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Integers and Rational Numbers: math test solutions, Grade 6 – download the PDF

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Test solutions Grade 6 : Integers and Rational Numbers — 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 Opposites and absolute values / 3 pts

  1. \( 13 \) and \( -6.4 \). (1 pt)
  2. \( 18 \) and \( \dfrac{7}{2} \). (1 pt)
  3. \( |-9| = 9 \gt 6 \), so \( -9 \) has the greater absolute value, but \( 6 \gt -9 \). (1 pt)

2 Ordering rational numbers / 4 pts

  1. In decimals: \( -2.4,\ 1.8,\ -3,\ -0.5,\ 0,\ 1.25 \). Order: \( -3 \lt -2.4 \lt -\dfrac{1}{2} \lt 0 \lt \dfrac{5}{4} \lt 1.8 \). (2 pts)
  2. Denominator 24: \( -\dfrac{20}{24} \) and \( -\dfrac{21}{24} \). Since \( -21 \lt -20 \), \( -\dfrac{7}{8} \lt -\dfrac{5}{6} \). (2 pts)

3 Temperatures in context / 3 pts

  1. \( 38 - (-12) = 50 \) degrees. (1 pt)
  2. \( -5 \gt -12 \), so the cold room is warmer. (1 pt)
  3. \( 9 - (-4) = 13 \) degrees. (1 pt)

4 Points and a rectangle / 4 pts

  1. E is in quadrant II, G in quadrant IV, H in quadrant III. (1 pt)
  2. Same y: \( 3 + 5 = 8 \). (1 pt)
  3. Same x: \( 4 + 2 = 6 \). (1 pt)
  4. The fourth vertex is \( (-3, -2) \). (1 pt)

5 Reflections / 4 pts

  1. Across the x-axis: \( (-7, -2) \) (1 pt). Across the y-axis: \( (7, 2) \) (1 pt).
  2. The image is \( (4, 3) \) (1 pt). Same x, opposite signs: \( 3 + 3 = 6 \) units (1 pt).

6 True or false? / 2 pts

  1. False: \( -15 \) is left of \( -4 \), so \( -15 \lt -4 \). (1 pt)
  2. True: both are 6 units from zero. (1 pt)
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