Grade 7 Math Practice Test: Proportional Relationships and Percent Problems
- Proportional Relationships and Percents
- 12 questions
- 15 minutes
This test covers unit rates with fractions, the constant of proportionality and percent problems such as discounts, sales tax, tips, simple interest and percent change. Tip: in a proportional relationship y = kx, and k is the value of y when x = 1.
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Question 1
Mia walks 12 mile in 14 hour. What is her speed in miles per hour?
Correct answer: B
Unit rate = miles ÷ hours = 12 ÷ 14 = 12 × 4 = 2 miles per hour. 18 multiplies the two fractions instead of dividing.
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Question 2
The table shows a proportional relationship between x and y.
x 2 5 8 y 7 17.5 28 What is the constant of proportionality of y to x?
Correct answer: D
Divide each y-value by its x-value: 7 ÷ 2 = 3.5, 17.5 ÷ 5 = 3.5 and 28 ÷ 8 = 3.5, so y = 3.5x. 27 is x ÷ y, the reciprocal of the constant.
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Question 3
Which equation represents a proportional relationship between x and y?
Correct answer: C
A proportional relationship has the form y = kx with nothing added, so its graph passes through the origin. In y = 4x + 1, x = 0 gives y = 1, so that relationship is not proportional.
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Question 4
A printer prints 84 pages in 6 minutes. At this rate, how many pages does it print in 15 minutes?
Correct answer: A
The unit rate is 84 ÷ 6 = 14 pages per minute, so in 15 minutes it prints 14 × 15 = 210 pages. 93 adds 9 pages because 15 is 9 more than 6, but proportional quantities are multiplied, not added.
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Question 5
The graph of a proportional relationship passes through the point (4, 10). Which point is also on the graph?
Correct answer: C
The constant is k = 10 ÷ 4 = 2.5, so y = 2.5x. For x = 6, y = 2.5 × 6 = 15. (5, 11) adds 1 to both coordinates, which does not keep the ratio the same.
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Question 6
A pair of sneakers costs $72. They are on sale for 25% off. What is the sale price?
Correct answer: A
The discount is 25% of $72 = $18, so the sale price is $72 − $18 = $54. $18 is the amount you save, not the price you pay.
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Question 7
A board game costs $40. The sales tax rate is 6.5%. What is the total cost including tax?
Correct answer: B
Tax = 0.065 × $40 = $2.60, so the total is $40 + $2.60 = $42.60. $46.50 adds $6.50 as if the tax were 6.5 dollars instead of 6.5% of the price.
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Question 8
A restaurant bill is $36. Dana leaves an 18% tip. How much is the tip?
Correct answer: D
18% of $36 = 0.18 × 36 = $6.48. $42.48 is the bill plus the tip, but the question asks only for the tip.
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Question 9
Last year a school club had 40 members. This year it has 50 members. What is the percent increase?
Correct answer: B
Percent change = amount of change ÷ original amount = 10 ÷ 40 = 0.25 = 25%. 20% divides by the new number (50), but the original amount always goes in the denominator.
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Question 10
The price of a bike dropped from $250 to $200. What is the percent decrease?
Correct answer: D
The price dropped by $50, and $50 ÷ $250 = 0.2 = 20%. 25% divides by the new price ($200) instead of the original price.
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Question 11
Ana deposits $500 in a savings account that earns 3% simple interest per year. How much interest will she earn in 4 years?
Correct answer: A
Simple interest = principal × rate × time = 500 × 0.03 × 4 = $60. $15 is the interest for one year only, and $560 is the account balance, not the interest.
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Question 12
The cost C, in dollars, of p pounds of apples is given by the equation C = 1.75p. What does 1.75 represent?
Correct answer: C
In an equation of the form y = kx, the constant k is the unit rate. Here k = 1.75, so 1 pound of apples costs $1.75; the total cost is C, not 1.75.
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