Free Printable Winter break pack - Math

1.

What are the zeros?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

2.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

3.

What are the factors AND solutions of x² + 2x – 3 = 0

a)

(x - 2)(x + 1); x=2, x=-1

b)

(x + 1)(x - 3); x=-1, x=3

c)

(x + 2)(x - 1); x=-2, x=1

d)

(x - 1)(x + 3); x=1, x=-3

4.

Factor and Solve

6x² + 17x + 12 = 0

a)

x = -4/3, x = -3/2

b)

x = 9, x = 8

c)

x = 4, x = 3

d)

x = -4, x = -3

5.

Factor and Solve

2x² - 3x - 2 = 0

a)

x = 1, x = -1

b)

x = -1/2, x = 2

c)

x = 1/2, x = 2

d)

x = 1/2, x = 1

6.

Solve the following by ISOLATION

$4\left(x-5\right)^2=12$

a)

$\left(4x+20\right)^2=12$

b)

$x=5\pm\sqrt[]{3}$

c)

$x=-5\pm\sqrt[]{3}$

d)

$x=5\pm\frac{1}{2}\sqrt[]{3}$

7.

Which method do you feel is the best way to solve the following?

$x^2-3x-54=0$

a)

Factor

b)

Isolation/Solve with Square Roots

c)

Complete the Square

d)

Quadratic Formula

8.

What are the steps to solving this by completing the square?

a² + 10a + 21 = 0

a)

Subtract 21 from both sides of the equation

b)

Add 25 to both sides of the equation

c)

Rewrite the left hand side as a (binomial)²

d)

Take the square root of both sides of the equation

e)

Subtract 5 from both sides of the equation

1)

2)

3)

4)

5)

9.

Complete the quadratic formula

Black question mark (a)

Blue question mark (b)

Red question mark (c)

Choose from the below words

$-b$

$b^2-4ac$

$2a$

$b$

$2b-4ac$

$b^2-4c$

$2$

$a^2$

$b^2-ac$

$2b$

10.

$2x^2+8x-7=0$

Use the quadratic formula to type an expression that will yield the solutions to the equation above.

You cannot type $\pm$ on the keyboard so instead put $+-$

DO NOT SIMPLIFY ANYTHING. JUST PLUG IN WITH PARENTHESES.

11.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

12.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

13.

Solve by the Square Root method: x² = 16

a)

± 4

b)

± 8

c)

4

d)

8

14.

Solve by the Square Root method:

-5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

15.

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

16.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

17.

Solve by using a method of your choice:

k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

18.

Solve $\left(x+5\right)^2-20=0$ , and leave your answer in the form $p\pm\sqrt[]{q}$

a)

$x=-5\pm\sqrt[]{20}$

b)

$x=5\pm\sqrt[]{20}$

c)

$x=5+\sqrt[]{20}$

d)

$x=-5-\sqrt[]{20}$

19.

Solve the equation:
5x² - 35x + 60 = 0

a)

x = 3, -4

b)

x = -3, 4

c)

x = 3, 4

d)

x = -3, -4

20.

How many solutions are there?

a)

0

b)

1

c)

2

d)

3

21.

In the quadratic formula, if b²-4ac>0, then the quadratic equation has

a)

two imaginary solutions

b)

two different real solutions

c)

two equal real solutions

d)

none of these

22.

In the quadratic formula, the expression
b²-4ac is called

a)

discrim

b)

determinant

c)

discriminant

d)

none of these

23.

The solutions of the quadratic equation
x²-5x+6=0 are

a)

x=1 or x=-6

b)

x=3 or x=2

c)

x=-3 or x= 2

d)

x=-1 or x=6

24.

To complete the perfect square trinomial in the expression x²-22x+_____, we need to add

a)

11

b)

44

c)

121

d)

144

25.

The solution of the quadratic equation
4x²-5x-9=0 are

a)

x=-1 or x=9/4

b)

x=1 or x=9/4

c)

x=2 or x=3

d)

x=-2 or x=-3

26.

