Free Printable MATH - HW SHEET 26

1.

Translate the phrase into an algebraic expression

"57 more than 3 times Kate's score" Use the variable g to represent Kate's score.

a)

57g + 3

b)

3g + 57

c)

3g − 57

d)

57 + 3g

2.

A number squared increased by 1

a)

1 + √2

b)

x²+ 1

c)

x²− 1

d)

_{√2 + 1}

3.

The difference of a number and 7

a)

7 − x

b)

x + 7

c)

x/7

d)

x − 7

4.

Kalia buys 5 items that cost d dollars each. She gives the cashier $60. Which expression represents the change she should receive?

a)

60 − 5d

b)

60 − d

c)

60 + 5d

d)

5d − 60

5.

Translate this phrase into an algebraic expression.

2 times the sum of a number and 15

Use the variable B to represent the unknown number.

a)

2(B+15)

b)

2B+15

c)

2B×15

d)

2×15B

6.

The expression (l + m) (2m + p) − 2m (p + m) can be simplified as

a)

2lm + lp

b)

2lm + lp − 2mp

c)

2lm + lp + mp

d)

2lm + lp − mp

7.

What is the product of (x² − y²) and (3x + 2y)?

a)

3x³ − 2y³ + 3x²y + 3xy²

b)

3x³ + 2y³ - 2x²y − 3xy²

c)

3x³ − 2y³ + 2x²y − 3xy²

d)

3x³ − 3y³ + 2x²y − 3xy²

8.

(x² - y²) × (x² + y²) = ______

a)

2x² + 2y²

b)

x⁴ - y⁴

c)

x⁴ + y⁴

d)

2x⁴

9.

$\left(a^2+2ab\ +b^2\right)$ is the expansion of

a)

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

b)

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

c)

$\left(a+b\right)^3$

d)

none of these

10.

Sunny earns $12, per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did Sunny earn this week?
Write your answer as an expression.

a)

12 - x + 15

b)

15 - x - 12

c)

12x - 15

d)

15x + 12

11.

Marco's mom gave him d dollars for his allowance one week. He also earned $14.55 for his newspaper route that week.
Write your answer as an expression.

a)

d - 14.55

b)

14.55 - d

c)

14.55 + d

d)

d + 14.55

12.

Sarah received $55, for her birthday. She used some of that money to buy 3 shirts priced at m dollars each. How much money does Sarah have left?
Write your answer as an expression.

a)

55 - 3m

b)

3m + 55

c)

55 + 3 + m

d)

55m - 3

13.

A large cheese pizza costs $18. Each topping you add on costs $1.50. How much would it cost to get a large cheese pizza with c toppings added?
Write your answer as an expression.

a)

c + 18

b)

18 + 1.50

c)

18 + 1.50c

d)

1.50c - 18

14.

A pizza delivery driver earns $12 an hour and works h hours per day. He also spends $ 12 a day on gas. How much money will the driver earn in one day.
Write your answer as an expression.

a)

12h-12

b)

12 + h + 12

c)

12/h - 12

d)

12h + 12

15.

Which phrase describes this expression?

6y + 4

a)

6 times the sum of y and 4

b)

The product of 6 and 4 times y

c)

4 more than the sum of 6 and y

d)

The product of 6 and y plus 4

16.

In an algebraic expression, what is the word that describes the letter that stands for an unknown number?

a)

term

b)

coefficient

c)

variable

d)

product

17.

A(n) __________________ consists of one or more numbers, variables, and operations.

a)

numeric expression

b)

term

c)

variable

d)

algebraic expression

18.

Which verbal expression represents the given expression?
3(4-x)

a)

four minus the number x divided by 3

b)

three times four less than a number x

c)

three times the quantity x less than four

d)

four subtracted from x times three

19.

Which set of words mean "exponent"?

a)

cubed, squared, increased, twice

b)

cubed, twice, squared, double

c)

cubed, squared, power

d)

cubed, squared, twice, triple

20.

"Twice the quantity of" means you will use ____________ to write the expression.

a)

addition

b)

subtraction

c)

division

d)

parenthesis

21.

Evaluate: 4=x/8

a)

2

b)

4

c)

32

d)

48

e)

8

22.

What is the value of: 1/2(8c-16)=4c-8

a)

c is not 2

b)

no solution

c)

0=-6

d)

Identity

e)

one solution

23.

Translate the sentence into an equation: “Eight more than four times a number is -12”

a)

8-4n=-12

b)

8+4/n=-12

c)

4n+8=12

d)

4n+8=-12

e)

4n-12=8

24.

