Differentiation: past paper questions

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• Question 24May/June 2026, paper 21Structured9 marks

  Find the coordinates of the turning points of the graph of $y=x^3-6x^2+7$.

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• Question 23Oct/Nov 2025, paper 21Structured4 marks

  Find the coordinates of the turning point on the graph of $y=7-2x-x^2$.

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• Question 25Oct/Nov 2023, paper 22Structured2 marksHas a diagram

  The derivative of $2a{x}^7+3x^k$ is $42x^6+15x^{k-1}$. Find the value of $a$ and the value of $k$.

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• Question 23May/June 2026, paper 22Structured7 marks

  The equation of a curve is $y=2x^2-11x+12$. Find the gradient of the tangent to the curve at $x=2$.

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• Question 22Oct/Nov 2025, paper 22Structured3 marks

  A graph with equation $y=x^2+bx+c$ has a minimum point at $(-5,12)$. Find the value of $b$ and the value of $c$.

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• Question 10Oct/Nov 2024, paper 42Structured9 marks

  A curve has the equation $y=x^3-9x^2-48x$. Differentiate $x^3-9x^2-48x$.

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• Question 11Oct/Nov 2023, paper 41Structured10 marks

  Differentiate $x^3-4x^2-3x$.

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• Question 20May/June 2026, paper 43Structured8 marks

  Find the coordinates of the turning points of the graph $y=8x^3-6x+5$.

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• Question 20Oct/Nov 2025, paper 43Structured4 marks

  $$y=x^3+3x^2-13x$$ Find $\frac{\mathrm{d}y}{\mathrm{d}x}$.

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• Question 10Oct/Nov 2024, paper 43Structured11 marks

  The diagram shows a sketch of the graph of $y=3+2x-x^2$.

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• Question 9Oct/Nov 2023, paper 42Structured8 marksHas a diagram

  The diagram shows a sketch of the graph of $y=4x^3-x^4$.

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• Question 22May/June 2025, paper 21Structured6 marks

  A curve has equation $y=x^n+q{x}^2+9x$. $$\frac{\mathrm{d}y}{\mathrm{d}x}=3x^2-12x+9$$ Find the value of $n$, and the value of $q$.

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• Question 8May/June 2024, paper 41Structured15 marks

  On the axes, sketch the graph of $y=x^2+7x-18$.

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• Question 11Oct/Nov 2023, paper 43Structured9 marksHas a diagram

  The diagram shows a sketch of $y=18+5x-2x^2$.

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• Question 21May/June 2025, paper 22Structured9 marksHas a diagram

  The diagram shows the graph of $y=3x-x^3$. The graph crosses the $x$-axis at $A$, at $O$ and at $B$. The turning points of the graph are at $P$ and at $Q$.

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• Question 11May/June 2024, paper 42Structured7 marks

  The point $(-1,6)$ lies on a curve. This curve has the derived function $\frac{\mathrm{d}y}{\mathrm{d}x}=-4x^3-9x^2+5$. Show that $(-1,6)$ is a stationary point of the curve.

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• Question 21May/June 2023, paper 21Structured6 marks

  A curve has equation $y=x^3-12x$. Find the gradient of the curve at the point $(1,-11)$.

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• Question 21May/June 2025, paper 23Structured6 marks

  Differentiate $x^3-3x^2+1$.

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• Question 10May/June 2024, paper 43Structured11 marks

  $y=x^7-7x^6$ Find the derivative of $y$ with respect to $x$.

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• Question 8May/June 2023, paper 42Structured13 marks

  Show that the equation $y=(x-4)(x+1)(x-2)$ can be written as $y=x^3-5x^2+2x+8$.

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• Question 26May/June 2025, paper 42Structured2 marks

  $$y=a{x}^{11}+3x^b$$ $$\frac{\mathrm{d}y}{\mathrm{d}x}=44x^{10}+18x^c$$ Find the values of $a$, $b$ and $c$.

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• Question 12May/June 2023, paper 43Structured8 marks

  The equation of a curve is $y=x^4-8x^2+5$. Find the derivative, $\left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)$, of $y=x^4-8x^2+5$.

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