Free Printable Algebra Final Exam Review

1.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

2.

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

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

∅

3.

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

a)

yes

b)

no

4.

$w^{15}\ \cdot\ \frac{1}{w^5}$

a)

w¹⁰

b)

w²⁰

c)

w³

d)

$\frac{1}{w^{75}}$

5.

15y² . (2y)³

a)

120y⁵

b)

120y⁶

c)

30y⁵

d)

30y⁶

6.

Using exponents, simplify the following expression:

(f^-6)(f¹⁰)

a)

f¹⁶

b)

f⁴

c)

1/f⁴

d)

1/f¹⁶

7.

Using exponents, simplify the following expression:

z^-3* z⁶ * z^-3

a)

1

b)

z⁶

c)

z⁵⁴

d)

1/z⁶

8.

Simplify the following expression:

(xyz)⁰ =

a)

0

b)

1

c)

xyz

d)

-1

9.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

10.

^simplify 5x³2x²

a)

10x⁵

b)

3x

c)

10x⁶

d)

7x⁵

11.

Use FOIL to solve: (p + 9)(4p + 2)

a)

9p x 4p + 2

b)

p to the 5th power minus seven

c)

-18p

d)

4p² + 38p + 18

12.

(x + 7)(x + 9)

a)

x² + 63x + 16

b)

x² + 16x + 63

c)

x² + 79

d)

x² + 16x + 2

13.

Factor the polynomial.
x²-4x-32

a)

(x-8)(x+4)

b)

(x-4)(x-32)

c)

(x+3)(x-4)

d)

x+2)(x+5)

14.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

15.

x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

16.

Factor the polynomial.
x²-4x-32

a)

(x-8)(x+4)

b)

(x-4)(x-32)

c)

(x+3)(x-4)

d)

x+2)(x+5)

17.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

18.

Factor
5x²-28x+32

a)

(3x-10)(x+6)

b)

(x-8)(5x-4)

c)

(5x-8)(x-4)

d)

(5x-8)(x+7)

19.

Solve for m by factoring.

a)

A

b)

B

c)

C

d)

D

20.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

21.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

22.

(3x + 4y - 3z) - (2x - 6y + 7z)

a)

x + 10y - 10z

b)

-x +10y - 10z

c)

x -10y - 10z

d)

-x -10y - 10z

23.

Subtract: (2a² + 5a + 3) -(a² - 3a - 4)

a)

3a² + 2a - 1

b)

a²+ 8a + 7

c)

3a²+ 8a + 7

d)

a² + 2a - 1

24.

y = 3x +2
y = 3x - 3
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

The same line

25.

Which line is perpendicular to
y = 2x - 7 ?

a)

y = -2x + 8

b)

y = ¹/₂x - 7

c)

y = ^-1/₂x + 2

d)

y = 2x - 3

26.

Solve the system of equations
4x+8y=20
-4x+2y=-30

a)

(-7,1)

b)

(2,-5)

c)

(-2,5)

d)

(7,-1)

27.

What is the solution to this equation?

a)

one solution

b)

no solution

c)

infinite solutions

d)

none of these

28.

Is the points (-4, 4) a solution to the system of equations?

a)

Yes

b)

No

29.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

D

30.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

_D

31.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

32.

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

33.

Use the quotient rule to simplify the monomial.

a)

4

b)

4y¹⁰

c)

4x

d)

4xy¹⁰

34.

Which of the following expressions is equivalent to (2x)³ ?

a)

(2x)(2x)(2x)

b)

2(x)(x)(x)

c)

2x + 2x + 2x

d)

2x⋅3

35.

(-5²)

a)

25

b)

-25

c)

10

d)

-10

36.

4x²- 64y²

a)

Unfactorable

b)

( 2x - 32y) (2 x + 32y)

c)

( 2x - 8y) (2 x - 8y)

d)

( 2x - 8y) (2 x + 8y)

37.

x²+ 81

a)

Unfactorable

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

38.

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

39.

$\sqrt{243}$

a)

$3\sqrt{3}$

b)

$9\sqrt{3}$

c)

$81\sqrt{3}$

d)

$3\sqrt{81}$

40.

Simplify the radical...
√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

41.

Simplify the expression

a)

6a⁵b³√6b

b)

2a⁵b³√54b

c)

3a⁵b³

d)

6√2a¹⁰b⁷

42.

a)

8

b)

9

c)

10

d)

11

43.

Challenge:
Find the GCF of 9u³v⁴w and 15u²v²w²

a)

9u²v²w

b)

9u³v⁴w²

c)

3u³v⁴w²

d)

3u²v²w

44.

The following polynomial is written in standard form:
7x³ - 11x² + 8x - 5

a)

True

b)

False

45.