Fill the blank space to complete the perfect square trinomial
x²-18x+____=(x- ____)²

a)

9 and 3 respectively

b)

81 and 9 respectively

c)

-9 and -3 respectively

d)

-81 and -9 respectively

27.

Solve the following quadratic equation...

x² - 2x - 15 = 0

a)

x = 5

x = -3

b)

x = -5

x = 3

c)

x = -15

x = 1

d)

x = 15

x = -1

28.

Solve the following quadratic equation...

x² - 14x + 24 = 0

a)

x = 12

x = 2

b)

x = 4

x = 6

c)

x = 3

x = 8

d)

x = 1

x = 24

29.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

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

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

30.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

31.

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

32.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

33.

When factorising

x² - 4x + 4 = 20,

what goes in the blank?

(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

34.

Solve by ANY method you have learned: x²−2x+11=0

a)

1±i√10

b)

1±√10

c)

-1±i√10

d)

-1±√10

35.

Which one does not belong?

a)

solutions

b)

factors

c)

x-intercepts

d)

zeroes

36.

Write an equation in Factored Form, whose solutions are 7 and 3.

a)

y = (x - 7)(x - 3)

b)

y = (x + 7)(x + 3)

c)

y = (x + 7)(x - 3)

d)

y = (x - 7)(x + 3)

37.

Write an equation in Factored Form, whose solutions are -7 and -3.

a)

y = (x - 7)(x - 3)

b)

y = (x + 7)(x + 3)

c)

y = (x + 7)(x - 3)

d)

y = (x - 7)(x + 3)

38.

Write an equation in Factored Form, whose solutions are $0$ and $-7$ .

a)

y = x(x + 7)

b)

y = x(x - 7)

c)

y = x( 7x )

d)

y = x( -7x )

39.

What are the x-intercepts for the graph?

a)

$x=3,\ 2$

b)

$x=-3,\ 2$

c)

$x=3,\ -2$

d)

$x=0$

40.

Write the equation for the graph in factored form.

a)

$y=\left(x+3\right)\left(x-2\right)$

b)

$y=\left(x-3\right)\left(x+2\right)$

41.

Which equation is CORRECT for the graph?

a)

$y=\left(x-1\right)\left(x+2\right)$

b)

$y=\left(x-1\right)\left(x-2\right)$

c)

$y=\left(x+1\right)\left(x+2\right)$

d)

$y=\left(x+1\right)\left(x-2\right)$

42.

Write the equation for the quadratic in factored form.

a)

$y=\left(x-3\right)^2$

b)

$y=\left(x+3\right)^2$

c)

$y=\left(x+3\right)\left(x-3\right)$

d)

$y=x-3$

43.

What is the x-intercept of the graph?

a)

x = 0

b)

x = 1

c)

x = 2

d)

x = 3

44.

Write a Quadratic equation in Standard Form, whose solutions are $7$ and $3$ .

a)

$y=x^2-10x+21$

b)

$y=x^2+10x+21$

c)

$y=x^2-10x-21$

d)

$y=x^2+10x-21$

45.

Write the equation for the graph in factored form.

a)

$y=\left(x-3\right)\left(x+4\right)$

b)

$y=\left(x+3\right)\left(x-4\right)$

c)

$y=\left(x+3\right)\left(x-3\right)$

d)

$y=\left(x+4\right)\left(x-4\right)$

46.

Which of the following statements are TRUE?

Select all that apply.

a)

The "a" value is positive.

b)

The y-intercept is positive.

c)

It has two zeros.

d)

The axis of symmetry is x = 1.

e)

The vertex is at (0, 5).

47.

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

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

48.

What piece of information does h identify in the following equation?
y=a(x-h)²+k

a)

y value of the vertex

b)

Axis of Symmetry

c)

Direction (facing up or down)

d)

x-intercept

49.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

50.

A parabola has a vertex at (-3,2).

Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

51.

a)

$y=x^2+4$

b)

$y=-x+4$

c)

$y=-x^2-4$

d)

$y=-x^2+4$

52.

