Free Printable Algebra 1 Final Review

1.

4 = 2(x + 3)

a)

1/2

b)

7/2

c)

-1

d)

5

2.

Solve: 5x - 14 = 8x + 4

a)

6

b)

-6

c)

-18/13

d)

10/3

3.

What is the first step to solve this equation:
11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

4.

2(3x+7) = x +10 +5x + 4

a)

2

b)

-4

c)

no solution

d)

all real numbers

5.

Solve:
5y+34 = -2(-7y+1)

a)

y = -4

b)

y = 9

c)

y = 4

d)

y = 36/19

6.

Solve the equation
-8x - 8 +3(x - 2) = -3x + 2

a)

x = -8

b)

x = 8

c)

x = 2

d)

x = -2

7.

Solve:
2x + 1 = 2x - 1

a)

No Solution

b)

x = 0

c)

Infinitely Many Solutions

8.

6x + 9 – x = 3x + 9 + x

a)

No Solution

b)

One Solution

c)

Infinite Solutions

9.

3(x-2) + 1 = 3x - 5

a)

No Solution

b)

One Solution

c)

Infinite Solutions

10.

Which property of real numbers was used to get from Step 3 to Step 4?

a)

Addition Property of Equality

b)

Subtraction Property of Equality

c)

Additive Inverse Property

d)

Substitution Property

11.

Which property justifies the work in solving this equation?

a)

Addition Property of Equality

b)

Additive Inverse Property

c)

Identity Property of Addition

d)

Subtraction Property of Equality

12.

Which property is shown below?
__________________________
7n = 21 then n = 3

a)

Division Property

b)

Sorcery

c)

Reduction of Multiples

d)

Distributive Property

13.

If y/4 = 5, then y = 20

a)

Multiplication Property of Equality

b)

Division Property of Equality

c)

Addition Property of Equality

d)

Subtraction Property of Equality

14.

-4x + 14 ≤ 54

a)

x ≥ - 10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

15.

Solve:
6x+10>5x-12

a)

x>2

b)

x<2

c)

x<-22

d)

x>-22

16.

Solve:
3(x - 2) < 2(x + 9)

a)

x<24

b)

x>12

c)

x<12

d)

x>24

17.

Solve:
4(2a + 3) < 3(a - 1)

a)

a<-3

b)

a>-3

c)

a<3

d)

a>3

18.

You want to spend at most $1200 on a new laptop. If you make a $400 down payment, then pay the same amount every month for 12 months. Which Inequality could be use to solve to find out how much you can pay each month.

a)

12x + 1200 > 400

b)

12x + 400 < 1200

c)

12x + 400 > 1200

d)

12x + 400 < 1200

19.

Which graph matches the inequality
-2 ≥ n?

a)

A

b)

B

c)

C

d)

D

20.

Consider the following scenario:

if x - 3y > 6

and 2x + 8 > x - 3y

then 2x + 8 > 6

a)

TRUE

b)

FALSE

21.

Based on the transitive property of inequality:

if 2x - 3 < 4

and x + 5 < 2x - 3

then x + 5 > 4

a)

TRUE

b)

FALSE

22.

3 = $\sqrt{b-1}$

a)

10

b)

16

c)

4

d)

no solution

23.

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

a)

8

b)

16

c)

4

d)

no solution

24.

$\sqrt{5x-36}+1=4$

a)

9

b)

10

c)

8

d)

no solution

25.

a)

9

b)

-9

c)

21

d)

-21

26.

Simplify:

a)

a

b)

b

c)

c

d)

d

27.

Simplify:

a)

a

b)

b

c)

c

d)

d

28.

Rewrite in exponential form:

a)

a

b)

b

c)

c

d)

d

29.

Rewrite in exponential form:

a)

a

b)

b

c)

c

d)

d

30.

Simplify:

a)

a

b)

b

c)

c

d)

d

31.

Solve for the indicated variable.

a)

A

b)

B

c)

C

d)

D

32.

Solve for the indicated variable.

a)

A

b)

B

c)

C

d)

D

33.

Solve for the indicated variable.

a)

A

b)

B

c)

C

d)

D

34.

Solve for the indicated variable.

a)

A

b)

B

c)

C

d)

D

35.

Solve for the indicated variable.

a)

A

b)

B

c)

C

d)

D

36.

What type of slope does the graph have?

a)

Zero

b)

Undefined

c)

Negative

d)

Positive

37.

Graph. y = -4

a)

a

b)

b

c)

c

d)

d

38.

Graph. x = 1

a)

a

b)

b

c)

c

d)

d

39.

What is the equation of this line?

a)

0

b)

undefined

c)

y = -2

d)

x = -2

40.

Graph. x = 1

a)

a

b)

b

c)

c

d)

d

41.

