Every direct and inverse proportion question from 5 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 2.8. 5 Extended-tier questions. Each question is labelled with its question paper code (for example 0580/23/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Algebra and Graphs past paper questions.
0580 Direct and Inverse Proportion past paper questions: Extended (Papers 2 and 4)
May/June 2026 · Paper 2 · 0580/23/M/J/26 · Q16
y is inversely proportional to x. When y = 5, x = 20. Find y when x = 4.
Show solution
- “y is inversely proportional to x” means y = k⁄x.
- Substitute y = 5 and x = 20: 5 = k⁄20, so k = 5 × 20 = 100.
- The formula is y = 100⁄x. When x = 4: y = 100⁄4 = 25
May/June 2026 · Paper 4 · 0580/42/M/J/26 · Q13
y is inversely proportional to x. When x = 6, y = 10.5. Find y when x = 9.
Show solution
- Inversely proportional means y = k⁄x, where k is a constant.
- Find k using x = 6 and y = 10.5: 10.5 = k⁄6, so k = 6 × 10.5 = 63.
- The formula is y = 63⁄x.
- When x = 9: y = 63⁄9 = 7
- Check: When x goes up, y should go down ✓
Oct/Nov 2025 · Paper 4 · 0580/41/O/N/25 · Q23
y is inversely proportional to √(x + 1). When x = 8, y = 3. Find y in terms of x.
Show solution
- “Inversely proportional to √(x + 1)” means y = k⁄√(x + 1) for some constant k.
- Substitute x = 8 and y = 3: √(8 + 1) = √9 = 3, so 3 = k⁄3.
- Multiply by 3: k = 9.
- y = 9⁄√(x + 1)
Oct/Nov 2025 · Paper 4 · 0580/42/O/N/25 · Q21
y is inversely proportional to (x + 2)². w is proportional to x. When y = 8, x = 3.5. When w = 15, x = 90. Find y in terms of w.
Show solution
- y is inversely proportional to (x + 2)², so y = k⁄(x + 2)².
- Use y = 8 and x = 3.5: 8 = k⁄5.5² = k⁄30.25, so k = 8 × 30.25 = 242.
- w is proportional to x, so w = mx. Use w = 15 and x = 90: 15 = 90m, so m = 1⁄6.
- So w = x⁄6, which means x = 6w.
- Replace x with 6w in the formula for y: y = 242⁄(6w + 2)²
May/June 2025 · Paper 2 · 0580/22/M/J/25 · Q20
y is inversely proportional to √x.
(a) When x = 9, y = 2. Find the value of y when x = 36.
(b) When x is increased by a factor of 4, the value of y changes by a factor of p. Find the value of p.
Show solution
- “Inversely proportional to √x” means y = k⁄√x.
- Substitute x = 9, y = 2: 2 = k⁄√9 = k⁄3, so k = 6.
- The formula is y = 6⁄√x. When x = 36: y = 6⁄√36 = 6⁄6 = 1
- If x is multiplied by 4, then √x is multiplied by √4 = 2.
- y = 6⁄√x, so doubling the bottom halves y.
- p = 1⁄2
Browse IGCSE Maths questions by topic
Book a free trial class
Tell us a little about your requirement.