Free Printable Algebra 2

1.

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

a)

16

b)

8

c)

-8

d)

-24

2.

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

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

3.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

4.

Bayside High School Orchestra performed two concerts to raise money for a

field trip. Tickets were $10 for adults and $7 for students and teachers. In

total, 300 people attended both concerts, and the orchestra raised $2400. The

number of teachers who came was a fourth of the number of students. Which

of the following systems can be used to represent this situation?

a)

10a+7s+7t=300

a+s+t=2400

t=4s

b)

10z+7s+7t=2400

a+s+t=300

t=4+s

c)

10a+7s+7t=2400

a+s+t=300

t=1/4(s)

d)

10a+7s+7t=2400

a+s+t=300

s=1/4(t)

5.

Write the system of inequalities for the given graph.

a)

y>4x-3

y>-2x+3

b)

y<4x-3

y>-2x+3

c)

y<4x-3

y>-2x+3

d)

y<4x-3

y>-2x+3

6.

Given the graph, determine which of the following are solutions to the system. [Could have more than one answer!]

a)

(4, -3)

b)

(-3, -7)

c)

(-4, 0)

d)

(1, -1)

7.

If

f\left(x\right)=x^3

is transformed into the graph of

h\left(x\right)=\left(x-6\right)^3-4

which of the following describes the transformation?

a)

f(x) is vertically stretched by a factor of 4 units to create the graph of h(x)

b)

f(x) is translated 4 units to the left and 6 units down to create the graph of h(x)

c)

f(x) is horizontally stretched by a factor of 6 units to create the graph of h(x)

d)

f(x) is translated 6 units to the right and 4 units down to create the graph of h(x)

8.

What is the positive solution to $-2\left|x+1\right|+6=0$ ?

a)

-4

b)

-2

c)

2

d)

4

9.

What is the solution to the following system of equations?

x + 2y + 4z = -8

5x + y + 3z = 10

2x + y + z = 6

a)

(-4, 2, 4)

b)

(2, 4, -4)

c)

(4, 2, -4)

d)

(4, 2, 4)

10.

|d + 3| = 6 - 2d

a)

d = 1, 9

b)

d = -1

c)

d = 1

d)

no solution

11.

What is the domain of the function shown in the graph?

a)

[-4,0]

b)

(-4,0)

c)

(-2,2]

d)

[-2,2)

12.

What is the domain of the graph?

a)

1≤ x ≤ 4

b)

1 < x < 4

c)

1≤ y ≤ 4

d)

1 < y < 4

13.

What is the range of the function?

a)

(1, 4)

b)

(-2, 4)

c)

[-2, 4)

d)

[-2, 4]

14.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

15.

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

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

16.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3x + 2y = 315
2x + 4y = 450

b)

3x + 2y = 450
2x + 4y = 315

c)

2x + 2y = 315
3x + 4y = 450

17.

Parallel Lines never intersect because...

a)

they have the same slopes.

b)

they have the same y-intercept.

c)

they have different slopes.

d)

they have different y-intercepts.

18.

Which point is a solution?

a)

(0, 6)

b)

(-3, 4)

c)

(1, 0)

d)

(-4, 3)

19.

Describe the transformation from f(x) to g(x).

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

g\left(x\right)=\frac{1}{x-2}+3

a)

Vertical shift up 3 and horizontal shift left 2.

b)

Vertical shift up 3 and horizontal shift right 2.

c)

Vertical shift down 3 and horizontal shift right 2.

d)

Vertical shift down 3 and horizontal shift left 2.

20.

$\left|2x-3\right|<7$

Which number line graph represents the solution to this inequality?

a)

b)

c)

d)

21.

What is the domain and range of the graph above?

a)

D:\left(-\infty,\infty\right)

R:\ y\le4

b)

$D:\left(-\infty,\infty\right)$
$R:\ y<4$

c)

$D:\left(-\infty,\infty\right)$
$R:\ y\ge4$

d)

$D:\ x\le4$
$R:\ \left(-\infty,\infty\right)$

22.

Solve the system of equations

a)

(-4, -2, 0)

b)

(2,0,4)

c)

(0,2,4)

d)

(4,2,0)

23.

Which point is a solution?

a)

(0, 6)

b)

(-3, 4)

c)

(1, 0)

d)

(-4, 3)

24.

Solve for x
l 2x−1 l +4 = 8

a)

x = 2.5 and x = -1.5

b)

x = 2 and x = -1

c)

x = -2 and x = 9

d)

No Solution

25.

Find the slope and y - intercept

y = 1/2x - 1

a)

slope: 1/2 y-intercept: -1

b)

slope: 2 y-intercept: -1

c)

slope: 1/2x y-intercept: 1

d)

slope: 2 y-intercept: 5

26.

Find the slope.

Hint: rise/run

a)

-5/3

b)

-3/5

c)

5/3

d)

5

27.

Which equation matches the graph?

a)

y = 2x

b)

y = 1/4 x + 2

c)

y = 1x + 4

d)

y = 2x - 3

28.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

29.

