IGCSE Mathematics 0580/12 May/June 2025 Past Paper with Answers

Question 1

Write the number twenty-four thousand and thirty-five in figures.

1. 24035
2. 24350
3. 2435
4. 240035

Question 2

Write two-fifths as a decimal.

1. 0.4
2. 0.25
3. 2.5
4. 0.04

Question 3

Write two-fifths as a percentage.

1. 40%
2. 25%
3. 4%
4. 52%

Question 4 · Answer A

√81 = 9 because 9 × 9 = 81. 8 is close but 8² = 64. 40.5 is 81÷2. 18 is 81÷4.5.

Question 5 · Answer A

10⁴ = 10 × 10 × 10 × 10 = 10000. 1000 is 10³. 40 is 10 × 4. 100000 is 10⁵.

Question 6 · Answer A

1 cm = 10 mm, so 6.5 cm = 6.5 × 10 = 65 mm. 0.65 mm divides by 10 instead. 650 mm multiplies by 100. 6.5 mm doesn't convert.

Question 7 · Answer A

Perpendicular lines meet at right angles, which is 90°. 180° is a straight line. 45° is half a right angle. 60° is a common angle but not for perpendicular lines.

Question 8 · Answer A

1 week = 7 days, so 8 weeks = 8 × 7 = 56 days. 48 uses 6 days per week. 64 uses 8 days. 80 uses 10 days.

Question 9 · Answer A

3/5 of 20 = 3/5 × 20 = 12 squares. 15 is 3/4 of 20. 8 is 2/5 of 20. 4 is 1/5 of 20.

Question 10 · Answer A

The reciprocal of 1/5 is 5/1 = 5. 0.2 is 1/5 as a decimal (not the reciprocal). -5 uses negative sign incorrectly. 1/5 is the original number.

Question 11 · Answer A

3⁻² = 1/3² = 1/9. 9 ignores the negative index. -9 confuses negative index with negative number. 1/6 calculates 1/(3×2).

Question 12 · Answer A

(8 − 6) ÷ 2 + 1 = 2 ÷ 2 + 1 = 1 + 1 = 2. 8 − (6 ÷ 2) + 1 = 2 gives 8 - 3 + 1 = 6. 8 − 6 ÷ (2 + 1) = 2 gives 8 - 2 = 6. 8 − (6 ÷ 2 + 1) = 2 gives 8 - 4 = 4.

Question 13 · Answer A

(2 + 3) × 4 − 5 = 5 × 4 − 5 = 20 − 5 = 15. 2 + 3 × (4 − 5) = 15 gives 2 + (-3) = -1. 2 + (3 × 4) − 5 = 15 gives 2 + 12 - 5 = 9. (2 + 3 × 4) − 5 = 15 gives 14 - 5 = 9.

Question 14 · Answer A

Convert to 24ths: 7/24, 8/24 (1/3), 9/24 (3/8), 10/24 (5/12). In order: 7/24, 1/3, 3/8, 5/12. 1/3, 7/24, 3/8, 5/12 swaps first two. 7/24, 3/8, 1/3, 5/12 has wrong middle order. 5/12, 3/8, 1/3, 7/24 is reversed.

Question 15 · Answer A

Surface area = 2(lw + lh + wh) = 2(4×3 + 4×2 + 3×2) = 2(12 + 8 + 6) = 2(26) = 52 cm². 24 cm³ is volume with wrong units. 26 cm² only adds once. 48 cm² uses wrong formula.

Question 16 · Answer A

Volume = l × w × h = 6 × 4 × 2 = 48 cm³. 48 cm² has wrong units. 24 cm³ is 6×4 only. 12 cm³ is 6×2 only.

Question 17 · Answer A

The mode is the most frequent value. 5 appears 3 times, 3 appears 2 times, others once. Mode = 5. 3 is the second most frequent. 4 is the median. 7 is the range.

Question 18 · Answer A

Range = highest − lowest = 18 − 3 = 15. 12 is the middle value. 11 is the mean. 18 is just the highest value.

Question 19 · Answer A

6 values, so median is average of 3rd and 4th: (8 + 11)/2 = 9.5. 8 is just the 3rd value. 10.33 is the mean. 11 is just the 4th value.

Question 20 · Answer A

Total = mean × count = 8 × 5 = 40. Sum of known = 5 + 6 + 9 + 12 = 32. Fifth = 40 − 32 = 8. 10 adds incorrectly. 7 subtracts wrong. 40 is just the total.

Question 21 · Answer A

67 × 99 = 67 × 100 − 67 = 6700 − 67 = 6633. 6700 is 67 × 100. 6767 is 67 × 101. 6600 is 67 × 100 − 100.

Question 22 · Answer A

A trapezium has exactly one pair of parallel sides. A parallelogram has 2 pairs. A rhombus is a special parallelogram. A kite has no parallel sides.

Question 23 · Answer A

A rectangle does NOT have all sides equal (that would be a square). All angles are 90°, Opposite sides are parallel, and Diagonals are equal in length are all true properties of rectangles.

Question 24 · Answer A

Area = ½(a + b) × h = ½(8 + 6) × 5 = ½ × 14 × 5 = 35 cm². 70 cm² forgets to halve. 40 cm² is 8 × 5. 30 cm² is 6 × 5.

Question 25 · Answer A

y = (3 + 2)(3 − 1) = 5 × 2 = 10. 4 is (3+1). 6 is (3+3). 8 is 5+3.

