Free Printable Core Alg 2 Quarter 1 Basics Gnarly Charlie

1.

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

2.

Find the sum (4x³- 5x²+ 3x) + (-2x³- x²+ 6x)

a)

2x³- 6x²- 9x

b)

2x³+ 6x²+ 9x

c)

-2x³- 6x²+ 9x

d)

2x³- 6x²+ 9x

3.

Find the sum (3x - 4) + (12x + 10)

a)

x - 12

b)

15x + 6

c)

36x + 40

d)

17x + 9,000

4.

Find the sum (9x + 17) + (19x - 27)

a)

28x + 44

b)

28x - 10

c)

-28x + 10

d)

-171x - 459

5.

Find the sum (2x + 5y) + (3x - 2y)

a)

3x + 5y

b)

5x + 3y

c)

5x + 7y

d)

7xy + 1xy

6.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

7.

Classify by number of terms:
9x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

8.

What is the standard form of the polynomial,
7x - 125 - 6x⁴ + 14x²

a)

125 + 7x - 14x² +6x⁴

b)

6x⁴ -14x² - 7x +125

c)

125 + 14x² + 7x - 6x⁴

d)

-6x⁴+ 14x² + 7x - 125

9.

What is the type of polynomial 3x⁴ + 2x² + 5x ?

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

10.

Which of these is in Standard Form?

a)

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

b)

$5-3x$

c)

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

d)

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

11.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

12.

Multiply
(x+5)²

a)

x²+25

b)

x²-25

c)

x²+10x+25

d)

x²-10x+25

13.

(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

14.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

15.

Label the polynomial

x^2\ -\ 4x\ +\ 8

a)

monomial

b)

trinomial

c)

binomial

d)

none of these

16.

The length of a rectangle is x - 5. The width is x + 1. What is the area?

a)

$x^2\ -\ 4x\ -\ 5$

b)

$2x\ -\ 4$

c)

$x^2\ +\ 6x\ -\ 5$

d)

none of these

17.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

18.

(x + 7)(x - 2)

a)

x² - 5x + 5

b)

x²- 9x - 14

c)

x² - 5x - 14

d)

x² + 5x - 14

19.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

20.

Multiply: 2x(-2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

21.

Multiply
x²(2x+3)

a)

x²+2x+3

b)

2x+3

c)

2x²+3x

d)

2x³+3x²

22.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

23.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

24.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

25.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

26.

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

a)

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

b)

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

c)

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

d)

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

27.

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

a)

$2a$

b)

$-2a+1$

c)

$2a\ +1$

d)

$-2a\ +\ 1a$

28.

5x²(2x - 3)

a)

5x² + 2x - 3

b)

10x³ - 15x²

c)

-5x2

d)

7x³ - 15x²

29.

Combine Like Terms:
4y + 3x³ + 2y + 8x³ - 6y

a)

11x³

b)

11x³ + 12y

c)

5x³

d)

11x⁶

30.

Divide

$\frac{-4a^{7\ }-\ 6a^5}{2a^3}$

a)

$2a^{4\ }+3a^2$

b)

$4a^{4\ }-\ 4a^2$

c)

$-2a^{7\ }-\ 3a^5$

d)

$-2a^{4\ }-3a^2$

31.

Divide

$\frac{\text{3}x^2-2xy}{\text{2x}}$

a)

$1.5x^{3\ }-x^2y$

b)

$1.5x\ -\ y$

c)

$1.5x\ +\ y$

d)

$1.5x\ -\ 2y$

32.

Divide

$\frac{15x^9-40x^6}{5x^3}$

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

33.

Divide

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

a)

$2a$

b)

$-2a+1$

c)

$2a\ +1$

d)

$-2a\ +\ 1a$

34.

Divide

$\frac{8x^8-8x^2-28x}{4x}$

a)

2x⁸- 8x²- 28x

b)

2x⁸- 2x²- 7x

c)

8x⁷- 8x - 28x

d)

2x⁷- 2x - 7

35.

Divide

$\frac{10x^8y^5}{4x^2y^5}$

a)

$6x^6y$

b)

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

c)

$\frac{5x^6y}{2}$

d)

$6x^6$

36.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

37.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

38.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

39.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

40.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

41.

x⁵⁄x³

a)

x²

b)

x

c)

1

d)

x⁸

42.

Simplify: (-5p)²

a)

-25p²

b)

25p²

c)

-5p²

d)

5p²

43.

