IGCSE Mathematics 0580/13 October/November 2025 Past Paper with Answers

Question 1

Write the number eight million, forty-two thousand and nine in figures.

1. 8042009
2. 842009
3. 8420009
4. 80042009

Question 2

Write in order, smallest first: 0.3, 3%, 3/10, 0.03

1. 0.03, 3%, 0.3, 3/10
2. 3%, 0.03, 0.3, 3/10
3. 0.03, 3%, 3/10, 0.3
4. 3/10, 0.3, 3%, 0.03

Question 3

Write down the value of 9².

1. 81
2. 18
3. 99
4. 27

Question 4 · Answer A

³√8 = 2 because 2 × 2 × 2 = 8. 4 is 8/2. 2.67 is 8/3. 512 is 8³.

Question 5 · Answer A

Negative × negative = positive. −8 × (−4) = 32. −32 ignores sign rule. −12 adds. 12 adds with wrong sign.

Question 6 · Answer A

90 = 2 × 45 = 2 × 9 × 5 = 2 × 3² × 5. 9 × 10 uses non-primes. 2 × 3 × 15 has 15. 2² × 3 × 5 has wrong power.

Question 7 · Answer A

09:25 to 12:25 = 3 hours. 12:25 to 12:08 = −17 min. 3h − 17min = 2h 43min. 3 hours 17 minutes adds wrong. 2 hours 17 minutes subtracts wrong. 3 hours 43 minutes adds both.

Question 8 · Answer A

In y = mx + c, gradient m = 4. 7 is y-intercept. 4/7 divides them. 11 adds them.

Question 9 · Answer A

Y-axis crossing at x = 0: y = 0 + 9 = 9. Point (0, 9). (9, 0) is x-intercept format. (0, 2) uses gradient. (−4.5, 0) is x-intercept.

Question 10 · Answer A

8x + 3x = 11x, −2y − 5y = −7y. Answer: 11x − 7y. 5x − 7y subtracts x terms. 11x + 3y adds y terms. 4xy combines illegally.

Question 11 · Answer A

6x − 3x = 17 − 5, 3x = 12, x = 4. x = 2.44 divides by 9. x = 12 is 3x. x = 7.33 divides by 3 wrong.

Question 12 · Answer A

Back bearing = 72° + 180° = 252°. 072° is original. 288° is 360 − 72. 108° is 180 − 72.

Question 13 · Answer A

0.00027 = 2.7 × 10⁻⁴ (4 places). 2.7 × 10⁻³ counts 3. 27 × 10⁻⁵ not standard form. 2.7 × 10⁴ positive power.

Question 14 · Answer A

A 5-sided polygon is a pentagon. Hexagon has 6, quadrilateral has 4, octagon has 8.

Question 15 · Answer A

Exterior angle = 360° ÷ 10 = 36°. 144° is interior angle. 1440° is sum of interior. 40° uses 9.

Question 16 · Answer A

P(black) = 1 − 0.3 − 0.45 = 0.25. 0.75 adds red and yellow. 0.15 subtracts wrong. 1.75 adds all.

Question 17 · Answer A

HCF = 5ab. So 5ab(2a − 3b). 5(2a²b − 3ab²), ab(10a − 15b), and 5ab(2a − 3) don't fully factorise.

Question 18 · Answer A

4⅓ = 13/3, 2⅚ = 17/6. 13/3 − 17/6 = 26/6 − 17/6 = 9/6 = 3/2 = 1½. 2½ adds. 1⅙ and 2⅙ calculate wrong.

Question 19 · Answer A

5n − 3 = 47, 5n = 50, n = 10. So 10th term. 9th term and 11th term off by one. 44th term uses 47−3.

Question 20 · Answer A

Actual = 12 × 40 = 480 cm = 4.8 m. 480 m doesn't convert to m. 0.3 m divides by 40. 48 m wrong conversion.

Question 21 · Answer A

From eq1: x = 10 − 2y. Sub: 3(10−2y) − y = 9, 30 − 7y = 9, y = 3, x = 4. Check: 4+6=10✓, 12−3=9✓

Question 22 · Answer A

C = 2πr = 2π × 5 = 10π cm. 25π cm is area formula. 5π cm is πr. 20π cm is 4πr.

Question 23 · Answer A

Radius = 6. A = πr² = π × 36 = 36π cm². 144π cm² uses diameter. 12π cm² is circumference. 6π cm² is πr.

Question 24 · Answer A

c² = 5² + 12² = 25 + 144 = 169. c = 13 cm. 17 cm adds. 169 cm forgets root. 7 cm subtracts.

Question 25 · Answer A

Mean = (5×5 + 15×12 + 25×8)/(25) = (25+180+200)/25 = 405/25 = 16.2. Closest is A. 15, 20, and 13.33 miscalculate.

Question 26 · Answer A

(x + 7)(x − 4) = x² − 4x + 7x − 28 = x² + 3x − 28. x² − 3x − 28 has wrong middle sign. x² + 11x − 28 adds coefficients. x² + 3x + 28 has wrong constant sign.

Question 27 · Answer A

Reflection in x = 0 (y-axis): x becomes −x, y stays same. (2,3)→(−2,3), etc. (2, −3), (4, −3), (3, −5) reflects in y=0. (−2, −3), (−4, −3), (−3, −5) reflects in both. (3, 2), (3, 4), (5, 3) swaps coordinates.

Question 28 · Answer A

Line of symmetry is midway between roots: (1 + 5)/2 = 3. So x = 3. y = 3 is wrong axis. x = 5 and x = 1 are the roots.

Question 29 · Answer A

V = πr²h = π × 16 × 9 = 144π cm³. 36π cm³ is πr²h/4. 72π cm³ is πr²h/2. 288π cm³ doubles.