What is the standard form of a quadratic?

a)

y = ax²+ bx + c

b)

y = a(x - h)² + k

c)

y = mx + b

d)

y = (x - h)(x - k)

53.

Convert the equation into standard form:

y = -5(x + 2)²- 10

a)

y = -5x²- 20x - 30

b)

y = -5x²- 4x - 10

c)

y = 25x² + 100x + 90

d)

y = 25x² - 10x - 30

54.

Write the equation of the parabola shown.

a)

y = 2x² + 4x - 5

b)

y = 2x² - 4x + 5

c)

y = 2x² + 4x + 5

d)

y = 2x² - 4x - 5

55.

a)

±72

b)

±12

c)

12

d)

No real solution

56.

Solve the equation:

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

a)

x = $\frac{13}{7}$

b)

x = $-\frac{5}{7}$

c)

x = $-\frac{25}{7}$

d)

x = $\frac{7}{5}$

e)

x = $-\frac{13}{3}$

57.

Solve the equation below:

a)

k = 152

b)

k = 176

c)

k = 5

d)

k = 27

58.

Which equation has x = 5 as the solution?

a)

x + 15 = 10

b)

2x = 5

c)

2x = 10

d)

2x - 3 = 15

59.

- 4x + 1 = 21

a)

x = 120

b)

x = 5

c)

x = 30

d)

x = - 5

60.

3x - 5 = - 26

a)

x = - 21

b)

x = 21

c)

x = - 7

d)

x = 61

61.

Solve: 3(x-4) = -3

a)

3

b)

-3

c)

5

d)

-5

62.

Solve: - 7(z - 6) = - 80

a)

$\frac{122}{7}$

b)

$\frac{7}{122}$

c)

$-\frac{38}{7}$

d)

$\frac{38}{7}$

63.

Janet wants to rent a U-Haul to move her mother. She spends $225 for the move. The U-Haul costs $45 up front and $1.50 a mile. What equation would you use to solve the number of miles her mother moved?

a)

225 = 45x + 1.5

b)

45 + 1.5x = 225

c)

45x + 1.5x = 225

d)

225 = 45(1.5) + 1.5x

64.

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

a)

x = -8

b)

x = 8

c)

x = 2

d)

x = -2

65.

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.

66.

A toy company spends $1500 per day for factory expenses plus $8 to make each teddy bear. They sell the teddy bears for $12 a piece. Which equation could be used to find the number of bears t the company has to sell in one day to equal its daily cost?

a)

1500 + 8t = 12

b)

12 + 8t = 1500

c)

1500 + 8t = 12t

d)

8t = 12t + 1500

67.

What is the first step in solving the equation 2a - 4(a - 5) = 10

a)

Add 4 to both sides

b)

Add the 2a and a

c)

Distribute 4 to a and -5

d)

Distribute -4 to a and -5

68.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

69.

2x - 3 + 4x = 27

a)

12

b)

4

c)

5

d)

15

70.

2x + 3(5x - 7) = 47

(enter the number only)

a)

1

b)

2

c)

3

d)

4

71.

$\frac{1}{2}$ x + 4 = 15

(enter the number only)

(a)

72.

Find the value of the unknown variable

a)

A

b)

B

c)

C

d)

D

73.

Solve: -7(x + 3) = -4(x - 6)

(a)

74.

Solve: $\frac{1}{2}$ (4x + 6) = 24

Enter the answer as a decimal to the nearest tenths place.

(a)

75.

Solve: 4(2x - 1) + 10 = 3(x - 3)

(a)

76.

Mary spent half of her allowance going to the movies. She washed the family car and earned an extra seven dollars this week. What is her weekly allowance if she ended with seventeen dollars?

a)

20

b)

48

c)

10

d)

12

77.

Jasmine feeds her cat 1/4 cup of food each day. There are 6 cups of cat food in the bag. How many days will the bag of cat food last?

(a)

78.

