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IGCSE Mathematics Past Papers & Drilling (Paper 4): Pythagoras, Trigonometry, Volume
TUTORZONE ORIGINAL DRILLING MOCK · CAMBRIDGE IGCSE MATHEMATICS (0580) PAPER 4
Written to the Cambridge 0580 syllabus (2025-2027): Paper 4 Calculator (Extended), 100 marks, 2 hours, 50% (structured and unstructured; scientific calculator required); plus Paper 2 Non-calculator (Extended, 100 marks, 50%). This is a Paper 4 drilling mock: 6 questions for 100 marks with answers and techniques.
What is in IGCSE Mathematics (0580) Paper 4?
Direct answer: Paper 4 Calculator (Extended), 100 marks, 2 hours, 50% (scientific calculator required).
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Paper 4 (Calculator, Extended) | Structured and unstructured, 100 marks | 50% | 2 hours |
| Paper 2 (Non-calculator, Extended) | Structured and unstructured, 100 marks | 50% | 2 hours |
IGCSE Mathematics Paper 4 drilling technique: show formula, substitution and units; round to the stated significant figures or decimal places; in trigonometry match sin/cos/tan to the correct sides; for statistics separate the mean (divide by n) from the median (order and take the middle).
How this paper was built
This is a TutorZone original drilling mock: the questions follow the Cambridge 0580 structure (Paper 4 Extended, 100 marks, 50%) and the answers are our own, not Cambridge past papers or marking references.
Every numeric answer was recomputed programmatically.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Paper 4 (Calculator, Extended) | 50% | about 20 min per question | calculation + explanation |
| Paper 2 (Non-calculator, Extended) | 50% | about 20 min per question | mental arithmetic + fractions |
How is the hypotenuse found?
Direct answer: sqrt(a^2 + b^2); for 2 cm and 5 cm it is 5.39 cm.
Paper 4: calculator drilling (6 questions, 100 marks)
Three-layer working; round as the question asks.
Question 1 (16 marks)
A right-angled triangle has legs of 2 cm and 5 cm. Find the hypotenuse (three significant figures).
Question 2 (17 marks)
Find sin 30 without a calculator and explain why sin 150 has the same value.
Question 3 (17 marks)
A cylinder has radius 3 cm and height 10 cm. Find its volume (pi = 3.142, three significant figures).
Question 4 (17 marks)
Find the mean and median of [4, 8, 15, 16, 23].
Question 5 (16 marks)
A bag has 3 red and 5 blue balls. Find P(red), and explain how to find P(red twice, without replacement).
Question 6 (17 marks)
Solve x^2 – 5x + 6 = 0 and explain how a calculator’s equation solver can check it.
How is a cylinder’s volume found?
Direct answer: V = pi r^2 h; r = 3 and h = 10 gives 282.8 cm^3.
Paper 4 answers
Question 1
Hypotenuse = sqrt(2^2 + 5^2) = sqrt(29) = 5.39 cm (16).
Question 2
sin 30 = 0.5 (8); 150 is in the second quadrant with the same opposite side (sine stays positive) (9).
Question 3
V = pi r^2 h = 3.142 x 9 x 10 = 282.8 cm^3 (17).
Question 4
Mean = 66 / 5 = 13.2 (8); median = 15 (9).
Question 5
P(red) = 3/8 = 0.375 (8); both red = (3/8) x (2/7) since without replacement the red count drops (8).
Question 6
Factorise (x-2)(x-3)=0, so x = 2 or 3 (10); substitute back to confirm both sides match (7).
Which topics does this paper drill?
Direct answer: Pythagoras, trigonometry, cylinder volume, mean and median, probability and quadratic equations.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Pythagoras as addition | sqrt(2+5) | sqrt(2^2+5^2) | 5.39 cm |
| Wrong trig sides | tan = adj/opp | tan = opp/adj | sin 30 = 0.5 |
| Median as mean | Average it | Order then take the middle | 15 |
How to use this paper
First drill: the full 2 hours on all 6 questions with no references.
Mark it: check formulas, substitution and rounding.
Second drill: redo three to seven days later, aiming to finish inside 1 h 45 min.
What should I do after drilling this paper?
Direct answer: log formula or rounding errors; redo in three to seven days; and drill Paper 2 (non-calculator).
FAQ
Is this a Cambridge past paper?
No. The questions and answers are TutorZone originals, not Cambridge past papers or marking references.
What is in IGCSE Mathematics Paper 4?
The calculator paper (Extended), 100 marks, 2 hours, 50%, requiring a scientific calculator.
How is the hypotenuse found?
sqrt(a^2 + b^2); for 2 and 5 it is 5.39 cm.
Official references
| Resource | What to check |
|---|---|
| Cambridge IGCSE Mathematics 0580 syllabus (2025-2027) | Confirm the paper marks and times |
| https://www.tutorzone.com.hk/en-igcse-mathematics-0580-paper-2-mock-2027/ | IGCSE Mathematics Paper 2 drilling mock |
Related: practice area · IGCSE Mathematics Paper 2 drilling mock
Next step: find a tutor / register as a tutor
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