Free Printable Mathematics for Mechatronics

1.

Which of these is an example of a rational number?

a)

√4

b)

√5

c)

√3

d)

√2

2.

Which of these is an example of an irrational number?

a)

√2

b)

√1

c)

√9

d)

√25

3.

Select the irrational numbers

a)

$\sqrt{50}$

b)

2

c)

$\pi$

d)

2.3454128904

4.

a)

7 and 8

b)

8 and 9

c)

17 and 18

d)

35 and 36

5.

Which number is between 7 and 8?

a)

√7

b)

√42

c)

√59

d)

√68

6.

Which property is used in this ? 8 + (3 + 4) =( 8 + 3) + 4

a)

Associative Addition

b)

Associative Multiplication

c)

Commutative Addition

d)

Commutative Multiplication

7.

Which property is used in this ? 9 x 2 = 2 x 9

a)

Commutative Property of Multiplication

b)

Associative Property of Multiplication

c)

Multiplicative Inverse property

d)

Distributive Property

8.

Which property is used in this ? 7 x (12-9) = (7 x 12) - (7 x 9)

a)

Commutative Property

b)

Associative Property

c)

Distributive Property

d)

Identity Property

9.

When we change the order of Integers. Their difference remains the same.

a)

True

b)

False

10.

Integers are closed under subtraction

a)

True

b)

False

11.

The product of odd number of negative integers is a negative integer

a)

True

b)

False

12.

The product of a positive and a negative integer is negative

a)

True

b)

False

13.

( -5) x ( 33) = 5 x (-33)

a)

True

b)

False

14.

(-20) x ( 5 - 3) = (-20) x ( - 2)

a)

True

b)

False

15.

Which of the following is the multiplicative identity for an integer a ?

a)

a

b)

1

c)

0

d)

-1

16.

Which property is used in this ? 8 + (3 + 4) =( 8 + 3) + 4

a)

Associative Addition

b)

Associative Multiplication

c)

Commutative Addition

d)

Commutative Multiplication

17.

Identify if the number is rational or irrational and convert to a decimal:

$1\ \frac{11}{12}$

a)

rational

b)

irrational

c)

1.92

d)

1.09

18.

Select all that apply that will classify the following number: -16

a)

NATURAL

b)

WHOLE

c)

INTEGER

d)

RATIONAL

19.

Select all that apply that will classify the following number: 4

a)

NATURAL

b)

WHOLE

c)

INTEGER

d)

RATIONAL

20.

Select all that apply that will classify the following number: -2.5

a)

NATURAL

b)

WHOLE

c)

INTEGER

d)

RATIONAL

21.

Select all that apply that will classify the following number: $\frac{1}{2}$

a)

NATURAL

b)

WHOLE

c)

INTEGER

d)

RATIONAL

22.

Select all that apply that will classify the following number: 0.3333...

a)

NATURAL

b)

WHOLE

c)

INTEGER

d)

RATIONAL

23.

Select all that apply that will classify the following number: -3

a)

NATURAL

b)

WHOLE

c)

INTEGER

d)

RATIONAL

24.

Select all that apply that will classify the following number: $-\frac{1}{2}$

a)

NATURAL

b)

WHOLE

c)

INTEGER

d)

RATIONAL

25.

Real numbers are ____.

a)

all of the number systems.

b)

fractions and decimals.

c)

natural numbers and whole numbers.

d)

irrational numbers.

26.

Rational numbers are ___.

a)

any integer, number, fraction, or decimal that does not have a denominator of zero.

b)

positive whole numbers, their opposites, and zero.

c)

all positive numbers, no fractions or decimals.

d)

the counting numbers.

27.

Integers are ___.

a)

the set of positive numbers, their opposites, and zero.

b)

any numbers, fractions, decimals, and integers that do not have zero as their demoniator.

c)

all positive numbers, no fractions or decimals.

d)

the counting numbers, with no negatives, decimals, or zero.

28.

Whole numbers are ____.

a)

all positive numbers including zero.

b)

positive whole numbers and their opposites.

c)

the counting numbers, no negatives, fractions, or decimals.

d)

numbers that can be positive, negative, fractions, or decimals.

29.

