7th grade Math
Georgia CRCT
Practice Study Guide
CCGPS Domain
/Algebra
(54 Questions )
Name: ______
Teacher: ______Period: _____
Grade: ______
* Show WORK on every problem *
“Answers Only” will NOT be accepted!!!
Standard
MCC7.EE.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients
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1.Simplify the expression: 45 + 16 2 4 – 6.
a. 24.5b. 13.25c. 47d. 29
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2.Simplify the expression:
a. –12b. 76c. 100d. 64
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3. Simplify the expression: ½(3³ + 7)
a. 8b. 17c. 44d. 5
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4. What is the value of this expression: a + b²
When a = –3 and b = 5 ?
a. / –28 / c. / 22b. / –13 / d. / 28
5. Which is equivalent to the expression below?
8p + 3 – 3p – 2 + 7w + 4
a. 12p + 9b. 5p + 7wc. 5p + 7w + 5 d. 11p + 1
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6.Write an equivalent expression for 3(x + 5) – 2
a. 8x + 3b. 15x – 2c. 3x + 13d. 8x – 2
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7.Subtract. 8 + 8w – (3w – 4)
a. 5w + 12b. 11w + 4c. 5w + 4d. 11w – 4
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8. Which of the following shows a simplified version of this expression?
2k + (–3h) – 6k + 2h
a. –4k – 2hb. –4k – hc. 4k – 5hd. 4k – h
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9. An equilateral triangle has a perimeter of 6x + 15. What is the length of each of the sides of the triangle?
a. 3x + 3b. 2x + 5c. 5x + 2d. 2x + 3
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Standard
MCC7.EE.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05ameans that “increase by 5%” is the same as “multiply by 1.05.”
MCC7.EE.4
Use variables to represent quantities in a real‐world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
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Use the following Key Words to help you translate phrases or problem situation into algebraic expressions for problems 10 - 12.
10. Which expression represents the phrase below?
74 less than a number n
a. 74 – nb. n ÷ 74c. n – 74d. 74 ÷ n
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11. If n stands for the unknown number, which expression represents the phrase below?
the sum of a number and eight, divided by four
a. n + b. c. d. + 4
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12. The number of comic books that Juan collected this year is 7 less than half the number of comic books he collected last year. He collected c comic books last year. Which expression represents the number of comic books he collected this year?
a. c –b. 7 –c. c –d. – 7
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13.Jamie and Ted both get paid an equal hourly wage of $9 per hour. This week, Ted made an additional $27 in overtime. Write an expression that represents the weekly wages of both if J = the number of hours that Jamie worked this week and T = the number of hours Ted worked this week?
a. 9 + J + T + 27b. 9(J – T) + 27c. 9J + (9T + 27)d. 9 – J + 9 – T + 27
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14.Maria bought a sweater that cost d dollars. She paid the clerk $40.00. She received $5.19 in change. Which equation represents this situation?
a. / 40.00 – d = 5.19 / c. / d – 40.00 = 5.19b. / 40.00 + d = 5.19 / d. / d – 5.19 = 40.00
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15. This season, the number of points Chris scored was 36 less than 4 times the number Paul scored. Chris scored 64 points this season. The equation below represents this situation.
4n – 36 = 64
What does n represent is this equation?
a. / the number of points Chris scored / c. / how many more points Chris scored than Paulb. / the number of points Paul scored / d. / how many points Chris and Paul scored in all
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16. The Johnson family stayed at a hotel for n nights. The cost was $75 per night plus a one-time fee of $25 because they brought their dog. Which expression represents the total cost of their hotel stay?
a. 75n + 25nb. 75n + 25c. 75+ 25nd. 75 + 25 + n
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17. Sally bought 5 books. Each book was the same price. After using a $15-off coupon, the total charge
was $30.
a. 5b + 15 = 30 b. 15b – 5 = 30c. 15b + 5 = 30d. 5b – 15 = 30
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18.Steve had r rocks in his collection. He separated his rocks into 5 equal piles. He now has 20 rocks in each pile. Which equation represents this situation?
a. r – 5 = 20b. r ÷ 5 = 20c. r + 5 = 20d. r · 5 = 20
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19. Annie had $26 dollars to spend on school supplies. After buying 10 pens, she had $14.30 left. How much did each pen cost?