Solve:

\frac{3}{5}h\ =27

a)

h = 27

b)

h = 135

c)

h = 45

d)

h = 16.2

25.

Solve:

$7+\frac{a}{3}=5$

a)

$a=-2$

b)

$a=-6$

c)

$a=3$

d)

$a=15$

26.

Solve the equation:
3(x - 1) = 2x + 9

a)

x = 12

b)

no solution

c)

x = 10

d)

x = 6

27.

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

a)

infinite solutions

b)

x = 1

c)

x = -1

d)

no solution

28.

Janeen's mother is 47. She is 26 years older than Janeen. Which equation can be used to find Janeen's age j?

a)

j + 26 = 47

b)

26j = 47

c)

j - 26 = 47

d)

47j = 26

29.

Which equation has x =2 as a solution?

a)

3 + x = 10

b)

11 + x = 13

c)

4x = 32

d)

5x =25

30.

a)

2

b)

4

c)

6

d)

8

31.

n+2=-14-n

a)

6

b)

8

c)

-8

32.

Solve the equation:
-5x = 25

a)

x = 20

b)

x = -20

c)

x = -5

d)

x = 5

33.

Which equation has w = 8 as the solution?

a)

8w= 64

b)

16w = 240

c)

16 - w = 9

d)

4 + w = 10

34.

Solve the proportion for n.

a)

18

b)

3

c)

2

d)

9

35.

Amina made a deposit of d dirhams in to her back account. Her old balance was AED100, and her new balance is AED280.

a)

d-100=280

b)

280-d=100

c)

100+d=280

d)

280+d=100

36.

Solve the equation. Check your solution.

a)

p = 80

b)

p = 45

c)

p = 180

d)

p = 5

37.

Solve the equation for x.

a)

6

b)

12

c)

0

d)

3

38.

the quotient of 12 and y plus 5 is 7

a)

(12 ÷ y) + 5 = 7

b)

(12 ÷ y) - 5 = 7

c)

(12 - y) + 5 = 7

d)

(12 + y) ÷ 5 = 7

39.

5(2x - 7) = 80

a)

x = 11.5

b)

x = 115

c)

x = 12

d)

x = 16

40.

Solve:
7x - 3x - 8 = 24

a)

8

b)

-8

c)

3.2

d)

4

41.

The length of a square can be determined by finding the square root of its area. If a square has an area of 81 m², what is the length of the square?

a)

8 m

b)

8.5 m

c)

9 m

d)

9.5 m

42.

Carlos completed x³ squats as part of his football workout. If x= 5, how many squats did he complete?

a)

10

b)

15

c)

25

d)

125

43.

The length of a side of a cube can be determined by finding the cube root of its volume. If a cube has a volume of 64 cm³, what is the length of a side?

a)

4 cm

b)

8 cm

c)

16 cm

d)

32 cm

44.

To determine the length of yarn needed for a project, Josie must solve $\frac{\sqrt{x}}{4}$
for x= 64. What is the solution?

a)

2

b)

4

c)

8

d)

16

45.

Mark multiplied a number by itself. He found a product of 30. What is the number, rounded to the nearest tenth?

a)

4.5

b)

5.4

c)

5.5

d)

15

46.

A square has an area of 50 square feet. What is the perimeter of the square, rounded to the nearest foot?

a)

7 ft

b)

28 ft

c)

49 ft

d)

100 ft

47.

A student is told that a moving car travels a distance x, where x, expressed in miles, is the solution to the equation (8 – x)² = 64. The student argues that the car can’t be moving, since x must equal zero. Which of the following describes the distance, x?

a)

A. The student is correct; x must equal zero.

b)

B. The student is incorrect; x can also be 8.

c)

C. The student is incorrect; x can also be 16.

d)

D. The student is incorrect; x can also be -8.

48.

A gallon has a volume of 231 cubic inches. If a gallon of milk was sold in a perfectly cubical container, to the nearest tenth of an inch, how high would the container be?

a)

6 inches

b)

6.1 inches

c)

6.2 inches

d)

6.3 inches

49.

Decide if each of the numbers listed below is a solution of the equation x³ = 512. Place a check mark to choose solution. The equation may have one solution, more than one solution, or no solution at all.

a)

-16

b)

-8

c)

8

d)

16

e)

32

50.

$\left(1\frac{2}{3}\right)^3=$

a)

$1\frac{8}{27}$

b)

$\frac{125}{27}$

c)

$\frac{25}{9}$

51.

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

a)

$-3+5$

b)

$9+125$

c)

$-3-5$

d)

$-9-125$

52.