Mark has two jobs. He worked 40 hours for $11.50 an hour at his first job this week and $6.50 an hour at his second job. How many hours did he work at the second job if he earned $502.25 for the week?

a)

35 hours

b)

40 hours

c)

6.5 hours

d)

4.5 hours

79.

Which of the following equations would have a solution of 3? (Choose all that apply.)

a)

3x = 9

b)

15x = - 45

c)

2x + 1 = 21

d)

7x - 6 = 15

e)

2(4x - 3) = 3x + 9

80.

Solve: $\frac{1}{2}x\ +\ 6\ =2\left(\frac{1}{3}x+\ 8\right)$

(a)

81.

Problem #4

Simplify the expression. Write your answer as a power.

$8^{10}\cdot8^4$

82.

Problem #6

Simplify the expression. Write your answer as a power.

$a^3\cdot a^3$

a)

$a^6$

b)

$a^0$

c)

$a^4$

d)

$a^9$

83.

Problem #8

Simplify the expression. Write your answer as a power.

$\left(\frac{2}{3}\right)^2\cdot\left(\frac{2}{3}\right)^6$

a)

$\left(\frac{2}{3}\right)^{12}$

b)

$\left(\frac{2}{3}\right)^8$

c)

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

d)

$\left(\frac{2}{3}\right)^3$

84.

Problem #10

Simplify the expression. Write your answer as a power.

$\left(-2.9\right)\cdot\left(-2.9\right)^7$

85.

Problem #12

Simplify the expression. Write your answer as a power.

$\left(b^{12}\right)^3$

a)

$b^{36}$

b)

$b^9$

c)

$b^{15}$

d)

$b^4$

86.

Problem #14

Simplify the expression. Write your answer as a power.

$\left(\left(-\frac{3}{4}\right)^5\right)^2$

87.

Problem #16

ERROR ANALYSIS: Correct the error in simplifying the expression.

a)

$r^{14}$

b)

$r^{24}$

c)

$r^2$

d)

$r^{10}$

88.

Problem #16

ERROR ANALYSIS: Describe the error in simplifying the expression.

a)

The exponents should not be added they should be divided.

b)

The exponents should not be added they should be subtracted.

c)

The exponents should not be added they should be multiplied.

d)

The exponents should be added.

89.

Problem #18

Simplify the expression.

$\left(-3v\right)^5$

a)

$243v^5$

b)

$-243v^5$

c)

$-15v^5$

d)

$-3v^5$

90.

Problem #20

Simplify the expression.

$\left(1.2m\right)^4$

a)

$-2.0736m^4$

b)

$-4.8m^4$

c)

$2.0736m^4$

d)

$4.8m^4$

91.

Problem #22

Simplify the expression.

$\left(-\frac{3}{4}p\right)^3$

a)

$-\frac{9}{12}p^3$

b)

$-\frac{27}{64}p^3$

c)

$-\frac{3}{4}p^3$

d)

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

92.

Problem #24 a

ARTIFACT: A display case for the artifact is in the shape of a cube. Each side of the display case is three times longer than the width of the artifact.

a. Write an expression for the volume of the case. Write your answer as a power.

a)

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

b)

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

c)

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

d)

$\left(3w\right)^3+6$

93.

Problem #24 b

ARTIFACT: A display case for the artifact is in the shape of a cube. Each side of the display case is three times longer than the width of the artifact.

b. Simplify the expression.

a)

$9w^2$

b)

$9w^3$

c)

$27w^3$

d)

$6w^3$

94.

Problem #26

Simplify the expression.

$16\left(\frac{1}{2}x\right)^4$

95.

Problem #28

CLOUDS: The lowest altitude of an altocumulus cloud is about $3^8$ feet. The highest altitude of an altocumulus cloud is about 3 times the lowest altitude. What is the highest altitude of an altocumulus cloud? Write your answer as a power.

_____ feet

96.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

97.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

98.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

99.

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

a)

add

b)

subtract

c)

multiply

d)

divide

100.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

101.