Simplify the expression.

a)

1

b)

g¹⁰

c)

g²⁵

d)

g

44.

Using the POWER RULE
Solve the following:
(3xy)²

a)

6x²y²

b)

3²x²y²

c)

3xy²

d)

3x²y

45.

Simplify

x⁻⁶

a)

$\frac{1}{x^6}$

b)

x⁶

c)

-x⁶

d)

$\frac{-1}{x^6}$

46.

$x^0\ =\$

a)

1

b)

y

c)

x

d)

0

47.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

48.

Simplify completely: 4²4³

a)

1024

b)

4⁶

c)

16⁵

d)

4⁵

49.

Simplify: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

50.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

51.

What is the missing number?

4 + (____ + 5) = (4 + 7) + 5

a)

4

b)

5

c)

16

d)

7

52.

The associative property means...

a)

You can group the numbers however you want.

b)

You can change a multiplication sign to a division sign.

c)

You can leave one of the numbers off.

d)

You can't solve the problem.

53.

Rewrite (9 x 6) x 5 using the associative property.

a)

270

b)

9 x 30

c)

9 x (6 x 5)

d)

5 x 9 + 5 x 6

54.

True or False:
When a problem has parentheses, I should always do the numbers inside of the parentheses last.

a)

True

b)

False

55.

Rewrite (9 x 6) x 5 using the associative property.

a)

270

b)

9 x 30

c)

9 x (6 x 5)

d)

5 x 9 + 5 x 6

56.

Which is an example of the Associative Property of Addition?

a)

7+(6+3)=7+(3x6)

b)

3x4 = 4x3

c)

7 + 3 = 13 + 7

d)

2+(3+4)=(2+3)+4

57.

What is the missing number?

6 + ____ = 7 + 6

a)

4

b)

13

c)

7

d)

9

58.

5 + 9 = 14, so 9 + 5 =

a)

11

b)

14

c)

15

d)

16

59.

3 x ____ = 9 x 3

a)

7

b)

9

c)

27

d)

11

60.

Which one of the following illustrates the Commutative Law of Addition?

a)

5 + 7 = 7 + 5

b)

5 + 7 = 4 + 8

c)

5 + 7 = 3 + 9

d)

5 + 7 = 10 + 2

61.

Which of the following illustrates the Commutative Law of Multiplication?

a)

3 x 4 = 6 x 2

b)

3 x 4 = 12 x 1

c)

3 x 4 = 2 x 6

d)

3 x 4 = 4 x 3

62.

What is the missing number?

8 + ____ = 2 + 8

a)

5

b)

10

c)

4

d)

2

63.

8 + 4 = 12, so 4+8 =

a)

12

b)

3

c)

4

d)

14

64.

What is the missing number?

4 x ____ = 6 x 4

a)

4

b)

6

c)

7

d)

24

65.

Name the Property
5(3+6) = (5*3) + (5*6)

a)

Distributive Property

b)

Commutative Property of Addition

c)

Commutative Property of Multiplication

d)

Addition Property of Zero

66.

Which Property says that order doesn't matter in addition and multiplication?

a)

Commutative Property

b)

Associative Property

c)

Identity Property

d)

Property Brothers

67.

This property tells us that you can move the parentheses when you are multiplying and the answer will not change.

a)

Associative Addition

b)

Associative Multiplication

c)

Commutative Addition

d)

Commutative Multiplication

68.

Which shows the Identity Property of Multiplication?

a)

3 + 1 = 4

b)

1 x 9 = 9

c)

18 - 1 = 17

d)

11 x 4 = 44

69.

How do you solve:
(2x⁵)(6x⁴)

a)

MULTIPLY coefficients
MULTIPLY exponents

b)

DIVIDE coefficients
SUBTRACT exponents

c)

Combine like terms

d)

MULTIPLY coefficients
ADD exponents

70.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

71.

Write using a single exponent: 10³ x 10⁵

a)

10¹⁵

b)

10⁸

c)

10²

d)

10⁶

72.

Write using a single exponent: (10⁴)⁵

a)

10²⁰

b)

10¹

c)

10⁹

d)

10⁶

73.

Write using a single exponent: $\frac{3^7}{3^3}$

a)

$3^{10}$

b)

$3^{21}$

c)

$3^4$

d)

$3^6$

74.

$10^{-5}$

Write using a positive exponent:

a)

$50$

b)

$10^5$

c)

$\frac{1}{10^5}$

d)

$10^9$

75.

