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IGCSE Additional Maths Past Papers & Drilling (Paper 1): Functions, Logs, Calculus
TUTORZONE ORIGINAL DRILLING MOCK · CAMBRIDGE IGCSE ADDITIONAL MATHEMATICS (0606) PAPER 1 (NON-CALCULATOR)
Written to the Cambridge 0606 syllabus (2025-2027): Paper 1 is non-calculator, 80 marks, 2 hours, 50%; Paper 2 is also 80 marks and 2 hours for 50%, but a scientific calculator is required. This is a Paper 1 drilling mock: 6 questions covering the 80 marks, with exact surd and fraction answers, worked steps and techniques.
May I use a calculator in IGCSE Additional Mathematics (0606) Paper 1?
Direct answer: No. Paper 1 is non-calculator (80 marks, 2 hours, 50%); Paper 2 is the one that requires a scientific calculator.
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Paper 1 (non-calculator) | Structured and unstructured questions, all compulsory, 80 marks | 50% | 2 hours |
| Paper 2 (scientific calculator required) | Structured and unstructured questions, all compulsory, 80 marks | 50% | 2 hours |
IGCSE Additional Mathematics Paper 1 drilling technique: with no calculator, answers should normally stay in surd or fraction form; show all necessary working because method marks are awarded; after solving a log equation check that each root is positive; for calculus rewrite into powers of x before differentiating or integrating.
How this paper was built
This is a TutorZone original drilling mock: the questions follow the Cambridge 0606 structure (Paper 1, 2 hours, 80 marks, no calculator) and the answers are our own, not Cambridge past papers or marking references.
Every numeric answer was computed independently before it was written (fg(2) = 9, gf(3) = 80, arc 7.2 cm, sector area 21.6 cm^2, 8C3 = 56, 8P3 = 336, definite integral 30), so the key cannot drift from the question data.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Paper 1 (non-calculator) | 50% | about 15-20 min a question; functions and logs first, calculus last | exact surd and fraction answers |
| Paper 2 (scientific calculator required) | 50% | write the formula before using the calculator; give 3 s.f. | formula, units and significant figures |
How are the two 0606 papers weighted?
Direct answer: Paper 1 and Paper 2 are worth 50% each; both are 80 marks, 2 hours and all questions are compulsory.
Paper 1: 6 demonstrated questions, 80 marks
No calculator; keep answers in surd or fraction form and show all working.
Question 1 (12 marks)
Given f(x) = 2x + 3 and g(x) = x^2 – 1. (a) Find fg(2). (b) Find gf(3). (c) Solve f(x) = g(x), giving the answers in surd form.
Question 2 (14 marks)
The curve y = x^2 – 6x + 5. (a) Find the coordinates of the stationary point and state whether it is a maximum or a minimum. (b) Find where the curve crosses the x-axis. (c) The equation x^2 + kx + 9 = 0 has equal roots; find the values of k.
Question 3 (14 marks)
(a) Solve log_2 x + log_2 (x – 6) = 4. (b) Explain why one of the roots must be rejected. (c) Simplify log_3 81 – log_3 3.
Question 4 (14 marks)
A sector has radius 6 cm and angle 1.2 radians. (a) Find the arc length. (b) Find the area of the sector. (c) Convert the angle to degrees, correct to three significant figures.
Question 5 (13 marks)
Three students are to be chosen from eight. (a) How many selections are possible if order does not matter? (b) How many arrangements are possible if the three take the posts of chair, vice-chair and secretary? (c) From five boys and four girls, how many ways are there to choose two boys and two girls?
Question 6 (13 marks)
(a) Given y = 3x^4 – 2x^-1 + 5, find dy/dx. (b) Hence find the gradient of the curve at x = 1. (c) Evaluate the definite integral of 3x^2 + 2 from x = 1 to x = 3.
Which topics does this paper drill?
Direct answer: functions and composite functions, quadratic functions and the discriminant, logarithmic equations, circular measure, permutations and combinations, and differentiation with a definite integral.
Paper 1 answers and working
Question 1
(a) g(2) = 2^2 – 1 = 3, so fg(2) = f(3) = 2(3) + 3 = 9 (4). (b) f(3) = 9, so gf(3) = g(9) = 81 – 1 = 80 (4). (c) 2x + 3 = x^2 – 1 gives x^2 – 2x – 4 = 0, so x = 1 ± √5 (4).
Question 2
(a) y = (x – 3)^2 – 4, so the stationary point is (3, -4); the coefficient of x^2 is positive, so it is a minimum (6). (b) x^2 – 6x + 5 = 0 gives (x – 1)(x – 5) = 0, so the curve crosses at x = 1 and x = 5 (4). (c) Equal roots need b^2 – 4ac = 0, so k^2 – 36 = 0 and k = 6 or k = -6 (4).
Question 3
(a) log_2[x(x – 6)] = 4, so x(x – 6) = 16, x^2 – 6x – 16 = 0 and (x – 8)(x + 2) = 0, giving x = 8 or x = -2 (8). (b) A logarithm is only defined for positive numbers, and x = -2 makes log_2 x meaningless, so it is rejected and x = 8 (4). (c) log_3 81 = 4 and log_3 3 = 1, so the answer is 3 (2).
Question 4
(a) Arc length = r-theta = 6 x 1.2 = 7.2 cm (4). (b) Area = half r^2 theta = 0.5 x 36 x 1.2 = 21.6 cm^2 (6). (c) 1.2 x 180/pi = 68.8 degrees (3 s.f.) (4).
Question 5
(a) 8C3 = 56 (4). (b) 8P3 = 336 (4). (c) 5C2 x 4C2 = 10 x 6 = 60 (5).
Question 6
(a) dy/dx = 12x^3 + 2x^-2 (6). (b) At x = 1: 12 + 2 = 14 (3). (c) The integral of 3x^2 + 2 is x^3 + 2x, so from 1 to 3 it is (27 + 6) – (1 + 2) = 30 (4).
How should I answer a non-calculator paper?
Direct answer: Keep answers exact in surd or fraction form and show all necessary working, because method marks are awarded.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Using a calculator | Copying a decimal straight in | The paper wants exact values | Keep surds or fractions |
| Skipping working | Writing the answer only | No method marks | Show every step |
| Not testing log roots | Quoting both roots | The negative root must be rejected | Check the domain of the log |
How to use this paper
First drill: put the calculator away and do all 6 questions inside 2 hours.
Mark it: highlight every question where missing working lost method marks.
Second drill: redo three to seven days later inside 1 h 40 min, then drill the calculator version in Paper 2.
What should I do after drilling this paper?
Direct answer: log every question where missing working lost method marks; redo in three to seven days; then drill again under the Paper 2 calculator rules.
FAQ
Is this a Cambridge past paper?
No. The questions and answers are TutorZone originals, not Cambridge past papers or marking references.
May I use a calculator in Paper 1?
No. Paper 1 of 0606 is non-calculator; Paper 2 requires a scientific calculator.
What grades are available?
A* to E only; candidates below the grade E threshold are unclassified.
Should answers be decimals?
Paper 1 usually wants exact values in surd or fraction form; where pi or trigonometry is involved the question states exact form or the required accuracy.
Official references
| Resource | What to check |
|---|---|
| Cambridge IGCSE Additional Mathematics 0606 page | Confirm the paper marks, times and calculator rules |
| https://www.tutorzone.com.hk/en-igcse-mathematics-0580-paper-4-mock-2027/ | IGCSE Mathematics 0580 Paper 4 drilling mock |
Related: practice area · IGCSE Mathematics 0580 Paper 4 drilling mock
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