Free Printable Algebra I Final Exam Review

1.

Which expression is equivalent to $\left(z+5\right)-\left(z^2-4z+6\right)$

a)

$z^2+5z+11$

b)

$-z^2+5z-1$

c)

$z^2+3z+11$

d)

$-z^2-3z+11$

2.

Which expression is equivalent to $\left(z+5\right)+\left(z^2-4z+6\right)$

a)

$z^2+5z+11$

b)

$-z^2+5z-1$

c)

$z^2-3z+11$

d)

$-z^2-3z+11$

3.

Simplify: $\frac{x^2y^5}{x^9y^5}$

a)

$x^2$

b)

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

c)

$\frac{1}{x^7}$

d)

$x^7$

4.

$\frac{\text{3}x^2-2xy}{\text{2x}}$

a)

$1.5x^{3\ }-x^2y$

b)

$1.5x\ -\ y$

c)

$1.5x\ +\ y$

d)

$1.5x\ -\ 2y$

5.

Match the following words to the best example from the given expression

$7x-2x^2+11$

a)

constant

1.

$11$

b)

coefficient

2.

$-2$

c)

term

3.

$7x$

d)

polynomial

4.

$7x-2x^2+11$

6.

Which expression is equivalent to the following?

4x^3y\left(-2x^3y^2+4x^2y\right)

a)

$8x^{11}y^5$

b)

$2x^6y^3+8x^5y^2$

c)

$-8x^6y^3+16x^5y^2$

d)

$-8x^9y^2+16x^6y$

7.

Multiply
(4x+3)(2x-1)

a)

8x²-2x-3

b)

8x-3

c)

8x²+6x-3

d)

8x²+2x-3

8.

A polynomial that has two terms is a:

a)

polynomial

b)

monomial

c)

binomial

9.

$Add:\ \ \left(9x^3+5x^2-3x\right)+\left(4x^3-8x^2+7x\right)$

a)

$5x^3-3x^2+4x$

b)

$13x^3-13x^2+4x$

c)

$13x^3-3x^2+4x$

d)

$14x^6$

10.

$Subtract:\ \ \left(6x^4-5x^3+2x^2-8x\right)\ -\ \left(4x^4+5x^3+3x^2+12x\right)$

a)

$10x^4-10x^3-x^2-20x$

b)

$2x^4-10x^3-x^2-20x$

c)

$2x^4-x^2-20x$

d)

$2x^4-20x$

11.

Write a linear equation in slope-intercept form give the point and slope. (-6, -11); slope = 1/2

a)

$y+6=\frac{1}{2}\left(x+6\right)$

b)

$x-2y=16$

c)

$y=\frac{1}{2}x-8$

d)

$y=\frac{1}{2}x-11$

12.

Write a linear equation in point-slope form given the point and slope: (5, -9), slope = -2/5

a)

$y+5=-\frac{2}{5}\left(x-9\right)$

b)

$y-5=-\frac{2}{5}\left(x+9\right)$

c)

$y-9=-\frac{2}{5}\left(x+5\right)$

d)

$y+9=-\frac{2}{5}\left(x-5\right)$

13.

What is the equation and slope of the line shown on the grid?

a)

y = 6; slope is -1

b)

x = 6; slope is zero

c)

y = 6; slope is 6

d)

x = 6; slope is undefined

14.

What is the slope of the line?

a)

m = 3/4

b)

m = 4/3

c)

m = -3/4

d)

m = -4/3

15.

Find the slope

a)

4/5

b)

5/4

c)

-5/4

d)

-4/5

16.

Find the slope of a line that passes through the given points:

(5,1) and (8,3)

a)

$\frac{2}{3}$

b)

$\frac{-2}{3}$

c)

$\frac{3}{-2}$

d)

$\frac{3}{2}$

17.

Given that the slope is 2/3 and the y intercept is -3 what is the equation of the line?

a)

y = 2/3x - 3

b)

y = 2/3x + 3

c)

y = -2/3x - 3

d)

y = -2/3x + 3

18.

Which equation is being represented by this line?

a)

y = -x + 2

b)

y = 1/2x + 2

c)

y = 3x -4

d)

y = -3x +2

19.

