Free Printable Algebra 1 Final Review

1.

Simplify each expression using exponential notation:

$\frac{6^3k^{15}}{6^7k^{19}}$

a)

$k^46^4$

b)

$\frac{k^4}{6^4}$

c)

$6^4k^4$

d)

$\frac{6^4}{k^4}$

2.

$\left(\frac{2}{5}\right)^2$

a)

$\frac{1}{4}$

b)

$\frac{4}{25}$

c)

$\frac{4}{10}$

d)

$\frac{2}{13}$

3.

$\left(\frac{a^4}{b^3}\right)^{-2}$

a)

$\frac{b^6}{a^8}$

b)

$\frac{b^9}{a^{16}}$

c)

$\frac{a^2}{b}$

d)

$\frac{a^8}{b^6}$

4.

Simplify:

\left(\frac{a^2b^3}{a^5b^{-1}}\right)^{-4}

a)

$-\left(\frac{a^{12}}{b^{16}}\right)$

b)

$\frac{a^{12}}{b^{16}}$

c)

$\frac{b^{16}}{a^{12}}$

d)

$\frac{b^4}{a}$

5.

Simplify: $\frac{30x^{12}y^{-5}}{5x^{-3}y^2}$

a)

$\frac{6x^2}{y^3}$

b)

$\frac{6x^{15}}{y^7}$

c)

$\frac{6x^9}{y^3}$

d)

$\frac{6x^{12}}{y^{-3}}$

6.

Which expressions are equal to:

2^7

a)

$2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2$

b)

2+2+2+2+2+2+2

c)

$2\cdot7$

d)

$\frac{2^9}{2^2}$

e)

$\frac{1}{2^{-7}}$

7.

Solve using the Quadratic Formula.

a)

A

b)

B

c)

C

d)

D

8.

Solve using the Quadratic Formula.

a)

A

b)

B

c)

C

d)

D

9.

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

10.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

11.

Solve by Factoring/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

12.

Solve using the method of your choice:

x² + 4x + 3 = 0

a)

x = 1 and x = 3

b)

x = 6 and x = -2

c)

x = -1 and x = -3

13.

What is one of the factors of

x² + 2x - 24 ?

a)

(x-12)

b)

(x+2)

c)

(x-6)

d)

(x-4)

14.

What are the coordinates of the vertex of the parabola given by the equation $y=2x^2-4x+3$ ?

a)

$\left(1,9\right)$

b)

$\left(-1,9\right)$

c)

$\left(1,1\right)$

d)

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

15.

Factor Completely: 6x² + 5x - 6

a)

6(x + 1)(x - 6)

b)

(6x + 6)(x - 1)

c)

(2x - 3)(3x + 2)

d)

(3x - 2)(2x + 3)

16.

Factor completely.
2n² + 13n + 15

a)

(5n - 9)(n - 3)

b)

(3n + 7)(n + 4)

c)

(2n + 3)(n + 5)

d)

Not factorable

17.

Factor 4y² – 9.

a)

(2y + 3)(2y – 3)

b)

prime

c)

(2y + 3)(2y + 3)

d)

(2y – 3)(2y – 3)

18.

Factor completely.

121x² - 49

a)

( 11x - 7 ) ²

b)

( 11x - 7 ) ( 11x - 7 )

c)

( 11x + 7 ) ( 11x - 7 )

d)

( 12x + 7 ) ( 12x - 7 )

19.

Solve

-8x < 48

a)

x < -6

b)

x > -6

c)

x < 6

d)

x > 6

20.

Who is this character?

a)

Mario

b)

Leonardo

c)

Luigi

d)

Toad

21.

Solve
-5m < 10

a)

m < -2

b)

m > -2

c)

m < -50

d)

m > -50

22.

Does the sign need to flip when solving?
-2x ≥ 22

a)

YES

b)

NO

23.

Solve for k.
2k - 9≤ -19

a)

k ≤ -5

b)

k ≤ 5

c)

k < -5

d)

k < 5

24.

Solve:

-2n>12

a)

n > -6

b)

n > 6

c)

n < -6

d)

n < 6

25.

When you divide both sides of an equality by a negative number the inequality sign "flips" or reverses?

a)

False

b)

True

26.

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.

27.

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.

28.

Which point below is NOT a part of the solution set?

a)

(0, 0)

b)

(0, 1)

c)

(-100, -3)

d)

(5, 10)

29.

Which of the following equations match the given graph?

a)

y ≤ -3/4 x + 3

b)

y ≥ -3/4 x + 3

c)

y < -3/4 x + 3

d)

y > -3/4 x + 3

30.

Which of the following equations match the given graph?

a)

y ≥ 2/5x + 1

b)

y ≥ -2/5x + 1

c)

y≤ 2/5x + 1

d)

y ≥ -2/5x - 1

31.

