Graphs of functions: past paper questions

Where the questions come from

• Question 8May/June 2026, paper 21Structured8 marks

  $P$ is the point $(0,4)$ and $Q$ is the point $(1,8)$. Find the coordinates of the midpoint of $PQ$.

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• Question 14Oct/Nov 2025, paper 23Structured2 marks

  The minimum point on a quadratic curve is $(-3,-5)$. Find the equation of the line of symmetry of the curve.

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• Question 22Oct/Nov 2024, paper 21Structured6 marksHas a diagram

  The graph of $y=(x+2)(x-1{)}^2$ is shown on the grid. Show that $y=(x+2)(x-1{)}^2$ can be written as $y=x^3-3x+2$.

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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 8May/June 2026, paper 42Structured11 marks

  The table shows some values, correct to 1 decimal place, for $y=x^3-2x^2-2$.

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• Question 11Oct/Nov 2025, paper 42Structured10 marks

  The table shows some values for $y=x^3-2x+3$. Where appropriate, values of $y$ are given correct to 2 decimal places. Complete the table.

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• Question 2Oct/Nov 2024, paper 42Structured13 marks

  The table shows some values for $y=x^3+4x^2-4$. Complete the table.

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• Question 7Oct/Nov 2023, paper 43Structured11 marks

  Complete the table of values for $y=3\cos 2x^{\circ }$.

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• Question 11May/June 2026, paper 43Structured10 marks

  The table shows some values for $y=3\times 2^x-5$ correct to 1 decimal place.

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• Question 13Oct/Nov 2025, paper 43Structured3 marks

  The point $(5,1024)$ lies on the curve $y=c^x$, where $c$ is a whole number. Find the $y$-coordinate of the point on the curve with $x$-coordinate $-2$.

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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 11May/June 2025, paper 21Structured5 marksHas a diagram

  The diagram shows the graph of $y=\mathrm{f}(x)$ and the point $P(-2,11)$. The tangent from $P$ touches the graph of $y=\mathrm{f}(x)$ at the point $(a,b)$. The values of $a$ and $b$ are integers.

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• Question 18May/June 2024, paper 22Structured3 marksHas a diagram

  The graph of $y=\mathrm{f}(x)$ is drawn on the grid. Draw the tangent to the graph at the point $x=3$.

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• Question 20May/June 2023, paper 21Structured7 marks

  The table shows some values for $y=3x^2-2x-1$. Complete the table.

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• Question 15May/June 2025, paper 22Structured6 marks

  The diagram shows the graph of $y=\frac{2}{x}-1$. Write down the coordinates of the point where the graph crosses the $x$-axis.

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• Question 5May/June 2024, paper 43Structured13 marksHas a diagram

  The diagram shows the graph of $y=\mathrm{f}(x)$ for values of $x$ from -3 to 3. Use the graph to find $\mathrm{f}(2)$.

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• Question 10May/June 2023, paper 43Structured12 marks

  The table shows some values for $y=2^x-3$.

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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 14May/June 2025, paper 41Structured11 marks

  The table shows some values for $y=5x^2-x^3-4$. Complete the table.

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