Natural numbers are ____.

a)

the counting numbers.

b)

positive fractions, decimals, and zero.

c)

positive numbers, their opposites, and zero.

d)

any number that can be written as a quotient of two numbers.

30.

How could this number be identified? (Select ALL the correct options)

-4.5

a)

rational number

b)

integer

c)

whole number

d)

natural number

31.

How could this number be identified? (Select ALL the correct options)

$\frac{2}{3}$

a)

rational number

b)

integer

c)

whole number

d)

natural number

32.

5+1 = 1+5

a)

Commutative Property of Addition

b)

Associative Property of Addition

c)

Inverse Property of Addition

d)

Distributive Property

33.

(5•2) • 4 = 5 • (2•4)

a)

Commutative Property of Multiplication

b)

Associative Property of Multiplication

c)

Transitive Property

d)

Symmetric Property

34.

9 + 0 = 9

a)

Reflexive Property

b)

Distributive Property

c)

Identity Property of Addition

d)

Inverse Property of Addition

35.

12 • 1/12 = 1

a)

Identity Property of Multiplication

b)

Associative Property of Multiplication

c)

Commutative Property of Multiplication

d)

Inverse Property of Multiplication

36.

$\pi$ • 0 = 0

a)

Property of Zero

b)

Distributive Property

c)

Reflexive Property

d)

Symmetric Property

37.

-3(a+c) = -3a-3c

a)

Transitive Property

b)

Distributive Property

c)

Symmetric Property

d)

Commutative Property of Multiplication

38.

t = t

a)

Substitution Property

b)

Transitive Property

c)

Reflexive Property

d)

Symmetric Property

39.

4x+3 = 15 , 15 = 4x+3

a)

Transitive Property

b)

Substitution Property

c)

Reflexive Property

d)

Symmetric Property

40.

If x+y = 4 and 4 = 3+1, then x+y = 3+1

a)

Transitive Property

b)

Reflexive Property

c)

Symmetric Property

d)

Substitution Property

41.

(x•y) • z = z • (x•y)

a)

Associative Property of Multiplication

b)

Commutative Property of Multiplication

c)

Multiplicative Inverse Property

d)

Identity Property of Multiplication

42.

a² + (b² + c²) = (a² + b²) + c²

a)

Commutative Property of Addition

b)

Zero Property

c)

Associative Property of Addition

d)

Identity Property of Addition

43.

1 • g³ = g³

a)

Inverse Property of Multiplication

b)

Zero Property

c)

Transitive Property

d)

Identity Property of Multiplication

44.

-x + x = 0

a)

Additive Inverse Property

b)

Identity Property of Addition

c)

Commutative Property of Multiplication

d)

Associative Property of Addition

45.

(x + y) • 0 = 0

a)

Substitution Property

b)

Distributive Property

c)

Zero Property

d)

Inverse Property of Multiplication

46.

3m(m + 4n - 6g) = 3m² + 12mn - 18mg

a)

Transitive Property

b)

Commutative Property of Multiplication

c)

Associative Property of Multiplication

d)

Distributive Property

47.

xyz = xyz

a)

Symmetric Property

b)

Reflexive Property

c)

Substitution Property

d)

Transitive Property

48.

q + p = 0 , 0 = q + p

a)

Transitive Property

b)

Reflexive Property

c)

Symmetric Property

d)

Substitution Property

49.

If s = d - 1 and d - 1 = -12, then s = -12

a)

Transitive Property

b)

Symmetric Property

c)

Multiplicative Inverse Property

d)

Reflexive Property

50.

If 2x + 4 = 10 and x = 3, then 2(3)+4=10

a)

Symmetric Property

b)

Substitution Property

c)

Transitive Property

d)

Distributive Property

51.

xyz • 1/xyz = 1

a)

Inverse Property of Addition

b)

Identity Property of Multiplication

c)

Zero Property

d)

Multiplicative Inverse Property

52.

Identify the property
a + b = b + a

a)

Identity of addtion

b)

commutative of addition

c)

associative of addition

d)

symmetric

53.

Identify the property
(a ⋅ b) ⋅ c = (c ⋅ b) ⋅ a

a)

commutative of multiplication

b)

identity of multiplication

c)

inverse of multiplication

d)

associative of multiplication

54.

