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Benchmark 1 Review (Equations, Exponents, Number Sense)

Total questions: 90

Worksheet time: 2hrs 30mins

Name
Class
Date
1.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
2.
(2ab)3
a)
23a3b3
b)
2ab3
c)
6a3b3
d)
6ab
3.
(y9)-2
a)
y18
b)
y11
c)
1/y18
d)
y9/2
4.
Evaluate the expression using the quotient rule.
a)
34
b)
1/34
c)
3-12
d)
332
5.
y⁻¹¹⋅y⁵
a)
1⁄y⁶
b)
y⁶
c)
-y⁶
d)
-1⁄y⁶
6.
a)
A
b)
B
c)
C
d)
D
7.
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
8.
Division Law states: keep the base the same and do this to the exponents.
a)
multiply
b)
add
c)
subtract
d)
divide
9.
Zero Exponent Law states that _____ becomes a 1.
a)
the exponent
b)
the base
c)
nothing
d)
the whole term
10.
Simplify:
x5 ÷ x2
a)
x7
b)
x3
c)
x10
d)
x2.5
11.
Simplify:
(x3)(x2)
a)
x5
b)
x6
c)
x
d)
x1.5
12.
Simplify:
2a7 ÷ 2a3
a)
a4
b)
1/a4
c)
2a4
d)
a7/3
13.
Simplify (-5.7)0
a)
1
b)
0
c)
-1
d)
-5.7
14.
(6x2)(-3x5)
a)
18x7
b)
-18x7
c)
18x10
d)
3x7
15.
According to exponent rules, when we multiply the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
16.
Simplify the following expression: 
xy-7
a)
1/(xy7)
b)
x/y7
c)
x7/y
d)
x7y
17.
(2x3y)6
a)
2x18y6
b)
64x18y6
c)
64x3y6
d)
2x3y6
18.
Make this negative exponent positive.
9-3
a)
93
b)
1/9-3
c)
1/93
d)
729
19.
How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?
a)
57
b)
56
c)
75
d)
5
20.
a)
49
b)
444
c)
421
d)
415
21.
a)
2560
b)
2517
c)
560
d)
517
22.
a)
0
b)
3
c)
1
d)
-1
23.
(3y⁴)²
a)
9y⁸
b)
9y⁶
c)
6y⁸
d)
6y⁶
24.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
25.

1a−5\frac{1}{a^{-5}}  

a)

a−5a^{-5}  

b)

a5\frac{a}{5}  

c)

a5a^5  

d)

5a\frac{5}{a}  

26.
5 less than a number is 15.
a)
x - 5 = 15
b)
5 - x = 15
c)
15 - x = 5
27.
Two more than 4 times a number is -18.
a)
4x + 2 = -18
b)
2x + 4 = -18
c)
18 = 4x +2
28.
Twice a number is 24.
a)
2n = 24
b)
2/n = 24
c)
2 + n = 24
d)
2 - n = 24
29.
What is the difference between an expression and equation?
a)
Expressions have an equal sign and equations do not have an equal sign
b)
Expressions do not have an equal sign and equations do have an equal sign
c)
There is not a difference
d)
Expressions do not have variables and equations have variables
30.
Translate: two times the sum of a number and five 
a)
2 + y + 5
b)
2y + 5 
c)
2(y + 5)
d)
2 - y + 5
31.
A number tripled subtracted from 60 is the same as 21.
a)
3c − 60 = 21
b)
60 − 3 = 21c
c)
60 − 3c = 21
d)
c(60 − 3) = 21
32.

Eight less than three times a number is equivalent to thirty four.

a)

3x - 8 = 34

b)

8x - 3 = 34

c)

8 - 3x = 34

d)

8 - x = 34

33.

Fifteen less than half a number is equivalent to eleven.

a)

(1/2)x + 15 = 11

b)

2x - 15 = 11

c)

15 - (1/2)x = 11

d)

(1/2)x - 15 = 11

34.

Twelve more than three quarters of a number is equal to thirty six.

a)

75x + 12 = 36

b)

(3/4)x + 12 = 36

c)

3x + 12 = 36

d)

25x + 12 = 36

35.

One quarter the difference of a number and twenty eight is equal to nine.

a)

(1/4)x - 28 = 9

b)

(1/4)(x - 28) = 9

c)

25x - 28 = 9

d)

(1/4)(x + 28) = 9

36.

