Georgia Online Formative Assessment Resource (GOFAR)
6th Grade VMath Algebra Review
Name:____________________________
Date: ____________________________
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1. All the students in sixth grade went on a field trip. The teacher put the students into groups of 25
students each. The table shows the numbers of boys and girls in each group. The number of boys and the
number of girls in Group 5 is unknown.
Part A
Write an equation to represent the number of boys, b , and the number of girls, g , that are in each group.
Part B
The number of students in the Group 5 can be found by using this information.
● There were more girls than boys.
● The number of boys was 2 more than 40% of the total students in the group.
How many boys are in Group 5? How many girls are in Group 5? Show your work using the equation from
Part A.
Part C
Create a coordinate grid and graph the data from the table that show a relationship between the number of
boys and the number of girls in each group. Include labels for the x -axis and y -axis. What do you notice
about the points on the grid?
If you knew the value of the x -coordinate, how could you determine the value of the y -coordinate? Show
your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
2. A scientist found the distance a bug traveled in four minutes and recorded it in a table.
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Part A
Write an expression with a value equal to the total distance the bug traveled. Use t to represent the
amount of time passed.
Part B
A second bug traveled 1.5 times as far as the first bug did during each minute.
Write a new expression with a value equal to the total distance the second bug traveled. Show your work.
Part C
● Create a coordinate graph to represent the distance traveled for both bugs. Label both axes and
create a title for your graph.
● Use the information in the table for the first bug and use a solid line to represent the distance the
first bug traveled during the four minutes on the coordinate grid.
● Use a dashed line to represent the distance the second bug traveled during the four minutes on the
same coordinate grid.
How can the points
answer.
and
have the same y -coordinate but different x -coordinates? Explain your
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
3. The total amount of money the chess club needs to attend a chess tournament is $500. The inequality
shows the amount of money, m , the members of the chess club need to raise in order to be able to attend
the chess tournament.
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Part A
What values of m make the inequality true? Explain how you know your values are correct.
Part B
The members of the chess club want to raise 30% more than the total amount needed to attend the chess
tournament in order to purchase new chess sets for the club. What is the new total amount that the
members need? Show your work or explain your answer.
Part C
The list shows the amount of money raised by each member of the chess club.
What is the median amount of money raised? Show your work.
What is the mean amount of money raised? Show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
4. Mr. Stevenson decided to buy several cowboy hats. He made a table to show the price of hats.
Part A
Write an equation to show the cost, C , of the cowboy hats Mr. Stevenson bought. Use n to represent the
number of cowboy hats he bought.
Part B
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Mr. Stevenson has $160. What is the greatest number of cowboy hats Mr. Stevenson can buy? Show your
work or explain your answer.
Part C
What is the difference, in dollars, between the mean price and median price of a hat from the list?
Would it cost more to buy 7 cowboy hats or 7 of the hats priced at the median hat price? Explain your
answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
5. A neighborhood group makes welcome baskets for new families in the neighborhood. Each basket
contains muffins, coupons for local stores, and a map of the area. The table shows the number of each item
needed for five welcome baskets.
Part A
Using the information in the table, what is the ratio of number of coupons to the number of muffins per
basket? Explain your answer.
Part B
All the baskets will have the same ratio of items. Complete the table to show the total number of each type
of item needed to make 12 baskets and 30 baskets. Show your work.
Part C
The muffins placed in the baskets cost $1.25 each, but the neighborhood group gets a 20% discount if they
purchase one dozen or more. What is the cost of one dozen of muffins before the 20% discount is applied?
Show your work.
Part D
Write an expression that can be used to determine the cost of ddozen muffins, including the discount.
Evaluate your expression for
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task.
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Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
6. Ms. Henderson’s 5 art classes are turning in their final projects for the year. The table shows the
numbers and type of project turned in during her first 4 classes.
Part A
Write the ratio of paintings to sculptures for each class. What is the ratio of the total number of paintings to
the total number of the sculptures for all of the classes? Explain your answer.
Part B
Ms. Henderson has 24 students in her fifth art class. The ratio of paintings to sculptures in this class is the
same as the ratio of paintings to sculptures for her first four classes combined.
Use the ratio you found in Part A to determine how many students in her fifth class are turning in each type
of project. Show your work or explain your answer.
Part C
In past years, the final projects have been submitted to a city-wide art contest.
● In past years, between 5% and 10% of Ms. Henderson’s students who submitted paintings have won
prizes.
