IGCSE Mathematics 0580/32 October/November 2025 Past Paper with Answers

Question 1

Write 200 as a product of its prime factors.

1. 2³ × 5²
2. 4 × 50
3. 2² × 5²
4. 8 × 25

Question 2

Find the HCF of 84 and 120.

1. 12
2. 4
3. 840
4. 24

Question 3

Find the LCM of 18 and 24.

1. 72
2. 6
3. 432
4. 48

Question 4 · Answer A

1⅔ = 5/3, 2¼ = 9/4. (5/3) × (9/4) = 45/12 = 15/4 = 3¾. 3 11/12, 2¼, and 4⅙ miscalculate.

Question 5 · Answer A

3½ = 7/2, 1¾ = 7/4. (7/2) ÷ (7/4) = (7/2) × (4/7) = 4/2 = 2. 6⅛ multiplies. 1¾ and 2½ wrong.

Question 6 · Answer A

4a + 3a = 7a, −2b + 5b = 3b. Answer: 7a + 3b. a + 3b, 7a − 7b, and 10ab have calculation errors.

Question 7 · Answer A

12x − 6 − 2x − 10 = 10x − 16. 10x + 4 adds wrong. 14x − 16 doesn't subtract 2x. 10x − 6 miscalculates constant.

Question 8 · Answer A

HCF = 3a. So 3a(2a + 3b). 3(2a² + 3ab), a(6a + 9b), and 3a(2a + 3) don't fully factorise.

Question 9 · Answer A

5x − 10 = 3x + 12, 2x = 22, x = 11. x = 1, x = 7, and x = −11 have calculation errors.

Question 10 · Answer A

8000 × 1.04² = 8000 × 1.0816 = $\$8652.80$. $\$8640$ uses simple interest. $\$8320$ uses 1 year. $\$8800$ uses wrong rate.

Question 11 · Answer A

25000 × 0.85² = 25000 × 0.7225 = $\$18062.50$. $\$17500$ uses simple. $\$21250$ is 1 year. $\$19125$ wrong.

Question 12 · Answer A

3.45 × 10⁵ = 345000 (5 places right). 34500 uses 10⁴. 3450000 uses 10⁶. 0.0000345 uses negative power.

Question 13 · Answer A

0.00084 = 8.4 × 10⁻⁴ (4 places). 8.4 × 10⁻³ counts 3. 84 × 10⁻⁵ not standard form. 8.4 × 10⁴ positive power.

Question 14 · Answer A

6.3 ÷ 9 = 0.7. 10⁴ ÷ 10⁻³ = 10⁷. 0.7 × 10⁷ = 7 × 10⁶. 7 × 10¹ subtracts powers. 7 × 10⁷ doesn't adjust. 0.7 × 10⁷ not standard form.

Question 15 · Answer A

y = 16 − 8 − 3 = 5. −3 is just constant. 13 adds. 9 miscalculates.

Question 16 · Answer A

Minimum at x = −b/(2a) = 6/2 = 3. Or roots at 1 and 5, midpoint is 3. −3 wrong sign. 6 and 5 are other values.

Question 17 · Answer A

x² − 5x + 6 = 0, (x−2)(x−3) = 0, x = 2 or x = 3. x = −2 and x = −3, x = 1 and x = 6, and x = 5 and x = 6 have wrong values.

Question 18 · Answer A

Arc = (60/360) × 2π × 15 = (1/6) × 30π = 5π cm. 30π cm is full circumference. 2.5π cm uses radius/2. 15π cm uses π × radius.

Question 19 · Answer A

Area = (90/360) × π × 100 = (1/4) × 100π = 25π cm². 100π cm² is full circle. 5π cm² is arc. 50π cm² uses wrong fraction.

Question 20 · Answer A

c² = 81 + 144 = 225. c = 15 cm. 21 cm adds. 225 cm forgets root. 10.5 cm halves.

Question 21 · Answer A

tan θ = 8/6 = 1.333. θ = tan⁻¹(1.333) = 53.1°. 36.9° is complement. 48.6° and 75° wrong calculations.

Question 22 · Answer A

Total = 12. P(blue) = 4/12 = 1/3. 4/12 not simplified. 1/2 is P(red). 2/3 is P(not green).

Question 23 · Answer A

P(BB) = (2/5) × (1/4) = 2/20 = 1/10. 4/25 uses replacement. 2/20 not simplified. 1/5 wrong.

Question 24 · Answer A

P(same) = 1/6 + 1/10 + 1/30 = 5/30 + 3/30 + 1/30 = 9/30 = 3/10. 1/1800 multiplies. 1/6 and 7/15 wrong.

Question 25 · Answer A

Vector from centre: (8−4, 6−2) = (4, 4). Multiply by 1/2: (2, 2). Add to centre: (6, 4). (4, 3), (2, 2), and (12, 10) wrong calculations.

Question 26 · Answer A

90° anticlockwise: (x, y) → (−y, x). (3, 5) → (−5, 3). (5, −3) is clockwise. (−3, −5) is 180°. (5, 3) swaps.

Question 27 · Answer A

Reflection in y = x: swap coordinates. (4, −2) → (−2, 4). (−4, 2), (2, −4), and (4, 2) apply wrong transformations.