Free Printable G@tt

1.

Express the following in Interval Notation
-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

2.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

3.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

4.

Express the following in Interval Notation
-9 < x < -8.5

a)

[-9, -8.5]

b)

[-9, -8.5)

c)

(-9, -8.5]

d)

(-9, -8.5)

5.

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

6.

Express the following interval in Set notation:
(-7, 15]

a)

-7 ≤ x ≤ 15

b)

-7 < x ≤ 15

c)

-7 ≤ x < 15

d)

-7 < x < 15

7.

Express the following interval in Set notation:
[14.2, 19.6)

a)

14.2 ≤ x ≤ 19.6

b)

14.2 < x ≤ 19.6

c)

14.2 ≤ x < 19.6

d)

14.2 < x < 19.6

8.

Express the following interval in Set notation:
(-63, -62)

a)

-63 ≤ x ≤ -62

b)

-63 < x ≤ -62

c)

-63 ≤ x < -62

d)

-63 < x < -62

9.

Look at the graph. Write the inequality in interval notation.

a)

(-2,5)

b)

(-∞,-2)⋃(5,∞)

c)

[-2,5]

d)

(-∞,-2]∪[5,∞)

10.

Write the following in interval notation
-7 ≤ x < 8

a)

(-7, 8)

b)

[-7, 8)

c)

[-7, 8]

d)

(-7, 8]

11.

Write the following in interval notation
x < 8

a)

(8, ∞)

b)

(8, -∞)

c)

(-∞, 8)

d)

[-∞, 8]

12.

Write the following in interval notation
x < 3 or x ≥ 5

a)

(3, -∞) or (∞, 5]

b)

[-∞, 3) or [5, ∞]

c)

(-∞, 3) or [5, ∞)

d)

(3, -∞] or [∞, 5]

13.

Write the following in interval notation
x > 6 and x ≤ 10

a)

(-∞, 6) and (10, ∞)

b)

[6, 10)

c)

(-∞, 6] and [10, ∞)

d)

(6, 10]

14.

Write the following in interval notation
x ≥ 100

a)

(0, 100] (Real quick)

b)

(∞, 100]

c)

[100, ∞)

d)

(∞, 100)

15.

Look at the Graph. Write the inequality in interval notation.

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

16.

When graphing b< 6 would you use an open or closed circle?

a)

open

b)

closed

17.

(-2,12) can be written in inequality notation as:

a)

-2 < x > 12

b)

-2 > x > 12

c)

-2 < x <12

d)

None of these

18.

Look at the picture. Which number line corresponds to [-2, 5]?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

19.

Look at the picture. Which graph best represents the solution set (-∞, -2) U (5, ∞)?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

20.

Look at the picture. Select the correct interval notation for the given number line.

a)

(-∞, -8) U (-4, ∞)

b)

(-∞, -8] U [-4, ∞)

c)

(-8, -4)

d)

[-8, -4]

21.

What is the sum of these fractions in lowest terms?

a)

5/12

b)

5/24

c)

6/12

d)

6/144

22.

What is the sum of these fractions in lowest terms?

a)

4/5

b)

3/20

c)

17/20

d)

4/20

23.

What is the difference of these fractions in lowest terms?

a)

7/9

b)

1/5

c)

12/20

d)

1/20

24.

What is the product of these fractions in lowest terms?

a)

1/3

b)

3/5

c)

3/6

d)

2/6

25.

What is the product of these fractions in lowest terms?

a)

20/50

b)

10/25

c)

2/5

d)

9/15

26.

What is the quotient of these fractions in lowest terms?

a)

6/40

b)

6/10

c)

3/5

d)

12/20

27.

What is the quotient of these fractions in lowest terms?

a)

1 3/5

b)

2/5

c)

1 3/5

d)

2/5

28.

Jenna had 1/6 of cake leftover. She wanted to share it among her 3 friends. How much cake would each friend get?

a)

18

b)

1/18

c)

9

d)

3/6

29.

