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Proportional Relationships and Slope: math test solutions, Grade 8 – download the PDF

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Test solutions Grade 8 : Proportional Relationships and Slope — Zyro the alien explorer of Planète Maths

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.

1 Unit rate / 3 pts

  1. 24 minutes \(= 0.4\) hour, so \(\dfrac{18}{0.4} = 45\) miles per hour. (1 pt)
  2. \(d = 45t\). (1 pt)
  3. \(45 \times 2.5 = 112.5\) miles. (1 pt)

2 Slope from two points / 4 pts

  1. \(m = \dfrac{-9 - 3}{2 - (-4)} = \dfrac{-12}{6} = -2\). (2 pts)
  2. Slope of \(BC\): \(\dfrac{-15 - (-9)}{5 - 2} = \dfrac{-6}{3} = -2\). Same slope and shared point \(B\), so \(A\), \(B\), \(C\) are on one line. (2 pts)

3 Reading a graph / 3 pts

  1. \(m = \dfrac{6 - 3}{4 - 2} = \dfrac{3}{2} = 1.5\). (1 pt)
  2. The line goes through the origin, so \(y = 1.5x\). (1 pt)
  3. \(1.5 \times 10 = 15\). (1 pt)

4 Two faucets / 4 pts

  1. \(\dfrac{36}{8} = 4.5\) gallons per minute. (1 pt)
  2. \(4.5 > 4.2\), so Faucet A is faster. (1 pt)
  3. A: \(\dfrac{63}{4.5} = 14\) minutes. B: \(\dfrac{63}{4.2} = 15\) minutes. (2 pts)

5 Similar triangles / 3 pts

  1. \(\dfrac{10}{8} = 1.25\). (1 pt)
  2. Both have a right angle and the same angle at the origin (the line makes the same angle with the horizontal), so their angles match and they are similar. (1 pt)
  3. \(\text{run} = \dfrac{35}{1.25} = 28\). (1 pt)

6 True or false? / 3 pts

  1. True: \(\dfrac{12}{3} = \dfrac{20}{5} = \dfrac{32}{8} = 4\). (1 pt)
  2. False: the slope is \(\dfrac{3}{2} = 1.5\), but \(\dfrac{6}{2} = 3 \neq 1.5\), so the line does not pass through the origin. (1 pt)
  3. False: the run is 0, so the line is vertical and the slope is undefined. (1 pt)
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