Identify the example of the

inverse property of multiplication.

a)

5 ⋅ 0 = 5

b)

5 ⋅ $\frac{1}{5}$ = 1

c)

5 - 5 = 0

d)

5 ⋅ 1 = 5

55.

Identify the example of the

identity property of addition.

a)

a + (-a) = 0

b)

a + a = 2a

c)

a + 0 = a

d)

a + b = b + a

56.

Identify the property
a(b + c) = ab + ac

a)

Associative of addtion

b)

Distributive

c)

Commutative of addition

d)

Inverse

57.

Identify the property
a + (-a) = 0

a)

Inverse of addition

b)

Identity of addtion

c)

associative of addition

d)

symmetric

58.

Identify this property.

$\frac{4}{5}\ \times\ \frac{5}{4}\ =\ 1$

a)

Multiplicative Inverse

b)

Multiplicative Identity

c)

Commutative

d)

Associative

59.

Identify the example that represents the

Multiplicative Property of Zero.

a)

-9 x 0 = 0

b)

-9 + 9 = 0

c)

9 - 9 = 0

d)

9 + 0 = 9

60.

What property is this?
1a = a

a)

Commutative Property of Multiplication

b)

Multiplicative Inverse

c)

Multiplicative Identity

d)

Distributive Property

61.

Identify this property.

$\frac{2}{3}\ +\ \left(-\frac{2}{3}\right)=0$

a)

Additive Identity

b)

Additive Inverse

c)

Multiplicative Property of 0

d)

Multiplicative Inverse

62.

Identify the property
a + b = b + a

a)

Identity of addtion

b)

commutative of addition

c)

associative of addition

d)

symmetric

63.

Identify the property
(a ⋅ b) ⋅ c = (c ⋅ b) ⋅ a

a)

commutative of multiplication

b)

identity of multiplication

c)

inverse of multiplication

d)

associative of multiplication

64.

Identify the example of the

inverse property of multiplication.

a)

5 ⋅ 0 = 5

b)

5 ⋅ $\frac{1}{5}$ = 1

c)

5 - 5 = 0

d)

5 ⋅ 1 = 5

65.

Identify the example of the

identity property of addition.

a)

a + (-a) = 0

b)

a + a = 2a

c)

a + 0 = a

d)

a + b = b + a

66.

Identify the property
a(b + c) = ab + ac

a)

Associative of addtion

b)

Distributive

c)

Commutative of addition

d)

Inverse

67.

Identify the property
a + (-a) = 0

a)

Inverse of addition

b)

Identity of addtion

c)

associative of addition

d)

symmetric

68.

Identify the additive inverse of

-7

a)

-7

b)

$-\frac{1}{7}$

c)

$\frac{1}{7}$

d)

7

69.

Identify this property.

For all real numbers, m = m.

a)

Symmetric

b)

Reflexive

c)

Transitive

d)

Substitution

70.

Identify this property.

If j = k, then k = j.

a)

Symmetric

b)

Reflexive

c)

Transitive

d)

Addition Property of Equality

71.

Identify this property.

If y = z and z = 4, then y = 4.

a)

Symmetric

b)

Transitive

c)

Reflexive

d)

Transgression

72.

Identify this property.

$\frac{4}{5}\ \times\ \frac{5}{4}\ =\ 1$

a)

Multiplicative Inverse

b)

Multiplicative Identity

c)

Commutative

d)

Associative

73.

Identify the example that represents the

Multiplicative Property of Zero.

a)

-9 x 0 = 0

b)

-9 + 9 = 0

c)

9 - 9 = 0

d)

9 + 0 = 9

74.

Identify this property.

$\frac{2}{3}\ +\ \left(-\frac{2}{3}\right)=0$

a)

Additive Identity

b)

Additive Inverse

c)

Multiplicative Property of 0

d)

Multiplicative Inverse

75.

What property is this?
1a = a

a)

Commutative Property of Multiplication

b)

Multiplicative Inverse

c)

Multiplicative Identity

d)

Distributive Property

76.

Identify this property.

a + (b + c) = (b + c) + a

a)

Commutative

b)

Associative

c)

Additive Identity

d)

Distributive

77.