Jordan made 1 2/3 qt of soup. More friends are coming to her party, so she needs to triple her recipe. How much total soup will she need?

a)

5

b)

1/5

c)

1 2/4

d)

3 2/3

30.

Jeremy bought 4 cups of soda. He let his sister drink 1 3/4 of it. How much soda does he have left?

a)

1

b)

3 3/4

c)

2

d)

2 1/4

31.

4¼ ÷ ¾

a)

5 ⅔

b)

6 ⅔

c)

10

d)

9⅗

32.

Sally baked 12 cupcakes for her friends. Each cupcake is ¾ pound. If she packed 6 cupcakes in each box, how much did 1 box weigh?

a)

$4\ \frac{1}{2}$ pounds

b)

$4\ \frac{3}{4}$ pounds

c)

16 pounds

d)

9 pounds

33.

Nick poured ¾ fluid ounce of vinegar into each of the ten 1-fluid-ounce test tubes to use in an experiment for Science Night. Each circle represents one fluid ounce. How many total fluid ounces of vinegar did Nick pour?

a)

3/4

b)

$7\ \frac{3}{4}$

c)

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

d)

$\frac{3}{40}$

34.

Laney uses $3\ \frac{4}{9}$ bags of red beads and $2\ \frac{1}{6}$ bags of yellow beads for a craft at summer camp. How many bags of red and yellow beads does Laney use for the craft?

a)

$6\ \frac{33}{54}$

b)

$5\ \frac{5}{18}$

c)

$5\ \frac{42}{54}$

d)

$5\ \frac{11}{18}$

35.

Simplify the expression:

$8\ -\ \left(3\ \frac{1}{3}\ +\ 2\ \frac{2}{5}\right)$

a)

$2\ \frac{11}{15}$

b)

$5\ \frac{11}{15}$

c)

$2\ \frac{4}{15}$

d)

$5\ \frac{3}{8}$

36.

Do the following operation.

2x^{2\ }-3x\ +4\ +\ 5x^{2\ }+\ \ 4x\ -8

(a)

37.

Do the following operation.

\left(4x^3\ +\ 3x^{2\ }+\ x\ \right)\ -\ \left(2x^{3\ }-4x^{2\ }+\ 3x\right)

(a)

38.

Do the following operation.

\left(x+3\right)\left(x-6\right)

(a)

39.

Do the following operation.

\left(2x+5\right)\left(x+3\right)

(a)

40.

Do the following operation.

\left(3x\ +3\right)+\left(2x\ -\ 9\right)

(a)

41.

Do the following operation.

-4x\left(x-2\right)

(a)

42.

Maritza saw on the board that the teacher had written $\left(x-3\right)\left(x+3\right)\ =\ x^{2\ }-9$ . She said, “I see what happened, so that means that $\left(x-2\right)\left(x+5\right)$ must equal $x^{2\ }-\ 10$ ." Use complete sentences and show your calculations to explain how you know if Maritza is right or wrong.

4 lines

43.

The length of a rectangle is $5x\ -\ 2$ and its width is $\ x\ +4$ . Show your calculations to find the area of the rectangle as a variable expression.

4 lines

44.

Create an addition problem in which the sum of TWO BINOMIALS is $x-4$ .

4 lines

45.

Raul was multiplying binomials. He found the product in one problem was $2x^{2\ }-\ 9x\ -\ 18$ . One of the binomials he was multiplying was $2x\ +\ 3$ . What was the other binomial?

4 lines

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

A

b)

B

c)

C

d)

D

49.

Add

a)

A.

b)

B.

c)

C.

d)

D.

50.

Subtract, factor, simplify

a)

A

b)

B

c)

C

d)

D

51.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

52.

$\frac{3b^2-6b}{b^2+2b-3}\cdot\frac{b^2-8b+7}{b-2}$

a)

$\frac{1}{b\left(b-2\right)}$

b)

$\frac{b-3}{3b^2\left(b+6\right)}$

c)

$b-8$

d)

$\frac{3b\left(b-7\right)}{b+3}$

53.