Simplify the following expression:

(xyz)⁰ =

a)

0

b)

1

c)

xyz

d)

-1

76.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

77.

X²⋅ X³⋅ X⁴⋅ X

a)

x⁹

b)

x²⁴

c)

x¹⁰

d)

x²⁵

78.

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

a)

add

b)

subtract

c)

multiply

d)

divide

79.

Simplify

a)

2x⁶

b)

2x

c)

2x⁵

d)

2x⁸

80.

Simplify the expression.

a)

1

b)

g¹⁰

c)

g²⁵

d)

g

81.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

82.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

83.

The sum of 8 and 3

a)

$8+3$

b)

$8\cdot3$

c)

$\frac{8}{3}$

d)

$8-3$

84.

Goku is at least as strong as Vegeta

a)

$Goku\ge Vegeta$

b)

$Vegeta\ge Goku$

c)

$Goku>Vegeta$

d)

$Goku\le Vegeta$

85.

Simplify the following expression:
(5 + 4x) + (2x - 8)

a)

13 + 6x

b)

6x - 3

c)

6x - 13

d)

6x + 3

86.

Simplify: (-4)²

a)

-8

b)

16

c)

-16

d)

8

87.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

88.

Simplify completely: 4²4³

a)

1024

b)

4⁶

c)

16⁵

d)

4⁵

89.

Simplify: (-5p)²

a)

-25p²

b)

25p²

c)

-5p²

d)

5p²

90.

Simplify: (2x/3)⁴

a)

(8x)/12

b)

(16x⁴)/81

c)

(8x)/81

d)

(2x⁴)/81

91.

Simplify: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

92.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

93.

Simplify: (6m⁷)/(4m³)²

a)

(6m)/16

b)

(3/8)m

c)

3/(8m)

d)

(3m)/4

94.

Simplify: x⁸/x²

a)

x¹⁶

b)

x⁴

c)

x⁵

d)

x⁶

95.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

96.

When using the Power to a Power rule, what are you supposed to do with the exponents? ex. $\left(x^9\right)^{12}$

a)

Add the exponents.

b)

Multiply the exponents.

c)

Subtract the exponents.

d)

Make it $12x^9$

97.

Simplify the following: $\left(4x^3\right)^4$

a)

$16x^7$

b)

$4^4x^7$

c)

$256x^{12}$

d)

$16x^{12}$

98.

The Quotient of Powers Property says, "to divide powers with the same base, _________ the exponents."

ex.

\frac{\text{}y^6}{\text{}y^3}

a)

Divide

b)

Add

c)

Multiply

d)

Subtract

99.

Anything raised to the zero power (except zero) is equal to what?

(a)

100.

Rewrite using a positive exponent.
7^-10

a)

¹/_7¹⁰

b)

7¹⁰

c)

¹/_7^-10

d)

-70

101.

Rewrite using a positive exponent.
g^-7

a)

¹/_g⁷

b)

g⁷

c)

¹/_g^-7

d)

-g⁷

102.

Rewrite using a positive exponent.
w^-13

a)

-w¹³

b)

¹/_w¹³

c)

¹/_w^-13

d)

w¹³

103.

Rewrite each expression with a negative exponent.
¹/_12⁴

a)

¹/_12^-4

b)

12⁴

c)

¹/_20,736

d)

12^-4

104.

Rewrite each expression with a negative exponent.
¹/_(-5)⁷

a)

(-5)⁷

b)

¹/_(-5)^-7

c)

(-5)^-7

d)

¹/_78,125

105.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

106.

Any number written to the 0 power is always 1
Example: 8⁰=1

a)

True

b)

False

107.

5^-2

a)

1/25

b)

1/5²

108.

Rewrite using a positive exponent.
(-5)^-4

a)

(-5)⁴

b)

¹/_(-5)^-4

c)

¹/_(-5)⁴

d)

-625

109.

Evaluate

a)

-1

b)

1/32

c)

-1/32

d)

1

110.

Write with positive exponents:

a)

a^-2

b)

a²

c)

$\frac{1}{a^2}$

d)

2a

111.

To get rid of a negative exponent you need to...

a)

Just erase it

b)

Find the reciprocal

c)

Multiply it by a negative

d)

Add a one to it

112.

Simplify x^-7

a)

-7

b)

-7x

c)

1/x⁷

d)

-1/x⁷

113.