a. $1.17b. $2.60c. $1.43d. $2.00
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20. The sum of three consecutive even numbers is 72. What is the correct equation? (n = number)
a. / n + 1 + n + 2 + n + 3 = 72 / c. / n + 2 + n + 4 + n + 6 = 72b. / 3n = 72 / d. / 72 ÷ 3n
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21.331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? (Use the box below to help you solve)
a. 54b. 64c. 42d. 49
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22.Taylor had $23 to spend on six notebooks. After buying them she had $11. How much did each notebook cost? (Use the box below to help you solve)
a. $4b. $6c. $2d. $5
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23.The school media specialist has catalogued of the new books in a shipment. If she has catalogued 52 books, what is the total number of books in the shipment?
a. 35b. 78c. 104d. 156
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24. Rudy wants to teach a hip-hop dance workshop. The cost of renting a dance studio is $109.50 plus $15 per person attending the workshop. Rudy can spend $318 at most to rent the space. What is the greatest number of people Rudy can allow to attend the workshop?
a. 13 peopleb. 14 peoplec. 28 peopled. 29 people
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Use the inequality word bank below to assist with problems 25 – 30.
25. A waitress earned $7 per hour at her job plus an additional $50 in tips on Friday. She earned more than $99 total. Which inequality best represents the situation, where h represents the number of hours she worked on Friday?
a. 7 + 50h > 99b. 7 + 50h ≥ 99c. 7h + 50 > 99d. 7h + 50 ≥ 99
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26. Joseph has at least 296 photos. He bought an album that holds 6 photos on each page. Which best describes the number of photo album pages he will use?
a. ≥ 50 pagesb. > 50 pagesc. < 50 pagesd. ≤ 50 pages
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27.Mandy’s monthly earnings consist of a fixed salary of $2800 and an 18% commission on all her monthly sales(s). To cover her planned expenses, Mandy needs to earn an income of at least $6400 this month.
Which inequality below, when solved will give the amount of sales Mandy needs to cover her planned expenses?
a. / 2800 + .18s > 6400 / c. / 2800 + .18s < 6400b. / 2800 + .18s ≤ 6400 / d. / 2800 + .18s ≥ 6400
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28. When John bought his new computer, he purchased an online computer help service. The help service has a yearly fee of $25.50 and a $10.50 charge for each help session a person uses. If John can at most spend $170 for the computer help this year, what is the maximum number of help sessions he can use this year? (Let xrepresent the number of online help service sessions per year)
Which inequality below, when solved, will give the maximum number of help session he can use this year?
a. 10.50 + 25.50x ≥ 170 / c. / 25.50 + 10.50x ≥ 170b. 25.50 + 10.50x ≤ 170 / d. / 10.50 + 25.50x ≤ 170
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29.What is the solution set of this inequality?
2n– 7 < 25
a. n > 16b. n < 16c. n > 9d. n < 9
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30. What is the solution set of this inequality?
–7d + 8 > 29
a. d > 3b. d > –3c. d < 3d. d < –3
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Standard
MCC7.RP.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks mile in each hour, compute the unit rate as the complex fraction miles per hour, equivalently 2 miles per hour.
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31.The ratio of the actual size of the rectangular patio to the blueprint was 4 feet (actual) to 1 inch (blueprint). If the blueprint showed the length of the patio was 6 inches in length and 4 inches in width, what would be the size of the actual patio?
a. / 16 feet long by 24 feet wide / c. / 8 feet long by 12 feet wideb. / 24 feet long by 16 feet wide / d. / 12 feet long by 8 feet wide
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32.Jamie had a ribbon that was 5feet long. Each piece she cut was 1feet long. How many pieces of ribbon did she cut?
a. 1b. 4c. 8d. 12
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33. Joey bought 3 pounds of chocolate for $10.35. What is the unit price per pound?
a. $3.45b. $4.65c. $6.65d. $7.35
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34. Ms. Richardson drove 75 miles in 1.5 hours. What was her speed in miles per hour?
a. 60 miles per hour b. 45 miles per hourc. 50 miles per hour d. 25 miles per hour
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35. Which of the follow shows the least expensive unit price?
a. / 4 peaches for $1.32 / c. / 6 peaches for $2.16b. / 5 peaches for $1.70 / d. / 7 peaches for $2.24
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Standard
MCC7.RP.2.a
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
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36.What value of x makes this proportion true? =
a. x = 72b. x = 36c. x = 90d. x = 54
------37. Which table represents a proportional relationship?
