Name:___________________________________
Review for Common Assessment Chapters 5, 6, and 7 (7th Gr)
1. A taxicab company charges $3.50 for each trip plus an additional $2.75 per mile traveled.
a.
Complete the table.
Miles
Traveled
Trip Charge
Mileage
Charge
Total Cost
6
$3.50
$16.50
$20.00
10
$3.50
18
$49.50
b.
Write an algebraic expression to represent the total cost.
c.
How much would it cost to ride a cab 5 miles?
2. Use the pan balance to answer each question.
a.
What will balance 1 rectangle? Explain your strategy.
b.
Use symbols to rewrite the representation shown on the balance. Let
determine what balances x.
3.
4. Evaluate the expression
for for
.
5. Solve 7x + 5 = −9 and verify your solution.
Fill in the unknown numbers to make each number sentence true.
6.
7.
=x and
=1 unit.Then,
8.
−3b + 4
b
4
−2
1
−5
Calculate each quotient.
9.
The table gives the lowest recorded temperature in five U.S. cities. Use this table to answer each question.
Lowest Recorded Temperatures (°°F)
Honolulu, HI
Huron, SD
Mobile, AL
Norfolk, VA
St. Louis, MO
53
−41
3
−3
−18
10. The lowest temperature recorded in Lexington, Kentucky, was 7 times the lowest temperature recorded in Norfolk.
What was Lexington’s lowest temperature?
Determine the unknown number.
11.
12.
__________
___________
Calculate each product or quotient.
13.
14. For each step of the simplification of the expression, identify the operation or property applied.
Number Property/Operation
15. Evaluate the expression
for
16.
Use the Distributive Property to rewrite each expression in its equivalent form.
17.
Rewrite each expression by factoring out the greatest common factor.
18. 5x + 15
19. 18r2 − 36r
Simplify each expression.
20. −5(7x − 9) − 22
Rewrite each expression by factoring out the greatest common factor.
21. 10pq + 8p
Simplify each expression by combining like terms.
22. 13p − 4p + 6q
23. What is a number that when you divide it by 3 and subtract 8 from the quotient, you get 12?
24. Solve −4x + 7 ≥ −5. Then, graph the solution on a number line.
Draw a two-color counter model to determine each product. Describe the expression in words.
25.
__________
26.
_____________
Complete a number line representation to determine each product.
27.
___________
28.
______________
Write each expression as a repeated addition sentence.
29.
Calculate each product.
30.
31.
Calculate each quotient.
32.
33.
For each step of the simplification of the expression, identify the operation or property applied.
34.
Solve each problem.
35. Tomas needs to cut a 15-foot steel pipe into
36. Eight divers recover
-foot pieces. How many
-foot pieces can he cut from the pipe?
ounces of gold from a sunken ship. How many ounces of gold will each diver get if they
divide the gold equally?
Evaluate each expression for the given value.
37. Evaluate
m for
38. Evaluate
for
.
.
Write the term that best completes each statement.
39. A ___________________ neither terminates nor repeats.
40. A _________________ has a finite number of digits, meaning that the decimal will end, or terminate.
41. ____________________can be used to signify the repeating digits in a repeating decimal.
42. A ____________________ is a decimal in which a digit, or a group of digits, repeats without end.
43. A _______________________ is a decimal that continues without end.
Convert each fraction to a decimal. Classify the decimal as terminating, non-terminating, repeating, or non-repeating.
If the decimal repeats, rewrite it using bar notation.
44.
45.
Define a variable and write an algebraic expression for each problem. Evaluate the expression for the given values.
46. The skating rink is running a promotion on skating lessons. For every ten lessons you take, you get one free lesson. If
you have already taken 4 lessons, how many free lessons will you get if you take:
a.
16 more lessons?
Evaluate each algebraic expression.
47.
a.
for
48.
a.
Complete each table.
49.
3b + 14
b
−5
−3
0
4
50.
v
1
2
5
−3.25
6.75 − 6v
Use the Distributive Property to rewrite each expression in its equivalent form.
51.
Rewrite each expression by factoring out the greatest common factor.
52.
Simplify each expression by combining like terms. If the expression is already simplified, state how you know.
53. −5y + 2y
Evaluate each expression for the given value. Choose whether or not to factor before evaluating.
54.
Evaluate each expression for the given value. Choose whether or not to combine like terms before evaluating.
55.
Determine whether the two expressions in each may be equivalent by evaluating for the given value.
56.
Determine whether the two expressions in each are equivalent by simplifying.
57.
Draw a picture to represent each situation. Label the unknown parts with variables and the known parts with their
values. Solve the problem and write an equation to represent the situation.
58. Lamar, Harris, and Tyler ran a 15-mile relay race as a team. Tyler ran 3 miles farther than Harris, and Lamar ran twice
as far as Harris. How many miles was each boy’s leg of the race?
