IGCSE Mathematics 0580/33 October/November 2025 Past Paper with Answers

Question 1

Write 300 as a product of its prime factors.

1. 2² × 3 × 5²
2. 4 × 75
3. 6 × 50
4. 2³ × 3 × 5

Question 2

Find the HCF of 90 and 150.

1. 30
2. 10
3. 450
4. 15

Question 3

Find the LCM of 14 and 21.

1. 42
2. 7
3. 294
4. 35

Question 4 · Answer A

2⅔ = 8/3, 1⅘ = 9/5. (8/3) × (9/5) = 72/15 = 24/5 = 4⅘. 3 7/15, 2⅖, and 5⅓ miscalculate.

Question 5 · Answer A

3¾ = 15/4, 1½ = 3/2. (15/4) ÷ (3/2) = (15/4) × (2/3) = 30/12 = 5/2 = 2½. 5⅝ multiplies. 2¼ and 3 wrong.

Question 6 · Answer A

7a + 2a = 9a, −4b + 6b = 2b. Answer: 9a + 2b. 5a + 2b, 9a − 10b, and 11ab have calculation errors.

Question 7 · Answer A

6x − 8 + 4x + 12 = 10x + 4. 10x − 20 adds wrong. 6x + 4 misses 4x. 10x + 20 wrong constant.

Question 8 · Answer A

HCF = 6a. So 6a(2a − 3b). 6(2a² − 3ab), 2a(6a − 9b), and a(12a − 18b) don't fully factorise.

Question 9 · Answer A

6x + 8 = 5x − 5, x = −13. x = 13 wrong sign. x = 3 and x = −3 wrong calculations.

Question 10 · Answer A

6000 × 1.05³ = 6000 × 1.157625 = $\$6945.75$. $\$6900$ uses simple interest. $\$6300$ uses 1 year. $\$7200$ uses wrong rate.

Question 11 · Answer A

600 × 0.75² = 600 × 0.5625 = $\$337.50$. $\$300$ uses simple. $\$450$ uses 1 year. $\$225$ uses wrong multiplier.

Question 12 · Answer A

7.2 × 10⁶ = 7200000 (6 places right). 720000 uses 10⁵. 72000000 uses 10⁷. 0.0000072 uses negative power.

Question 13 · Answer A

0.00095 = 9.5 × 10⁻⁴ (4 places). 9.5 × 10⁻³ counts 3. 95 × 10⁻⁵ not standard form. 9.5 × 10⁴ positive power.

Question 14 · Answer A

2.5 × 4 = 10 = 1 × 10. 10³ × 10⁻⁵ = 10⁻². Total: 1 × 10⁻¹. 1 × 10⁻² doesn't adjust. 10 × 10⁻² not standard. 1 × 10⁸ adds powers.

Question 15 · Answer A

y = 1 + 3 + 2 = 6. 0 is when x=1 or x=2. 2 is constant only. −2 miscalculates.

Question 16 · Answer A

Vertex at x = −b/(2a) = 4/2 = 2. −2 wrong sign. 4 is −b/a. 1 is constant.

Question 17 · Answer A

x² = 2, x = ±√2 ≈ ±1.41. x = ±2 solves x² = 4. x = 2 only forgets negative. x = 4 is 2².

Question 18 · Answer A

Area = ½ × 8 × 3 = 12 cm². Volume = 12 × 15 = 180 cm³. 360 cm³ forgets ½. 24 cm³ is just area. 12 cm³ is ½ area.

Question 19 · Answer A

TSA = 2(20) + 30 + 40 + 50 = 40 + 120 = 160 cm². 120 cm² forgets triangles. 140 cm² forgets one rectangle. 200 cm² doubles.

Question 20 · Answer A

c² = 400 + 441 = 841. c = 29 cm. 41 cm adds. 841 cm forgets root. 20.5 cm averages.

Question 21 · Answer A

tan θ = 15/8 = 1.875. θ = tan⁻¹(1.875) = 61.9°. 28.1° is complement. 58.0° and 45° wrong calculations.

Question 22 · Answer A

Total = 8. P(green) = 5/8. 3/8 is P(yellow). 5/3 and 8/5 are ratios not probabilities.

Question 23 · Answer A

P(R then B) = (4/7) × (3/6) = 12/42 = 2/7. 12/49 uses replacement. 12/42 not simplified. 1/7 wrong.

Question 24 · Answer A

P(same) = 2/7 + 1/7 = 3/7. 2/49 multiplies. 1/7 is just P(BB). 4/7 is P(different).

Question 25 · Answer A

180° rotation: (x, y) → (−x, −y). (2, 5) → (−2, −5). (5, 2) swaps. (−5, −2) swaps and negates. (2, −5) reflects in x-axis.

Question 26 · Answer A

Reflection in y = x swaps coordinates: (1, 4) → (4, 1). (−1, −4) and (−4, −1) negate. (1, −4) reflects in x-axis.

Question 27 · Answer A

Vector from centre: (3−1, 2−1) = (2, 1). Multiply by 3: (6, 3). Add to centre: (7, 4). (9, 6), (10, 7), and (4, 3) wrong calculations.