Twice the sum of four times and number and ten is equal to seventy two.

a)

4x + 10 = 72

b)

2(x + 10) = 72

c)

2(4x + 10) = 72

d)

8x + 10 = 72

37.
Translate the statement into an equation:
The sum of three times a number and ten is equal to eight times the number.
a)
3 + 10 = 8
b)
3x + 10 = 8
c)
3x + 10 = 8x
d)
3(x + 10) = 8x
38.
A gymnastics center charges a $60 registration fee and $15 per class. Olivia registers to take a class and pays a total of $210. Which equation can be used to determine how many classes Olivia signed up for?  
a)
60 - 15x = 210 
b)
15x - 60 = 210
c)
15x + 60 = 210 
d)
210 + 15x = 60 
39.
Eight less than three times a number is equivalent to ten more than one and half times the same number. 
a)
3x - 8 = 0.5x + 10 
b)
8 - 3x = 1.5x + 10 
c)
3x - 8 = 1.5x + 10
d)
8 - 3x = 0.5x + 10
40.

Seven times the sum of four more than twice a number is equal to three less than the product of eight and that same number.

a)

7(2n + 4) = 8n - 3

b)

7(2n + 4) = 3 - 8n

c)

7(2n) + 4 = 3 - 8n

d)

7(4) + 2n = 8n - 3

41.

Five times the sum of a number tripled and two is equal to nine more than the same number.

a)

5(3x + 2) = 9x

b)

5(3x + 2) = x + 9

c)

5(3x) + 2 = 9 - x

d)

5(2) + 3x = 9

42.

The product of eight and a number increased by five is equal to the product of nine and the same number decreased by 10

a)

8c - 5 = 9c + 10

b)

5c + 8 = 9c - 10

c)

8 + 5c = 10 - 9c

d)

8c + 5 = 9c - 10

43.

A ice cream cone cost $3 plus an additional $0.50 per scoop. James paid a total of $4.50, which equation below models this situation.

a)

3x + 0.50 = 4.50

b)

0.50x = 7.50

c)

0.50x + 3 = 4.50

d)

4.50 + 0.50x = 3

44.

The cinema charges $15 for popcorn and an additional $0.10 for each extra squirt of butter. If Joey paid a total of $17, which equation model's this situation?

a)

0.10x + 15 = 17

b)

15x + 0.10 = 17

c)

17x + 0.10 = 15

d)

0.10x + 17 = 15

45.

6 less than a number is nine.

a)

9 - 6 = m

b)

m - 6 = 9

c)

m - 9 = 6

d)

6 - m = 9

46.
What is set of numbers that includes all positive and negative whole numbers?
a)
Whole Numbers
b)
Integers
c)
Rational Numbers
d)
Natural Numbers
47.
What is the set of numbers that includes fractions?
a)
Whole numbers
b)
Integers
c)
Rational Numbers
d)
Natural Numbers
48.
What is the set of numbers that includes repeating decimals?
a)
Rational Numbers
b)
Irrational Numbers
49.
What is the set of numbers that includes π?
a)
Rational Numbers
b)
Irrational Numbers
50.
What is the set of numbers that doesn't include 0?
a)
Whole Numbers
b)
Real Numbers
c)
Irrational Numbers
d)
Natural Numbers
51.
Which name does not apply to this number?
- √100
a)
integer
b)
rational number
c)
whole number
d)
real number
52.
Which name does not apply to this number?
√ 24
a)
real number
b)
irrational number
c)
rational number
53.
Which name does not apply to this number?
7/8
a)
rational number
b)
real number
c)
whole number
54.
Which name does not apply to this number?
-17.84
a)
rational number
b)
real number
c)
irrational number
55.
Which name does not apply to this number?
 -10
a)
whole number
b)
integer
c)
real number
d)
rational number
56.

Select all Rational numbers

7/8 13\sqrt[]{13}   8.23481256... .45 7.343434... −438-4\frac{3}{8}  

a)

7/8 .45 7.343434.... −4 38-4\ \frac{3}{8}  

b)

13\sqrt[]{13}   8.23481256...

c)

none of them

d)

all of them

57.

Is the number 1225\sqrt[]{1225}  rational or irrational? Explain

a)

Irrational since it is a square root

b)

Irrational since it is a non repeating decimal

c)

Rational since it equals a terminating decimal

d)

Rational since it repeats

58.

Which one is not a perfect square/irrational?

49    121     15    4\sqrt[]{49}\ \ \ \ \sqrt[]{121}\ \ \ \ \ \sqrt[]{15}\ \ \ \ \sqrt[]{4}  

a)

49\sqrt[]{49}  

b)

121\sqrt[]{121}  

c)

4\sqrt[]{4}  

d)

15\sqrt[]{15}  

59.
Convert 0.444... to a fraction.
a)
4/10
b)
4.4/99
c)
4/9
d)
2/5
60.
Convert 0.252525... to a fraction.
a)
25/9
b)
25/99
c)
25/100
d)
1/4
61.
Convert 0.769769769... to a fraction.
a)
769/999
b)
769/1000
c)
769/100
d)
769/99
62.
a)
3/10
b)
1/3
c)
1/9
d)
30/99
63.