What is the equation of the graph?

a)

y = -5

b)

y = 5

c)

x = -5

d)

x = 5

20.

What is the equation of the line that goes through the points (2, 9) and (3, 1) ?

a)

y= 8x - 5

b)

y= -8x + 25

c)

y= (1/8)x - 2

d)

y= (-1/8)x + 1

21.

What is an equation of line that is perpendicular to the line y = -3x + 5?

a)

$y\ =\ -3x\ +\ 7$

b)

$y=\frac{1}{3}x\ +2$

c)

$y\ =\frac{2}{3}x\ -3$

22.

Identify the form of this linear equation

y=mx+b

a)

point-slope

b)

slope-intercept

c)

standard

23.

Identify the form of this linear equation

y-y_1=m\left(x-x_1\right)

a)

point-slope

b)

slope-intercept

c)

standard

24.

Which graphs represent linear functions? Select all that apply.

a)

b)

c)

d)

25.

Identify the y-intercept for the function:

y = -3x

a)

(0, -3)

b)

(0, 0)

c)

(0, 1)

d)

(0, -1)

26.

Which equation represents the following graph?

a)

y = 3x + 2

b)

y = -2x + 3

c)

y = 2x + 3

d)

y = -3x + 2

27.

The start up cost to join eTunes music is $7.95 plus $0.95 per song downloaded. Write a linear equation that could be used to find how many songs he downloaded.

a)

y = 0.95x + 7.95

b)

y = 7.95x + 0.95

c)

y = 0.95x - 7.95

d)

y = - 0.95x + 7.95

28.

Which equation represents the total cost of a repair by an electrician after x hours?
An electrician charges $90 per hour plus a $50 travelling fee.

a)

y = 50 - 90x

b)

y = 90x + 50

c)

y = -50x + 90

d)

y = -90 - 50x

29.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

30.

3x + 2(4x - 4) = 3

a)

4

b)

3

c)

2

d)

1

31.

Solve the equation:
3x - x + 2 = 4(2x - 1)

a)

infinite solutions

b)

x = 1

c)

x = -1

d)

no solution

32.

Solve for x:

\frac{\left(3x-3\right)}{-7}=-45

a)

x = 106

b)

x = -106

c)

x = 16

d)

x = -16

33.

Solve

2\left(4w-1\right)=-10\left(w-3\right)+4

a)

2

b)

-2

c)

0

d)

-1

34.

Identify the number of solutions the equation has.

4x + 5 = 2(2x +3)

a)

one solution

b)

no solution

c)

Identity (infinite solutions)

d)

two solutions

35.

Solve:
3x + 15 = 3(x + 5)

a)

No Solution

b)

x = 15

c)

Infinitely Many Solutions

36.

Label the parts of the equation

a)

Slope

b)

Y-Intercept

1

2

1)

2)

37.

Label the parts of the equation

a)

y-coordinate

b)

Slope

c)

x-coordinate

1

2

3

1)

2)

3)

38.

If two lines are parallel their slopes are ____________

a)

the same.

b)

negative reciprocals of each other.

39.

Are these lines parallel?
y = 12x + 4
y = 12x +14

a)

YES

b)

NO

40.

Are these lines parallel?

y = (-1/2)x + 1

y = (1/2)x - 5

a)

YES

b)

NO

41.

Write a slope that is parallel to this equation:

$y-7=2\left(x-5\right)$

42.

2x + 7 < -11

a)

x < 2.5

b)

x < - 2.5

c)

x ≤ -9

d)

x<-9

43.

Pick the correct inequality.

a)

A

b)

B

c)

C

d)

D

44.

Which number line best represents the solution to the inequality 5w ≥ 30

a)

A

b)

B

c)

C

d)

D

45.

-4x + 14 ≤ 54

a)

x ≥ - 10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

46.

What inequality is graphed?

a)

x > 2 and x ≤ −3

b)

x > 2 and x < −3

c)

x > 2 or x ≤ −3

d)

x > 2 or x < −3

47.