Rewrite the following expression using a positive exponent: $g^{-7}$

a)

$\frac{1}{g^7}$

b)

$g^7$

c)

$-\frac{1}{g^7}$

d)

$-g^7$

114.

Simplify the following expression: $\frac{1}{x^{-7}}$

a)

$x^7$

b)

$7x$

c)

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

d)

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

115.

Rewrite the following expression with positive exponents only: $\frac{1}{3^{-4}}$

a)

$12$

b)

$\frac{1}{-12}$

c)

$-3^4$

d)

$3^4$

116.

r²⋅ r

a)

r³

b)

r²

c)

2r³

d)

11r²

117.

Simplify: x ∙ x ∙ x ∙ x ∙ x ∙ x

a)

x⁶

b)

6x

c)

x³

d)

6x⁶

118.

x^{20 .} x¹⁰

a)

x³⁰

b)

x²⁰⁰

c)

2x³⁰

d)

x¹⁰

119.

If the bases are the same when multiplying, then you....

a)

Multiply the exponents

b)

Subtract the exponents

c)

Add the exponents

d)

Divide the exponents

120.

4²* 4²

a)

16⁴

b)

4²

c)

4⁴

d)

8²

121.

2 * 2² *2²

a)

2⁴

b)

8⁴

c)

36

d)

2⁵

122.

When multiplying two powers that have the same base, you can ___________ the exponents.

a)

Subtract

b)

Divide

c)

Add

d)

Multiply

123.

What is the base in 2⁸ ?

a)

8

b)

2

124.

6r *5r²

a)

30r³

b)

30r²

c)

11r³

d)

11r²

125.

7v³*10u³v⁵

a)

70u³v⁶

b)

17u³v⁸

c)

70u³v⁸

d)

none of the above

126.

7u²v⁵ * 9uv³

a)

16u²v⁸

b)

63u³v¹⁵

c)

63uv⁸

d)

63u³v⁸

127.

uv * 4uv⁵

a)

4u²v⁶

b)

u²v⁶

c)

2u*4v

d)

4uuvvv

128.

What is the exponent form for the factors
5 x 5 x 5?

a)

3⁵

b)

5³

129.

Exponents use.....

a)

repeated addition

b)

repeated division

c)

repeated multiplication

d)

repeated subtraction

130.

What is equivalent to

3x^2y\cdot6xy^3

a)

$9x^3y^4$

b)

$9x^3y^3$

c)

$18x^3y^4$

d)

$18x^3y^3$

131.

What is equivalent to

5m^4n^3\cdot8m^5n^4z

a)

$40m^9n^7$

b)

$13m^8n^7z$

c)

$13m^9n^7z$

d)

$40m^9n^7z$

132.

How do you correctly say 4³

a)

4 squared

b)

3 quadrupled

c)

4 cubed

d)

4 to the power of 2

133.

Solve the following in exponential form: $8^2$ x 8

a)

$8^3$

b)

$64^2$

c)

$64^3$

d)

$8^2$

134.

Multiply

2^9\cdot2^4

a)

$4^{13}$

b)

$2^{13}$

c)

$2^{36}$

d)

$4^{36}$

135.

a)

4³

b)

4¹⁵

c)

1³

d)

1¹⁵

136.

a)

1¹⁰

b)

1²⁶

c)

z¹⁰

d)

z²⁶

137.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

138.

a)

y¹⁴

b)

y¹⁰

c)

1¹⁴

d)

1¹⁰

139.

a)

2y²⁴

b)

2¹⁰

c)

2y¹⁰

d)

2y¹⁴

140.

a)

8x⁴

b)

8x⁸

c)

6x⁴

d)

6x⁸

141.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

142.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

143.

a)

1²²

b)

1³⁰

c)

6²²

d)

6³⁰

144.

a)

b⁵

b)

b

c)

b^-1

d)

b⁶

145.

a)

3⁴

b)

1/3⁴

c)

3^-12

d)

3³²

146.

a)

1

b)

g¹⁰

c)

g²⁵

d)

g

147.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

148.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

149.

4⁹ / 4⁶

a)

4³

b)

4¹⁵

c)

1³

d)

1¹⁵

150.

In 2³what is the base?

a)

2

b)

3

c)

2³

151.

In 2³what is the exponent?

a)

2

b)

3

c)

2³

152.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

153.

a)

1¹⁰

b)

1²⁶

c)

z¹⁰

d)

z²⁶

154.

a)

1/p²

b)

p⁴

c)

1/p⁴

d)

p

155.

