IGCSE Mathematics 0580/33 May/June 2025 Past Paper with Answers

Question 1

Write 180 as a product of its prime factors.

1. 2² × 3² × 5
2. 4 × 9 × 5
3. 2 × 3 × 30
4. 2³ × 3 × 5

Question 2

Find the HCF of 48 and 60.

1. 12
2. 4
3. 240
4. 6

Question 3

Find the LCM of 12 and 18.

1. 36
2. 6
3. 216
4. 72

Question 4 · Answer A

7a − 3a = 4a, 2b + 5b = 7b. Answer: 4a + 7b. 10a + 7b adds a terms. 4a − 3b subtracts b terms. 11ab combines unlike terms.

Question 5 · Answer A

15x − 10 − 8x − 2 = 7x − 12. 7x − 8 adds −10 and −2 wrong. 23x − 12 adds x terms. 7x + 12 has wrong sign.

Question 6 · Answer A

HCF = 4ab. So 4ab(2a + 3b). 4(2a²b + 3ab²), 2ab(4a + 6b), and ab(8a + 12b) don't fully factorise or use wrong HCF.

Question 7 · Answer A

3.27 × 10⁴ = 32700 (move decimal 4 places right). 327000 uses 10⁵. 3270 uses 10³. 0.000327 uses negative power.

Question 8 · Answer A

0.00072 = 7.2 × 10⁻⁴ (4 places). 7.2 × 10⁻³ uses 3. 72 × 10⁻⁵ not standard form. 7.2 × 10⁴ positive power.

Question 9 · Answer A

8.4 ÷ 4.2 = 2, 10⁶ ÷ 10² = 10⁴. Answer: 2 × 10⁴. 2 × 10⁸ adds powers. 2 × 10³ subtracts wrong. 4.2 × 10⁴ doesn't divide numbers.

Question 10 · Answer A

4x = 25 − 9 = 16, x = 4. x = 8.5 is (25−9)÷2. x = 16 forgets to divide. x = 3.5 uses wrong subtraction.

Question 11 · Answer A

12x − 8 = 2x + 10, 10x = 18, x = 18/10 = 9/5. x = 2 rounds. x = −1 has sign error. x = 18/10 not simplified.

Question 12 · Answer A

From eq2: x = 12 − 4y. Sub: 3(12−4y) + 2y = 16, 36 − 12y + 2y = 16, −10y = −20, y = 2, x = 4. Check: 3(4)+2(2)=16✓, 4+4(2)=12✓

Question 13 · Answer A

Frequency polygons use class midpoints. Midpoint of 20-30 is (20+30)/2 = 25. 20 and 30 are boundaries. 50 is sum.

Question 14 · Answer A

Mean = (5×5 + 15×10 + 25×15)/(5+10+15) = (25+150+375)/30 = 550/30 ≈ 18.3. Closest is 17. 20, 15, and 10 are incorrect calculations.

Question 15 · Answer A

x ≥ −2 includes −2. x < 3 excludes 3. So: −2, −1, 0, 1, 2. −2, −1, 0, 1, 2, 3 includes 3. −1, 0, 1, 2 excludes −2. −2, −1, 0, 1 excludes 2.

Question 16 · Answer A

5x − 3x < 10 − 2, 2x < 8, x < 4. x > 4 has wrong inequality sign. x < 6 uses wrong arithmetic. x < 1.5 divides wrong.

Question 17 · Answer A

c² = 8² + 15² = 64 + 225 = 289, c = 17 cm. 23 cm adds. 289 cm forgets root. 12 cm subtracts.

Question 18 · Answer A

Area = ½ × 6 × 10 = 30 cm². 60 cm² forgets ½. 16 cm² adds. 136 cm² finds c² + area.

Question 19 · Answer A

tan θ = 7/10 = 0.7, θ = tan⁻¹(0.7) = 35.0°. 55.0° is complement. 44.4° uses wrong ratio. 70.0° doubles.

Question 20 · Answer A

y = 8/4 = 2. 32 multiplies. 4 uses same value. 0.5 inverts.

Question 21 · Answer A

6 = k/2, so k = 12. 3 is 6/2. 8 is 2+6. 4 is 6−2.

Question 22 · Answer A

10/x = 4, x = 10/4 = 2.5. x = 0.4 is 4/10. x = 6 is 10−4. x = 40 is 10×4.

Question 23 · Answer A

25% of 80 = 20. Sale price = 80 − 20 = $\$60$. $\$100$ adds. $\$55$ uses 31.25%. $\$20$ is just the discount.

Question 24 · Answer A

Increase = 12. Percentage = (12/40) × 100 = 30%. 23.1% uses 52 as base. 12% is just 12. 130% is ratio × 100.

Question 25 · Answer A

Horizontal line means distance isn't changing, so the object is stationary. The object is moving at constant speed would be a diagonal line. The object is accelerating and The object is decelerating would be curves.

Question 26 · Answer A

Speed = distance/time = 90/1.5 = 60 km/h. 135 km/h multiplies. 91.5 km/h adds. 45 km/h uses 2 hours.

Question 27 · Answer A

Speed = gradient. Steepest gradient = fastest speed. The horizontal section is zero speed. The curved section shows changing speed. The lowest section is about position not speed.

Question 28 · Answer A

Arc = (72/360) × 2π × 10 = (1/5) × 20π = 4π cm. 20π cm is full circumference. 2π cm uses wrong formula. 72π cm uses angle directly.

Question 29 · Answer A

Area = (60/360) × π × 36 = (1/6) × 36π = 6π cm². 36π cm² is full circle. 12π cm² uses wrong fraction. 2π cm² uses arc formula.

Question 30 · Answer A

Perimeter = arc + 2r = 3π + 10 cm. 3π cm is just arc. 8π cm adds wrong. (3π + 5) cm only adds one radius.