Convert the following decimal into a fraction. 

0.36‾0.\overline{36}  

a)

4/9

b)

4/11

c)

4/13

d)

3/13

64.

14 + 35v = 3v + 14

a)

One Solution

b)

No Solution

c)

Infinite Solutions

65.

36 - 7p = -7p + 35

a)

One Solution

b)

No Solution

c)

Infinite Solutions

66.

-2v + 4 = -3 -2v

a)

No Solution

b)

Infinite Solutions

c)

One Solution

67.

-2v + 4 = -3 -2v

a)

No Solution

b)

Infinite Solutions

c)

One Solution

68.

3 + 5n = 5n + 3

a)

One Solution

b)

No Solution

c)

Infinite Solutions

69.

30 + 6p = 7p + 37

a)

No Solution

b)

Infinite Solutions

c)

One Solution

70.

8x + 38 = -3 (-6 - 4x)

a)

No Solutions

b)

Infinite Solutions

c)

One Solution

71.
What is the solution to this equation?
a)
one solution
b)
no solution
c)
infinite solutions
d)
none of these
72.
Solve:
2x + 1 = 2x - 1
a)
No Solution
b)

One Solution

c)
Infinitely Many Solutions
73.
Solve:
3x + 15 = 3(x + 5)
a)
No Solution
b)

One Solution

c)
Infinitely Many Solutions
74.

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

3x - 8 = 3(x - 4) + 1

a)

one

b)

no solutions

c)

infinite solutions

75.

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

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

a)

one

b)

no solutions

c)

infinite solutions

76.
What is the solution to the equations?
a)
one solution
b)
no solution
c)
infinite solutions
d)
none of these
77.

Between what 2 whole numbers is 6\sqrt{6}  ?

a)

1 and 2

b)

2 and 3

c)

3 and 4

d)

4 and 5

78.

Between what 2 whole numbers is 35\sqrt{35}  ?

a)

2 and 3

b)

3 and 4

c)

4 and 5

d)

5 and 6

79.
Which statement is true? 
a)
The number ⅚ is irrational
b)
The number 0.345345345 is irrational
c)
The number (4π/16π) is irrational
d)
The number (√11)² is rational
80.
Put in order of least to greatest.
√5, 3, 2½, √8
a)
3, 2½, √8, √5
b)
2½, 3, √5, √8
c)
√5, 3, 2½, √8
d)
√5, 2½, √8, 3
81.
List the following numbers from least to greatest:
-64 , 3.5 , √27 , 6.666...
a)
-64 , 3.5 , √27 , 6.666...
b)
3.5 , √27 , 6.666..., -64
c)
3.5, -64, √27, 6.666...
d)
6.666, √27, -64, 3.5
82.
A rectangle has a perimeter of 70 feet. Its length is five more than twice its width. Which equation can be used to determine the width of the rectangle? 
a)
2x + 5 = 70 
b)
3x + 5 = 70 
c)
6x + 10 = 70 
d)
5x + 2 = 70
83.
A rectangle has a perimeter of 100 inches. Its length is one more than two and a half times its width. Which equation can be used to determine the width of the rectangle? 
a)
2.5x + 1 = 100 
b)
3.5x + 1 = 100 
c)
5x + 2 = 100 
d)
7x + 2 = 100 
84.

The  40\sqrt[]{40}   is between which two integers?

a)

6 & 7, but is closer to 7.

b)

5 & 6, but is closer to 5.

c)

5 & 6, but is closer to 6.

d)

6 & 7, but is closer to 6.

85.

Which of the following letters represents −4-\sqrt[]{4}  on the number line?

a)

A

b)

C

c)

D

d)

F

86.

Which of the following letters best represents 7\sqrt[]{7}  on the number line?

a)

B

b)

E

c)

C

d)

A

87.

Which of the following letters best represents 38\sqrt[]{38}  on the number line?A

a)

B

b)

E

c)

C

d)

A

88.

Which number is not a perfect cube?

a)

8

b)

30

c)

125

d)

216

89.

Approximate the cube root to the nearest tenths place.

a)

1.8

b)

1.2

c)

2.4

d)

3

90.

Approximate the cube root to the nearest tenths place.

a)

4.6

b)

4.1

c)

4.9

d)

11.1

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