IGCSE Mathematics 0580/32 May/June 2025 Past Paper with Answers

Question 1

Write down the mathematical name for a polygon with 8 sides.

1. Octagon
2. Hexagon
3. Heptagon
4. Decagon

Question 2

Work out the size of one interior angle of a regular octagon.

1. 135°
2. 120°
3. 144°
4. 108°

Question 3

The sum of the interior angles of a polygon is 1440°. How many sides does it have?

1. 10
2. 8
3. 9
4. 12

Question 4 · Answer A

2/5 × 3/8 = 6/40 = 3/20. 6/40 not simplified. 5/13 and D add instead of multiply.

Question 5 · Answer A

3½ = 7/2, 1¼ = 5/4. 7/2 ÷ 5/4 = 7/2 × 4/5 = 28/10 = 14/5 = 2⅘. 4⅜ multiplies. 2⅖ and 1¾ calculate wrong.

Question 6 · Answer A

2(3x + 4) + 5(x − 1) = 6x + 8 + 5x − 5 = 11x + 3. 11x + 9 adds 8+5. 8x + 3 misses 5x. 11x − 1 subtracts wrong.

Question 7 · Answer A

HCF = 5a. 15ab ÷ 5a = 3b, 20a² ÷ 5a = 4a. So 5a(3b − 4a). 5(3ab − 4a²), a(15b − 20a), and 5a(3b − 4) don't fully factorise.

Question 8 · Answer A

6x − 15 = 4x + 7, 2x = 22, x = 11. x = 4 doesn't expand correctly. x = −4 and x = 1 have sign errors.

Question 9 · Answer A

Any non-zero number to power 0 equals 1. 0 confuses with x×0. 7 is 7¹. 70 concatenates.

Question 10 · Answer A

4⁻³ = 1/4³ = 1/64. 64 ignores negative. -64 confuses negative index with negative value. 1/12 calculates 1/(4×3).

Question 11 · Answer A

(2x³)⁴ = 2⁴ × x¹² = 16x¹². 8x¹² is 2³. 16x⁷ adds indices. 2x¹² doesn't raise 2 to power.

Question 12 · Answer A

y⁴ × y² = y⁶, then y⁶ ÷ y³ = y³. y⁹ adds all. y²⁴ multiplies. y subtracts wrong.

Question 13 · Answer A

Interest = 5000 × 0.02 × 4 = $\$400$. Total = $\$5400$. $\$400$ is just interest. $\$5408$ uses compound interest. $\$5800$ uses 4% per year.

Question 14 · Answer A

6000 × 1.03² = 6000 × 1.0609 = $\$6365.40$. $\$6360$ uses simple interest. $\$6180$ uses 1 year. $\$7128.54$ uses 9%.

Question 15 · Answer A

Angle = (25/100) × 360° = 90°. 25° uses frequency as angle. 45° halves incorrectly. 72° uses 20% formula.

Question 16 · Answer A

Green and Yellow both have frequency 15 (highest). This is bimodal. Green only lists one. 15 gives frequency not category. Red is not highest.

Question 17 · Answer A

Back bearing = 85° + 180° = 265°. 085° is the original. 275° adds 190°. 095° adds 10°.

Question 18 · Answer A

15 km ÷ 2 = 7.5 cm. 30 cm multiplies by 2. 15 cm doesn't convert. 13 cm subtracts 2.

Question 19 · Answer A

y = 25 − 20 + 3 = 8. 3 just uses constant. -2 subtracts wrong. 13 adds all.

Question 20 · Answer A

x² − 2x − 3 = 0, (x+1)(x−3) = 0, x = −1 or x = 3. x = 1 and x = −3 has signs wrong. x = 0 and x = 3 includes 0. x = −1 and x = −3 has both negative.

Question 21 · Answer A

x² − 4 = 5, x² = 9, x = ±3. x = −1 and x = 1 solves x² = 1. x = −2 and x = 2 solves x² = 4. x = −9 and x = 9 uses x² = 81.

Question 22 · Answer A

V = πr²h = π × 64 × 10 = 640π cm³. 80π cm³ is πrh. 160π cm³ is 2πrh. 1280π cm³ doubles.

Question 23 · Answer A

V = ⅓πr²h = ⅓ × π × 36 × 10 = 120π cm³. 360π cm³ forgets ⅓. 60π cm³ uses ⅓πrh. 180π cm³ uses ½.

Question 24 · Answer A

Distance = √[(4−1)² + (6−2)²] = √[9 + 16] = √25 = 5. 7 adds differences. 25 doesn't take root. 3 is just x-difference.

Question 25 · Answer A

P is 2 units left of x=5. Image is 2 units right, at x = 7. y stays same. (7, 4). (3, 6) reflects in y. (−3, 4) reflects in y-axis. (5, 4) is on mirror line.

Question 26 · Answer A

Point is 2 above y=1. Image is 2 below, at y = −1. x stays same. (2, −1). (2, 5) goes wrong direction. (−2, 3) reflects in y-axis. (0, 3) reflects in x=1.

Question 27 · Answer A

P(blue) = 6/10 = 3/5. 2/5 is P(red). 6/4 has ratio inverted. 2/3 simplifies wrong.

Question 28 · Answer A

P(R then B) = 3/5 × 2/4 = 6/20 = 3/10. 6/25 uses replacement. 6/20 not simplified. 1/5 is wrong calculation.

Question 29 · Answer A

P(RR) + P(BB) = (4/7 × 3/6) + (3/7 × 2/6) = 12/42 + 6/42 = 18/42 = 9/21. 12/21 is different colours. 6/21 is just P(BB). 7/21 is wrong.