Free Printable SUMMER -TEST 3 Algebra 1

Worksheets

SUMMER -TEST 3 Algebra 1

Total questions: 100

Worksheet time: 25hrs 50mins

Name

Class

Date

Solve the literal equation for the given variable.

2A/h

2/(h)

2Ah

Ah/2

Solve for a.

a = pw

a = p/w

a = w/p

a = w + p

Solve for v

C = xv + x

(C-x)/x = v

(C+x)/x = v

(-C-x)/x = v

(Cx)/x = v

(2.5+h)f

g=1

f(5+h)/2

(5f+h) / 2

b = 3A - a - c

b = -3A + a - c

b = -3A - a - c

b = 2A - c

Solve for h

V = πr²h for h

V/(πr²) = h

V - πr² = h

V + πr² = h

V/π = h

4w-10

-2w+10

2w-10

-4w + 10

Solve 2x - 3 = 1

-2

Solve 3x - 7 = 32

-13

-12

10.

Solve -5t + 9 = 24

-3

11.

Solve -3x + 5 = -16

-7

12.

Solve 2x -7 = -23

-8

-7

13.

Solve 9 + 3x = 10

2/3

1/3

-1/3

14.

Solve 12 - 6y = 24

-2

-3

15.

Solve 7 - 3y = 22

-5

-15

16.

Solve 12 - 6y = 24

-1

-2

-3

-4

17.

"difference of"

ADD

SUBTRACT

MULTIPLY

DIVIDE

18.

4 less than x

4 - x

x - 4

-4x

19.

m plus the product of 6 and n

m + 6n

m - 6 + n

6m + n

m + 6 + n

20.

How would you translate
x - 5 = 12 into words?

x - 5 = 12

The product of x and 5 is twelve

x less than 5 is 12

Five less than x is 12.

21.

Translate the sentence into an equation:
Four more than six times a number is 18.

4 + 6x = 18

4x + 6 = 18

6x + 4 = 18

not enough info

22.

Translate the sentence into an equation.
Seven subtracted from n is 18

n + 7 = 18

7 - n = 18

n - 7 = 18

n + 7 = 18n

23.

Write an algebraic expression for:
three times a number plus 16

3(16)+n

16n+3

3n+16

24.

Translate this phrase into an algebraic expression.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.

8 - 4m

8m - 4

8m + 4

4m - 8

25.

"total"

ADD

SUBTRACT

MULTIPLY

DIVIDE

26.

"times"

ADD

SUBTRACT

MULTIPLY

DIVIDE

27.

r less than 5

r - 5

5 - r

r + 5

5 + r

28.

Translate this phrase into an algebraic expression.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.

8 - 4m

8m - 4

8m + 4

4m - 8

29.

the sum of 3 times a number and 7

3 - 7n

3n - 7

3n + 7

3 / 7n

30.

5 more than the product of 7 and s

7s + 5

5 - 7 + s

7(s - 5)

5 - 7s

31.

Solve:
3(x - 2) = 18

6.7

-4

32.

8v - 4(v + 8) = 8

-4

33.

2x - 3 + 4x = 27

34.

6 (-6 -5v) = 84

-3

-5

-4

35.

1 = 1 + 6b + 2b

36.

6x + 3(-x + 11) = 3

-10

-15

37.

Solve -20 = -4x - 6x

x = -2

x = 10

x = 2

x = -10

38.

Solve the equation for y.
2x + 3y = 4

y = (4-2x)/3

y = (2x-4)/3

x = (4-3y)/2

y = (4-2x)/ -3

39.

Solve the equation for w. ^{x = w / a}

w = a / x

w = x / a

w = ax

x = wa

40.

Solve the equations for y.
2x - 4y = 7

y = (7+2x)/ -4

y = (7-2x) / 4

y = (7-2x)/ -4

y = (7+2x)/ 4

41.

Add the polynomials.

(2x + 5y) + (3x − 2y)

3x + 5y

5x + 3y

5x + 7y

7xy + 1xy

42.

Find the sum.

(3y² + y³ − 5) + (4y² − 4y + 2y³ + 8)

3y³+ 7y²− 4y + 3

4y² + 3y³ − y + 3

-y⁴ + 2y³− y − 4

4y³+ 3y²− 3y + 1

43.

(x³− x²+ 4) − (3x³− 2x²+ 3)

-2x³− 3x²+ 7

-2x³+ x²+ 1

2x³− 3x³− 1

4x³− 3x²+ 7

44.