What's the base?
y⁵

a)

5

b)

y

78.

Which is the expanded form of
5³

a)

3 x 3 x 3

b)

5 x 5

c)

5 x 5 x 5

d)

5 x 3

79.

What is the exponential form of
4 x 4 x 4 x 4 x 4 x 4

a)

6⁴

b)

4²

c)

4⁶

d)

4 x 6

80.

Rewrite the following expression in exponential form:

2*2*2*5*5*5*5

a)

3*2*4*5

b)

8*625

c)

2³*5⁴

d)

3²*4⁵

81.

m*m*m*m*p*p*p*q*q*q*q*q

a)

4m*3p*5q

b)

m⁴p³q⁵

c)

4^m3^p5^q

d)

12mpq

82.

According to exponent rules, when we multiply terms with the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

83.

Power to a Power Law states: keep the base the same and do this to the exponents.

a)

multiply

b)

add

c)

subtract

d)

divide

84.

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

a)

add

b)

subtract

c)

multiply

d)

divide

85.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

86.

Simplify the following expression:

7⁵* 7² =

a)

7⁷

b)

7⁵

c)

49⁹

87.

Simplify the expression:
(a⁵)(a⁴)

a)

a²⁰

b)

a⁹

c)

a¹

88.

Simplify the expression in exponential form:
(5⁴)^{3
Hint: Expand it out}

a)

5¹

b)

5⁷

c)

5¹²

89.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

90.

Simplify the expression:
(5⁸) ÷ (5²)

a)

5⁶

b)

5¹⁰

c)

5⁴

d)

5¹⁶

91.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

92.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

93.

Which expression is NOT equivalent to $3^8$ ?

a)

$\left(3^6\right)\left(3^2\right)$

b)

$\left(3^4\right)^2$

c)

$\left(3^4\right)\left(3^4\right)$

d)

$\left(3^4\right)^4$

94.

4⁵5⁴

a)

20⁹

b)

Can't simplify

c)

20¹

95.

Simplify the expression in exponential form:
134⁰

a)

0

b)

134

c)

1

96.

z⁰

a)

z

b)

0

c)

1

97.

How do you feel rewriting expressions using the laws of exponents to generate equivalent expressions.

a)

Rules of exponents are easy.

b)

With a little of more practice I can master it.

c)

Need lots of practice. They are not that easy .

d)

I still don't get it. Those rules are really confusing.

98.

Simplify 5³⋅5⁴

a)

5⁷

b)

5⁻¹

c)

5¹²

d)

5

99.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

100.

Solve and Simplify (no exponent)

2^0

a)

$0$

b)

$1$

c)

$2$

d)

$\frac{1}{2}$

101.

3⁴x 3⁷

a)

9²⁸

b)

3²⁸

c)

3¹¹

d)

9¹¹

102.

Simplify:
(x³)(x²)

a)

x⁵

b)

x⁶

c)

x

d)

x^1.5

103.

How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?

a)

5⁷

b)

5⁶

c)

7⁵

d)

5

104.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

105.

Simplify: $x^3\cdot x^4$

a)

$x^{12}$

b)

$x^7$

c)

$x^1$

d)

$x^{\frac{4}{3}}$

106.

Solve using the product law of exponents

Resolver utilizando la ley de productos de los exponentes

(5⁵)(5³)

a)

25⁸

b)

5¹⁵

c)

25¹⁵

d)

5⁸

107.

Solve using the product law of exponents.

(Espanol) Resolver utilizando la ley de productos de los exponentes.

(10¹²)(10⁴)

a)

10¹⁶

b)

10⁴⁸

c)

100¹⁶

d)

100⁴⁸

108.

Simplify.

Simplificar.

(x⁴) (x)

a)

2x⁴

b)

x

c)

x⁵

d)

x⁴

109.

Simplify

w⁵(w^x)w⁷

a)

w^35x

b)

w¹³

c)

w^12x

d)

w^{12 + x}

110.

5²·5⁵=

a)

5⁷

b)

5³

c)

5^-7

d)

5^-3

111.

x³·x⁴=

a)

x⁷

b)

x¹

c)

x^-7

d)

x^-1

112.

n⁰ =

a)

1

b)

0

113.