Simplify 4^-2=

a)

1/16

b)

-16

c)

1/4

d)

-42

102.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

103.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

104.

a)

b)

c)

d)

105.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

106.

a)

b)

c)

d)

107.

a)

b)

c)

d)

108.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

109.

Write with positive exponents:

1/a^-2

a)

a^-2

b)

a²

c)

1/a¹

110.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

111.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

112.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

113.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

114.

Simplify

a)

x⁴/3

b)

3x¹⁰

c)

36x¹⁰

d)

3x⁴

115.

Simplify: $2^{-4}$

a)

$-8$

b)

$-16$

c)

$-\frac{1}{8}$

d)

$\frac{1}{16}$

116.

According to exponent rules, when we simplify (x²)⁵ we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

117.

(-4³)²

a)

-4⁶

b)

-4⁵

c)

-4

d)

-4⁻¹

118.

Simplify (4xy⁴)³

a)

64x³y¹²

b)

64xy¹²

c)

12x³y¹²

d)

7x⁴y⁷

e)

16x⁴y⁷

119.

Simplify (-2r³p²m)³

a)

-8r⁹p⁶m³

b)

8r⁹p⁶m³

c)

-6r⁶p⁵m³

d)

6r⁹p⁶m³

120.

"D" matches with which property?

Choose the correct answer choice.

Answer choices:

1. Commutative Property

2. Associative Property

3. Identity Property

4. Inverse Property

5. Property of Zero

6. Distributive Property

7. Reflexive Property

8. Symmetric Property

9. Transitive Property

a)

1

b)

2

c)

5

d)

6

121.

D matches with which property?

Type the NUMBER only of the answer.

Answer choices:

1. Commutative Property

2. Associative Property

3. Identity Property

4. Inverse Property

5. Property of Zero

6. Distributive Property

7. Reflexive Property

8. Symmetric Property

9. Transitive Property

(a)

122.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

123.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

124.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

125.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

126.

a)

b)

c)

d)

127.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

128.

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

a)

add

b)

subtract

c)

multiply

d)

divide

129.

Classify

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

130.

Classify by the DEGREE:
3x - 2

a)

1

b)

2

c)

3

d)

4

131.

Polynomial or not?
5x⁴ - 7x

a)

polynomial

b)

not a polynomial

132.

Polynomial or not?

a)

polynomial

b)

not a polynomial

133.

Rewrite the polynomial in standard form:-5 + 4m

a)

-5 + 4m

b)

4m - 5

c)

-4m + 5

d)

4m² - 5

134.

What is the degree classification of this polynomial?
x²+4x-8

a)

binomial

b)

trinomial

c)

quadratic

d)

cubic

135.

Which is an example of a cubic binomial?

a)

x³+5

b)

x²+3

c)

x²+5x-6

d)

5x³

136.

What is the leading coefficient of the following polynomial?
5x²-3x+6

a)

2

b)

-3

c)

5

d)

6

137.

Which is an example of a linear polynomial?

a)

x²-5

b)

6x+4

c)

5x⁵

d)

2x³-9x²

138.

Classify the polynomial by its degree.
x² + 2x³ - 4

a)

A
binomial

b)

B
trinomial

c)

C
quadratic

d)

D
cubic

139.

Classify the polynomial by its number of terms.
4x² - 2

a)

A
monomial

b)

B
binomial

c)

C
trinomial

d)

D
polynomial

140.

What is the degree of the polynomial?
x³y²- 7x²y + 3

a)

A
1

b)

B
3

c)

C
5

d)

D
7

141.

Which is an example of a cubic monomial?

a)

A
x³ + 5

b)

B
x² + 3

c)

C
x² + 5x - 6

d)

D
5x³

142.

How many terms are in the following polynomial?
_3xy_{- 2y + 8x - 7z -16}

a)

A
1

b)

B
2

c)

C
4

d)

D
5

143.

Add:
(3x² - 3x + 2) + (x² - 2x + 1)

a)

A
4x³-2x²+2

b)

B
4x² - 5x + 3

c)

C
-2x³+2x+2

d)

D
4x³-2x²-2

144.