When solving inequalities you must _________________ the inequality when ____________________ by a negative.

a)

flip; dividing

b)

ignore; multiplying and dividing

c)

flip; multiplying

d)

flip; multiplying and dividing

48.

Match the following

a)

The coordinate where the function crosses the x-axis. At this point, y=0.

1.

x-intercept

b)

The coordinate where the function crosses the y-axis. At this point, x=0.

2.

y-intercept

c)

Measure of how STEEP a line is, can be found using rise/run

3.

SLOPE

d)

Slope-intercept form

4.

y=mx+b

e)

Standard Form

5.

Ax+By=C

49.

What is the y-intercept in the equation x + 2y = 4

a)

1/2

b)

2

c)

4

d)

-4

50.

Determine the y-intercept for the following equation
4x + 2y = -12

a)

-24

b)

-6

c)

-12

d)

2

51.

Find the x and y intercepts
4x - 5y = 40

a)

x intercept is 10
y intercept is 8

b)

x intercept is 10
y intercept is 20

c)

x intercept is 8
y intercept is 10

d)

x intercept is 10
y intercept is -8

52.

Find the x-intercept of
3x - 7y = 21

a)

3

b)

7

c)

-3

d)

-7

53.

Name the x- and y-intercepts for the equation:
2x + y = 6

a)

(0, 3) and (6, 0)

b)

(0, -3) and (-6, 0)

c)

(3, 0) and (0, 6)

d)

(-3, 0) and (0, -6)

54.

The solution (x, y) to a system of equations is the point where they...?

a)

Run off the graph

b)

Don't touch

c)

Intersect

d)

Exist

55.

What is the solution to the system?

a)

(3, -1)

b)

(2, -6)

c)

No Solution

d)

(6, -2)

56.

-4x-2y=-12
4x+8y=-24

a)

(5,6)

b)

(6,-6)

c)

(6,-2)

d)

(4,-3)

57.

This system has _____ solutions

a)

no

b)

1

c)

2

d)

Infinitely many

58.

Which point is a solution?

a)

(0, 6)

b)

(-3, 4)

c)

(1, 0)

d)

(-4, 3)

59.

Match the system to the graph (solution set is on the left)

a)

y ≤ 3x and y ≤ -2x + 4

b)

y > 3x and y > -2x + 4

c)

y < 3x and y > -2x + 3

d)

y > 3x and y < -2x + 4

60.

Which system of inequalities is shown?

a)

y ≥ -x - 1
y < x + 4

b)

y < -x - 1
y ≥ x + 4

c)

y > -x - 1
y ≥ x + 4

d)

y > -x - 1
y ≥ x + 3

61.

The equations of two lines are:
2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?

a)

x=8

b)

x=3

c)

x=11

d)

x=5

62.

Solve for x and y
y = 2x + 1
y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

63.

A set of ordered pairs is called what?

a)

Coordinates

b)

Relation

c)

Function

d)

Vertical Line Test

64.

A relation where every input yields one and only one output is called what?

a)

Relation

b)

Linear

c)

Exponential

d)

Function

65.

Is this table a function or not a function?

a)

Function

b)

Not a Function

66.

Does the graph represent a function?

a)

Yes, because the vertical line test shows there are no repeating input values

b)

No, because the vertical line test shows there are repeating input values

67.

Is this a function?

a)

Yes

b)

No

68.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

69.

What is the range of the function shown?

a)

{10, 19, 26}

b)

{-3, 0, 4}

c)

{-3, 0, 4, 10, 19, 26}

d)

{0, 16}

70.

What is the domain of the function graphed?

a)

x < 5

b)

x ≥ 1

c)

x > 0

d)

All real numbers

71.

What is the domain of the graph?

a)

{-4, 0, 2, 4}

b)

{-5, -4, -3, -1}

c)

{-5, -4, -3, -1, 0, 2, 4}

d)

All real numbers

72.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

73.

Factor completely: 2x²+22x+60

a)

(2x+10)(x+6)

b)

(x+5)(x+6)

c)

2(x+1)(x+30)

d)

2(x+5)(x+6)

74.

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)

75.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

76.

Write using a single exponent: 10³ x 10⁵

a)

10¹⁵

b)

10⁸

c)

10²

d)

10⁶

77.