Which ordered pair makes the inequality 2x + 4y > 600 true?

a)

(50, 100)

b)

(150, 100)

c)

(200, 25)

d)

(100, 75)

32.

Which ordered pair is NOT a solution to y ≥ -x + 1?

a)

(2,1)

b)

(0,2)

c)

(-4,4)

d)

(-1,6)

33.

Consider the equation:
y=-x+4
Identify the slope and y-intercept.

a)

m=4, b=-x

b)

m=-x, b=4

c)

m=1, b=4

d)

m=-1, b=4

34.

What is the y-intercept in the equation y= -2x + 5

a)

-2

b)

3

c)

5

d)

Cannot be Determined

35.

What does the x intercept represent?

a)

The length of the race

b)

The amount of time it took Trish to run the race.

36.

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)

37.

^{What is the x- intercept of the line?}

a)

(1, 0)

b)

(2, 0)

c)

( -1, 0)

d)

(-2, 0)

38.

What is the x-intercept shown on the graph?

a)

(2, 0)

b)

(-2, 0)

c)

(0, 3)

d)

(3, 0)

39.

What is the y-intercept shown on the graph?

a)

(0, -2)

b)

(3, 0)

c)

(0, 3)

d)

None of these.

40.

Who is this character?

a)

Seinfeld

b)

Mario

c)

Luigi

d)

Kramer

41.

What is the y-intercept of the equation?
y = 3x - 12

a)

y = 1 or (0, 1)

b)

y = 12 or (0, 12)

c)

y = -1 or (0, -1)

d)

y = -12 or (0, -12)

42.

Find the slope of the line.

a)

-5/4

b)

5/4

c)

-4/5

d)

4/5

43.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

2/1

d)

-2/1

44.

Find the slope of the line.

a)

1/4

b)

-1/4

c)

-4/1

d)

4/1

45.

Write the equation of the line.

a)

y=1/3x-1

b)

y=3/2x -1

c)

y=3x-1

d)

y=2/3x-1

46.

Write the equation for the line.

a)

y= -1x+3

b)

y= 4x+3

c)

y=1/4x+3

d)

y= -4x+3

47.

What is f(6) for the function f(x)=3x-8

a)

-8

b)

10

c)

-144

d)

answer not here

48.

What is $f\left(0\right)$ for the function $f\left(x\right)=2x+3$

a)

2x

b)

-3

c)

3

d)

10

49.

$f\left(x\right)=5x-12$ What is $f\left(-4\right)$

a)

-32

b)

-3

c)

-12

d)

3

50.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

51.

Complete the square for

x² - 12x + ____

a)

144

b)

36

c)

- 36

d)

24

52.

Complete the square.

x² + 6x + ____

a)

9

b)

12

c)

36

d)

- 9

53.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

54.

Given the perfect square trinomial, identify the equivalent expression

x²+14x+49

a)

(x+14)²

b)

(x+49)²

c)

(x-7)²

d)

(x+7)²

55.

Complete the Square and solve the equation.
m² - 16m = -59

a)

8

b)

8 ± √ 5

c)

± √ 13

d)

-8 ± √ 5

56.

Simplify $\frac{-2x^{-4}}{x^6}$

a)

$-\frac{2}{x^{10}}$

b)

$\frac{1}{2x^{24}}$

c)

$-2x^2$

57.

Solve the system by using the substitution method

a)

$\left(3,\ 6\right)$

b)

$\left(6,\ 3\right)$

c)

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

d)

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

58.

Solve this system by substitution.

a)

(1, -4)

b)

(1, 4)

c)

(-4, -7)

d)

(-7, -4)

59.

Solve the system by elimination.

a)

(-8,5)

b)

(8,-5)

c)

(8,5)

d)

(-8,-5)

60.

Who is this character?

a)

Daisy

b)

Minnie

c)

Apple

d)

Peach

61.

Solve the system by elimination.

a)

(2,5)

b)

(-2,5)

c)

(-2,-5)

d)

(2,-5)

62.

Is the pictured graph exponential growth, exponential decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

63.

Given y=3^xdetermine the y-intercept

a)

(0,1)

b)

(0,3)

c)

No Y-intercept

d)

y=1

64.

What function is present?

a)

Absolute Value

b)

Exponential Decay

c)

Linear Equation

d)

Exponential Growth

65.

Which graph is an exponential function?

a)

red

b)

blue

c)

green

d)

none

66.

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

a)

(.27)^x

b)

.27

c)

13

d)

3.51

67.

a)

100

b)

√20

c)

10√2

d)

2√10

68.

a)

3√2

b)

√6

c)

6

d)

2√3

69.

a)

2√5

b)

10

c)

5√2

d)

√10

70.