● More than 15% of her students who submitted sculptures have won prizes.
What is the minimum number of students for all 5 classes expected to win a prize for each type of project
based on past years? Show your work or explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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7. A hand is a measure used to describe a horse’s height. One hand is equivalent to four inches.
Part A
Complete the table to show n , the number of inches for h hands.
Part B
Write an equation to show the relationship between the number of hands, h , and the number of inches, n .
Part C
How would the values in the second column change if you converted hands, h , to feet, f ?
Complete the table to show the number of feet in hands.
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Write an equation to show the relationship between the number of hands, h , and the number of feet, f .
Part D
Tammy rode a horse that was at least 5 feet tall. What is the shortest the horse could be, in inches? What
is the shortest the horse could be, in hands? Show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
8. Which expression correctly uses the distributive property to rewrite the expression 7(y +5)?
A)5 + 7y
B)5(7 + y)
C)7y+ 35
D)12(7 + y)
9. Ralph simplified the expression
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Which of the following properties of the real numbers did Ralph use?
A)associative property of multiplication
B)commutative property of multiplication
C)distributive property
D)multiplicative identity property
10. Which ordered pair below will be a point on the graph of the equation
y = 2x + 3?
A)(2, 3)
B)(5, 1)
C)(3, 9)
D)(1, -1)
11. A car rental company will rent out a sport utility vehicle for $22.50 per day plus $0.50 per mile driven.
Gloria rented this vehicle for three days and was billed $200. How many miles did Gloria drive?
A)211.25 miles
B)223 miles
C)265 miles
D)272.5 miles
12. Susan buys 2 CDs. Each CD costs $10.99 plus 6% tax. How much change will Susan receive if she gives
the cashier $30.00?
A)$6.70
B)$7.70
C)$8.02
D)$23.30
13. Judy spent $4.55 on oranges that cost $0.65 each. If x = the number of oranges, what equation would
determine how many oranges Judy purchased?
A)$0.65x = $4.55
B)$4.55x =$0.65
C)
=x
D)$4.55 – $0.65 = x
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14. If
and
in which quadrant of the xy-plane does the point (r, s) lie?
A)quadrant I
B)quadrant II
C)quadrant III
D)quadrant IV
15. Gabriel is 2 years older than his sister, Leeann. Which of the following graphs correctly represents the
relationship between Gabriel's age and Leeann's age, in years?
A)
B)
C)
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D)
16.
Sampson finds that for every hour he lifts weights, he burns 400 calories. Which proportion should Sampson use t
A)
=
B)
=
C)
=
D)
=
17.
In a box of blocks, there are r red blocks, b blue blocks, and y yellow blocks. Which fraction expresses the ratio of
blocks?
A)
B)
C)
D)
18. What is the ratio of the length of a side of an equilateral triangle to its perimeter?
A)3 : 1
B)1 : 1
C)1 : 2
D)1 : 3
19.
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The recipe for a fruit salad calls for 5 bananas, 3 peaches, 2 apples, 1 pear, 8 strawberries, 1 cantaloupe,
and 2 oranges.
What is the ratio of peaches to the total?
A)1:22
B)2:22
C)3:22
D)8:22
20.
In Ms. Miller's class there are 18 girls and 10 boys. Find the ratio of boys to girls.
A)1:2
B)5:9
C)3:5
D)7:10
21.
On the high school cheerleading squad, there are 3 girls with blonde hair, 5 girls with brown hair and 1 girl
with red hair. Find the ratio of girls with blonde hair to girls with brown or red hair.
A)1:3
B)1:2
C)3:5
D)4:5
22. There are 30 red marbles and 150 blue marbles in a box. What is the ratio of blue marbles to
red marbles?
A)
B)
C)
D)
23. Nancydetermined that 48 out of the 108 students in tenth grade play a musical instrument.
What fraction of the students plays a musical instrument?
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A)
B)
C)
D)
24. Darnell caught 4 fish in 2 hours. At that rate, how many fish will he catch in 6 hours?
A)4 fish
B)8 fish
C)10 fish
D)12 fish
25. Find the next number in the pattern.
8, 64, 512, _____
A)568
B)960
C)1,024
D)4,096
26. How would you write
A)0.25
as a decimal?