Add to Simplify:
(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

145.

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

a)

7x - 7x + 5x²

b)

5x²+ 2x - 2

c)

5x²

d)

5x² + 6x + 8

146.

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

a)

11a³ - 4a² - 14a - 7

b)

5a³ - 4a² - 14a - 7

c)

5a³ - 4a² - 20a - 7

d)

5a³ - 9a² - 20a - 7

147.

Combine like terms to simplify:
(5x + 2) + (4x + 5)

a)

9x -7

b)

-9x-11

c)

9x+7

d)

x+7

148.

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

149.

Add or Subtract to Simplify:
(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

150.

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

a)

2x² + x + 2

b)

x + 2

c)

2x² + x - 10

d)

x - 10

151.

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

a)

-5x⁵ + 2x³ - 6x

b)

7x⁵ - 6x

c)

-5x³ + 2x² - 6x

d)

-5x⁵ - 6x

152.

Simplify the expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

153.

Simplify the expression
-6x - 5(10x + 3)

a)

-56x - 15

b)

-56x+15

c)

44x+15

d)

-44x-15

154.

Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

a)

4b⁴ - 2b³ + 7

b)

5b⁴ - 2b³ + 4

c)

b⁴ - 2b³ + 7

d)

5b⁴ - 2b³ + 7

155.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

156.

(x +2)(x + 3)

a)

x² + 5x + 6

b)

x² + x + 6

c)

x² + 5x + 5

d)

x² + 6x + 6

157.

(2x - 1)(x + 2)

a)

2x² + 3x - 2

b)

2x² - 5x - 2

c)

2x² + 3x + 2

d)

2x² - 5x + 2

158.

Multiply
(4x+3)(2x-1)

a)

8x²-2x-3

b)

8x-3

c)

8x²+6x-3

d)

8x²+2x-3

159.

Multiply
x²(2x+3)

a)

x²+2x+3

b)

2x+3

c)

2x²+3x

d)

2x³+3x²

160.

Multiply
(4x+3)(2x-1)

a)

8x²-2x-3

b)

8x-3

c)

8x²+6x-3

d)

8x²+2x-3

161.

(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

162.

(x-3)(x²+2x+7)

a)

x³-x²+x-21

b)

x³+5x+13x-21

c)

x³-3x²+7x-21

d)

x²+2x-3

163.

5x(2x³+6)

a)

10x⁴+30x

b)

10x³+30x

c)

7x⁴+11x

164.

Divide:
(9x² + 6x) ÷ 3x

a)

3x + 2

b)

3x² + 2x

c)

5x²

d)

3x + 6

165.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

166.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

167.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

168.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

169.

Simplify $\frac{45x^{15}}{9x^{10}}$

a)

$5x^{1.5}$

b)

$36x^5$

c)

$5x^5$

d)

$36x^{1.5}$

170.

$\frac{18y^{6\ }+9y^{4\ }-12y^2}{3y^2}$

a)

$6y^2\ +3y^2\ -4y^2$

b)

$15y^{4\ }+6y^2\ -\ 9$

c)

$6y^{4\ }+3y^2-4$

d)

$6y^{3\ }-3y^2\ +4y$

171.

a)

1/m²

b)

m²

c)

m⁸

d)

1/m⁸

172.

$\frac{-12a^{4\ }+\ 6a^3}{6a^3}$

a)

$2a$

b)

$-2a+1$

c)

$2a\ +1$

d)

$-2a\ +\ 1a$

173.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

174.

Simplify. Assume no denominator is equal to 0.

$\frac{24mn^{-9}}{12mn^{-11}}$

**Remember: Divide/reduce coefficients, subtract exponents, and then move negative exponents to the opposite spot.**

a)

$\frac{12m^2}{n^{20}}$

b)

$2n^2$

c)

$2mn^2$

175.

Simplify. Assume no denominator is equal to 0.