Solve the system of equations.
x + 5y = -27
-2x - 5y = 24

a)

(3, 6)

b)

(-3, -6)

c)

(-3, -4)

d)

(3, -6)

71.

Find the slope of the line that passes through:
(-3, -4) and (7, 6)

a)

0

b)

Undefined

c)

-1

d)

1

72.

^{What is the solution?}

a)

1

b)

-2

c)

(1, 2)

d)

(1, -1)

73.

What is the equation of a line with a zero slope that goes through the point
(6, 7) ?

a)

x = 6

b)

x = 7

c)

y = 6

d)

y = 7

74.

What would the graph of the equation x = -4 look like?

a)

Horizontal line

b)

Vertical line

c)

Slanted line

d)

No way to tell

75.

What would the graph of y = 8 look like?

a)

Horizontal line

b)

Vertical line

c)

Slanted line

d)

No way to tell

76.

Find the equation that represents the line going through (0, 2) and (-4, 0).

a)

y = 1/2 x - 4

b)

y = 1/2 x + 2

c)

y = 2x + 2

d)

y = -2x - 4

77.

Find the equation of the line that passes through the points:
(-4, -2) and (-3, 5)

a)

y = ¹/₇ x + 26

b)

y = 7x + 26

c)

y = -7x + 26

d)

y = -7x - 26

78.

Find the equation of the line that passes through the points:

(2, 2) and (3, 4)

a)

y = 2x + 2

b)

y = -2x - 2

c)

y = -2x + 2

d)

y = 2x - 2

79.

Write the equation of the line with slope -2 through the point (7, −1).

a)

y = −2x + 15

b)

y = −2x − 15

c)

y = −2x + 13

d)

y = −2x − 13

80.

Who is this character?

a)

Cutie

b)

Toad

c)

Bubba

d)

Genie

81.

What is the y-intercept of
2x-5y=35?

a)

(0,-7)

b)

(-7,0)

c)

(35/2, 0)

d)

(0,35/2)

82.

What is the x-intercept of
x+4y=7?

a)

(7/4, 0)

b)

(0, 7/4)

c)

(7, 0)

d)

(0,7)

83.

What information is enough to be able to graph a line?

a)

two points

b)

slope and y-intercept

c)

x- and y-intercepts

d)

a point and a dream

84.

Name the x- and y-intercepts for the equation:
5x - 3y = 15

a)

(3, 0) and (0, -5)

b)

(0, 3) and (-5, 0)

c)

(5, 15) and (15, 3)

d)

(0, -3) and (5, 0)

85.

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

86.

Which system of linear inequalities is represented by the graph?

a)

y≤2x-1
y>-2x+3

b)

y>2x-1
y≤-2x+3

c)

y<2x-1
y≥-2x+3

d)

y≤2x-1
y>2x+3

87.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

88.

Solve the equation, if possible.
$2a-6\left(a-4\right)=\ -4$

a)

7

b)

identity

c)

0

d)

-5

89.

Solve the equation, if possible.
$6m+5-3m=7\left(m-1\right)$

a)

3

b)

no solution

c)

identity

d)

5

90.

Does the equation open up or down?
Y = -3x² +7x - 2

a)

up

b)

down

91.

Solve using square roots.
k² - 6 = 43

a)

k = √37

b)

k = 37 or - 37

c)

k = 7, k = -7

d)

no solution

92.

Solve using square roots.
4m² - 100 = 0

a)

m=25, -25

b)

m=96

c)

m=5, -5

d)

m=-96

93.

Sovle for x using approximation:

5^x= 45

a)

x = 9

b)

x = 2.9

c)

x = 2.23

d)

x = 3.7

94.

Solve for x using approximation:

7^x = 42

a)

x = 1.12

b)

x = 6

c)

x = 2.14

d)

x = 1.88

95.

What is the correct graph for the equation y = - 0.5x²+ 2

a)

b)

c)

d)

96.

If we have the equation y = ax²+ bx + c,

how can we can find the x-coordinate of the vertex?

a)

-a

b)

-b/a

c)

b/2a

d)

-b/2a

97.

What is the vertex of y = x²+ 4x + 3?

a)

(2, 1)

b)

(-2, 1)

c)

(0, 0)

d)

(-2, -1)

98.

Does the equation open up or down?
Y = -3x² +7x - 2

a)

up

b)

down

c)

both

d)

neither

99.

What is the y intercept for the equation:
y = -8x² + 3x - 7

a)

(0, -8)

b)

(0, 3)

c)

(-8, -7)

d)

(0, -7)

100.

Who is this character?

a)

Kim K

b)

Wario

c)

Waluigi

d)

Birdo

Algebra 1 Final Review

Total questions: 100

Worksheet time: 7hrs 49mins

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