B)0.35
C)0.75
D)0.85
27. If $55 of a $220 budget is spent on clothes, what percent of the budget is spent on clothes?
A)25%
B)55%
C)85%
D)95%
28. Old Faithful, the famous geyser in Yellowstone National Park, erupts every hour and sends 15,000
gallons of steam and boiling water into the air. At the end of one entire day, how many gallons of water
and steam would Old Faithful have sent into the air?
A)360,000 gallons
B)180,000 gallons
C)153,000 gallons
D)36,000 gallons
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29. The profits and losses of six different stores are shown in the table below.
Store
A
B
C
D
E
F
Net Profit/Loss $250 -$184 -$256 $198 $346 -$120
What is the range of the data for Net Profit/Loss among the six stores?
A)$602
B)$370
C)$148
D)$90
30.
Larry wants to visit his cousin who lives 320 miles away and expects to drive 55 miles per hour the entire way. W
house?
A)17 minutes
B)3 hours
C)5 hours
D)6 hours
31.
The first three figures in a pattern are shown below.
How many cubes should be used to make the seventh figure?
A)21
B)28
C)36
D)119
32. Pizzas take 20 minutes to cook. Four pizzas can be cooked at one time in the pizza oven. How long
would it take to cook 10 pizzas?
A)40 minutes
B)50 minutes
C)60 minutes
D)80 minutes
33. What is the next number in the following pattern?
18, 17, 15, 14, 12, 11, 9, ?
A)7
B)8
C)9
D)10
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34. In every carton of eggs, there are 12 eggs. If c equals the number of cartons and e equals the number
of eggs, which equation shows the direct proportion of cartons to eggs?
A)e = 12c
B)c = 12e
C)e = c + 12
D)c = e – 12
35.
A group of friends went on a hiking trip. The group recorded their progress on the graph. If the rate
remains the same, how far would the group have hiked after five hours?
A)5.5 miles
B)6.5 miles
C)7.5 miles
D)8.5 miles
36.
The graph shows the time it took Hannah to walk a certain distance. What was Hannah's constant of
variation?
A)100 feet per minute
B)200 feet per minute
C)500 feet per minute
D)1000 feet per minute
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37.
The graph represents the number of super balls, y, produced per second, x. Using the graph, determine the
ratio of super balls produced per second.
A)1 superballs/second
B)2 superballs/second
C)3 superballs/second
D)4 superballs/second
38.
Julie can make 12 chairs in 6 hours. What is Julie's constant of proportionality for making one chair?
A) hour
B) hour
C)1 hour
D)2 hours
39.
Jeanette's car uses 15 gallons of gas for every 360 miles she drives. How far can Jeanette's drive with 6
gallons of gas?
A)17 miles
B)25 miles
C)72 miles
D)144 miles
40.
For every 3 books Paige sells, she earns $25. How much money will Paige earn if she sells 11 books?
A)$6.81
B)$91.67
C)$125.37
D)$275.00
41.
Three-fourths of the members of student council are female. There are 36 females in student council. What
is the total membership?
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A)40
B)48
C)63
D)80
42.
In a town, a middle school has 45 classrooms. This amount is 30% of all the classrooms in the entire town.
How many total classrooms are in the town?
A)67
B)75
C)135
D)150
43.
One-third of the fish in an aquarium are blue. There are 10 blue fish in the aquarium. How many total fish
are in the aquarium?
A)13
B)10
C)30
D)60
44.
If the line containing these points is plotted on a coordinate plane, what should the graph look
like?
A)
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B)
C)
D)
45. At a golf course, a worker placed 216 golf balls equally into 9 buckets. What is the ratio of golf balls to
buckets?
A)
B)
C)
D)
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Answer Key :
1.
2.
3.
4.
5.
6.
7.
8. C)7y+ 35
9. C)distributive property
10. C)(3, 9)
11. C)265 miles
12. A)$6.70
13. A)$0.65x = $4.55
14. D)quadrant IV
15. A)
16. D)
=
17. D)
18. D)1 : 3
19. C)3:22
20. B)5:9
21. B)1:2
22. C)
23. C)
24. D)12 fish
25. D)4,096
26. C)0.75
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27. A)25%
28. A)360,000 gallons
29. A)$602
30. D)6 hours
31. C)36
32. C)60 minutes
33. B)8
34. A)e = 12c
35. D)8.5 miles
36. B)200 feet per minute
37. B)2 superballs/second
38. B) hour
39. D)144 miles
40. B)$91.67
41. B)48
42. D)150
43. C)30
44. A)
45. A)
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