Simplify:

$\frac{10x^{12}y^4z^8}{15x^9y^3z^6}$

a)

$\frac{2x^3y}{3z^2}$

b)

$\frac{2x^3yz^2}{3}$

c)

$\frac{10y^2}{15x^4z^8}$

d)

$\frac{3x^3yz^2}{2}$

156.

Simplify:

$\frac{36w^{10}h^{15}}{9w^{14}h^7}$

a)

$\frac{4w^4}{h^8}$

b)

$\frac{h^8}{4w^4}$

c)

$4w^{24}h^{22}$

d)

$\frac{4h^8}{w^4}$

157.

Simplify:

$\frac{m^{17}}{m^{25}}$

a)

$m^8$

b)

$\frac{1}{m^8}$

c)

$m^{-11}$

d)

$\frac{1}{m^7}$

158.

Simplify:

$\frac{36x^{20}y^{12}z^9}{\left(2x^3y^7z^4\right)^2}$

a)

$18x^{17}y^8z^5$

b)

$\frac{9y^2}{x^{14}z}$

c)

$\frac{9x^{14}z}{y^2}$

d)

$\frac{9z}{x^{14}y^2}$

159.

Simplify:

$\frac{42k^8h^{11}c^5}{28k^6h^{24}c^2}$

a)

$\frac{7k^2c^2}{2h^{12}}$

b)

$\frac{2h^{13}c^3}{3k^2}$

c)

$\frac{3h^{11}}{4k^4c^{10}}$

d)

$\frac{3k^2c^3}{2h^{13}}$

160.

Simplify:

$\frac{\left(2w^9p^8d^2\right)^3}{4w^{14}pd^5}$

a)

$2w^{13}p^{23}d$

b)

$2w^{10}p^{30}d^2$

c)

$4w^{11}p^{20}d^4$

d)

$\frac{4w^{18}d^3}{p^{17}}$

161.

Simplify:

$\frac{8x^{15}y^7w^9}{6x^{20}y^3w^2}$

a)

$\frac{3x^5}{4w^7y^4}$

b)

$\frac{4x^3w^9}{3y^{14}}$

c)

$\frac{4y^4w^7}{3x^5}$

d)

$\frac{4x^{35}y^{20}}{3w^{22}}$

162.

Simplify:

$\frac{p^{40}}{p^{33}}$

a)

$p^7$

b)

$\frac{1}{p^7}$

c)

$p^{73}$

d)

$\frac{1}{p^{73}}$

163.

Simplify:

$\frac{w^{-18}}{w^3}$

a)

$w^{21}$

b)

$\frac{1}{w^6}$

c)

$w^9$

d)

$\frac{1}{w^{21}}$

164.

Simplify: $\frac{21x^5y^2}{3xy^2}$

a)

$7x^4y$

b)

$18x^4y$

c)

$18x^4$

d)

$7x^4$

165.

r²⋅ r

a)

r³

b)

r²

c)

2r³

d)

11r²

166.

Simplify: x ∙ x ∙ x ∙ x ∙ x ∙ x

a)

x⁶

b)

6x

c)

x³

d)

6x⁶

167.

x^{20 .} x¹⁰

a)

x³⁰

b)

x²⁰⁰

c)

2x³⁰

d)

x¹⁰

168.

If the bases are the same, then you....

a)

Multiply the exponents

b)

Subtract the exponents

c)

Add the exponents

d)

Divide the exponents

169.

4²* 4²

a)

16⁴

b)

4²

c)

4⁴

d)

8²

170.

2 * 2² *2²

a)

2⁴

b)

8⁴

c)

36

d)

2⁵

171.

When multiplying two powers that have the same base, you can ___________ the exponents.

a)

Subtract

b)

Divide

c)

Add

d)

Multiply

172.

What is the base in 2⁸ ?

a)

8

b)

2

173.

6r *5r²

a)

30r³

b)

30r²

c)

11r³

d)

11r²

174.

7v³*10u³v⁵

a)

70u³v⁶

b)

17u³v⁸

c)

70u³v⁸

d)

none of the above

175.

7u²v⁵ * 9uv³

a)

16u²v⁸

b)

63u³v¹⁵

c)

63uv⁸

d)

63u³v⁸

176.

uv * 4uv⁵

a)

4u²v⁶

b)

u²v⁶

c)

2u*4v

d)

4uuvvv

177.

