Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Differentiation — exam questions
10 original Incandio exam-style questions on differentiation, 27 marks, about 33 minutes of writing. Each one carries the command word, the tariff and the specification statement it assesses, exactly as a paper presents them. This is an original Incandio practice question, written to reflect the structure and demands of the qualification. It is not an official Pearson Edexcel past-paper question.
This is the practice set for Differentiation — the module that teaches it. Read the module first if the idea is new; come here when you want to find out whether you can turn it into marks. Completely free, no account needed to read.
What these questions ask of you
5 command words run through this set, and on Pearson Edexcel International GCSE Mathematics A each one means something precise. Answering the wrong command is the commonest way a candidate who understands the module still loses the mark.
- Write down (1–2 marks)
- a value that needs no working — read off, recalled or stated
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- Work out (1–5 marks)
- a calculated result, with the working that produced it
- Show that (2–5 marks)
- every step of a derivation to a value that is already printed in the question Misread as: stating the printed answer again instead of deriving it
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 3.4. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording.
The 10 questions
Answer them on paper, then open the module's exam practice to have them marked. The mark scheme, the accepted and rejected answers and the annotated model answer are in Incandio and are not printed here — an answer beside its question is not practice.
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(1)Write down
y = x⁵. Write down dy/dx.
(Total for Question 1 = 1 mark)
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(2)Find
y = 4x³ + 9. Find dy/dx.
(Total for Question 2 = 2 marks)
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(2)Find
y = x² + 7x − 2. Find dy/dx.
(Total for Question 3 = 2 marks)
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(1)Explain why
The curves y = x² and y = x² + 6 have the same derivative. Explain why.
(Total for Question 4 = 1 mark)
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(3)Work out
y = x³ − 4x² + 5. Work out the gradient of the curve at the point where x = 3.
gradient of the curve = ............................
(Total for Question 5 = 3 marks)
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(3)Find
y = x² − 10x + 3. Find the coordinates of the turning point of this curve.
(Total for Question 6 = 3 marks)
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(3)Show that
y = 2x³ − 6x + 1. Show that the curve is flat at x = 1 and at x = −1.
(Total for Question 7 = 3 marks)
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(3)Find
y = 12x − x³ has a turning point where x is positive. Find the coordinates of that point.
(Total for Question 8 = 3 marks)
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(4)Find
The curve y = x² − 4x + 7 has a tangent at the point where x = 3. Find the equation of that tangent.
(Total for Question 9 = 4 marks)
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(5)Find
A curve has equation y = x³ − 6x² + 9x + 2. Find the coordinates of the two stationary points, and determine which is the maximum.
coordinates of the stationary points = ............................
(Total for Question 10 = 5 marks)
Have them marked, then defend the answer
Practice tells you the mark; teaching it back tells you whether you understand it. On Incandio a topic counts as mastered only once you have taught it and defended it.
- Mark these questions — 10 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
- Teach it — explain differentiation to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Isaac Newton over three rounds, marked against descriptors you can read first.
Completely free. No subscriptions, no paywalls, no account needed to start.
Back to the module
- Differentiation — The gradient of a curve at a single point — the power rule, and why it works. Higher Tier, and genuinely on this specification.
- All of Incandio Mathematics · Incandio Exam Practice