Free Printable Final Review MATH 4

1.

What type of number is 13?

a)

Imaginary

b)

Rational

c)

Integer

d)

Whole

e)

Real

2.

What type of number is -7/3?

a)

Irrational

b)

Integer

c)

Rational

d)

Whole

e)

Real

3.

π is a rational number

a)

True

b)

False

4.

0 is an integer

a)

True

b)

False

5.

How would 0.333333... be classified?

a)

rational and real

b)

integer, rational, real

c)

irrational and real

d)

only irrational

6.

Which number is an irrational number?

a)

-15 / 7

b)

square root of 88

c)

square root of 25

d)

0.3333....

7.

Simplify. |18 - 9|

a)

18

b)

9

c)

27

d)

-9

8.

What values of x make the statement true?

|x| = 5

a)

5 and 0

b)

15

c)

5 and -5

d)

5

9.

What is the absolute value of

$\left|-7.8\right|$

a)

7.8

b)

1

c)

-1

d)

-7.8

10.

Find and explain the error.
5 - 3 + 2
5 - 5
0

a)

There is no error.

b)

Addition was done first and you should have subtracted first

c)

There is a subtraction error

11.

Simplify the following:
-8 + (15 - 3) ÷ 4

a)

-5

b)

1

c)

-11

d)

11

12.

Evaluate each expression.
| x + 9 | = -5

a)

-14

b)

-4

c)

{-14, -4}

d)

no solution

13.

Solve the following expression: (remember * means multiply)
6+|-6-3|+2*3

a)

-21

b)

21

c)

3

d)

-3

14.

Solve for x:
5x - 14 = 8x + 4

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

15.

-3x − 4 < 5

a)

x > -3

b)

x < -3

c)

x < (1 ⁄ 3)

d)

x > (1 ⁄ 3)

16.

Pick the correct letter for:
6 > x

a)

A

b)

B

c)

C

d)

D

17.

When you graph an inequality, you used a closed dot when you use which symbols?

a)

≤, ≥

b)

<, >

18.

When graphing an inequality, you use an open dot when you use which symbol?

a)

<, >

b)

≤, ≥

19.

3(x+2) = 15

a)

13

b)

7

c)

4.33333

d)

3

20.

Solve the equation: 4x - 5x + 9 = 5x - 9

a)

x=3

b)

x=-3

c)

x=-9

d)

x=9

21.

In order to solve an equation, we must get variables on one side of an equation, and constants on the opposite side.

a)

False

b)

True

22.

What do I need to do first? Distribute or Combine Like Terms?

a)

Distribute

b)

Combine like terms

23.

Simplify the expression (this means distribute and/or combine like terms):

a)

-6x + 5 = 42

b)

-12x - 18 = 42

24.

Show your work:

a)

b)

25.

Solve the equation.

a)

x = 2

b)

x = -5

26.

Do I need to distribute, combine like terms, or both?

a)

Distribute

b)

Combine like terms

c)

Both

27.

Simplify the expression (this means distribute and/or combine like terms):

a)

9x + 5 = 14

b)

7x + 7 = 14

28.

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

a)

No Solution

b)

x = 15

c)

Infinitely Many Solutions

29.

What is the solution to this equation?

a)

one solution

b)

no solution

c)

infinite solutions

d)

none of these

30.

What is the solution to the equations?

a)

one solution

b)

no solution

c)

infinite solutions

d)

none of these

31.

Evaluate this expression using the quotient of powers rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

32.

(x²)⁶

a)

x¹²

b)

x⁸

c)

x²⁶

d)

x⁴

33.

a)

True

b)

False

34.

The negative exponent rule states: $a^{-n}=?$

a)

$a^n$

b)

$\frac{1}{a^n}$

c)

$n^a$

d)

$\frac{1}{n^a}$

35.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

36.

a)

b)

c)

d)

37.

a)

m⁴

b)

m⁶

c)

m¹⁰

d)

1/m⁶

38.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

39.