Simplify each expression.

(6b³ + 6 − b⁴) − (8b³ − 6b⁴ + 2)

4b⁴ − 2b³ + 7

5b⁴ − 2b³ + 4

b⁴ − 2b³ + 7

5b⁴ − 2b³ + 7

45.

Simplify:

2x ( -2x − 3)

-4x − 3

x² − 3

-4x² − 6x

-4x − 6

46.

(x +2)(x + 3)

x² + 5x + 6

x² + x + 6

x² + 5x + 5

x² + 6x + 6

47.

Multiply

(4x + 3)(2x − 1)

8x²− 2x − 3

8x − 3

8x²+ 6x − 3

8x²+ 2x − 3

48.

(x − 3)(x²+ 2x + 7)

x³− x²+ x − 21

x³+ 5x + 13x − 21

x³− 3x²+ 7x − 21

x²+ 2x − 3

49.

Find the Quotient

(2x³ − 5x² − 3x + 7) ÷ (x − 2)

2x²− 9x + 15

2x² − x − 5

2x² − 9x − 21

2x² + x + 5

50.

Find the remainder

(2x³ − 5x − 7) ÷ (x + 2)

-9

-13

-1

51.

Add the polynomials.

(2x + 5y) + (3x − 2y)

3x + 5y

5x + 3y

5x + 7y

7xy + 1xy

52.

Find the sum.

(3y² + y³ − 5) + (4y² − 4y + 2y³ + 8)

3y³+ 7y²− 4y + 3

4y² + 3y³ − y + 3

-y⁴ + 2y³− y − 4

4y³+ 3y²− 3y + 1

53.

(x³− x²+ 4) − (3x³− 2x²+ 3)

-2x³− 3x²+ 7

-2x³+ x²+ 1

2x³− 3x³− 1

4x³− 3x²+ 7

54.

Simplify each expression.

(6b³ + 6 − b⁴) − (8b³ − 6b⁴ + 2)

4b⁴ − 2b³ + 7

5b⁴ − 2b³ + 4

b⁴ − 2b³ + 7

5b⁴ − 2b³ + 7

55.

Simplify:

2x ( -2x − 3)

-4x − 3

x² − 3

-4x² − 6x

-4x − 6

56.

(x +2)(x + 3)

x² + 5x + 6

x² + x + 6

x² + 5x + 5

x² + 6x + 6

57.

Multiply

(4x + 3)(2x − 1)

8x²− 2x − 3

8x − 3

8x²+ 6x − 3

8x²+ 2x − 3

58.

(x − 3)(x²+ 2x + 7)

x³− x²+ x − 21

x³+ 5x + 13x − 21

x³− 3x²+ 7x − 21

x²+ 2x − 3

59.

Find the Quotient

(2x³ − 5x² − 3x + 7) ÷ (x − 2)

2x²− 9x + 15

2x² − x − 5

2x² − 9x − 21

2x² + x + 5

60.

Find the remainder

(2x³ − 5x − 7) ÷ (x + 2)

-9

-13

-1

61.

The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person whose mass is 75 kg?

50 kg water

72 kg water

94 kg water

150 kg water

62.

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

y=1344x

y=100x

y=5.25x

y=4/21x

63.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

58.5

64.

If y = 15 when x = 12 find y when x = 32.

-40

-5

65.

Is the given table a direct variation? If so, what is the constant?

Yes; 1/4

Yes; 4

Yes; 2

66.

What is the equation of the line in the graph?

y = 3

x = 3

x = 0

67.

Which equation represents the following graph?

y = 3x + 2

y = -2x + 3

y = 2x + 3

y = -3x + 2

68.

What is the function of the table?

y=3x+1

y=4x-2

y=x+1

y=x+7

69.

y=x-6
What is the missing number?

70.

What is the equation of the linear function?

y = -3x + 10

y = -3x + 16

y = 3x + 10

y = 3x + 16

71.

Which equation matches the table?

y = x

y = 5x

y = x - 4

y = x + 4

72.

Which situation can be represented by y=12x-4?
*Hint: Pay attention to your sign for your y-intercept*

The number of eggs, y, in x dozen eggs for sale after 4 dozen eggs are sold

The cost, y, of buying x movie tickets that sell for $8 each

The cost, y, after a $4 discount, of buying x T-shirts that sell for $12 each

The number of inches, y, in an x-foot-tall tree after cutting off 4 feet

73.

