Name: _____________________________________ Due Date: 1- 4-15 Pd: ____
Units 1-4 Benchmark Study Guide
Students use this guide to prepare for your semester exam; it will take place Jan 7-8.
YOU MUST SHOW YOUR THINKING/WORK TO GET FULL CREDIT ON EACH QUESTION!! (2 PTS EACH)
Write the rational number as a decimal.
1. 
3
11
̅̅̅̅
A. 0. 27
̅̅̅̅
B. −0. 27
C. 0.311
D. −3.11
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2. – 3
13
20
A. 0.65
B. -0.65
C. 3.65
D. -3.65
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3.
2
5
A. 0.25
B. 0.4
C. 0.8
D. 0.2
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13
4. − 100
A. -0.13
B. 1.3
C. 0.13
D. -0.013
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Add or subtract. Write fractions in simplest form.
5. 5.73  3.56
A. 2.17
B. 9.29
C. -9.29
D. -2.17
1
6. 
5
1
 2
3
3
2
A. −4
B. − 3
C. 4
D.
2
3
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2
1
7. 2 5 − 3 2
1
9
A. 1 10
B. 5 10
1
9
C. −1 10
D. −5 10
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3
1
full. After breakfast the jug is
full. Find the difference of the amounts
12
4
before breakfast and after breakfast.
8.A gallon jug of milk is
A.
C.
2
B.
3
1
D.
16
5
6
7
12
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9.You buy a bag of dog food for $12.59 and a bottle of dog shampoo for $4.75. How much more did the
dog food cost than the shampoo?
A. $4.59
B. $17.18
C.$12.00
D. $7.84
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Multiply. Write fractions in simplest form.
 2 
 5 
1
4
10.    1 
A. - ½
B. ¾
C. ½
D. – ¾
2
11. 0.15   0.6
A. 0.09
B. -0.09
C. 0.9
D. -0.9
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2
12. A recipe calls for 1 3 cups of sugar. If you want to triple the recipe how much sugar do you need?
2
A. 3 3 cups
B. 6 cups
C. 5 cups
D. 5 3 cups
1
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Divide. Write fractions in simplest form.
13.  4.2  12
A. -2.85714
B. -0.35
C. 0.35
D. 2.85714
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14. 
A.
C.
2  8
  
7  21 
16
147
16
B. – 147
3
3
D. – 4
4
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15.How many
2
-ounce packages of peanuts can be made with 8 ounces of peanuts?
3
A. 5
B. 12
C. 8
D. 15
Mixed Problem Solving:
16. A 10.5-gallon aquarium is
A. 7 gallons
2
full. How many more gallons of water does it take to fill the aquarium?
3
B. 3.5 gallons
3
C. 15 ¾ gallons
D. 10 gallons
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17. Your bank account has a balance of $45.24. This is $51.35 more than yesterday. What was your
account balance yesterday?
A. $96.59
B. $6.11
C. -$96.59
D. -$6.11
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18. It costs $2.75 to enter an arcade. Each game costs $1.25. You have $14. How many games can you
play?
A. 12
B. 11
C. 10
D. 9
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19. How many 0.45-ounce packages of cinnamon can be made with 3.15 ounces of cinnamon?
A. 1 ½
B. 3.6
C. 3
D. 7
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20. On Monday Kayla ran 1 ½ miles and on Tuesday she ran 2 ¼ miles. How much further did she run
on Tuesday?
A. 1 ¾
B. ½
C. 3 ¾
D. ¾
21. Solve the following equation and choose the correct solution for n.
9n + 7 = 61
22. Portia is reading a novel that has a total of 363 pages. So far, she has read 195 pages. Portia is
reading at an average rate of 28 pages per hour. If she continues reading at this rate, how many
more hours must she read to finish this novel?
a. 6 hours
b. 7 hours
c. 8 hours
d. 9 hours
e. 10 hours
4
23. Factor out the following expression using the Greatest Common Factor:
24x –72
a. 24(x - 72)
b. 12(2x – 6) c. 12(– 2x + 6)
d. 9(15x –8)
e. –72(24x)
24. What is the solution to the inequality shown below?
–2x + 3 > 7
a. x < –5
b. x < –2
c. x > 2
d. x < 3
d. x > –2
25. Simplify the expression using the distributive property and combining like terms.
–10y + 3(4y + 10x)
26. Simplify:
(– 9c –12) – (2c – 4)
a. –11c – 8
b. –7c – 16
c. –11c – 16
d. –7c – 8
27. The Armstrong family went to dinner, and spent “x” dollars on food and drinks. If they left a
20% tip, which of the following expressions could be used to calculate the cost of the meal
including tip?