What kind of slope would this line have?

a)

positive

b)

negative

c)

zero

d)

undefined

42.

Find the slope of the line that goes through the points

(−11,−5) and (1,−12)

a)

$-\frac{5}{8}$

b)

$\frac{16}{11}$

c)

$\frac{1}{6}$

d)

$-\frac{7}{12}$

43.

Find the slope of the line that goes through the points

(−1,−2) and (−3,−4).

a)

1

b)

2

c)

3

d)

4

44.

Which of these represents point-slope form of a linear equation?

a)

y - y₁ = m(x - x₁)

b)

Ax + By = C

c)

y = mx + b

45.

Write the equation in point-slope form of the line that passes through the given point and has the given slope:
(-2, -1); m= -3

a)

y + 1 = -3(x - 2)

b)

y + 1 = -3(x + 2)

c)

y - 1 = 3(x - 1)

d)

y + 2 = -3(x + 1)

46.

Write the equation in point-slope form of the line that passes through the given point and has the given slope:
(-2, -1); m= -3

a)

y + 1 = -3(x - 2)

b)

y + 1 = -3(x + 2)

c)

y - 1 = 3(x - 1)

d)

y + 2 = -3(x + 1)

47.

What is the slope?

a)

1/3

b)

-3

c)

3

d)

-1/3

48.

Slope is know as rise/

a)

run

b)

fall

c)

none

d)

rise

49.

In the equation y=mx+b, what does the m represent?

a)

slope

b)

y-intercept

c)

linear

d)

point-slope

50.

How would you write the equation with a slope of 2/3 and a y-intercept of -3

a)

y=3/2x+3

b)

y=2/3-3

c)

y=2/3x-3

d)

y=2/3x+3

51.

What is the slope of the line that passes through the points (0, -5) and (3, 2)?

a)

-7/3

b)

5/3

c)

3/7

d)

7/3

52.

Determine the slope of the line passing through (-3, 4) and (1, -2).

a)

-3/2

b)

3/2

c)

2/3

d)

-2/3

53.

Find the slope of the line passing through the points (2, 3) and (5, 7).

a)

4/3

b)

2/3

c)

7/3

d)

5/3

54.

What does 'b" represent in y=mx=b

a)

y-intercept

b)

mushroom

c)

nothing

d)

slope

55.

What is the slope in the equation: y = 4x + 3

a)

3

b)

4x

c)

4

d)

x

56.

What is the y-intercept in the following equation: y = - 4x - 5

a)

- 4

b)

- 4x

c)

5

d)

- 5

57.

If m=3 and b=6, what is the correct slope intercept equation?

a)

y = 3 + 6

b)

y = 3x - 6

c)

y = 3x + 6

d)

y = 6x + 3

58.

Find the slope from the table:

a)

-0.4

b)

-2.5

c)

2.5

d)

0.4

59.

What is the slope-intercept form formula?

a)

y = kx

b)

y = mx + b

c)

I = Prt

60.

Which equation is in standard form?

a)

y = mx + b

b)

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

c)

Ax + By = C

d)

$m=\frac{y_2-y_1}{x_2-x_1}$

61.

What is the first thing you would do to write 2x - y = 7 in slope intercept form?

a)

Add y to both sides

b)

Subtract 2x from both sides

c)

Divide both sides by 2

d)

Subtract 7 from both sides

62.

Write x + 5y = 10 in slope intercept form.

a)

$y=-5x\ +\ 2$

b)

$y\ =\ -\frac{1}{5}x\ +\ 5$

c)

$y\ =\ 5x\ +\ 2$

d)

$y\ =\ -\frac{1}{5}x\ +\ 2$

63.

Write x + 5y = 10 in slope intercept form.

a)

$y=-5x\ +\ 2$

b)

$y\ =\ -\frac{1}{5}x\ +\ 5$

c)

$y\ =\ 5x\ +\ 2$

d)

$y\ =\ -\frac{1}{5}x\ +\ 2$

64.

Which represents -2x - 3y = 12 in slope intercept form.

a)

$y\ =\ -\frac{2}{3}x\ -\ 4$

b)

$y\ =\ \frac{2}{3}x\ -\ 4$

c)

$y\ =\ -\frac{2}{3}x\ +\ 4$

d)

$y\ =\ \frac{2}{3}x\ +\ 4$

65.

What is the solution to the system?

a)

(0, 3)

b)

(1, -1)

c)

(-3, 1)

d)

(1, 3)

66.

Will the solution (-3, -7) make the following system of equations a true statement?

y = 4x + 5

y = x – 4

a)

YES

b)

NO

67.

What is the solution to this system?

y = 2x + 1

y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

68.