Frank opened a savings account. He already deposited $400. He plans to save $20 each month and his mom will help him out and save $5 each month. Which equation could be used to find A, the total amount in his account after x months?

y = 400x + 20

y = 25x + 400

y = (400+5)x + 20

y = 25(400x + 5)

74.

A fitness club opens with 80 members. Each month the membership increases by 15 members. Which equation represents the relationship between the number of months the club has been opened, x, and the total fitness club membership, y?

y=15x

y=15x+80

y=x+15

y=80x+15

75.

Which of the following situations could be descried by the equation y= -25x + 120

There are 120 people in the football stadium, and 25 more are entering each hour.

A plumber charges $25 for a house call and $120 per hour.

A teacher has 120 students. Her third period has 25 students

There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

76.

Randy charges his tenants $400 each month to rent his houses plus $600 security deposit. In the new year, the property taxes increased on the area where he rents so as a result he must increase the rate of change by $25 to ensure his profits are not harmed. What equation best represents how much his tenants will now have to pay?

y = 425x + 600

y = 425 + 600x

y = 400x + 625

y = 400 + 625x

77.

What does the slope represent in this situation?

The sloth runs 1 feet in 3 minutes

The sloth runs 3 feet in 1 minute

The sloth runs fast

The sloth runs 6 feet in 1 minute

78.

At what rate did the rain fall?

2 cm per hour

¹/₄ cm per hour

¹/₂ cm per hour

4 cm per hour

79.

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

80.

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

infinite solutions

x = 1

x = -1

no solution

81.

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

no solution

infinite solutions

x = 6

x = 0

82.

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation.

g(x) is shifted up 6 units

g(x) is shifted down 6 units

g(x) is shifted left 6 units

g(x) is shifted right 6 units

83.

A student graphed f(x) = x and g(x) = ⅓f(x). Which statement is true?

The graph of f is steeper than the graph of g.

The graph of f is less steep than the graph of g.

The graph of f is shifted 2 units up to create the graph of g.

The graph of f is shifted 2 units to the right to create the graph of g.

84.

Describe the transformation from the parent function y = x to the new function y = 3x + 5

Steeper; Shift up 5 units

Steeper; Shift down 5 units

Flatter; Shift up 5 units

Flatter; Shift down 5 units

85.

Where is the y-intercept?

3/4

-3/4

86.

What is the y intercept of this graph?

-2

87.

Write in slope intercept form
5x - 3y = -9

y = (5/3)x - 3

y = (5/3)x + 9

y = (5/3)x + 3

y = (3/5)x + 3

88.

what is the slope intercept form for the equation -2x + 8y = 2

y = -2x + 8

y = 1/4x + 1/4

y = -1/4x - 1/4x

y = 2/8x + 4

89.

y=-3x+1

y=3x+1

y=1/3x+1

y=-1/3x-1

90.

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

$10

$15

$20

91.

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

Sugar Cookies $5
Oatmeal Cookies $3

Sugar Cookies $4
Oatmeal Cookies $8

Sugar Cookies $2
Oatmeal Cookies $6

Sugar Cookies $3
Oatmeal Cookies $6

92.

-x + 2y = 3

93.

What is the solution?

(1, -1)

(-1, 1)

(0, -2)

(0, 1)

94.

Solve the system of equations.
y = 4x+1
3x + 2y = 13

(1, 5)

(5, 1)

(0.25, 2)

∅

95.

Solve for x and y
3x + 2y = 16
7x + y = 19

(-2,5)

(-2,-5)

(2,-5)

(2,5)

96.

Find the slope of the line that passes through:
(2, 4) and (6, 12)

1/2

-1/2

-2

97.

Find the slope of the line that passes through:
(10, 1) and (5, 2)

1/5

-1/5

-5

98.

What is the RANGE?

0 ≤ x < 3

0 < y ≤ 3

-2 ≤ y < 1

-2 ≤ y ≤ 1

99.

What is the DOMAIN?

0 ≤ x < 3

0 < x ≤ 3

-2 ≤ x ≤ 1

-2 ≤ y ≤ 1

100.

Solve:
7x + 19 = -2x + 55

14.8

8.2

-4

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SUMMER -TEST 3 Algebra 1

Total questions: 100

Worksheet time: 25hrs 50mins

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