Question 26 · Answer A

The x-intercepts occur when y = 0, so (x + 3)(x − 2) = 0. This gives x = −3 or x = 2. x = 3 and x = −2, x = −3 and x = −2, and x = 3 and x = 2 have signs confused.

Question 27 · Answer A

The x-coordinate of the vertex is halfway between the roots. Roots are x = 1 and x = 5. Vertex x = (1 + 5)/2 = 3. 2 and C are not midpoint. 5 is a root.

Question 28 · Answer A

The line of symmetry is x = (−1 + 3)/2 = 1. y = 1 is wrong axis. x = −1 and x = 3 are the x-intercepts, not the line of symmetry.

Question 29 · Answer A

The minimum of y = (x + 2)(x − 4) is at x = 1, y = 3 × (−3) = −9. Since y = 5 is above the minimum, the horizontal line will cross the parabola twice.

Question 30 · Answer A

n² + 20 = 45, so n² = 25, n = 5 (positive). 25 is n². 12.5 is 25/2. 6.7 is √45.

Question 31 · Answer A

Area = ½ × base × height = ½ × 5 × 4 = 10 cm². 20 cm² forgets to halve. 9 cm² is 5+4. 18 cm² is 9×2.

Question 32 · Answer A

Moving right adds to x: −2 + 3 = 1. Moving down subtracts from y: 5 − 4 = 1. New coordinates: (1, 1). (−5, 9), (1, 9), and (−5, 1) have sign errors.

Question 33 · Answer A

(3, −2) + (5, −7) = (3 + 5, −2 + (−7)) = (8, −9). (−2, 5) subtracts instead of adds. (8, 5) and (−2, −9) have mixed errors.

Question 34 · Answer A

Point (3, 4) is 2 units above y = 2. Reflected point is 2 units below y = 2, at (3, 0). (−3, 4) reflects in y-axis. (3, −4) reflects in x-axis. (1, 4) reflects in x = 2.

Question 35 · Answer A

For enlargement SF 3 from origin: multiply each coordinate by 3. (2, 1) → (6, 3). (5, 4) adds 3. (2/3, 1/3) divides by 3. (6, 1) only multiplies x.

Question 36 · Answer A

For 90° anticlockwise about origin: (x, y) → (−y, x). So (3, 1) → (−1, 3). (1, −3) is 90° clockwise. (−3, −1) is 180°. (1, 3) swaps coordinates only.

Question 37 · Answer A

38.7 ≈ 40, 4.2 ≈ 4, 19.8 ≈ 20. Estimate = (40 × 4) ÷ 20 = 160 ÷ 20 = 8. 160 forgets to divide. 0.8 divides by 200. 6 uses wrong values.

Question 38 · Answer A

48 = 2⁴ × 3, 72 = 2³ × 3². HCF = 2³ × 3 = 8 × 3 = 24. 12 is a factor but not highest. 144 is LCM. 6 is too small.

Question 39 · Answer A

Primes between 20 and 30: 23 and 29. 21 = 3 × 7, 25 = 5², 27 = 3³ are not prime.

Question 40 · Answer A

Open circle at 1 means 'not including 1' so >. Filled circle at 6 means 'including 6' so ≤. Thus 1 < x ≤ 6. 1 ≤ x < 6, 1 < x < 6, and 1 ≤ x ≤ 6 have wrong inequality symbols.

Question 41 · Answer A

The overlap is the intersection, A ∩ B (elements in both A AND B). A ∪ B is union (in A or B or both). A' is complement of A. A − B is A without B.

Question 42 · Answer A

1 2/3 = 5/3, 2 1/4 = 9/4. (5/3) × (9/4) = 45/12 = 15/4 = 3 3/4. 2 1/6 adds instead of multiplies. 3 11/12 and 4 1/2 are calculation errors.

Question 43 · Answer A

Nearest mm = nearest 0.1 cm. Half of 0.1 = 0.05. Bounds: 5.8 − 0.05 = 5.75, 5.8 + 0.05 = 5.85. 5.7 cm ≤ length < 5.9 cm uses nearest cm. 5.79 cm ≤ length < 5.81 cm uses 0.01. 5.8 cm ≤ length ≤ 5.8 cm gives no range.

Question 44 · Answer A

HCF of 12a and 8ab is 4a. 12a ÷ 4a = 3, 8ab ÷ 4a = 2b. So 12a + 8ab = 4a(3 + 2b). 4(3a + 2ab), 2a(6 + 4b), and a(12 + 8b) don't fully factorise.

Question 45 · Answer A

(3x + 2)(x − 5) = 3x² − 15x + 2x − 10 = 3x² − 13x − 10. 3x² − 15x − 10 doesn't combine middle terms. 3x² − 13x + 10 and 3x² + 17x − 10 have sign errors.

Question 46 · Answer A

Check: 2(3) + 3(2) = 6 + 6 = 12 ✓. 4(3) − 2 = 12 − 2 = 10. Using elimination or substitution methods to solve simultaneously.

Question 47 · Answer A

Large arc = π × 10 = 10π. Small arc = π × 6 = 6π. Straight edges = 2(10 − 6) = 8. Perimeter = 10π + 6π + 8 = 16π + 8. 16π cm forgets straight edges. (10π + 6π + 8) cm doesn't simplify. (16π + 4) cm uses wrong straight length.