Which function is graphed?

a)

f(x) = 2|x + 2| -4

b)

f(x) = 2|x - 4| + 2

c)

f(x) = |x + 2| - 4

d)

f(x) = -2|x - 4|

30.

Which function is graphed?

a)

f(x) = -3|-x + 1| + 4

b)

f(x) = -|x - 1| + 4

c)

f(x) = -5|x + 1| + 4

d)

f(x) = -3|x - 4| + 1

31.

What are all the x-intercepts?

a)

(-2.55, 0), (2.55, 0)

b)

(-3,0), (-2,0), (2,0), (3,0)

c)

(0, 36)

d)

(-∞,∞)

32.

What are the coordinates of the y-intercept?

a)

(-3, 0)

b)

(0, -3)

c)

(2, 1)

d)

y=-3

33.

If g(x) = 2x² - 4, find g(-2)

a)

-8

b)

-12

c)

4

d)

0

34.

Factor out the GCF:
12x + 6

a)

6(2x + 1)

b)

3(4x + 2)

c)

6x(2x + 1)

d)

2(6x + 3)

35.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

36.

Factor:
x² - 5x - 14

a)

(x - 2)(x + 3)

b)

(x - 2)(x + 7)

c)

(x + 2)(x - 7)

d)

(x - 2)(x - 3)

37.

Which of the following is a factor of x²-10x+24?

a)

x-4

b)

x+4

c)

x+6

d)

x-2

38.

Solve for X:

(x-5)(x+6)=0

a)

{5,5 }

b)

{ -5,-5 }

c)

{ -5,-6 }

d)

{5,-6 }

39.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

40.

x² - 6x - 7 = 0

a)

{-1, 7}

b)

{-3, -1}

c)

{5, 6}

d)

{-3, 3}

41.

Factor Completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

42.

3x²+9x-30=0

a)

x= 2, -5

b)

x= 5, -2

c)

x= -5, -2

43.

Factor:
2x² + 11x + 14

a)

(x + 7)(2x + 2)

b)

(x + 2)(2x + 7)

c)

(x + 14)(2x + 1)

d)

(x + 1)(2x + 14)

44.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

45.

$x^2-100=0$

a)

$\left\{25,4\right\}$

b)

$\left\{-50,2\right\}$

c)

$\left\{-10,10\right\}$

d)

$\left\{0,100\right\}$

46.

Factor completely: x²+16x+64

a)

(x+4)(x+16)

b)

(x-8)(x-8)

c)

(x+2)(x+32)

d)

(x+8)(x+8)

47.

Factor completely: x²-13x+40

a)

(x-5)(x-8)

b)

(x+5)(x+8)

c)

(x-4)(x-10)

d)

(x-2)(x-20)

48.

Factor:
2x² + 13x + 15

a)

(2x + 1)(x + 15)

b)

(x + 3)(x + 5)

c)

(2x - 3)(x - 5)

d)

(2x + 3)(x + 5)

49.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

50.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x)= x²

c)

f(x) = |x|

d)

f(x) = ab^x

51.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x)= x²

c)

f(x) = |x|

d)

f(x) = ab^x

52.

What type of function is shown?

a)

exponential

b)

linear

c)

quadratic

d)

square root

53.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x) = x²

c)

f(x) =√(x)

d)

f(x) =∛(x)

54.

Which parent function matches the graph?

a)

f(x) = √(x)

b)

f(x) = ∛(x)

c)

f(x) = |x|

d)

f(x) = a⋅b^x

55.

Name the parent function.

a)

constant

b)

quadratic

c)

linear

d)

exponential

56.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

57.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

58.

Name the parent function.

a)

cube root

b)

square root

c)

quadratic

d)

linear

59.

Name the parent function.

a)

quadratic

b)

cubic

c)

square root

d)

logarithmic

60.

Domain is:

a)

All x values, from left to right.

b)

All y values, from bottom to top.

c)

All x values from bottom to top.

d)

All y values from left to right.

61.

Range is:

a)

All x values, from left to right.

b)

All y values, from left to right.

c)

All y values, from bottom to top.

d)

All x values, from bottom to top.

62.

Solve the system of equations by substitution.

a)

(3, -24)

b)

(0, 4)

c)

(-24, 3)

d)

No solution

e)

Infinite solutions

63.

Which graph represents a system of equations with no solution?

a)

b)

c)

d)

64.

Which graph represents a system of equations with infinite solutions?

a)

b)

c)

d)

65.

Solve the system of equations by substitution.

a)

(-6, 10)

b)

(-2, 10)

c)

(-2, 7)

d)

(-6, 8)

66.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

67.

Solve this system of equations by graphing.

y = 2x

y = 3x + 1

a)

(-1, -2)

b)

(2, 1)

c)

(2, 4)

d)

(-2, -3)

68.

