Every IGCSE Additional Mathematics topic, with free past-paper-style questions and full mark schemes. Pick a chapter to practise its questions, or generate a complete 0606-format paper in seconds, from easy warm-ups to A*-level "brutal" papers.
Generate a free Additional Mathematics paper →Functions · Quadratic functions · Factors of polynomials · Equations, inequalities & graphs · Simultaneous equations · Logarithmic & exponential functions
Straight-line graphs · Coordinate geometry of the circle · Circular measure · Trigonometry
Paper 1 · Non-calculator (80 marks · 2h); Paper 2 · Calculator (80 marks · 2h).
A mixed set from across the syllabus. Questions marked A* challenge come from the hardest bank.
A circle has centre C(3, 2) and passes through the point P(6, 6).
Find the equation of the circle.
Find the equation of the tangent to the circle at P.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (x − 3)2 + (y − 2)2 = 25 radius 5 B1 (x − 3)2 + (y − 2)2 = 25 B1 | 2 |
| (b) | tangent gradient CP = 43 B1 tangent gradient −34 M1 y − 6 = −34(x − 6) A1 | 3 |
A boat travels at 8 m/s in still water. It heads due north across a river flowing at 6 m/s due east.
Find the resultant speed and the angle between the boat’s path and the bank.
| Part | Answer and marking points | Marks |
|---|---|---|
| 10 m/s; 53.1° Pythagoras M1 10 m/s A1 tan θ = 8/6 M1 53.1° A1 | 4 |
A team of 4 is to be chosen from 9 people, including Ali and Bea.
Find the number of different teams.
Find the number of teams that include Ali but not Bea.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 126 126 B1 | 1 |
| (b) | 35 7C3 M1 35 A1 | 2 |
The first term of a geometric progression is 24 and the common ratio is 23.
Find the sum to infinity.
Find the least number of terms whose sum exceeds 99% of the sum to infinity.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 72 a ÷ (1 − r) M1 72 A1 | 2 |
| (b) | 12 1 − rn > 0.99 M1 logs M1 12 A1 | 3 |
A particle moves in a straight line. Its displacement, s m, from O after t s is s = 2t3 − 15t2 + 24t.
Find the times when the particle is instantaneously at rest.
Find the acceleration when t = 5.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | t = 1 and t = 4 v = dsdt M1 v = 0 solved M1 t = 1, 4 A1 | 3 |
| (b) | 30 m s−2 a = dvdt = 12t − 30 M1 30 A1 | 2 |
f(x) = (x + 3)2 + 7 for x ≥ −3
State the range of f.
Find f−1(x) and state its domain.
Describe how the graphs of y = f(x) and y = f−1(x) are related.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | f(x) ≥ 7 f(x) ≥ 7 B1 | 1 |
| (b) | −3 + √(x − 7), x ≥ 7 swap x and y and rearrange M1 f−1(x) = √(x − 7) − 3 A1 domain x ≥ 7 B1 | 3 |
| (c) | reflection in y = x reflection in the line y = x B1 | 1 |
No. They are original questions written to match the IGCSE Additional Mathematics 0606 syllabus and the style of real Cambridge papers, so you can practise beyond the past papers you have already done.
Yes. Every question on these pages has its answer, and every generated paper comes with a full Cambridge-style mark scheme you can download as a PDF.
Yes. Choose the paper (Paper 1 Non-calculator, Paper 2 Calculator), the topics, the marks and the difficulty, and the generator builds a fresh paper with the same number and style of questions as the real exam.
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