Cube of an odd number is

a)

An odd number

b)

An even number

c)

A prime number

d)

None of the above

53.

Cube of an even number is..

a)

An even number

b)

An odd number

c)

A prime number

d)

None of the above

54.

$^3\sqrt{\frac{1000}{343}}=$

a)

100/7

b)

10/7

c)

10/49

d)

100/49

55.

$^3\sqrt{\frac{1}{216}}=$

a)

1/8

b)

1/6

c)

1/16

d)

1/216

56.

The inverse operation for SQUARING a number is finding the CUBE root?

a)

true

b)

false

57.

Find the square root.

a)

4/5

b)

2/3

c)

-4/5

d)

-2/3

58.

$3r^2+7=37$

a)

$\pm10$

b)

$\pm\sqrt{10}$

c)

$\sqrt{10}$

d)

$\pm5$

59.

$10x^2-6=1434$

a)

$\pm12$

b)

$\pm\sqrt{12}$

c)

$\pm2\sqrt{3}$

d)

$12$

60.

$49n^2+6=70$

a)

$\pm\frac{8}{7}$

b)

$\pm\sqrt{\frac{8}{7}}$

c)

$\frac{8}{7}$

d)

$\pm\frac{7}{8}$

61.

Simplify 5³⋅5⁴

a)

5⁷

b)

5⁻¹

c)

5¹²

d)

5

62.

Simplify (2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

63.

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

a)

add

b)

subtract

c)

multiply

d)

divide

64.

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

a)

add

b)

subtract

c)

multiply

d)

divide

65.

How would you write 4.3756 x 10⁴in standard form?

a)

437,560,000

b)

0.00043756

c)

43,756

d)

4,3756

66.

How would you write 0.0005 in scientific notation?

a)

50 x 10⁵

b)

5 x 10^-4

c)

5 x 10^-3

d)

.5 x 10³

67.

How do you write
8.317 x 10⁶in standard form?

a)

8, 371, 000

b)

83, 170, 000

c)

837, 100

d)

8, 317, 000

68.

Simplify using a positive exponent.
9^-3

a)

9³

b)

1/9^-3

c)

1/9³

d)

729

69.

Fill in the blank with the correct exponent to make the statement true.
3^{16 =}(3⁸)(3^_)

a)

2

b)

8

c)

4

d)

1

70.

When writing a number in scientific notation, the first number must be at least 1, but less than 10. (1 < x < 10)

a)

False

b)

True

71.

Scientific Notation is made up of two number parts. The second part must be an exponent with of base 10.

a)

True

b)

False

72.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

73.

Which is greater? 1.111 x 10¹⁵ or 9.999 x 10³ ?

a)

They are equivalent.

b)

There is no way to determine which is greater. The numbers are too big to understand.

c)

1.111 x 10¹⁵ is greater because of the larger exponent

d)

9.999 x 10³ is greater because 9.999 is larger than 1.111

74.

Simplify

a)

8^-9

b)

8^-3

c)

8³

d)

8⁹

75.

Which of the following is NOT equivalent to (2³)² ?

a)

2⁵

b)

2⁶

c)

64

d)

2³ x 2³

76.

The average person blink 2.88 x 10⁴ times a day. How many times does a person blink in year (365 days)? Write your answer in scientific notation

a)

367.88 x 10⁴

b)

1.0512 x 10⁷

c)

1051.2 x 10⁴

d)

3.6788 x 10⁷

77.

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

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

78.

The mean distance from the sun to Earth is 9.29 x 10⁷ miles. Jupiter's mean distance from the sun is 4.8388 x 10⁸ miles. What is the difference between these two distances in miles?

a)

4.3092 x 10¹

b)

3.9098 x 10⁷

c)

3.9098 x 10⁸

d)

5.7678 x 10⁸

79.

The mass of he sun is 1.989 x 10³⁰ kilograms. The mass of the earth is 5.98 x 10²⁴ kilograms. How many times bigger is the sun than the earth?

a)

3.326 x 10⁵

b)

3.326 x 10⁶

c)

1.99 x 10³⁰

d)

1.99 x 10⁶

80.

In Australia, the people use approximately 2,240,000,000 pounds of bread in a year. How can we write this number in scientific notation?

a)

2.240 x 10^-9

b)

224 x 10⁶

c)

2.2 x 10⁶

d)

2.240 x 10⁹

81.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

82.

Divide:
(6.9 x 10⁷) / (2.3 x 10^-3)

a)

3 x 10¹⁰

b)

3 x 10⁴

c)

3 x 10^-4

d)

3 x 10^-11

83.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

84.

a)

x⁴

b)

x⁸

c)

x¹²

d)

x²⁰

85.