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

a)

$\frac{x-8}{x+10}$

b)

$\frac{x+10}{x-8}$

c)

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

d)

$\frac{5}{x+3}$

54.

$\frac{40v+48}{35v+42}\cdot\frac{v-7}{3v^2-21v}$

a)

$\frac{v+6}{7v}$

b)

$v-8$

c)

$\frac{8}{21v}$

d)

$\frac{v+4}{4}$

55.

$\frac{7n+42}{6n+24}\div\frac{n^2+3n-18}{6n-18}$

a)

$\frac{7}{n+4}$

b)

$\frac{24}{7n^2}$

c)

$\frac{8n\left(n+2\right)}{n+8}$

d)

$\frac{4}{n-8}$

56.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

57.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

58.

State the EXCLUDED VALUES of the rational expression:

$\frac{3\left(x-5\right)}{\left(x-2\right)\left(x+1\right)}\cdot\frac{x^2-3x+9}{4\left(x-7\right)}$

a)

$x\ne5,\ 6,\ -1$

b)

$x\ne-2,\ 1,\ -7$

c)

$x\ne3,\ 5,\ 9$

d)

$x\ne2,\ -1,\ 7$

59.

Add the rational expressions:

\frac{3x-5}{x+5}+\frac{4x-3}{x+5}

a)

$\frac{x+2}{x+5}$

b)

$\frac{12x-15}{x+5}$

c)

$\frac{7x+8}{x+5}$

d)

$\frac{7x-8}{x+5}$

60.

DIVIDE the rational expressions:

\frac{4x^2}{5x^4}\div\frac{2x^5}{3x^{10}}

a)

$\frac{6x^3}{5}$

b)

$\frac{2}{5x^7}$

c)

$\frac{5x^3}{6}$

d)

$\frac{6x^9}{5}$

61.

DIVIDE the rational expressions:

\frac{1}{x-7}\div\frac{x+5}{x^2-4x-21}

a)

$\frac{x+3}{x+5}$

b)

$\frac{x-7}{x+3}$

c)

$\frac{x+6}{5}$

d)

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

62.

Simplify

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

63.

Multiply

a)

A.

b)

B.

c)

C.

d)

D.

64.

a)

x^1/2

b)

x³

c)

x²

d)

x^-2

65.

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

a)

add

b)

subtract

c)

multiply

d)

divide

66.

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

a)

add

b)

subtract

c)

multiply

d)

divide

67.

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

a)

add

b)

subtract

c)

multiply

d)

divide

68.

5x³2x²

a)

10x⁵

b)

3x

c)

10x⁶

d)

7x⁵

69.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

70.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

71.

According to exponent rules, when we multiply powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

72.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

73.

n⁴⋅n⁷

a)

n¹¹

b)

n4

c)

n²⁸

d)

n7

74.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

75.

Rewrite using a positive exponent.
w^-13

a)

-w¹³

b)

¹/_w¹³

c)

¹/_w^-13

d)

w¹³

76.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

77.

Simplify.
4a^-2 ⋅ 2ab³

a)

8b³/a³

b)

4b³/a

c)

6b³/a

d)

8b³/a

78.

Simplify (-4x)⁰

a)

-4x

b)

-4

c)

1

d)

-1

79.

Simplify y⁰

a)

y

b)

0

c)

1

d)

1y

80.

Simplify

a)

x²⁸y¹² / x²y

b)

x²⁸y¹² / x⁸y⁴

c)

x²⁰y⁸

81.

Simplify

a)

9a³/6b³

b)

9a³/8b³

c)

27a³/8b³

d)

6a³/5b³

82.

Who is this?

a)

Elsa

b)

Aurora

c)

Snow White

d)

Cinderella

83.

What does this symbol represent?

a)

turn around

b)

walk in a triangle

c)

recycle

d)

loop around

84.