I. 0.2x
II. x + 0.2
a. II and IV
III. x + 0.2x
b. III and V
c. IV and VI
IV. x – 0.2x
V. 1.2x
d. I and II
e. IV and V
VI. 0.8x
28. Which expressions can be used to represent the perimeter(P) and area(A) of the rectangle
below?
7
3m + 5
a. P = 20m + 24
a = 12m + 15
b. p = 6m + 24
a = 10m + 12
c. p = 3m + 12
a = 21m + 35
d. p = 6m + 24
a = 21m + 35
5
29. Brad bought a skateboard
for $2 less than half its original
price. If he paid $21.50, which
skateboard did he buy?
a.
b.
c.
d.
Skateboard
Go Green
Speedster
Up and Down
With the Flow
Price ($)
45
47
43
41
Go green
Speedster
Up and Down
With the Flow
30. Marilyn bought a dress that was 15% off the original price. If “d” represents the original cost of
the dress, which expressions could be used to find the price Marilyn pays for the dress after the
discount?
I. d – 15
a. II and IV
II. d – 0.15d
b. I and V
III. 1.15d
IV. 0.85d
c. III and VI
V. 1 – 0.85d
VI. 0.85d + 1
d. II and III
e. I and V
31. The perimeter of the equilateral (all sides are the same length) triangle EFG can be
represented by the expression 15x – 3. Which expression could be used to represent each side
length of the triangle?
a. 3x – 1
b. 5x + 1
c. 2x + 5
d. 5x – 1
32. Which inequality has the solution graphed on the number-­­line below:
a. –4x – 5 ≤ –1
b. 3x + 7 ≥ 4
c. –5x + 4 ≥ 9
d. 6x – 10 ≤–4
6
33. The perimeter of a rectangle is 60cm. The length of the rectangle is 16 cm. Which equation
and solution would be used to calculate the width of the rectangle?
a. 2w + 32 = 60 ; w = 14
b. 32w + 16 = 60; w = 1.375
c. 32 – 2w = 60; w = 24
d. 2w + 16 = 60; w = 22
34. As sales employee, you are paid $75.00 per week, plus an additional $5.00 per sale. This week
you have set a goal to make at least $130.00. Choose an inequality that represents the number of
sales you need to make, and describes the solution set.
a. 75x + 5 ≥ 130; you must make 11 or more sales to reach your goal.
b. 5x + 75 ≥ 130; you must make 11 or more sales to reach your goal.
c. 5x + 75 ≤ 130; you must make 11 or less sales to reach your goal.
d. 75x – 130 ≤ 5; You must make exactly 11 sales to reach your goal.
35. Find the solution to the equation: ⅗x – 12 = –3
36. A local band is asked to play at the town’s Halloween festival. They will earn $100 plus an
additional 15% of ticket sales. Which of the following equations could be used to calculate “e”; the
bands total earnings if “t” represents the number of tickets sold?
a. e = 100t +15
b. e = 100 + 15t
c. e = 100 + 0.15t
d. t = 100e + 0.15
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37. Four women are training for a marathon. Each expression below represents the total distance
that each woman ran one day. Let “d” represent their total distance, and “m” represent the length
of a marathon. Which women ran the farthest?
a. Molly: d = 0.65m
b. Pamela: d = m – 0.2m
c. Angie: d = 0.7m
d. Lindsay: d = m – 0.36m
38. A bench is being centered on a wall. The wall is 2.7 m long and the bench is 1.8 m wide. Write
an equation to match the situation and find how much of the wall should be on each side of the
bench? Draw a picture to help you.
a. 2.7 - 1.8x = 2; 0.5 m on each side
b. 2x + 1.8 = 2.7; 0.45 m on each side
c. 2x - 1.8 = 2.7; 1.75 m on each side
d. 2.7 - 2x = 1.8; 0.55 m on each side
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