Simplify:

(x³)(x²)

a)

x⁵

b)

x⁶

c)

x

114.

How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?

a)

5⁷

b)

5⁶

c)

7⁵

d)

5

115.

$\left(9y\right)^3$

a)

$9y^3$

b)

$9^3y$

c)

$27y^3$

d)

$729y^3$

116.

Simplify the expression using exponential notation:

$\left(a^4\right)^3$

a)

$a^{12}$

b)

$a^7$

c)

$a$

d)

$a^{15}$

117.

Simplify the expression using exponential notation:

$\left(y^8\right)^5$

a)

$y^{13}$

b)

$y^{40}$

c)

$y^3$

d)

$y^{85}$

118.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

119.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

120.

What is the quotient?

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

121.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

122.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

123.

(2x³ + 7x² - 6x - 8) ÷ (x + 4)

a)

2x² - x - 2

b)

2x³ - x² - 2x

c)

2x² + 15x + 54 + 208/x+4

d)

2x³ + 15x² + 54x + 208

124.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

125.

What is the remainder when x⁴ - 5 is divided by x + 3?

a)

76

b)

81

c)

7

126.

What is the remainder of (4x³ - 3x² - 4x +2) ÷ (x - 3)?

a)

-71

b)

71

c)

145

127.

What is the remainder of (x³ - 5x² - 8x +1) ÷ (x + 1)?

a)

-13

b)

1

c)

3

128.

What is the remainder when n³ - 7 is divided by n + 5 ?

a)

118

b)

132

c)

-132

129.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

130.

Find the quotient:

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

131.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

132.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

133.

-2x²+4x+48 ÷ x+4

a)

-2x+12

b)

2x+12

c)

-4x+9

d)

4x+9

134.

x²-6x+8 ÷ x-2

a)

x-6

b)

x-9 R=2

c)

x-4

d)

x-8 R=3

135.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

136.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

137.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

138.

Which term is missing in this problem?
2x³ + 5x² + 9 ÷
x + 3

a)

x⁴

b)

x³

c)

x²

d)

x

139.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

a)

True

b)

False

140.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

141.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

142.

How can I tell, when doing synthetic division, if the binomial is a FACTOR of the dividend?

a)

The remainder is zero

b)

They are all factors

c)

We can't tell

d)

The remainder is a constant

143.

What does this tell me?

a)

f(-2)= -27 and -27 is the remainder

b)

-2 is a solution of the function

c)

(x+2) is a factor of the function

d)

(x-2) is a factor of the function

144.

Was this problem done correctly?

a)

Yes

b)

No

145.

It's time to write the answer. What goes in the yellow area?

a)

$n-9$

b)

9

c)

-9

d)

$6n^2-48n-58$

146.

What is the next step in synthetic division?

a)

Multiply the 9 and 6

b)

Add the 9 and 6

c)

Bring down the -48

147.

What is the next step in synthetic division?

a)

Add the -48 to the 54

b)

Multiply the 54 and 6

c)

Divide the 54 by 6

d)

Bring down the -58

148.

if f(x) = x³+8x+24, then find f(-2) using synthetic division.

a)

12

b)

8

c)

0

d)

-6

149.

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division.

a)

0

b)

10

c)

15

d)

-7

150.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

151.

When p(x) = 9x⁴- 45x³+ 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

a)

p(2) = 656

b)

p(2) = 652

c)

p(2) = -64

d)

p(2) = -368

152.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

153.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

154.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

155.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

156.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

157.

Which term is missing in this problem?
2x³ + 5x² + 9 ÷
x + 3

a)

x⁴

b)

x³

c)

x²

d)

x

158.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

159.

It's time to write the answer. What goes in the yellow area?

a)

$n-9$

b)

9

c)

-9

d)

$6n^2-48n-58$

160.

What is the next step in synthetic division?

a)

Multiply the 9 and 6

b)

Add the 9 and 6

c)

Bring down the -48

161.

What is the next step in synthetic division?

a)

Add the -48 to the 54

b)

Multiply the 54 and 6

c)

Divide the 54 by 6

d)

Bring down the -58

162.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

163.