Simplify the following expression using exponent rules.

$\frac{\left(2x^3\right)\left(8x^5\right)}{4x^6}$

a)

$4x^8$

b)

$4x^2$

c)

$4x^{14}$

d)

$2.5x^2$

85.

Simplify the following expression using exponent rules.

$\frac{32x^6}{4x^2}$

a)

$8x^4$

b)

$8x^8$

c)

$6x^4$

d)

$6x^8$

86.

Simplify the following expression using exponent rules.

$\frac{x^{-5}y^3}{xy^2}$

a)

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

b)

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

c)

$x^{-4}y$

d)

$x^6y^5$

87.

$\left(x^a\right)^{b\ }=\ x^{\left(a\cdot b\right)}$

This rule says that to raise a power to a power you need to multiply the exponents.

a)

Product Rule

b)

Quotient rule

c)

Power Rule

d)

Negative Exponent Rule

e)

Zero exponent Rule

88.

Simplify the following expression using exponent rules.

$\frac{20x^7}{10x^5}$

a)

$10x^{-2}$

b)

$2x^2$

c)

$2x^{12}$

d)

$10x^{12}$

89.

Simplify the following expression using exponent rules.

$\frac{x^8z^{10}}{x^6z^3}$

a)

$x^{14}z^{13}$

b)

$\frac{x^2}{z^7}$

c)

$\frac{x^{14}}{z^7}$

d)

$x^2z^7$

90.

Simplify the following expression using exponent rules.

$(-7y^2)(5y^4)$

a)

$-35y^6$

b)

$-2y^6$

c)

$-35y^8$

d)

$-2y^8$

91.

Simplify the following expression using exponent rules.

$(y^9)^{-2}$

a)

$y^{18}$

b)

$y^{11}$

c)

$\frac{1}{y^{18}}$

d)

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

92.

Rewrite this expressions so there are no negative exponents.

$9^{-3}$

a)

$9^3$

b)

$\frac{1}{9^{-3}}$

c)

$\frac{1}{9^3}$

d)

$729$

93.

According to the product rule, when we MULTIPLY exponents with the same base, we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

94.

Simplify the expression in exponential form: (5⁴)³

a)

5¹

b)

5⁷

c)

5¹²

95.

Simplify the expression in exponential form:
134⁰

a)

0

b)

134

c)

1

96.

Simplify the following expression using exponent rules.

$4x-7x^{3\ }+8xy-x+y+4xy=$

a)

$9x^7y^3$

b)

$-3x^3+4xy+x-y$

c)

$-7x^{3\ }+15xy^2$

d)

$-7x^3+12xy+3x+y$

97.

Simplify the following expression using exponent rules.

$\left(a^5\right)\left(a^4\right)$

a)

$a^{20}$

b)

$a^9$

c)

$a^1$

98.

Simplify:

$\frac{y^{10}}{y^{-5}}$

a)

$y^{15}$

b)

$y^2$

c)

$y^5$

d)

$2\ y^5$

99.

Simplify

$x^2\cdot x^3\cdot x^4\cdot x$

a)

$x^9$

b)

$x^{10}$

c)

$x^{24}$

d)

$x^{25}$

100.

$\frac{1}{3^5}$ is the same as

a)

$3^{-5}$

b)

$15$

c)

$3^5$

d)

$\frac{3}{5}$

101.

Which two exponent rules do you need to use to simplify this expression?

a)

Product Rule and Quotient Rule

b)

Power Rule and Negative Exponent Rule

c)

Power Rule and Product Rule

d)

Zero Rule and Power Rule

102.

According to quotient rule, when we DIVIDE the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

103.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

104.

Simplify: $\frac{50r^6n^{-7}}{2n^2r^4}$

a)

$25r^4n^5$

b)

$\frac{25r^4}{n^5}$

c)

$\frac{25r^2}{n^9}$

d)

$25r^2n^{-9}$

G@tt

Total questions: 104

Worksheet time: 12hrs 21mins

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