Differentiation — AS & A Level Further Mathematics (9231) questions by topic
Implicit and parametric differentiation runs through this small topic: showing that dy/dx = -1/6 at a given point on an implicit logarithmic curve, and showing that dy/dx simplifies to a stated expression for parametric curves defined with inverse trigonometric functions.
Show and find are the two command words across 8 questions from 2023 to 2024 papers, worth from 6 to 8 marks, so each answer is a single sustained chain-rule derivation reaching a fixed target expression. With no examiner-report extracts logged for this topic, submitting each implicit or parametric derivation for instant marking is the way to confirm every product-rule and chain-rule term is present before the stated result is reached.
May–June 2024, Paper 21
It is given that x = sin^(-1)(t) and y = tcos^(-1)(t), for 0 <= t < 1. Show that dy/dx = -t + sqrt(1 - t^2)cos^(-1)(t).
Answer this question and get it marked →May–June 2024, Paper 22
It is given that x = sin^(-1)(t) and y = tcos^(-1)(t), for 0 <= t < 1. Show that dy/dx = -t + sqrt(1 - t^2)cos^(-1)(t).
Answer this question and get it marked →May–June 2024, Paper 23
The curve C has equation x^3 + 2xy + 8y^3 = -12. Show that, at the point (-2, -1) on C, dy/dx = -1/2.
Answer this question and get it marked →October–November 2024, Paper 21
It is given that x = 1 + 1/t and y = cos^(-1) t for 0 < t < 1. Show that dy/dx = t^2 / sqrt(1 - t^2).
Answer this question and get it marked →October–November 2024, Paper 22
The curve C has equation 4y^2 + 4 ln(xy) = 1. Show that, at the point (2, 1/2) on C, dy/dx = -1/6.
Answer this question and get it marked →October–November 2024, Paper 23
It is given that x = 1 + 1/t and y = arccos(t) (that is, y = cos^(-1) t) for 0 < t < 1. Show that dy/dx = t^2 / sqrt(1 - t^2).
Answer this question and get it marked →May–June 2023, Paper 23
The curve C has equation 4y^3 + (x + y)^6 = 109. Show that, at the point (-4, 3) on C, dy/dx = 1/17.
Answer this question and get it marked →October–November 2023, Paper 22
It is given that x = 1 + 1/t and y = te^t. Show that dy/dx = -e^t(t^3 + t^2).
Answer this question and get it marked →Other AS & A Level Further Mathematics topics
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