Ratios and Proportional Relationships: math test solutions, Grade 7 – download the PDF

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Test solutions with the detailed point scale. Add up your points and spot what to review.

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

Sommaire

a) $ \dfrac{3/8}{1/12} = \dfrac{3}{8} \times 12 = \dfrac{36}{8} = 4.5 $ miles per hour. (2 pts)

b) $ 18.75 \div 2.5 = 7.5 $: $7.50 per pound (1 pt). $ 3.5 \times 7.5 = 26.25 $: the cost is $26.25 (1 pt).

a) $ \dfrac{10.5}{3} = \dfrac{17.5}{5} = \dfrac{28}{8} = \dfrac{42}{12} = 3.5 $. The quotients are all equal, so it is proportional. (2 pts)

b) $ k = 3.5 $: the printer uses 3.5 grams of filament per minute. (1 pt)

c) $ y = 3.5x $. (1 pt)

a) The points lie on a straight line that goes through $ (0, 0) $ (the quotients $ \dfrac{3}{2}, \dfrac{9}{6}, \dfrac{15}{10} $ are all 1.5). (1 pt)

b) $ (1, 1.5) $: the drone climbs 1.5 feet each second. (1 pt)

c) $ y = 1.5x $. (1 pt)

a) $ 120 \times 0.70 = 84 $: the sale price is $84. (2 pts)

b) $ 84 \times 1.06 = 89.04 $: the final cost is $89.04. (2 pts)

a) $ 2 + 7 = 9 $ parts, and $ 45 \div 9 = 5 $ cups per part. Concentrate: 10 cups; water: 35 cups. (2 pts)

b) $ 63 \div 9 = 7 $, so concentrate: $ 2 \times 7 = 14 $ cups. (1 pt)

a) It is the constant of proportionality: each room needs 0.75 gallon of paint. (1 pt)

b) $ 0.75x = 6 $, so $ x = 8 $ rooms. (1 pt)

Test yourself: quick challenge for Grade 7