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Dependent and Independent Variables: math test solutions, Grade 6 – download the PDF

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Test solutions Grade 6 : Dependent and Independent Variables — 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 Identify the variables / 3 pts

  1. Independent: hours. Dependent: gallons used. (1 pt)
  2. Independent: number of players. Dependent: number of bottles. (1 pt)
  3. Independent: speed. Dependent: distance traveled in one hour. (1 pt)

2 Smoothie bar / 4 pts

  1. \( c = 7n \). (1 pt)
  2. \( n \) 2 4 6 8
    \( c \) 14 28 42 56

    (1 pt)

  3. \( c = 7 \times 11 = 77 \) dollars. (1 pt)
  4. \( 7n = 91 \), so \( n = 13 \) smoothies. (1 pt)

3 Find the rule / 3 pts

  1. Each output is 5 more than its input: \( y = x + 5 \). (1 pt)
  2. \( y = 20 + 5 = 25 \). (1 pt)
  3. The rate of change is 1. The graph is not through the origin because \( x = 0 \) gives \( y = 5 \), not 0. (1 pt)

4 Planting tulips / 4 pts

  1. The number of hours \( n \) is independent and goes on the horizontal axis. (1 pt)
  2. The points go up by 8 for each hour: 8 bulbs per hour. (1 pt)
  3. \( b = 8n \). (1 pt)
  4. \( b = 8 \times 6 = 48 \) bulbs. (1 pt)

5 Constant rate or not? / 3 pts

  1. Table A goes up by 3 each time, so the rate is 3. (1 pt)
  2. Table B goes up by 3, then 4, then 5. These changes differ. (1 pt)
  3. Table A: \( y = 3x \), so \( k = 3 \). (1 pt)

6 Renting a bus / 3 pts

  1. \( c = 12r + 40 \). (1 pt)
  2. \( c = 12 \times 5 + 40 = 100 \) dollars. (1 pt)
  3. \( 12r + 40 = 172 \), so \( 12r = 132 \) and \( r = 11 \) riders. (1 pt)
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