

88.

Which is the y-intercept?

a)

$\left(0,\ -5\right)$

b)

$\left(1,\ 0\right)$

c)

$\left(3,\ 4\right)$

d)

$\left(5,\ 0\right)$

e)

$\left(6,\ -5\right)$

89.

What is the axis of symmetry for this graph?

a)

y=2

b)

x=2

c)

x=0

d)

y=0

90.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

91.

What is the vertex?

a)

(4,-4)

b)

(2,0)

c)

(0,2)

d)

(6,0)

92.

Find the zeros of the equation:
(x+10)(x-2) = 0

a)

10 and 2

b)

-2 and 10

c)

-10 and 2

d)

-2 and -10

93.

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

94.

Find the axis of symmetry for
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

95.

What's the axis of symmetry of y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

96.

Find the vertex of
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

97.

Find the vertex of f(x)= -2x²-16x+3.

a)

(4, -93)

b)

(-4, 35)

c)

(-4,99)

d)

(8,3)

98.

The equation for the axis of symmetry line is x = -b/(2a)

a)

true

b)

false

99.

Find the vertex y = x² - 2x - 5

a)

V(-2, 10)

b)

V(-1, 15)

c)

V(1, -6)

d)

V(1, -12)

100.

Find the vertex y = - x² - 14x - 59

a)

V(-6, 4)

b)

V(-7, -10)

c)

V(14, 12)

d)

V(7, 4)

101.

Find the vertex y = x² - 12x + 46

a)

V(3, -7)

b)

V(3, 7)

c)

V(6, 10)

d)

V(6, -3)

102.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

103.

2d² = 8

a)

4

b)

-2

c)

-4, 4

d)

-2, 2

104.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

105.

What is another word that describes the zeroes of a quadratic function?

a)

y-intercepts

b)

vertex

c)

x-intercepts

d)

maximum

106.

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

107.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

108.

A function has a discriminant of 25.
______________
How many solutions does it have?

a)

0

b)

1

c)

2

d)

5

109.

ax²+bx+c=0 is the standard form of a quadratic equation.

a)

True

b)

False

110.

Solve using the Quadratic Formula:

x²+ 6x + 9 = 0

a)

x = −3, 3

b)

x = −3

c)

x = 3

d)

No Solution

111.

Solve using the Quadratic Formula:

15x²+ 22x = −8

a)

x = −2/3, 4/5

b)

x = 2/3, −4/5

c)

x = 2/3, 4/5

d)

x = −2/3, −4/5

112.

Solve by factoring:

x² - 5x - 2 = 4

a)

x = 6 or x = -1

b)

x = -6 or x = 1

c)

x = -6 or x = 5

d)

Cannot be factored

113.

Solve by factoring:

x²- 2x - 3 = 0

a)

x = 1 or x = 6

b)

x = -1 or x = 3

c)

x = -5 or x = -4

d)

x = 1 or x = -3

114.

Solve by factoring:

x² - 13v + 42 = 0

a)

x = -6 or x = -7

b)

x = 6 or x = -5

c)

x = 6 or x = 7

d)

x = -6

115.

Solve by factoring:

x² - 6x + 11 = 6

a)

x = 1 or x = 5

b)

x = -3 or x = -8

c)

x = 8 or x = -5

d)

x = -1 or x = -5

116.

Solve using square roots:

-7x² = -91

a)

x = 1 or x = -1

b)

No real solutions.

c)

x = 3.6

d)

x = 3.6 or x = -3.6

117.

Solve using square roots:

5x² + 6 = 186

a)

x = 1.3 or x = -1.3

b)

x = 6 or x = -6

c)

No real solutions

d)

x = 6

118.

Solve using square roots:

x² + 7 = 89

a)

x = 9.8

b)

No real solution

c)

x = 9.1

d)

x = 9.1 or x = -9.1

119.

Solve using square roots:

10x² + 3 = -17

a)

x = 6.7 or x = -6.7

b)

x = 2.25 or x = -2.25

c)

x = -2 or x = 2

d)

No real solution

120.

Solve using the Quadratic Formula:

4x² + x - 95 = 0

a)

x = 7 or x = -6

b)

x = 5 or x = -6

c)

x = 4.75 or x = -5

d)

x = -4.75 or x = 5

121.

Solve using Quadratic Formula:

12x² - 3x - 13 = -5

a)

x = 3 or x = -2

b)

x = 3.6 or x = -5.6

c)

x = .95 or x = -.70

d)

x = 5.6 or x = -3.6

122.

Solve using Quadratic Formula:

x² - 11x - 80 = 0

a)

x = 2 or x = -4

b)

x = 2 or x = -1.3

c)

x = 16 or x = -5

d)

x = 1-6 or x = 5

123.

Solve using Quadratic Formula:

2x²- 3x - 42 = 2

a)

No real solution

b)

x = -1.3 or x = -2.7

c)

x = -0.4 or x = -0.7

d)

x = 5.5 or x = -4

Algebra II Final exam review

Total questions: 123

Worksheet time: 4hrs 30mins

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