A.
x / 3 / 5 / 7 / 9Y / 6 / 9 / 12 / 15
B
x / 1 / 2 / 6 / 8y / 5 / 8 / 18 / 45
C
x / 4 / 6 / 10 / 16Y / 6 / 10 / 15 / 32
D
x / 2 / 6 / 8 / 12Y / 10 / 30 / 40 / 60
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38.What is the constant rate of change of the table below?
Minutes / 5 / 15 / 25 / 35Feet / 15 / 45 / 75 / 105
a. / 9 feet per minute / c. / 6 feet per minute
b. / 3 feet per minute / d. / 12 feet per minute
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39. What value of w makes this proportion true? =
a. w = 40b. w = .04c. w = 4d. w = .4
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40. Which pair of ratios does not form a true proportion?
a. / 6:14 and 15:45 / c. / andb. / 6 to 10 and 15 to 25 / d. / 12:15 and 40:50
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Standard
MCC7.RP.2b
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
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41. Mrs. Klein drove 112 miles in 3½ hours. What was Mrs. Klein’s speed in miles per hour?
a. 36 miles per hour b. 32 miles per hour c. 16 miles per hourd. 42 miles per hour
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Use the function table for questions 42 and 43 .
The table shows the relationship between the side lengths of a regular octagon and its perimeter.
Side Length, s(inches) / Perimeter, p
(inches)
1 / 8
2 / 16
3 / 24
4 / 32
5 / 40
42.Which equation shows the relationship between the side length and the perimeter of a regular octagon?
a. P = s + 8b. P = sc. p = 8sd. p = 8s + 8
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43. If a regular octagon has side lengths of 9 inches, what is it perimeter?
a. 64 inchesb. 48 inchesc. 56 inchesd. 72 inches
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Use the graph for questions 44– 46.
44.Which equation shows the relationship between the number of video games purchased, x, and the cost, y ?
a. y = xb. y = 2xc. y = 10xd. y = 20x
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45. What is the unit cost of a video game?
a. / $20 per video game / c. / $5 per video gameb. / $10 per video game / d. / $2 per video game
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46.How much will it cost to purchase 8 video games?
a. $180b. $160c. $140d. $20
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Standard
MCC7.RP.2c
Represent proportional relationships by equations. For example, if total cost tis proportional to the number nof items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
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47. Sally rides 30 miles in 2 hours. Which equation shows the relationship between the distance, d, and the time, t, that she rides?
a. d = 2tb. d = 15tc. d = 30td. d = 32t
------48.Cynthia bought 3 pounds of apples for $2.67. Which ratio is proportional to 3 pounds at $2.67?
a. / / c. /b. / / d. /
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Standard
MCC7.RP.2d
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r)where r is the unit rate.
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49.The point (1.5, 0.15) is on the graph below. What does that point represent?
a. / A call that lasts 0.15 minute will cost $1.50 / c. / The unit rate is $0.15 per minuteb. / A call that lasts 1.5 minutes will cost $0.15 / d. / The unit rate is $1.50 per minute
Standard
MCC7.RP.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
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50.Appliances at Discount City Store are on sale for 70% of the original price. Eli has a coupon for an 18% discount on the sale price. If the original price of a microwave oven is $500, how much will Eli pay for the oven before tax?
a. $440b. $287c. $260d. $240
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51.Find the percent of change of 10 ft to 7 ft. Describe the percent of change as an increase or decrease.
a. 10% decreaseb. 70% increasec. 30% decreased. 7% increase
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52. You and your friend went out to lunch and your total bill (before taxes) was $37.50. You enjoyed your service and want to leave a tip of $20%. What is your tip amount?
a. $7.00b. $75.00c. $7.50d. $8.00
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53. John went into Home Depot to purchase items to fix his Bicycle. His total bill (before taxes) was $46.60. If the tax rate is 7%. What is his total cost of his purchase? (round to the nearest hundredth)
a. $3.26b. $48.50c. $93.20d. $49.86
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54. The price of this year model iPhone rose from $400 to $500. What was the percent increase in the price?
a. 25%b. 20%c. 50%d. 30%
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