Write using a single exponent: (10⁴)⁵

a)

10²⁰

b)

10¹

c)

10⁹

d)

10⁶

78.

Write using a single exponent: $\frac{3^7}{3^3}$

a)

$3^{10}$

b)

$3^{21}$

c)

$3^4$

d)

$3^6$

79.

$10^{-5}$

Write using a positive exponent:

a)

$50$

b)

$10^5$

c)

$\frac{1}{10^5}$

d)

$10^9$

80.

Simplify the following expression:

(xyz)⁰ =

a)

0

b)

1

c)

xyz

d)

-1

81.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

82.

Simplify

a)

2x⁶

b)

2x

c)

2x⁵

d)

2x⁸

83.

Simplify:

9x^6y^2\cdot5x^2y^3

a)

$14x^8y^5$

b)

$14x^{12}y^6$

c)

$45x^8y^5$

d)

$45x^{12}y^6$

84.

Simplify:

\frac{x^{-7}}{x^{12}}

a)

$\frac{1}{x^5}$

b)

$x^5$

c)

$x^{19}$

d)

$\frac{1}{x^{19}}$

85.

Simplify the following:

$\left(\frac{x^3}{x^2}\right)^4$

a)

$x^4$

b)

$x^{20}$

c)

$x^8$

d)

$x^{10}$

86.

Simplify the following:

$x^{-5}$

a)

$x^{-5}$

b)

1

c)

$\frac{1}{x^5}$

d)

5x

87.

Simplify the following (CAREFUL!!!):

$\frac{x^{12}}{x^{-2}}$

a)

$x^{14}$

b)

$x^{-6}$

c)

$x^{10}$

d)

$\frac{1}{x^6}$

88.

$\left(6x^2\right)\left(3x^{-5}\right)$

a)

$\frac{18}{x^{10}}$

b)

$18x^3$

c)

$\frac{18}{x^3}$

d)

$\frac{1}{18x^3}$

89.

Which scatter plot shows a linear relationship between x and y?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

90.

What is a line of best fit used for?

a)

To make predictions

b)

To make the graph look pretty

c)

To connect the points

d)

To make it look like you know what you are doing

91.

The graph shows a line of best fit for data collected on the amount of income earned by lawn companies in relation to the number of yards mowed. What is the equation of the line of best fit?

a)

y = (3/2) x

b)

y = 30x

c)

y = 30x + 300

d)

y = (3/2)x + 300

92.

$\left|x\right|=\ -\ 5$

a)

5

b)

-5

c)

5 or -5

d)

no solution

93.

Solve for x

$|x+3|=1$

Don't forget to choose two answers!

a)

-4

b)

4

c)

2

d)

-2

e)

I am not sure.

94.

Solve for x:

$|2x-3|=5$

Choose two answers.

a)

4

b)

-1

c)

1

d)

-4

e)

I am not sure.

95.

What is the perimeter of the rectangle?

a)

x²+8x-5

b)

2x²+16x-10

c)

2x²+10x-8

d)

6x-2

96.

Sara wants to build a new ﬂower garden and has decided on the following dimensions. Which equation would help her decide how much wood to use for the perimeter of the ﬂower garden? (5 min)

a)

$4x^2+5x+7$

b)

$8x^2+10x+14$

c)

$20x^2+27x−8$

d)

$20x^3+32x^2−5x−8$

97.

Lap 3 - 5 min

Sara is trying to ﬁll the ﬂower garden she built. Which equation could she used to help determine how much dirt she need to ﬁll the ﬂower garden?

a)

$4x^2+5x+7$

b)

$8x^2+10x+14$

c)

$20x^2+27x−8$

d)

$20x^3+32x^2−5x−8$

98.

Evaluate -2x + -3y if x = 10 and y = -6

a)

18

b)

-38

c)

12

d)

-2

99.

Evaluate the expression.

a)

3

b)

5.57

c)

-6

d)

-3

100.

Evaluate the expression.

a)

1

b)

3.74

c)

7

d)

49

Algebra I Final Exam Review

Total questions: 100

Worksheet time: 8hrs 20mins

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