$\frac{-9f^{-1}g^8h^{-3}}{6g^2h^9}$

a)

$\frac{-3g^6}{2fh^{12}}$

b)

$-3fg^{10}h^6$

c)

$\frac{-54fg^{16}}{h^{27}}$

176.

Simplify. Assume no denominator is equal to 0.

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

**Remember: When dividing monomials, subtract exponents of like variables.**

a)

$x^2y^8$

b)

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

c)

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

177.

Simplify $\frac{-24y^8}{4y^2}$

a)

$6y^6$

b)

$-6x^6$

c)

$-6y^4$

d)

$-6y^6$

178.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

179.

Factor:

7x+49

a)

$7x\left(x+49\right)$

b)

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

c)

$49\left(x+7\right)$

d)

$x\left(7+49\right)$

180.

Factor:
$5a^2-15$

a)

$5\left(a^2-15\right)$

b)

$5a\left(a-15\right)$

c)

$5\left(a^2-3\right)$

d)

$5a\left(a-3\right)$

181.

$12c^2-20a^2$

Factor:

a)

$2\left(6c^2-10a^2\right)$

b)

$4\left(3c^2-5a^2\right)$

c)

$2a^2c^2\left(6-10\right)$

d)

$4\left(ca\right)^2\left(3-5\right)$

182.

$64-40ab$

Factor:

a)

$4\left(16-10ab\right)$

b)

$4ab\left(16-10ab\right)$

c)

$8ab\left(8-5ab\right)$

d)

$8\left(8-5ab\right)$

183.

$36a^2+24a$

Factor:

a)

$12a\left(3a+2\right)$

b)

$a\left(36a+24\right)$

c)

$12\left(3a^2+2a\right)$

d)

$a^2\left(36+24a\right)$

184.

Factor:
$18x^4-12x^2$

a)

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

b)

$x^2\left(18x^2-12\right)$

c)

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

d)

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

185.

Factor:

12ab^3+20b

a)

$4ab\left(3b+5\right)$

b)

$b\left(12ab^2+20\right)$

c)

$4b\left(3ab^2+5\right)$

d)

$12b\left(ab^2+2\right)$

186.

$10x^2+5x$

a)

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

b)

$5x\left(2x+1\right)$

c)

$10x^2\left(1x+2x\right)$

d)

$5x^2\left(2x^2+1\right)$

187.

Factor:

14x-21x^2

a)

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

b)

$x\left(14-21x^2\right)$

c)

$14x\left(1-2x\right)$

d)

$7x\left(2-3x\right)$

188.

Factor:
$81m+48mn$

a)

$3m\left(27+16n\right)$

b)

$m\left(81+48n\right)$

c)

$3\left(27+16n\right)$

d)

$mn\left(81+48n\right)$

189.

Factor:
$8ab-56a$

a)

$8a\left(b-7\right)$

b)

$8\left(ab-7a\right)$

c)

$a\left(8b-56\right)$

d)

$8ab\left(1-7b\right)$

190.

Factor:
$a^2b^2+a$

a)

$a^2\left(b^2+1\right)$

b)

$ab\left(ab+1\right)$

c)

$a\left(ab^2+1\right)$

d)

$a\left(b^2+1\right)$

191.

Factor:
$15xy+30x^2y^2$

a)

$xy\left(15+30xy\right)$

b)

$15\left(xy+2x^2y^2\right)$

c)

$15xy\left(1+2xy\right)$

d)

$5xy\left(3+6xy\right)$

192.

Factor:
$36ab^2-48a^2b$

a)

$a^2b^2\left(16a-38b\right)$

b)

$6ab\left(6b-8a\right)$

c)

$12ab\left(3a-4b\right)$

d)

$12ab\left(3b-4a\right)$

193.

Factor:
$x^3y^2+x^2y+x$

a)

$xy\left(x^2y+x+1\right)$

b)

$x\left(x^2y^2+xy+1\right)$

c)

$x\left(x^3y+x^2+1\right)$

d)

$y\left(x^3y+x^2+x\right)$

194.