According to exponent rules, when we raise the exponents to another power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

40.

According to exponent rules, when we divide the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

41.

Rewrite using a positive exponent.
7^-10

a)

¹/_7¹⁰

b)

7¹⁰

c)

¹/_7^-10

d)

-70

42.

Which number is the BASE?

2³= 8

a)

2

b)

3

c)

8

43.

a)

b)

c)

d)

44.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

45.

What does this symbol ( ∩ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

46.

What does this symbol ( ∪ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

47.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∪ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

48.

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

49.

Solve: |x + 3| < 8

a)

x > 5 or x < -11

b)

-11 < x < 5

c)

x > 11 or x < -5

d)

5 < x < 11

50.

Solve: |x - 3| > 8

a)

x > 5 or x < -11

b)

-11 < x < 5

c)

x > 11 or x < -5

d)

-5 < x < 11

51.

Write the following in interval notation

x < 8

a)

(8, ∞)

b)

(-∞, 8)

c)

(8, -∞)

d)

[-∞, 8]

52.

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

53.

Which compound inequality represents the graph?

a)

m < -1 OR m > 2

b)

-1 < m < 2

c)

m > -1 OR m < 2

54.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

55.

(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

56.

(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

57.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

58.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

59.

Factor:

(x² - 2x - 15)

a)

(x - 5)(x + 3)

b)

(x + 3)(x + 5)

c)

(x - 3)(x - 5)

d)

(x - 15)(x - 2)

60.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 25 ) ( x - 25 )

d)

Prime

61.

Factor Completely:

20x³- 25x²+ 4x - 5

a)

(5x²- 5)(4x + 1)

b)

5(x²- 1)(4x + 5)

c)

(5x²+ 1)(4x - 5)

d)

(5x²+ 1)(4x - 1)

62.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

63.

Factor
d² - 10d + 25

a)

(d + 5) (d - 5)

b)

(d - 15) (d + 10)

c)

(d + 5) (d - 20)

d)

(d - 5) (d - 5)

64.

What is the GCF of the following?

12x^3+9yx

(a)

65.

What is the first question you ask yourself when factoring a polynomial?

a)

How many terms does it have?

b)

Is there a GCF?

c)

What strategy should I use?

d)

Why do I have to learn this?!?!?!

66.

Factor 25x² - 81.

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

cannot be factored

67.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

68.

Factor $27x^3-343$

a)

$\left(3x+7\right)\left(3x^2+21x+49\right)$

b)

$\left(3x+7\right)\left(9x^2-21x+14\right)$

c)

$\left(3x-7\right)\left(3x^2+10x+49\right)$

d)

$\left(3x-7\right)\left(9x^2+21x+49\right)$

69.

$Simplify:\ \ \frac{x^2+6x-7}{x^2-49}$

a)

$\frac{x-1}{x+7}$

b)

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

c)

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

d)

$\frac{x+1}{x-7}$

70.

$Simplify:\ \ \frac{x^2-25}{x^2-6x+5}$

a)

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

b)

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

c)

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

d)

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

71.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

72.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

73.

Alison has factored the numerators and denominators and multiplied across. She must be…

a)

Adding or Subtracting Rational Expressions

b)

Multiplying Rational Expressions

c)

Dividing Rational Expressions

74.

Bob has factored the denominators and made sure there is a common denominator. He must be...

a)

Adding or Subtracting Rational Expressions

b)

Multiplying Rational Expressions

c)

Dividing Rational Expressions

75.

Julie has factored the numerators and denominators and multiplied by the reciprocal (keep it, flip it, multiply it). She must be…

a)

Adding or Subtracting Rational Expressions

b)

Multiplying Rational Expressions

c)

Dividing Rational Expressions

76.

Add and Simplify

a)

b)

c)

d)

77.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

78.

Subtract

a)

A

b)

B

c)

C

d)

D

79.

