Proportional Relationships: Grade 7 Math Test Answer Key – PDF Download

Question 1: Table A (2 points)

The pairs are (2, 5), (3, 7.5), (5, 12.5) and (8, 20). \(\frac{5}{2}=2.5\), \(\frac{7.5}{3}=2.5\), \(\frac{12.5}{5}=2.5\), \(\frac{20}{8}=2.5\). Proportional, \(k=2.5\).

Scoring: 1 point for checking all the ratios; 1 point for the conclusion with \(k=2.5\).

Question 2: Table B (2 points)

\(\frac{2}{1}=2\), \(\frac{5}{2}=2.5\), \(\frac{8}{3}\approx 2.67\), \(\frac{11}{4}=2.75\). The ratios are not equal. Not proportional.

Scoring: 1 point for computing at least three ratios correctly; 1 point for the correct conclusion.

Question 3: Distance and time (2 points)

The line passes through the origin and the ratios are equal: \(\frac{3}{2}=\frac{6}{4}=\frac{9}{6}=1.5\). Proportional, \(k=1.5\) miles per hour.

Scoring: 1 point for recognizing a line through the origin or equal ratios; 1 point for \(k=1.5\) with units.

Question 4: Graph B (2 points)

The line is straight, but it crosses the \(y\)-axis at \((0,1)\), not at \((0,0)\). Also \(\frac{3}{1}=3\) and \(\frac{5}{2}=2.5\) are different. It is not proportional.

Scoring: 1 point for the conclusion; 1 point for a correct reason (misses the origin or unequal ratios).

Question 5: Printer (2 points)

(a) \(k=\frac{45}{9}=5\). 5 pages per minute

(b) The point \((1,5)\) means that the printer prints 5 pages in 1 minute.

Scoring: 1 point for each part.

Question 6: Gym membership (2 points)

\(\frac{30}{1}=30\), \(\frac{40}{2}=20\), \(\frac{50}{3}\approx 16.67\). The ratios are different, and 0 months would cost $20 rather than $0. Not proportional.

Scoring: 1 point for correct ratios or noting the starting fee; 1 point for the conclusion.

Question 7: Flour and loaves (2 points)

Loaves per cup: \(\frac{3}{2}=1.5\), so \(k=1.5\). Cups per loaf: \(\frac{2}{3}\), so \(k=\frac{2}{3}\).

\(1.5\) loaves per cup; \(\frac{2}{3}\) cup per loaf.

Scoring: 1 point for each constant.

Question 8: Missing values (2 points)

\(k=\frac{14}{4}=3.5\). Check: \(\frac{21}{6}=3.5\). Missing \(x\): \(28: 3.5=8\). Missing \(y\): \(3.5\times 10=35\).

\(x=8\) and \(y=35\)

Scoring: 1 point for each missing value.

Question 9: Reading a point (2 points)

(a) \(k=\frac{10}{4}=2.5\). $2.50 per ounce

(b) \(2.5\times 6=15\). $15

Scoring: 1 point for each part.

Question 10: Who is faster? (2 points)

Ethan: \(\frac{6}{2}=3\) mph. Noah: \(\frac{12}{5}=2.4\) mph. \(3-2.4=0.6\).

Ethan is faster, by 0.6 mile per hour.

Scoring: 1 point for both speeds; 1 point for the correct comparison and difference.

⬇ Download the Grade 7 Proportional Relationships test answer key (PDF, 98 KB)

See every chapter on the Grade 7 math page.