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Scale Drawings and Similar Figures: math test solutions, Grade 7 – download the PDF

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Test solutions Grade 7 : Scale Drawings and Similar Figures — 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 Scale and lengths / 4 pts

  1. \( 3.5 \times 6 = 21 \) m. (1 pt)
  2. \( 90 \div 6 = 15 \) cm. (1 pt)
  3. 6 m = 600 cm, so the ratio is 1 : 600. (2 pts: 1 for the conversion, 1 for the ratio)

2 Two rectangles / 4 pts

  1. \( 10 \div 4 = 2.5 \). (1 pt)
  2. \( 7 \times 2.5 = 17.5 \) cm. (1 pt)
  3. ABCD: \( 2 \times (4 + 7) = 22 \) cm; A′B′C′D′: \( 2 \times (10 + 17.5) = 55 \) cm, which is \( 22 \times 2.5 \). (1 pt)
  4. ABCD: \( 28 \) cm²; A′B′C′D′: \( 10 \times 17.5 = 175 \) cm². \( 175 \div 28 = 6.25 = 2.5^2 \). The area is multiplied by 6.25. (1 pt)

3 Distances on a map / 3 pts

  1. \( 3.25 \times 12 = 39 \) mi. (1.5 pts)
  2. \( 78 \div 12 = 6.5 \) in. (1.5 pts)

4 A living room plan / 4 pts

  1. \( 7 \times 2 = 14 \) ft and \( 5 \times 2 = 10 \) ft. (1 pt)
  2. \( 14 \times 10 = 140 \) ft². (1 pt)
  3. \( 7 \times 5 = 35 \) cm². (1 pt)
  4. \( 35 \times 2^2 = 35 \times 4 = 140 \), which matches the actual area. (1 pt)

5 Similar triangles / 3 pts

  1. \( 15 \div 5 = 3 \). (1 pt)
  2. \( 12 \times 3 = 36 \) and \( 13 \times 3 = 39 \). (1 pt)
  3. \( 30 \times 3^2 = 270 \). (1 pt)

6 True or false? / 2 pts

  1. False: the area is multiplied by \( 3^2 = 9 \). (1 pt)
  2. True: only lengths are scaled; angle measures do not change. (1 pt)
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