Factor:

8m^2n^2-24mn^3+16mn

a)

$8\left(m^2n^2-3mn^3+2mn\right)$

b)

$8mn\left(mn-3mn+2mn\right)$

c)

$8mn\left(mn-3n^2+2\right)$

d)

$mn\left(8mn-24n^2+16\right)$

195.

Factor:

10x^3y^2-2xy^2+14xy

a)

$xy\left(10x^2y-2y+14\right)$

b)

$2xy\left(5x^2y-y+7\right)$

c)

$2xy\left(10x^2y-y+7\right)$

d)

$xy\left(5x^2y-y+7\right)$

196.

Factor:

9xz^3+18yz^2+24z^2

a)

$3z^2\left(3xz+6y+8\right)$

b)

$9z^2\left(xz+2y+3\right)$

c)

$3z\left(3xz^2+6yz+24z\right)$

d)

$9z\left(xz^2+2yz+3z\right)$

197.

Factor:

16x^6y+16x^2y^4+32x^3y^2

a)

$16x^2y\left(x^3+y^4+2xy\right)$

b)

$16xy\left(x^6+xy^3+2x^2y\right)$

c)

$16x^2y\left(x^4+y^3+2xy\right)$

d)

$16x^2y\left(x^4+y^3+2\right)$

198.

Evaluate f(2).

a)

f(2) = 5

b)

f(2) = 12

c)

f(2) = 10

d)

f(2) = 0.5

199.

Evaluate f(6).

a)

f(6) = 18

b)

f(6) = 12

c)

f(6) = 10

d)

f(6) = 1

200.

What is x if
f(x) = -2?

a)

4

b)

0

c)

3

d)

8

201.

Evaluate f(33)

a)

33

b)

11

c)

10

d)

8

202.

Evaluate for f(2)

a)

-3

b)

0

c)

4

d)

7

203.

Find the value of f(x), given x = -1

a)

0

b)

1

c)

2

d)

-1

204.

Find the value of f(x), given x = 3

a)

0

b)

1

c)

2

d)

-1

205.

a)

Function

b)

Not a Function

206.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

207.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

208.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

209.

What is the RANGE?

a)

(-∞, ∞)

b)

(-2, ∞)

c)

[-2, ∞)

d)

(-∞, 0) U (0, ∞)

210.

What is the range?

a)

(-4,5]

b)

[-4,5)

c)

(-3,3)

d)

[-3,3]

211.

What is the domain of the graph?

a)

[-7, 5)

b)

(-7, 5]

c)

[-3, 1)

d)

(-3, 1]

212.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D:{-4, 0, 1, 2}
R:{-4, -3, 1}

c)

D:{0, 1, 2, 3, 4}
R:{1, -3, -4}

213.

Give the range of the set of ordered pairs: (2, 11), (9, -3), (7, 21), (-8, 6)

a)

{2, 9, 7, -8}

b)

{11, -3, 21, 6}

c)

-8 < x < 9

d)

-3 < y < 21

214.

Which set of ordered pairs is not a function?

a)

(1, 3), (2, 7), (3, 8), (4, 11)

b)

(2, 3), (4, 9), (3, 8), (4, 15)

c)

(1, 2), (3, 5), (6, 9), (7, 11)

d)

(-9, 4), (-6, 3), (-2, 8), (0, 21)

215.

For the function: f(x) = 7(x - 11), f (16) = _____

a)

5

b)

35

c)

16

d)

28

216.

Which graph is not a function?

a)

b)

c)

d)

217.

What is a function?

a)

A relation that maps every domain value to exactly one range value.

b)

A relation that maps every range value to exactly one domain value.

c)

Any set of ordered pairs.

d)

Any graph of x and y values.

218.

What is the test to determine if a graph represents a function?

a)

Horizontal line test

b)

Vertical line test

c)

Heidelberg Uncertainty Test

d)

Obi Wan Kenobi Test

Winter break pack - Math - Grade 11

Total questions: 218

Worksheet time: 21hrs 1mins

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