The following diagrams represent ski hills. Rank the hills in order of their steepness, from least to greatest.
Answer: Slopes: A = 6070 ≈ 0.86, B = 60110 ≈ 0.55, C = 80100 = 0.8. From least to greatest steepness: B, C, A.
Step-by-step solution
Idea: Steepness is the slope riserun (height ÷ horizontal distance). Turn each into a decimal and compare.
- Hill A: slope = 6070 = 67 ≈ 0.857.½ mark
- Hill B: slope = 60110 = 611 ≈ 0.545.½ mark
- Hill C: slope = 80100 = 45 = 0.8.½ mark
- 0.545 < 0.8 < 0.857, so the order from least to greatest steepness is B, C, A.½ mark
B (6/11) < C (4/5) < A (6/7): least to greatest steepness is B, C, A.
Check: A and B have the same height, but A covers it in a shorter run, so A must be steeper than B ✓. C (0.8) sits between them ✓.
Answer to write in the exam
Slope = riserun
A: 6070 ≈ 0.857; B: 60110 ≈ 0.545; C: 80100 = 0.8
0.545 < 0.8 < 0.857
∴ Order (least to greatest): B, C, A
Common mistakes that cost marks
- Ranking by height alone: C is tallest but not steepest.
- Dividing run by rise (7060 etc.), which reverses the order.
How this can come in the exam
MCQ (1 mark)
A slide rises 3 m over 4 m and a ramp rises 2 m over 5 m. Which is steeper and what is its slope?
- Ramp, 0.4
- Slide, 0.75
- Slide, 1.33
- Both equal
Show answer
(B) Slide, 0.75
Slide 34 = 0.75 > ramp 25 = 0.4.
Try one yourself
Rank by steepness (least first): P rises 30 m over 90 m, Q rises 40 m over 100 m, R rises 25 m over 50 m.
Show answer
P ≈ 0.33, Q = 0.4, R = 0.5 ⇒ P, Q, R.
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We can also solve this using a pair of linear equations.
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