What is the exponent form for the factors
5 x 5 x 5?

a)

3⁵

b)

5³

178.

Exponents use.....

a)

repeated addition

b)

repeated division

c)

repeated multiplication

d)

repeated subtraction

179.

What is equivalent to

3x^2y\cdot6xy^3

a)

$9x^3y^4$

b)

$9x^3y^3$

c)

$18x^3y^4$

d)

$18x^3y^3$

180.

What is equivalent to

5m^4n^3\cdot8m^5n^4z

a)

$40m^9n^7$

b)

$13m^8n^7z$

c)

$13m^9n^7z$

d)

$40m^9n^7z$

181.

How do you correctly say 4³

a)

4 squared

b)

3 quadrupled

c)

4 cubed

d)

4 to the power of 2

182.

Solve the following in exponential form: $8^2$ x 8

a)

$8^3$

b)

$64^2$

c)

$64^3$

d)

$8^2$

183.

Multiply

2^9\cdot2^4

a)

$4^{13}$

b)

$2^{13}$

c)

$2^{36}$

d)

$4^{36}$

184.

What is equivalent to

2^4

a)

8

b)

16

c)

4

d)

2

185.

Exponents use.....

a)

repeated addition

b)

repeated division

c)

repeated multiplication

d)

repeated subtraction

186.

What is equivalent to

3x^2y\cdot6xy^3

a)

$9x^3y^4$

b)

$9x^3y^3$

c)

$18x^3y^4$

d)

$18x^3y^3$

187.

What is equivalent to

\left(2a^2b\right)^3

a)

$8a^6b^3$

b)

$4a^4b^2$

c)

$2a^2b^3$

d)

$8a^6b^2$

188.

What is equivalent to

6^4

a)

36

b)

1296

c)

216

d)

6

189.

What is equivalent to

5m^4n^3\cdot8m^5n^4z

a)

$40m^9n^7$

b)

$13m^8n^7z$

c)

$13m^9n^7z$

d)

$40m^9n^7z$

190.

What is equivalent to

\left(3x^2yz\right)^4

a)

$81x^8y^4z^4$

b)

$12x^8y^4z^4$

c)

$81x^4y^8z^4$

d)

$12x^4y^4z^4$

191.

What is equivalent to

7^3

a)

49

b)

343

c)

21

d)

7

192.

What is equivalent to

3ab^6\cdot x^5y^7

a)

$4ab^6x^5y^7$

b)

$3ab^6x^5y^7$

c)

$3b^6x^5y^7$

d)

$4b^6x^5y^7$

193.

What is equivalent to

\left(2x^2y^3z\right)^2

?

a)

$6x^6y^4z^2$

b)

$4x^4y^6z^2$

c)

$4x^2y^4z$

d)

$2x^2y^3z^2$

194.

$\frac{81x^9-54x^6+27x^3}{9x}$

a)

$9x^9-6x^6+3x^3$

b)

$9x^8-6x^5+3x^2$

c)

$9x^{10}-6x^7+3x^4$

d)

$81x^8-6x^5+3x^2$

195.

$\frac{75x^8+50x^4+30x^3+5x^2}{5x^2}$

a)

$15x^8+10x^4+6x^3+x^2$

b)

$15x^6+10x^2+6x$

c)

$15x^{10}+10x^6+6x^5+x^4$

d)

$15x^6+10x^2+6x+1$

196.

$\frac{16x^8+24x^6-40x^4}{4x^3}$

a)

$4x^5+6x^3-10x$

b)

$4x^8+6x^6-10x^4$

c)

$12x^5+20x^3-44x$

d)

$4x^{11}+6x^9-10x^7$

197.

Which is another way of correctly expressing
(x - 3)(x - 3)?

a)

(x² - 3²)

b)

(x² - 3)

c)

(x + 3)(x - 3)

d)

(x - 3)²

198.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

199.

Factor
x²+ 12x + 36

a)

(x + 6)(x +6)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 6)(x - 6)

200.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

201.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

202.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

203.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

204.

Factor Trinomial Completely:
2x² + 12x + 16

a)

2(x + 8)(x + 6)

b)

(2x + 4)(2x + 2)

c)

2(x + 2)(x + 4)

d)

2(x² + 6x + 8)

205.

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

206.

x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

207.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Prime

208.

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

209.

x²+ 81

a)

Prime

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

210.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

211.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

212.

