IGCSE Mathematics 0580/11 May/June 2025 Past Paper with Answers

Question 1

What is 20045 written in words?

1. Twenty thousand and forty-five
2. Two thousand and forty-five
3. Twenty thousand four hundred and five
4. Two hundred thousand and forty-five

Question 2

What is 7836 rounded to the nearest ten?

1. 7840
2. 7830
3. 7800
4. 7900

Question 3

Convert 4523 centimetres into metres.

1. 45.23 m
2. 452.3 m
3. 4.523 m
4. 0.4523 m

Question 4 · Answer A

Cost = 8 × $\$0.35$ = $\$2.80$. Change = $\$5$ - $\$2.80$ = $\$2.20$

Question 5 · Answer A

Check: 4 + (-3) = 1 ✓ and 4 × (-3) = -12 ✓

Question 6 · Answer A

An even number is divisible by 2. 82 ÷ 2 = 41, so 82 is even.

Question 7 · Answer A

36 = 6², so 36 is a square number.

Question 8 · Answer A

48 ÷ 12 = 4, so 12 is a factor of 48.

Question 9 · Answer A

29 has only two factors: 1 and 29, so it is prime.

Question 10 · Answer A

The reciprocal of a number n is 1/n. Reciprocal of 8 = 1/8

Question 11 · Answer A

(3 + 2) × 5 - 5 = 5 × 5 - 5 = 25 - 5 = 20

Question 12 · Answer A

2 - 4 × (3 + 2) = 2 - 4 × 5 = 2 - 20 = -18.

Question 13 · Answer A

Cost = price per book × number of books = 12 × b = 12b

Question 14 · Answer A

Total = blue pens + black pens = m + 9

Question 15 · Answer A

60% = 60/100 = 6/10 = 3/5

Question 16 · Answer A

7/100 = 7 ÷ 100 = 0.07

Question 17 · Answer A

45 - 38 = 7, 38 - 31 = 7, 31 - 24 = 7. The rule is subtract 7.

Question 18 · Answer A

The rule is subtract 6. 10 - 6 = 4, then 4 - 6 = -2

Question 19 · Answer A

Common difference = 5, so coefficient of n is 5. When n=1: 5(1) + c = 7, so c = 2. nth term = 5n + 2

Question 20 · Answer A

The destination is at the maximum distance, which is 30 km.

Question 21 · Answer A

Time at location = 10:45 - 10:00 = 45 minutes

Question 22 · Answer A

They arrive home when the distance from home is 0, which is at 12:30.

Question 23 · Answer A

Time = distance ÷ speed = 24 ÷ 48 = 0.5 hours = 30 minutes

Question 24 · Answer A

Volume of cube = side³ = 5³ = 125 cm³

Question 25 · Answer A

$4x + 7 = 2x - 3$. Subtract $2x$: $2x + 7 = -3$. Subtract $7$: $2x = -10$. Divide by $2$: $x = -5$

Question 26 · Answer A

Negative × negative = positive. -6 × -7 = 42

Question 27 · Answer A

Adding a negative is the same as subtracting. -5 + (-9) = -5 - 9 = -14

Question 28 · Answer A

When multiplying with same base, add powers: $n + 3 = 8$, so $n = 5$

Question 29 · Answer A

A cuboid has 6 faces, so its net must have 6 rectangles.

Question 30 · Answer A

Collect like terms: 8x - 2x = 6x and 3y - 7y = -4y. Answer: 6x - 4y

Question 31 · Answer A

HCF of 8 and 12 is 4. Factor out: 8a + 12b = 4(2a + 3b)

Question 32 · Answer A

Common factor is $ab$. $a^2b - 3ab = ab(a - 3)$

Question 33 · Answer A

Round: $38.7 \approx 40$, $21.2 \approx 20$, $2.89 \approx 3$, $4.12 \approx 4$. Calculate: $\frac{40+20}{3 \times 4} = \frac{60}{12} = 5$

Question 34 · Answer A

Alternate angles are equal. The alternate angle is 65°.

Question 35 · Answer A

Corresponding angles are equal. The corresponding angle is 72°.

Question 36 · Answer A

Angles in triangle sum to 180°. Third angle = 180 - 55 - 75 = 50°

Question 37 · Answer A

P(blue) = number of blue ÷ total = 3/10

Question 38 · Answer A

P(Head) = 1/2. P(Head and Head) = 1/2 × 1/2 = 1/4

Question 39 · Answer A

The coordinates (2.5, 40) mean x = 2.5 and y = 40.

Question 40 · Answer A

When one variable increases and the other decreases, it is negative correlation.

Question 41 · Answer A

A line of best fit should pass through the middle of the scattered points.

Question 42 · Answer A

Read the y-value from the line at x = 10, which is 25.

Question 43 · Answer A

Angle at centre = 2 × angle at circumference. So angle ACB = 84° ÷ 2 = 42°

Question 44 · Answer A

HCF = 2¹ × 5¹ = 10 (take lowest power of common factors)

Question 45 · Answer A

LCM = 2² × 3² = 4 × 9 = 36 (take highest power of all factors)

Question 46 · Answer A

90° clockwise: (x, y) → (y, -x). So (3, 2) → (2, -3)

Question 47 · Answer A

Moving right is positive x, moving down is negative y. Vector is (5, -3)

Question 48 · Answer A

Multiply coordinates by scale factor: (2×3, 1×3) = (6, 3)

Question 49 · Answer A

2¼ + 1⅔ = 9/4 + 5/3 = 27/12 + 20/12 = 47/12 = 3 11/12

Question 50 · Answer A

47000 = 4.7 × 10⁴ (move decimal 4 places left)

Question 51 · Answer A

10⁻⁴ means move decimal 4 places left: 3.2 × 10⁻⁴ = 0.00032

Question 52 · Answer A

Add equations: 4x = 12, so x = 3. Then 3 - 2y = -1, 2y = 4, y = 2