Rational functions and graphs — AS & A Level Further Mathematics (9231) questions by topic
Asymptote-finding for rational curves defines this topic: finding the equations of the asymptotes of a quotient of two quadratics, showing a curve has no vertical asymptotes before stating its horizontal asymptote, and finding asymptotes for a curve containing a parameter a greater than 5/2.
Find, sketch, show and draw lead the command words across 14 questions from 2023 to 2025 papers, worth from 13 to 16 marks, the narrowest and highest mark band in this syllabus set, so each response is a substantial, multi-part sketch-and-justify task. With no examiner-report extracts logged for this topic, submitting each asymptote derivation and sketch for instant marking is the way to confirm both vertical and horizontal or oblique asymptotes are correctly justified before the curve is drawn.
May–June 2025, Paper 11
The curve C has equation y = (2x^2 - 5x)/(2x^2 - 7x - 4). Find the equations of the asymptotes of C.
Answer this question and get it marked →May–June 2025, Paper 12
The curve C has equation y = (2x^2 - 5x)/(2x^2 - 7x - 4). Find the equations of the asymptotes of C.
Answer this question and get it marked →May–June 2025, Paper 13
The curve C has equation y = (x^2 + a)/(x + a), where a is a positive constant. Find the equations of the asymptotes of C.
Answer this question and get it marked →May–June 2024, Paper 12
The curve C has equation y = (x^2 + ax + 1)/(x + 2), where a 5/2. Find the equations of the asymptotes of C.
Answer this question and get it marked →May–June 2024, Paper 13
The curve C has equation y = (x + 1)/(x^2 + 3). Show that C has no vertical asymptotes and state the equation of the horizontal asymptote.
Answer this question and get it marked →October–November 2024, Paper 11
The curve C has equation y = (4x^2 + x + 1)/(2x^2 - 7x + 3). Find the equations of the asymptotes of C.
Answer this question and get it marked →October–November 2024, Paper 12
The curve C has equation y = (x^2 + 3)/(x^2 + 1). Show that C has no vertical asymptotes and state the equation of the horizontal asymptote.
Answer this question and get it marked →October–November 2024, Paper 13
The curve C has equation y = (4x^2 + x + 1)/(2x^2 - 7x + 3). Find the equations of the asymptotes of C.
Answer this question and get it marked →May–June 2023, Paper 11
The curve C has equation y = (x^2 + 2x - 15)/(x - 2). Find the equations of the asymptotes of C.
Answer this question and get it marked →May–June 2023, Paper 12
The curve C has equation y = (x^2 + 2x - 15)/(x - 2). Find the equations of the asymptotes of C.
Answer this question and get it marked →May–June 2023, Paper 13
The curve C has equation y = (x^2 + 2x + 1)/(x - 3). Find the equations of the asymptotes of C.
Answer this question and get it marked →October–November 2023, Paper 11
The curve C has equation y = f(x), where f(x) = (x^2 + 2) / (x^2 - x - 2). Find the equations of the asymptotes of C.
Answer this question and get it marked →October–November 2023, Paper 12
The curve C has equation y = f(x), where f(x) = x^2 / (x + 1). Find the equations of the asymptotes of C.
Answer this question and get it marked →October–November 2023, Paper 13
The curve C has equation y = f(x), where f(x) = (x^2 + 2) / (x^2 - x - 2). Find the equations of the asymptotes of C.
Answer this question and get it marked →Other AS & A Level Further Mathematics topics
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