Factor:
n²+ 10n + 25

a)

(n + 5)(n - 5)

b)

(n + 25)(n + 1)

c)

(n - 5)²

d)

(n + 5)²

213.

Is this a perfect square trinomial?
x² + 18x + 9

a)

Yes

b)

No

214.

Is this a perfect square trinomial?
x² + 14x + 49

a)

Yes

b)

No

215.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

216.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

217.

Factor
x² - 5x - 36

a)

(x - 4)(x + 9)

b)

(x - 6)(x + 6)

c)

(x + 4)(x - 9)

d)

(x -12)(x + 3)

218.

Factor
k² - 2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

219.

Factor:
x² + 0x - 144

a)

(x + 12)²

b)

(x - 12)(x + 12)

c)

(x - 12)²

d)

12²

220.

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

221.

Factor Completely
$v^2+11v+28$

a)

$\left(v-7\right)\left(v+4\right)$

b)

$\left(v+7\right)\left(v-4\right)$

c)

$\left(v+6\right)\left(v+3\right)$

d)

$\left(v+7\right)\left(v+4\right)$

222.

$x^2-5x+6$ Factor Completely

a)

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

b)

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

c)

$x\left(x-10\right)$

d)

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

223.

Factor Completely
$n^2-12n+35$

a)

$4\left(n+9\right)\left(n+10\right)$

b)

$\left(n-7\right)\left(n-5\right)$

c)

$\left(n-7\right)\left(n+5\right)$

d)

Not Factorable

224.

Factor Completely
$k^2+2k\ -63$

a)

$\left(k-7\right)\left(k+9\right)$

b)

$\left(k+3\right)\left(k+4\right)$

c)

$\left(k-3\right)\left(k-9\right)$

d)

$\left(k-7\right)\left(k-9\right)$

225.

Factor Completely
$m^2+11m+10$

a)

$4\left(m-3\right)\left(m+10\right)$

b)

$\left(m+10\right)\left(m-1\right)$

c)

$\left(m+10\right)\left(m+1\right)$

d)

$\left(m-10\right)\left(m+1\right)$

226.

Factor Completely
$m^2-6m-27$

a)

$\left(m+7\right)\left(m-2\right)$

b)

$\left(m+3\right)\left(m-9\right)$

c)

$6m\left(m+8\right)$

d)

$\left(m+3\right)\left(m+9\right)$

227.

Factor Completely
$x^2-4x+3$

a)

$\left(x-3\right)\left(x+1\right)$

b)

$\left(x-7\right)\left(x+4\right)$

c)

$\left(x-3\right)\left(x-1\right)$

d)

$\left(x+3\right)\left(x-1\right)$

228.

Factor Completely
$5x^2+20x-105$

a)

$5\left(x-3\right)\left(x+7\right)$

b)

$5\left(x+3\right)\left(x-7\right)$

c)

$5\left(x-3\right)\left(x-7\right)$

d)

Not Factorable

229.

Factor Completely
$6p^2+90p+300$

a)

$6\left(p+5\right)\left(p+10\right)$

b)

$5\left(p-6\right)\left(p-10\right)$

c)

$6\left(p+5\right)\left(p-10\right)$

d)

$\left(p+8\right)\left(p+9\right)$

230.

What is the GCF of the trinomial?
3x²- 9x -120

a)

3

b)

2

c)

6

d)

9

231.

Factor using GCF or monomial factoring:

2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

232.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

233.

Which expression is equivalent to

the polynomial: k²+7x+10?

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

234.

Which expression shows the factors of: n² + 16n + 63?

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

235.

Which expression is a factor of: k² -2k - 24

a)

(k-6)

b)

((k+2)

c)

(k-1)

d)

(k-5)

236.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

237.

Which expression shows the

factors of: x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

238.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

239.

The trinomial 4x²-20x + 25 is factorable.

Which of these is the correct factorization?

a)

(2x+5)(2x-5)

b)

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

c)

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

d)

$\left(x-5\right)\left(4x-5\right)$

240.

Factor:

2x² + 3x - 9

a)

2(x + 3)(x - 3)

b)

(2x - 3)²

c)

(x + 3)(2x - 3)

d)

(2x + 3)(x - 3)

241.

Which function is equivalent to: h(x)= 3x² + 10x - 8?

a)

h(x)=(3x + 2)(x + 4)

b)

h(x)=(7x + 5)(x + 2)

c)

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

d)

h(x)=(7x - 3)(x - 4)

242.

The area of a rectangle painting is (x²+ 9x - 36) square units.