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

a)

add

b)

subtract

c)

multiply

d)

divide

86.

Write $3.45\times10^{-3}$ in standard notation.

a)

3,450

b)

0.00345

c)

0.000000345

d)

0.345

87.

Write $9.06\times10^{-5}$ in standard notation.

a)

0.0000906

b)

0.906

c)

0.0096

d)

0.0000000906

88.

Write 0.00000202 in scientific notation.

a)

$2.02\times10^{-7}$

b)

$2.2\times10^{-6}$

c)

$2.02\times10^{-6}$

d)

$2\times10^6$

89.

Estimate:

$\sqrt{20}$

a)

Between 4.4 - 4.5

b)

Between 10.1 - 10.2

c)

Between 4.8 - 4.9

d)

Between 10.8 - 10.9

90.

$\frac{4.8\times10^8}{2.4\times10^6}$

a)

200

b)

20

c)

2000

d)

20000

91.

Find the next item in the pattern:
-3, 6, -12, 24, ...

a)

36

b)

-36

c)

48

d)

-48

92.

Generate the first 4 terms of the sequence with the following n^th term rule...

3n + 7

a)

10, 13, 16, 19...

b)

7, 10, 13, 16...

c)

10, 14, 18, 22...

d)

10, 17, 24, 31...

93.

Is this table a function or not a function?

a)

Function

b)

Not a Function

94.

a)

multiply by 4

b)

divide by 4

c)

add 30

d)

subtract 6

95.

What number belongs in the blank?
18,24,___,36,42

a)

28

b)

31

c)

30

d)

35

96.

What is the rule for this pattern?
32,36,40,44

a)

add 4

b)

multiply 2

c)

subtract 4

d)

divide by 2

97.

How would you describe this pattern's rule?
4, 11, 18, 25, 32, 39

a)

Add 8

b)

Add 6

c)

Subtract 8

d)

Add 7

98.

Give the next three terms in the following number pattern:
3; 5; 7; 9; ...

a)

10; 11; 12

b)

13; 15; 17

c)

10; 12; 14

d)

11; 13; 15

99.

Give the next three terms in the following number pattern:
-2; -6; -18; ...

a)

-36; -54; -72

b)

-54; -162; -486

c)

-27; -36; -54

d)

-72; -288; -1152

100.

Determine the equation connecting x and y in the given table.

a)

$y=x+2$

b)

$y=2x$

c)

$y=\frac{1}{2}x$

d)

$y=3x$

101.

Determine the value of a.

a)

39

b)

15

c)

26

d)

36

102.

Determine the value of b.

a)

100

b)

25

c)

26

d)

15

103.

Which of the following best represents the relationship of the table?

a)

y = -4x + 2

b)

y = -5x + 2

c)

y = -5x + 6

d)

y = -4x - 4

104.

What could be the rule the number machine uses?

a)

n + 5 = t

b)

n ÷ 5 = t

c)

n x 5 = t

d)

n – 5 = t

105.

For lunch, Amanda had a hamburger and some potato chips. The hamburger totaled 325 calories and each chip had 12 calories. Write a liner equation to represent the situation.

a)

y = 12 + 325

b)

y = 12x + 325

c)

y = 325 - 12x

d)

y = 325x + 12

106.

How many squares are in Figure 4?

a)

10

b)

11

c)

12

d)

13

e)

14

107.

How many squares are in Step 5?

a)

30

b)

31

c)

32

d)

33

e)

34

108.

How many counters would come next?

a)

5

b)

7

c)

9

d)

11

109.

What would be the next two figures in this pattern?

a)

star, star

b)

square, square

c)

star, square

d)

square, star

110.

Coach Benefield wrote the following number pattern: 37, 30, 23, 16,

What number would come next if the pattern continued?

a)

8

b)

7

c)

9

d)

10

111.

What are the missing numbers in this pattern?
23, 33, ___, 53, ___, 73

a)

32, 62

b)

42, 63

c)

43, 63

d)

42, 62

112.

Find the next number in the pattern.
10, 11, 9, 10, 8, ____

a)

12

b)

9

c)

10

d)

8

113.

Which choice uses the same subtraction rule as the pattern shown?

42,32,22,12,2

a)

29,22,15,8,1

b)

11,9,7,5,3

c)

39,30,21,12,3

d)

47,37,27,17,7

114.

80,___, 70, 65, 60, ___, 50
Is this a growing or repeating pattern?

a)

Growing

b)

Repeating

115.

What is the pattern growing by
10, 8, 6, 4, 2

a)

+2

b)

-2

c)

+5

d)

-5

116.