$\left(5\times6\right)\div\left(10-5\right)$

a)

5

b)

6

c)

30

d)

1

164.

$20\div\left(17-7\right)$

a)

1

b)

2

c)

10

d)

5

165.

$30\div\left(2+3\right)+10^2$

a)

110

b)

115

c)

106

d)

1

166.

$\left(7\times2\right)\div7\ \times\ 2$

a)

1

b)

14

c)

7

d)

2

167.

14 + (22 - 2) =

a)

34

b)

37

c)

40

d)

44

168.

20 x 2 - (100 - 90)

a)

22

b)

30

c)

34

d)

100

169.

Solve: (32 ÷ 8) + 26 - 10

a)

10

b)

20

c)

30

170.

20 + (7 – 2) × 2 =

a)

30

b)

29

c)

44

d)

40

171.

90 - 5² × 2

a)

15

b)

40

c)

195

d)

140

172.

(2 + 40) ÷ 2 – 15

a)

19

b)

6

c)

16

d)

42

173.

$6^2-3\cdot4$

a)

20

b)

26

c)

24

d)

30

174.

9 ÷ 3 + (7 × 5) × 1 + 15 =

a)

50

b)

51

c)

53

d)

52

175.

Solve using PEMDAS rules:

7 x 2 + 6

a)

20

b)

21

c)

22

d)

23

176.

$\left(6+4\right)^2-\left(5\div1\right)^2$

a)

75

b)

100

c)

5

d)

150

177.

$28-\left(49\div7^2\right)$

a)

49

b)

27

c)

50

d)

28

178.

$3\div\left(2-1\right)^{ }\times3^2$

a)

27

b)

6

c)

3

d)

100

179.

$\left(4\times2-2\right)^2+2$

a)

20

b)

6

c)

36

d)

38

180.

$\left(5\times6-2\right)\div\left(7-5\right)$

a)

16

b)

15

c)

14

d)

13

181.

$6+12\div\left(10-7\right)$

a)

11

b)

10

c)

12

d)

3.6

182.

$\left(4\right)\left(7+1\times3\right)$

a)

39

b)

96

c)

42

d)

40

183.

A gift shop had 500 colored pencils. The shop sold 3 sets of 20 colored pencils, 6 sets of 12 colored pencils, and 10 sets of 18 colored pencils. Which expression shows how many colored pencils are left?

a)

3 × 20 + 6 × 12 + 10 × 18 – 500

b)

500 – [3 × (20 + 6) × (12 + 10) × 18)]

c)

500 + [(3 × 20) + (6 × 12) + (10 × 18)]

d)

500 – [(3 × 20) + (6 × 12) + (10 × 18)]

184.

A gift shop had 500 colored pencils. The shop sold 3 sets of 20 colored pencils, 6 sets of 12 colored pencils, and 10 sets of 18 colored pencils. Which expression shows how many colored pencils are left?

a)

3 × 20 + 6 × 12 + 10 × 18 – 500

b)

500 – [3 × (20 + 6) × (12 + 10) × 18)]

c)

500 + [(3 × 20) + (6 × 12) + (10 × 18)]

d)

500 – [(3 × 20) + (6 × 12) + (10 × 18)]

185.

Multi-Step

A company can produce 300 ballpoint pens or 550 gel pens each hour. Each weekday, the company produces ballpoint pens for 5 hours and gel pens for 8 hours. How many pens does the company produce in 5 weekdays?

a)

7,500

b)

24,500

c)

29,500

d)

5,900

186.

Which expression has a value of 4?

a)

[(4 × 5) + (9 + 7)] + 9

b)

[(4 × 5) + (9 + 7)] ÷ 9

c)

[(4 × 5) − (9 + 7)] × 9

d)

[(4 + 5) + (9 + 7)] − 9

187.

Simplify the numerical expression.

14 + [(2 × 5) + (3 × 8)]

a)

15

b)

48

c)

5

d)

10

188.

Simplify the numerical expression.

5 × [(8 + 2) − (16 − 9)]

a)

15

b)

48

c)

5

d)

10

189.

Simplify the numerical expression.

40 ÷ [(18 − 9) − (13 − 12)]

a)

15

b)

48

c)

5

d)

10

190.