Which of the following could be the dimensions of the painting?

a)

(x + 12)units

by (x - 3) units.

b)

(x + 9) units

by (x - 4)units

c)

(x - 12) units

by (x + 3) units

d)

(x - 9)units

by (x - 4)units

243.

What are the factors of: x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

244.

Factor
k² - 2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

245.

Which factorization below is the complete factorization of the trinomial: $5x^2+10x-15?$

a)

5(x - 3)(x +1)

b)

5x(x+3)(x-1)

c)

5(x + 3)(x - 1)

d)

5x(x- 3)(x+1)

246.

What is the complete factorization of 3x²-3x - 18?

a)

3(x -2)(x - 3)

b)

3(x +3)(x -2)

c)

3x(x -3-6)

d)

3(x + 2)(x - 3)

247.

Factor completely.
3x² + 10x - 8

a)

(3x + 2)(x + 4)

b)

(7x + 5)(x + 2)

c)

(3x - 2)(x + 4)

d)

(7x - 3)(x - 4)

248.

A box in the shape of a rectangular prism

is represented by the polynomial a² - a - 12,

where a is measured in centimeters.

Which measure might represent the box?

a)

(a - 4)cm and

(a + 3)cm.

b)

(a + 6)cm and

(a - 4)cm

c)

(a - 6)cm and

(a + 4) cm

d)

(a + 4) cm and

(a - 3)cm

249.

$x^2-x-20$

Which of the following is the complete factorization?

a)

(x-2)(x-10)

b)

(x-1)(x+20)

c)

(x+5)(x+4)

d)

(x-5)(x+4)

250.

1.1

Which answer matches the question?

a)

That we are not our own but belong, body and soul, both in life and death, to God and to our Savior Jesus Christ.

b)

God is the creator and sustainer of everyone and everything. He is eternal, infinite, and unchangeable in his power and perfection, goodness and glory, wisdom, justice, and truth. Nothing happens except through him and by his will.

c)

That we are not our own but belong, body and soul, both in life and death, to God.

d)

God created us male and female in his own image to know him, love him, live with him, and glorify him. And it is right that we who were created by God should live to his glory.

e)

That we are not our own but our souls, both in life and death, to God and to our Savior Jesus Christ.

251.

2.1

Which answer matches the question?

a)

That we are not our own but belong, body and soul, both in life and death, to God and to our Savior Jesus Christ.

b)

God is the creator and sustainer of everyone and everything. He is eternal, infinite, and unchangeable in his power and perfection, goodness and glory, wisdom, justice, and truth. Nothing happens except through him and by his will.

c)

That we are not our own but belong, body and soul, both in life and death, to God.

d)

God created us male and female in his own image to know him, love him, live with him, and glorify him. And it is right that we who were created by God should live to his glory.

e)

That we are not our own but our souls, both in life and death, to God and to our Savior Jesus Christ.

252.

1.2

Which question matches the answer?

"That we are not our own but belong, body and soul, both in life and death, to God and to our Savior Jesus Christ."

a)

What is our only hope in life and death?

b)

What is God?

c)

How many persons are there in God?

d)

How and why did God create us?

e)

What is our only certainty in life and death?

253.

2.2

Which question matches the answer?

"God is the creator and sustainer of everyone and everything. He is eternal, infinite, and unchangeable in his power and perfection, goodness and glory, wisdom, justice, and truth. Nothing happens except through him and by his will."

a)

What is our only hope in life and death?

b)

What is God?

c)

How many persons are there in God?

d)

How and why did God create us?

e)

What is our only certainty in life and death?

254.

1.3

What scripture is this catechism based on?

a)

Romans 14:7–8

b)

John 14:7–8

c)

Matthew 14:7–8

d)

Mark 14:7–8

e)

Luke 14:7–8

255.

2.3

What scripture is this catechism based on?

a)

Psalm 86:8-10,15

b)

Psalm 85:8-10,15

c)

Psalm 86:7-10,15

d)

Psalm 80:8-10,15

e)

Core Alg 2 Quarter 1 Basics Gnarly Charlie

Total questions: 255

Worksheet time: 63hrs 45mins

Romans 14:7–8

John 14:7–8

Matthew 14:7–8

Mark 14:7–8

Luke 14:7–8

Psalm 86:8-10,15

Psalm 85:8-10,15

Psalm 86:7-10,15

Psalm 80:8-10,15

Psalm 86:8-10,13

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