Which choice uses the same addition rule as the pattern shown?

5,12,19,26,33

a)

9,18,27,36,45

b)

6,15,24,33,42

c)

9,16,23,30,37

d)

9,14,19,24,29

117.

Given the following tile pattern, how many tiles would be in the 5th shape?

a)

b = 8

b)

b = 11

c)

b = 7

d)

b = 9

118.

How many blocks will be in the 4th term?

a)

The next term will have 16 blocks

b)

The next term will have 15 blocks.

c)

The next term will have 14 blocks.

d)

This is the end of the pattern.

119.

😝 ❤ 😝 ❤ 😝 ❤

a)

😝

b)

❤

120.

😝 😲 😝 😲 😝 😲 😝

a)

😝

b)

😲

121.

Derrick is 4 years older than his brother. The sum of their ages is 30. How old is Derrick?

a)

13

b)

17

c)

30

d)

5

122.

9 (x + 3) - 14x -15 = 52

a)

-8

b)

8

c)

7.5

d)

-9.8

123.

$2+3p=2+4p-p$

a)

$p=-4$

b)

$p=-9$

c)

All real numbers

d)

$p=-16$

124.

x + 6 = 7x - 42

a)

x=8

b)

x=20

c)

x=9

d)

x=15

125.

What is the solution to the equation 3(2x - 5) = x + 10?

a)

9

b)

6

c)

8

d)

5

126.

Solve:
C = 2πr, for r

a)

C/(2π) = r

b)

C + 2π = r

c)

C - 2π = r

d)

2πC = r

127.

ax + c = R
(solve for x)

a)

ax = R + c

b)

ax = R - c

c)

x = a(R-c)

d)

x = (R-c) / a

128.

Solve for x:

a)

x = yb - v

b)

x = by - v

c)

x = by + v

129.

Solve -2 = 4r + s for s.

a)

s = -2 + 4r

b)

s = 2 - 4r

c)

s = -2 - 4r

d)

s = 2 + 4r

130.

Find the solution.

8x\ +\ 4\ -10x\ =\ 3\ -\ 9x\ +\ 15

a)

x = 2

b)

x = -1

c)

x = 12

d)

x = 6

131.

Solve for w.

-4\left(3w\ +\ 4\right)\ -\ 14\ =\ 3\left(2w\ -\ 4\right)\ -\ 9w

a)

w = -4

b)

w = -2

c)

w = 1

d)

w = 5

132.

solve for x

a)

5

b)

-25

c)

15

d)

1/5

133.

$\frac{1}{5}\left(x-3\right)=\frac{3}{4}$

a)

27/4

b)

29/4

c)

31/4

d)

33/4

134.

Make and solve the equation:

Six friends all use $2 off coupons to buy themselves movie tickets. They spend a total of $42. What is the price of one movie ticket without the coupon?

a)

$7

b)

$8

c)

$9

d)

$10

135.

Which of the following is false with respect to an algebraic equation?

a)

An algebraic equation is an equality involving variables.

b)

The LHS of an algebraic equation is equal to its RHS for all values of the variables.

c)

An algebraic equation can have variables on both side of the equality sign.

d)

An algebraic equation can have one or more terms.

136.

What is the LCM (Least Common Multiple) that you would multiply everything by to get rid of the fractions?

\frac{3}{4}\left(x-4\right)\ +\ 3=\frac{1}{8}\left(x-16\right)\

a)

2

b)

4

c)

8

d)

12

137.

What would be the solution for this equation?

\frac{3}{4}\left(x-4\right)\ +\ 3=\frac{1}{8}\left(x-16\right)\

a)

$x=-32$

b)

$x=-\frac{16}{5}$

c)

The equation has no solution.

d)

$x=1$

138.

Solve for L. $A\ =\ \pi r^2+\pi rL$

a)

$\frac{A+\pi r^2}{\pi r}$

b)

$\frac{A-\pi r^2}{\pi r}$

c)

$\frac{A}{\pi r}-\pi r^2$

d)

$A-r$

139.

$pV=nRT$

solve for R

a)

$R=\frac{pV}{nT}$

b)

$R=\frac{p}{n}+\frac{V}{T}$

c)

$R=pV-nT$

d)

$R=\frac{(pV-n)}{T}$

140.

Solve the linear equation.

4 ( x - 9 ) - ( x - 12 ) = 2x - 15

a)

x = 33

b)

x = 11

c)

x = 9

d)

x = 3

MATH - HW SHEET 26

Total questions: 140

Worksheet time: 12hrs 40mins

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