Simplify the numerical expression.

[(15 + 5) + (5 × 2)] ÷ 3

a)

15

b)

48

c)

5

d)

10

191.

Simplify the numerical expression.

[(21 − 13) + (32 − 24)] × 4

a)

64

b)

19

c)

9

d)

51

192.

Simplify the numerical expression.

49 − [(3 × 4) + (9 × 2)]

a)

64

b)

19

c)

9

d)

51

193.

Simplify the numerical expression.

32 + [(11 − 7) + (5 × 3)]

a)

64

b)

19

c)

9

d)

51

194.

Simplify the numerical expression.

[(6 × 9) − (7 × 4)] − 17

a)

64

b)

19

c)

9

d)

51

195.

Simplify the numerical expression.

[(13 − 9) × 3] + [(14 − 8) × 2]

a)

64

b)

19

c)

29

d)

24

196.

Simplify the numerical expression.

[(2 × 6) + 3] + [35 − (7 × 3)]

a)

64

b)

19

c)

29

d)

24

197.

Fred’s Car Dealership has a three-floor parking garage with cars for sale. Each floor has 3 rows of 5 compact cars and 4 rows of 8 sedans.

Write an expression you can use to find the number of cars in Fred’s garage.

Simplify the expression.

a)

3 + 5 + (4 × 8 × 3)

b)

[(3 × 5) + (4 × 8)] × 3

c)

141

d)

104

198.

A carpenter has a supply of 84 large and small boards for the cabinets he builds. One week, he uses 3 sets of 8 small boards. Then he buys 3 more sets of 6 large boards.

Write an expression you can use to find the number of boards the carpenter has now.

Simplify the expression.

a)

[84 − (3 × 8)] + (3 × 6)

b)

84 + (3 × 8) + (3 × 6)

c)

78

d)

126

199.

Which expression has a value of 1?

a)

30 + [(9 × 2) + (4 × 3)]

b)

30 ÷ [(9 × 2) + (4 × 3)]

c)

30 − [(9 × 2) + (4 × 3)]

d)

30 × [(9 + 2) − (4 + 3)]

200.

Which expression has a value equal to the value of the expression 4 × [(12 + 4) − (12 ÷ 3)]?

a)

(4 × 12) + 4

b)

4 × (16 − 4)

c)

4 + (12 × 4)

d)

4 × 12 + 4

201.

The school math coach takes an inventory of math materials. He counts the materials for 5 different classes. Each class has 7 boxes of 10 pattern blocks, 6 boxes of 9 rulers, and 3 boxes of 2 calculators. Which expression shows the number of math materials?

a)

5 × [(7 × 10) + (6 × 9) + (3 × 2)]

b)

5 + [(7 × 10) + (6 × 9) + (3 × 2)]

c)

5 × 7 × 10 + 6 × 9 + 3 × 2

d)

[(7 × 10) + (6 × 9) + (3 × 2)] ÷ 5

202.

At the beginning of the year, the teacher’s supply closet contained 250 markers. In September, 5 sets of 6 black markers, 4 sets of 5 red markers, and 6 sets of 3 yellow markers are used. Which expression shows the number of markers left?

a)

250 + [(5 × 6) + (4 × 5) + (6 × 3)]

b)

(250 − 5) × 6 + [(4 × 5) + (6 × 3)]

c)

250 + [(5 + 6) × (4 + 5) × (6 + 3)]

d)

250 − [(5 × 6) + (4 × 5) + (6 × 3)]

203.

Multi-Step

The principal conducted a school assembly every school day for a week. On Monday, 78 students attended. Then 6 classes with 25 students in each class attended each day for the next three days. On Friday, 8 classes with 32 students in each class attended the assembly. How many students attended the assembly?

a)

606

b)

484

c)

706

d)

784

204.

Multi-Step

Employees from a local store donated picnic supplies for the end of the school year picnic. They donated 20 packs of 12 forks, 10 packs of 12 spoons, 5 packs of 10 knives, and 175 paper plates. How many picnic items were donated?

a)

244

b)

410

c)

585

d)

695

Mathematics for Mechatronics

Total questions: 204

Worksheet time: 6hrs 13mins

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