Which of these is in Standard Form?

a)

$4x^2+12x-13x^3$

b)

$5-3x$

c)

$2x^4-12x^2+5x-9$

d)

$5x^5+4x^{\text{4}}+12x^3-23x+15$

46.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

47.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

48.

m²-10m=0

a)

m=0 and m=-10

b)

m=1 and m=10

c)

m=0 and m=10

d)

m=1 and m=-10

49.

a)

{49,-49}

b)

{8,-8}

c)

{7,-7}

d)

No Solution

50.

a)

{9.49,-9.49}

b)

{9,-9}

c)

{3,-3}

d)

No Solution

51.

Solve using square roots.

a)

A

b)

B

c)

C

d)

D

52.

Which of the following inequalities matches the given graph?

a)

y ≥ 2/5x + 1

b)

y ≥ -2/5x + 1

c)

y≤ 2/5x + 1

d)

y ≥ -2/5x - 1

53.

Which of the following inequalities matches 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

54.

√24

a)

4√6

b)

2√6

c)

6√2

d)

2√12

55.

√125

a)

5√5

b)

25√5

c)

5√25

d)

5√2

56.

Simplify the radical...

√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

57.

√75x²

a)

5x²√3

b)

5x

c)

5x√3x

d)

5x√3

58.

√500x⁸y²

a)

10x⁴y√5

b)

10x⁴y²√5

c)

50x⁴y

d)

100x⁴y√5

59.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

60.

√121

a)

11

b)

12

c)

21

d)

121

61.

∛8

a)

2

b)

-2

c)

±2

d)

None

62.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

63.

Simplify this expression.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

64.

Factor:
2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

65.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

66.

What is the factored form of x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

67.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

68.

Solve the equation by factoring:
x² + x - 20 = 0

a)

x = -5 and 4

b)

x = 4 and 5

c)

x = 5 and -4

d)

x = -4 and -5

69.

Solve by factoring

x² + 10x = -25

a)

x = -5

b)

x = ±5

c)

x = 5

d)

x = 0

70.

x² - 9

a)

(x + 3) (x - 3)

b)

(x - 3) (x - 3)

c)

(x + 3) (x - 6)

d)

Can't factor using Diff. of Squares

71.

Find the quotient:

a)

x + 10

b)

x - 10

c)

x - 5

d)

x + 4

72.

Find the quotient:

a)

7n - 5

b)

7n

c)

7

d)

n - 5

73.

a)

A

b)

B

c)

C

d)

D

74.

Find the vertex y = x² - 2x - 5

a)

V(-2, 10)

b)

V(-1, 15)

c)

V(1, -6)

d)

V(1, -12)

75.

a)

A

b)

B

c)

C

d)

D

76.

Find the zeros of this quadratic.

a)

b=4/5, b=3

b)

b=4, b=-3

c)

b=1/5, b=3

d)

b=4/5, b=-3

77.

What are the zeros?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

78.

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

79.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

80.

True or false:
The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

81.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

82.

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)

Subtract the 21

83.

Solve for x:
(x+6)²=49

a)

x=7,12

b)

x=±7

c)

x=1,-13

d)

x=43,-55

84.

3. Solve the equation
4x²- 25 = 0

a)

5/2, -5/2

b)

5/2, 5/2

c)

-5/2, -5/2

d)

-5/2, 5/2

85.

Solve by completing the square:
x² + 6x = 55

a)

x = -14, 2

b)

x = 14, -2

c)

x = -5, 11

d)

x = 5, -11

86.

What are the roots of the function
f(x)= (x - 2)(x + 3)?

a)

x = - 2 or x = 3

b)

x = 2 or x = -3

c)

The are no real roots

d)

x = 2 or x = 3

87.

What is the equation for the axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

88.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

89.

Does y = -4x² have a maximum or minimum value?

a)

maximum

b)

minimum

90.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

91.

What is the formula to find the vertex of a parabola?

a)

x = -b/2

b)

x = -b

c)

x = -b / (2a)

d)

x = -b / 2

92.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

none of these

93.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

94.

What is the vertex?

a)

(-2,0)

b)

(0,0)

c)

(0,-4)

d)

(2,0)

95.

Select the answer that has a, b, and c correctly labeled:

y=-x^2+2x-9

a)

a= 1, b= 2, c= -9

b)

a= 2, b= -1, c= 9

c)

a= -9, b= 2, c= -1

d)

a= -1, b= 2, c= -9

96.

Which direction will this parabola open?

y=2x^2+8x-16

a)

upwards

b)

downwards

97.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

98.

.How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

99.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

a)

Minimum value, because the a value is positive

b)

Maximum value, because the b value is positive

c)

Maximum value, because the a value is positive

d)

Minimum value, because the c value is negative

100.

What is the vertex?

a)

(5,2)

b)

(2,5)

c)

(-2,5)

d)

(-5,2)

Algebra Final Exam Review

Total questions: 100

Worksheet time: 6hrs 25mins

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