Extended · 100 marks · 2h. Each generated paper follows the 0580 Paper 4 · Calculator format, with the same number and style of questions as the real exam, and comes with a Cambridge-style mark scheme.
Generate Paper 4 · Calculator →The probability that it rains on any day is 0.6. The weather on different days is independent.
Find the probability that it rains on exactly one of two days.
Find the probability that it rains on at least one of three days.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.48 2 × 0.6 × 0.4 M1 0.48 A1 | 2 |
| (b) | 0.936 1 − 0.43 M1 0.936 A1 | 2 |
OAB is a triangle with OA = a and OB = b.
P is the point on AB such that AP : PB = 2 : 1.
Q is the point on OB such that OQ = 23b.
The lines OP and AQ intersect at X.
Find OP in terms of a and b.
By writing OX = λOP and AX = μAQ, find the values of λ and μ.
Find the ratio OX : XP in its simplest form.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 13a + 23b a + 23(b − a) M1 13a + 23b A1 | 2 |
| (b) | λ = 34, μ = 34 OX = a + μ(−a + 23b) M1 equate coefficients of a and of b M1 two correct equations A1 λ = 34 A1 μ = 34 A1 | 5 |
| (c) | 3 : 1 3 : 1 B1 | 1 |
The exchange rate is 1 euro (€) = 0.86 pounds (£).
Change €400 into pounds.
Change 412.80 pounds into euros.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 344.00 344.00 B1 | 1 |
| (b) | €480.00 ÷ 0.86 M1 480.00 A1 | 2 |
Expand and simplify (x − 7)(x − 1).
Factorise completely 45x2y + 25xy2.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x2 − 8x + 7 x2 − 8x + 7 B2 B1 for three of four terms | 2 |
| (b) | 5xy(9x + 5y) 5xy(9x + 5y) B2 B1 for a correct partial factorisation | 2 |
The diagram shows shape A and shape B on a grid.
Describe fully the single transformation that maps shape A onto shape B.
On the grid, reflect shape A in the line y = −3. Label the image C.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | Translation by the vector 22 Translation B1 22 B1 | 2 |
| (b) | Image C drawn with vertices (−2, −4), (1, −4), (−1, −6) Correct image B2 B1 for reflection in another horizontal line or correct reflection of the line y = −3 with one vertex wrong | 2 |
A parallelogram has area 72 cm² and base 8 cm. Find its perpendicular height.
| Part | Answer and marking points | Marks |
|---|---|---|
| 9 cm 72 ÷ 8 M1 9 A1 | 2 |
All IGCSE Mathematics papers and topics
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in