A Level Further Mathematics 9231, topic 1.2

Rational functions and graphs: past paper questions

21 Cambridge A Level Further Mathematics 9231 questions on Rational functions and graphs (1.2) from 21 papers, 2023 to 2026. Open the paper or try a question free.

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Questions: 21
Papers: 21
Years: 2023 to 2026
Total marks: 301
Average per question: 14.3 marks
Largest question: 16 marks

By type: Structured 21

How hard the questions are

Recall0
Apply21
Analyse0
Not banded0

Derived from the command word Cambridge prints in each question, banded by a fixed table beside the syllabus's own definitions. A question printing no command word is unbanded: unknown, not middling.

Command words

findApply21 questions
sketchApply21 questions
make a simple freehand drawing showing the key features, taking care over proportions
show thatApply9 questions

Where the questions come from

By year

20263
20256
20246
20236

By session

May/June12
Oct/Nov9

By paper

Paper 121

Questions on this topic

Showing 19 of 21, spread across the years. Open one to write your answer and have it marked.

Question 6May/June 2026, paper 11Structured14 marks
The curve $C$ has equation $y = \frac{x^{2} - x + 2}{4 x + 4}$ . Find the equations of the asymptotes of $C$ .
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Question 7Oct/Nov 2025, paper 11Structured14 marks
The curve $C$ has equation $y = \frac{x + 2}{x^{2} + 3 x + 1}$ . Find the equations of the asymptotes of $C$ .
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Question 6Oct/Nov 2024, paper 11Structured13 marks
The curve $C$ has equation $y = \frac{4 x^{2} + x + 1}{2 x^{2} - 7 x + 3}$ . Find the equations of the asymptotes of $C$ .
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Question 7Oct/Nov 2023, paper 11Structured15 marks
The curve $C$ has equation $y = f (x)$ , where $f (x) = \frac{x^{2} + 2}{x^{2} - x - 2}$ . Find the equations of the asymptotes of $C$ .
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Question 6May/June 2026, paper 12Structured14 marks
The curve $C$ has equation $y = \frac{x^{2} - x + 2}{4 x + 4}$ . Find the equations of the asymptotes of $C$ .
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Question 7Oct/Nov 2025, paper 12Structured14 marks
The curve $C$ has equation $y = \frac{x^{2} + x + 1}{x + 1}$ . Find the equations of the asymptotes of $C$ .
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Question 6Oct/Nov 2024, paper 12Structured15 marks
The curve $C$ has equation $y = \frac{x^{2} + 3}{x^{2} + 1}$ . Show that $C$ has no vertical asymptotes and state the equation of the horizontal asymptote.
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Question 7Oct/Nov 2023, paper 12Structured16 marks
The curve $C$ has equation $y = f (x)$ , where $f (x) = \frac{x^{2}}{x + 1}$ . Find the equations of the asymptotes of $C$ .
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Question 6May/June 2026, paper 13Structured14 marks
The curve $C$ has equation $y = \frac{x + 1}{x^{2} + x + 1}$ . Show that $C$ has no vertical asymptotes and state the equation of the horizontal asymptote.
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Question 6Oct/Nov 2024, paper 13Structured13 marks
The curve $C$ has equation $y = \frac{4 x^{2} + x + 1}{2 x^{2} - 7 x + 3}$ . Find the equations of the asymptotes of $C$ .
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Question 7Oct/Nov 2023, paper 13Structured15 marks
The curve $C$ has equation $y = f (x)$ , where $f (x) = \frac{x^{2} + 2}{x^{2} - x - 2}$ . Find the equations of the asymptotes of $C$ .
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Question 7May/June 2025, paper 11Structured15 marks
The curve $C$ has equation $y = \frac{2 x^{2} - 5 x}{2 x^{2} - 7 x - 4}$ . Find the equations of the asymptotes of $C$ .
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Question 6May/June 2024, paper 11Structured15 marks
The curve $C$ has equation $y = \frac{x^{2} + a x + 1}{x + 2}$ , where $a > \frac{5}{2}$ . Find the equations of the asymptotes of $C$ .
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Question 6May/June 2023, paper 11Structured15 marks
The curve $C$ has equation $y = \frac{x^{2} + 2 x - 15}{x - 2}$ . Find the equations of the asymptotes of $C$ .
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Question 6May/June 2024, paper 12Structured15 marks
The curve $C$ has equation $y = \frac{x^{2} + a x + 1}{x + 2}$ , where $a > \frac{5}{2}$ . Find the equations of the asymptotes of $C$ .
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Question 6May/June 2023, paper 12Structured15 marks
The curve $C$ has equation $y = \frac{x^{2} + 2 x - 15}{x - 2}$ . Find the equations of the asymptotes of $C$ .
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Question 6May/June 2025, paper 13Structured14 marks
The curve $C$ has equation $y = \frac{x^{2} + a}{x + a}$ , where $a$ is a positive constant. Find the equations of the asymptotes of $C$ .
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Question 6May/June 2024, paper 13Structured13 marks
The curve $C$ has equation $y = \frac{x + 1}{x^{2} + 3}$ . Show that $C$ has no vertical asymptotes and state the equation of the horizontal asymptote.
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Question 7May/June 2023, paper 13Structured13 marks
The curve $C$ has equation $y = \frac{x^{2} + 2 x + 1}{x - 3}$ . Find the equations of the asymptotes of $C$ .
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