Subtract:
$\frac{5x-3}{x+2}-\frac{3x-1}{x+2}$

a)

$\frac{2x-4}{x+2}$

b)

$\frac{8x-4}{x+2}$

c)

$\frac{2x-2}{x+2}$

d)

$\frac{2x-2}{0}$

80.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

81.

Solve for y $\frac{y+2}{3}-\frac{y-1}{4}=\frac{2}{3}$

a)

y = -9

b)

y = -3

c)

y=1

d)

y = 3

82.

Simplify

\sqrt{24}

a)

$4\sqrt{6}$

b)

$2\sqrt{6}$

c)

$6\sqrt{2}$

d)

$6\sqrt{4}$

83.

Simplify:

\sqrt{x^{15}}

a)

$x^{7.5}$

b)

$x^{14}\sqrt{x}$

c)

$x^7\sqrt{x}$

84.

Simplify:

a)

√12

b)

(4√3)/3

c)

√3

d)

(2√3)/3

85.

Simplify:

a)

√5

b)

(√14)/2

c)

√7

d)

Cannot be simplified

86.

√3 × √15 =

a)

3√5

b)

5√3

c)

2√7

d)

√17

87.

a)

8√6

b)

8√12

c)

12√6

d)

12√12

88.

Question 1

a)

10

b)

8

c)

16

d)

4

89.

Question 3

a)

20

b)

11

c)

4

d)

-2

90.

(x + 7)(x + 9)

a)

x² + 63x + 16

b)

x² + 16x + 63

c)

x² + 79

d)

x² + 16x + 2

91.

Simplify:

a)

8x⁹

b)

8x³

c)

8x⁴√x

d)

8x³√x

92.

Simplify
$\sqrt{6}\left(\sqrt{6}+\sqrt{10}\right)$

a)

$6+2\sqrt{15}$

b)

$8\sqrt{15}$

c)

$\sqrt{96}$

d)

$6\sqrt{6}+2\sqrt{15}$

93.

Simplify
$\left(2+\sqrt{3}\right)\left(8-\sqrt{3}\right)$

a)

$13+6\sqrt{3}$

b)

$13-6\sqrt{3}$

c)

$19+10\sqrt{3}$

d)

$19-10\sqrt{3}$

94.

Given the quadratic

f\left(x\right)=2x^2-8x+13

, what is the "b" value?

a)

b = 2

b)

b = -8

c)

b = 13

d)

b = 8

95.

What is the value of -(-7)?

a)

-7

b)

7

c)

8

d)

-8

96.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

97.

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

98.

What should you do first in solving this equation?

x² + 6x - 13 = 3

a)

Factor

b)

Write down: a = 1, b = 6, c = -13

c)

Subtract 3 from both sides.

d)

Add 3 to both sides.

99.

What is the name of this property?

a)

Zero Exponent Property

b)

Zero Product Property

c)

Commutative Property

d)

Zero Sum Property

100.

What is this formula?

a)

This is the standard formula.

b)

This is the quadratic formula.

c)

This is the square root formula.

d)

This is the Pythagorean formula

101.

Solve by taking the square root:

x² = 49

a)

-7

b)

7

c)

49

d)

±7

102.

Solve by the Extraction of Roots method: (x - 2) ² = 49

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

103.

Find the answer using substitution: Please list your answer as a coordinate (x,y)

(a)

104.

Solve the given systems of equations using elimination: Write you answer as a coordinate (x,y).

(a)

105.

x - y = -2
y = -2

a)

(1,-2)

b)

(-1,-2)

c)

(-4,-2)

d)

(4,-2)

106.

x = - 3
2x + 3y = 6

a)

(4,3)

b)

(-4,3)

c)

(-3,4)

d)

(3,-4)

107.

Solve this system by substitution.

a)

(1, -4)

b)

(1, 4)

c)

(-4, -7)

d)

(-7, -4)

Final Review MATH 4

Total questions: 107

Worksheet time: 6hrs 57mins

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