Problem Set
Determine what will balance one rectangle. Explain your solution. Then rewrite each representation as an equation.
59.
Solve each two-step equation. State the inverse operations, in the correct order of operations, you used to isolate the
variable. Check your solution.
60. 72 = 5h + 22
Solve each riddle using equations.
61. What is a number that when you multiply it by 7 and add 25 to the product, you get 46?
Problem Set
Write a sentence to describe how to apply inverse operations to solve each equation. Then, solve the equation and
verify your solution.
62.
Write an equation to represent each situation. Define your variables, solve the equation, and verify your solution.
63. The student council ordered 1000 pencils embossed with the school name to give to honor roll
students. If they give each honor roll student two pencils and they have 840 pencils left after the first quarter, how
many students are on the honor roll in the first quarter?
64. Javier has a collection of 125 comic books. He gives each of his 3 friends the same number of
comic books and keeps his favorite 38 comic books for himself. How many comic books did he give to each of his
friends?
Solve each equation using the Distributive Property.
65.
66.
Write an equation to represent each situation. Define your variables and solve the equation.
67. Susana bought a laptop for $500. It was marked $50 off because it was out of the box and slightly scratched. She also
got a 25% student discount, which was taken off of the original price. What was the original price of the laptop?
A list of possible solutions for each inequality is shown. Choose the solutions that make the inequality true. Then, list
three additional solutions to the inequality.
68.
69.
Solve each inequality and then graph the solution.
70. 8x > 56
71. 2x + 4 ≤ 20
72. −500 ≤ 11x − 60
Review for Common Assessment Chapters 5, 6, and 7 (7th Gr)
Answer Section
1. a.
b.
Miles
Traveled
Trip Charge
Mileage Charge
Total Cost
6
$3.50
$16.50
$20.00
10
$3.50
$27.50
$31.00
18
$3.50
$49.50
$53.00
Let x represent the number of miles traveled.
c.
It will cost $17.25
2. a.
Four squares will balance 1 rectangle.
I subtracted 5 squares from each side, which left 2 rectangles on one side and 8 squares on the other
side. Then, I divided 8 squares into 2 equal groups of 4.
b.
3.
4.
5.
6.
−6
7.
−27
8.
9.
10. −21°F
11. 20
12. −8
13.
b
−3b + 4
4
−8
−2
10
1
1
−5
19
14.
Number Property/Operation
Commutative Property of Addition
Addition
Addition
15.
16.
17.
18. 5(x + 3)
19. 18r ( r − 2)
20.
21. 2p(5q + 4)
22. 9p + 6q
23.
The number is 60.
24.
25. −12
The expression
26. −10
The expression
27. −15
means 2 groups of (−6).
means the opposite of 2 groups of 5.
28. 15
29.
30.
31.
32.
33.
34.
35.
Tomas can cut 6 pieces from the pipe.
36.
Each diver will get
37.
38.
ounces of gold.
39. non-repeating decimal
40. terminating decimal
41. Bar notation
42. repeating decimal
43. non-terminating decimal
44. The decimal equivalent is 0.15. The decimal is terminating.
45. The decimal equivalent is 0.108108… or
. The decimal is non-terminatingand repeating.
46.
Let a represent the number of additional lessons you take;
a.
You will get 2 free lessons with 16 more lessons
47. a.
48. a.
49.
b
3b + 14
−5
−1
−3
5
0
14
4
26
50.
51.
52.
v
1
2
5
−3.25
6.75 − 6v
0.75
−5.25
−23.25
26.25
53. −3y
54.
55.
56.
. The expressions may be equivalent.
57.
. The expressions are not equivalent.
58.
Harris ran 3 miles, and Lamar and Tyler each ran 6 miles.
59. I subtracted 2 squares from each side which left 3 rectangles on one side and 18 squares on the other side.
Then, I divided each side by 3 which left 1 rectangle on one side and 6 squares on the other side.
60. Subtract first, and then divide.
Check:
61.
The number is 3.
62. First add 12 to each side, then divide each side by −5.
Verify the solution by substituting −6 for x in the equation.
63. 1000 − 2s = 840
Let s represent the number of honor roll students.
There are 80 students on the honor roll in the first quarter.
Verify the solution by substituting 80 for s in the equation.
64.
Let c represent the number of comic books each friend received.
Javier gives each of his friends 29 comic books.
Verify the solution by substituting 29 for c in the equation.
65.
66.
67.
Let x represent the original price of the laptop.
The original price of the laptop was $733.33.
68. The numbers −2, −1, 0, 1, 2, 3, 4, and 5 make the inequality true.
Answers will vary. Three additional solutions for the inequality are −3, −4, and −5.
69. The number 7 makes the inequality true.
Answers will vary. Three additional solutions for the inequality are 8, 9, and 10.
70.
71.
72.