Solve the system.

a)

(2, -2, 3)

b)

(2, 1, 4)

c)

(-2, 2, -3)

d)

No Solution

69.

Solve the system.

a)

(5, -6, 3)

b)

(2, 3, -1)

c)

(-4, 2, 5)

d)

No Solution

70.

Determine which ordered triple is a solution of the systems of equations?
2x+y=0
x+3y-z=-11
7x+5y+4z=21

a)

(0,0,11)

b)

(1,-2,6)

c)

(-1,2,-16

d)

(0,1,-14)

71.

Express the following in Interval Notation
-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

72.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

73.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

74.

Express the following interval in Set notation:
[3, 5]

a)

3 ≤ x ≤ 5

b)

3 < x ≤ 5

c)

3 ≤ x < 5

d)

3 < x < 5

75.

Express the following interval in Set notation:
(-7, 15]

a)

-7 ≤ x ≤ 15

b)

-7 < x ≤ 15

c)

-7 ≤ x < 15

d)

-7 < x < 15

76.

Look at the graph. Write the inequality in interval notation.

a)

(-2,5)

b)

(-∞,-2)⋃(5,∞)

c)

[-2,5]

d)

(-∞,-2]∪[5,∞)

77.

Write the following in interval notation
-7 ≤ x < 8

a)

(-7, 8)

b)

[-7, 8)

c)

[-7, 8]

d)

(-7, 8]

78.

Look at the Graph. Write the inequality in interval notation.

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

79.

When graphing b< 6 would you use an open or closed circle?

a)

open

b)

closed

80.

Determine the transformation

a)

left 3, up 2

b)

right 3, up 2

c)

left 3, down 2

d)

right 3, down 2

81.

Determine the transformation

a)

Left 5, up 1

b)

Left 5, down 1

c)

Right 5, up 1

d)

Right 5, down 1

82.

Determine the transformation

a)

down 2

b)

flip, down 2

c)

flip, left 2

d)

left 2

83.

Determine the Domain

a)

x > 5

b)

x > -5

c)

All Reals

d)

x > 1

84.

Solve for x
l 5x l = 40

a)

x = 8 and x =-8

b)

x = 35 and x = -35

c)

Only x = 8

d)

No Solution

85.

Solve for x
l 2x−1 l = 9

a)

x = 5 and x =-4

b)

x = 5 and x = -5

c)

Only x = 5

d)

No Solution

86.

Solve for x
l 4x−3 l = 17

a)

x = 5 and x =-3.5

b)

x = 0 and x = -5

c)

x = 10 and x = -10

d)

No Solution

87.

Solve for x
l x−6 l + 4= 10

a)

x = 12 and x = 0

b)

x = 3 and x = -3

c)

x = -12 and x = 0

d)

No Solution

88.

Solve |x – 12| - 3 = 11.

a)

x = -2 and x = -26

b)

x = -2 and x = 26

c)

x = 3 and x = 25

d)

x = 4 and x = -7

89.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

90.

Is this set of ordered pairs a function or not a function?

a)

Function

b)

Not a Function

91.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

92.

Is the graph pictured a function?

a)

Yes

b)

No

93.

a)

Function

b)

Not a Function

94.

.

a)

Function

b)

Not a Function

95.

a)

Function

b)

Not a Function

96.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(5, 1)

c)

(-1, -3)

d)

(20, -5)

97.

Which point is a solution?

a)

(0, 6)

b)

(-3, 4)

c)

(1, 0)

d)

(-4, 3)

98.

Identify all solutions for the graph

a)

(2, 3)

b)

(4, -2)

c)

(2, -4)

d)

(-2, 0)

99.

How can I tell if an inequality will have a solid line?

a)

It has an equal sign.

b)

The symbol is greater than.

c)

The symbol has "or equal to."

d)

You just guess.

100.

This graph represents the inequality y < 3, TRUE or FALSE?

a)

TRUE

b)

FALSE

101.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

102.

Which ordered pair(s) is a solution to the given system?

a)

(5, -5)

b)

(0,0)

c)

(-5, -2)

d)

(3,-3)

103.

Given the system, determine a solution.

a)

No solution

b)

Infinite solutions

c)

(-5, 5)

d)

(5, -5)

104.

Which system of inequalities matches the graph?

a)

y > 2x - 4
y < 2

b)

y < 2x - 4
y < 2

c)

y > 2x - 4
y < 2

d)

y < 2x - 4
y < -2

105.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

106.

Factor completely.
2m² + 2m - 1

a)

(7m - 6)(m + 5)

b)

(2m + 1)(m + 1)

c)

(2m - 1)(m +1)

d)

(2m + 7)(m - 10)

107.

Factor completely.
5x² - 7x + 2

a)

5(x - 2)(x + 1)

b)

(5x - 2)(x + 1)

c)

(7x - 1)(x - 4)

d)

(5x - 2)(x - 1)

108.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

Algebra 2 - Fall Exam!

Total questions: 108

Worksheet time: 6hrs 53mins

Similar Resources on Wayground