Differentiate: y = x³.
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Differentiation Topical Past Papers.
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These Differentiation Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Algebra and graphs (E2.12) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Estimate gradients of curves; differentiate functions of the form axⁿ (and sums of these); apply differentiation to find gradients, stationary points and distinguish between maxima and minima.
Differentiate: y = x³.
Find dy/dx if y = 5x².
[1 mark]Differentiate y = 2x³ − 4x + 7.
[2 marks]Find the gradient of the curve y = x² + 3x at the point where x = 2.
[2 marks]What is dy/dx when y = 5?
Consider the curve y = x³ − 3x + 1.
Find dy/dx.
[1 mark]Find the x-coordinates of the stationary points of the curve.
[2 marks]y = x² − 4x. Find the x-coordinate of the stationary point and state whether it is a maximum or a minimum.
[2 marks]A rectangle has width x and length (12 − 2x), where 0 < x < 6. Find the value of x that gives the maximum possible area.
[2 marks]