Will the solution (-3, -7) make the following system of equations a true statement?
y = 4x + 5
y = x – 4

a)

YES

b)

NO

69.

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

a)

Sugar Cookies $5
Oatmeal Cookies $3

b)

Sugar Cookies $4
Oatmeal Cookies $8

c)

Sugar Cookies $2
Oatmeal Cookies $6

d)

Sugar Cookies $3
Oatmeal Cookies $6

70.

The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3.
Solve:
x + y = 55
x - y = 3

a)

(26, 23)

b)

(26, 29)

c)

(29, 26)

d)

(29, 32)

71.

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

a)

4x + 6y = 3
13.5x - 13y = 6

b)

x + y = 4
x - y = 6

c)

4x + 6y = 13
3x + 7y = 13.5

d)

4x - 6y = 13
3x - 7y = 13.5

72.

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situation?

a)

x + y = 15
4x + 2y = 44

b)

4x + 2y = 15
x + y = 44

c)

x = 2y + 44
4x = y + 15

d)

2x - 4y = 44
x - y = 15

73.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

74.

What is the solution to the system of equations graphed below?

a)

No Solution

b)

Infinite Solutions

c)

One Solution: (0, 4)

d)

One Solution: (0, 6)

75.

What is the solution to the system of equations graphed below?

a)

No Solution

b)

Infinite Solutions

c)

One Solution: (0, 2)

d)

One Solution: (2, 6)

76.

What is the value of the y-coordinate of the solution to the system of equations
x-2y=1
x+4y=7

a)

1

b)

-1

c)

3

d)

4

77.

Solve the system of equations.

a)

(-23, 4)

b)

(-4, -3)

c)

(-2, -4)

d)

No solution

e)

Infinite solutions

78.

An inequality using a > or a < has a ___________ line

a)

invisible

b)

solid

c)

dashed

79.

Is (3,-4) a solution to this system?

a)

yes

b)

no

80.

Pick the ordered pair that is NOT a solution

a)

(0,0)

b)

(1,-1)

c)

(2,0)

d)

(4,-4)

81.

Consider the function y<2x+3. Which is true?

a)

The line would be solid with shading above.

b)

The line would be dashed with shading above.

c)

The line would be solid with shading below.

d)

None of these.

82.

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

83.

Given: y < 4x + 3

Would you draw a solid or dashed line?

a)

Solid

b)

Dashed

84.

Given: y < 4x + 3

Would shade above or below the line?

a)

Above

b)

Below

85.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

86.

Will my line be solid?
5 ≥ x

a)

Yes

b)

No

87.

Pick ALL correct answers.

Which are solutions to the system?

a)

(-5,4)

b)

(-5,-2)

c)

(0,10)

d)

(5,10)

e)

(0,-5)

88.

Which system is graphed?

a)

y>-\frac{1}{4}x-3

y>2x+6

b)

$y>\frac{1}{4}x-3$
$y\le-2x+6$

c)

$y\le-2x+6$
$y<-\frac{1}{4}x-3$

d)

$y\le-2x+6$
$y>-\frac{1}{4}x-3$

89.

Combine like terms
3x + 2x + 3y - 7y

a)

5x + 10y

b)

5x + 4y

c)

5x - 4y

d)

5x -10y

90.

Simplify by combining like terms:
4x² - 3x + 11 -2x

a)

4x² - 5x + 11

b)

11x + 11

c)

16x² - 5x + 11

d)

10x²

91.

Which of these are like terms in the following expression:
(3x + 7 - 9x) + (24y + 2x²)

a)

7, 24y

b)

3x, 9x

c)

3x, -9x

d)

3x, -9x, 2x²

92.

Simplify the expression:
-2x² - x + 1 - x² + 3x - 5

a)

-2x² + 2x - 6

b)

-3x² + 2x - 4

c)

2x² + 2x + 4

d)

-3x² + 4x - 4

93.

A monomial has _?_ term.

a)

one

b)

two

c)

three

d)

many

94.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

95.

(5x+1)(x+4)

a)

5x² + 19x − 4

b)

5x² + 21x + 4

c)

5x² + 4

d)

5x² − 19x − 4

96.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

97.

Simplify the expression.
x³(2x²+3x)

a)

2x⁵+3x⁴

b)

2x⁶+3x³

c)

5x⁹

d)

5x

98.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

99.

Add or Subtract to Simplify:
(4x²+ x) - (x²+ 2x)

a)

3x²- x

b)

4x²+ 2x

c)

3x² + 3x

d)

3x² + 2x

100.

Add or Subtract to Simplify:
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

101.

Rewrite using a positive exponent.
7^-10

a)

¹/_7¹⁰

b)

7¹⁰

c)

¹/_7^-10

d)

-70

102.

Rewrite each expression with a negative exponent.
¹/_(-5)⁷

a)

(-5)⁷

b)

¹/_(-5)^-7

c)

(-5)^-7

d)

¹/_78,125

103.

Simplify.
2^-3⋅ 2^-4

a)

¹/₁₂₈

b)

2^-7

c)

2¹²

d)

2⁷

104.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

105.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

106.

Factor x²-2x-15

a)

(x+5)(x-3)

b)

(x-5)(x-3)

c)

(x-5)(x+3)

d)

(x+5)(x+3)

107.

Factor x² + 7x + 12

a)

(x + 2)(x + 10)

b)

(x + 3)(x + 4)

c)

(x + 4)(x + 5)

d)

(x + 4)(x + 6)

108.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

109.

Factor:
p² - 14p

a)

p(1 - 14)

b)

2p(p - 7)

c)

p²(1-14)

d)

p(p - 14)

110.

Which is another way of correctly expressing
(x - 3)(x - 3)?

a)

(x² - 3²)

b)

(x² - 3)

c)

(x + 3)(x - 3)

d)

(x - 3)²

111.

x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

112.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

113.

Factor
n²-13n+40

a)

(n-5)(n-8)

b)

(n+5)(n-8)

c)

(n-5)(n+8)

d)

(n+6)(n+1)

114.

Factor the expression completely:

x^2-49

a)

Not Factorable

b)

$\left(x-7\right)\left(x+7\right)$

c)

$\left(x-7\right)^2$

d)

$\left(x+7\right)^2$

115.

Factor the expression completely:

25x^2+4

a)

Not Factorable

b)

$\left(5x-2\right)\left(5x+2\right)$

c)

$\left(5x-4\right)\left(5x-1\right)$

d)

$\left(5x+4\right)\left(5x+1\right)$

116.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Move 21 to the right and change to a negative

117.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

118.

To solve by completing the square, what needs to be moved in this equation? $x^2=6x+8$

a)

Move the $6x$

b)

Move the $8$

c)

Move the $x^2$

119.

Complete the square for

x² - 14x + ____

(find the missing value that goes in the blank)

a)

- 196

b)

49

c)

- 49

d)

28

120.

Is this a perfect square trinomial?
x² + 18x + 9

a)

Yes

b)

No

121.

Factor the perfect square trinomial
x² + 14x + 49

a)

(x+7)²

b)

(x+7)(x-7)

c)

(x-7)²

d)

(x+14)²

122.

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

123.

What is the vertex of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

124.

What is the y-intercept of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

125.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

126.

What are the zeros of the parabola?

a)

1, 5

b)

3, -5

c)

3, 0

d)

-6, 1

127.

Does this graph have maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

128.

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

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

129.

In vertex form,

f(x) = a(x - h)²+ k

what does the h stand for?

a)

the y-coordinate of the vertex

b)

the x-coordinate of the vertex

c)

the x-intercept

d)

the y-intercept

130.

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

a)

x = -b/2a

b)

x = (-b ±√b² - 4ac)/2a

c)

y = ax² + bx + c

d)

y = a(x - h)² + k

131.

Which of the following equations matches STANDARD FORM of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

132.

√24

a)

4√6

b)

2√6

c)

6√2

d)

2√12

133.

√28

a)

7√2

b)

7√4

c)

4√7

d)

2√7

134.

√45

a)

3√5

b)

5√3

c)

9√5

d)

5√9

135.

√125

a)

5√5

b)

25√5

c)

5√25

d)

5√2

136.

Simplify √72

a)

8√3

b)

6√2

c)

3√8

d)

4√8

137.

What is the definition of function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

138.

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.

139.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

140.

Is this table a function or not a function?

a)

Function

b)

Not a Function

141.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

142.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

143.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

144.

What is x if

f(x) = -1?

a)

4

b)

0

c)

3

d)

6

145.

What is the range of the graph?

a)

-4 ≤ x ≤ 3

b)

3 ≤ x ≤ -3

c)

-2 ≤ x ≤ 10

d)

-3 ≤ x ≤ 10

146.

What is the domain of the graph?

a)

-3 ≤ x ≤ 3

b)

3 ≤ x ≤ -3

c)

-2 ≤ x ≤ 10

d)

-3 ≤ x ≤ 10

147.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

148.

Which ordered pair could you add to the following list of points to create a function? (3, 5) (4, 9) (2, 5)

a)

(3, 7)

b)

(4, 1)

c)

(1, 9)

d)

(2, 6)

149.

Solve using the quadratic formula:

4x²+ 4x + 1 = 0

a)

x = -½

b)

x = -2

c)

x = 0

d)

x = ½

150.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

Algebra 1 Final Review

Total questions: 150

Worksheet time: 12hrs 31mins

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