◈ Oracle PrepSign Up Free
A-LevelMathematicsDifferentiation9709/31 · Oct/Nov 2025 · Q75 Marks

The parametric equations of a curve are x = t² - ln(t+1), y = t/(2t+1)

  1. (a)Obtain a simplified expression for dy/dx in terms of t.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

  1. [B1] State dx/dt = 2t - 2/(2t+1)
  2. [M1] Use correct quotient rule or correct product rule
  3. [A1] Obtain dy/dt = (2t+1).1-t(2) / (2t+1)² oe
  4. [M1] Use dy/dx = (dy/dt) / (dx/dt)
  5. [A1] Obtain answer 1 / (2(t+1)(2t-1)(t+1))

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2025 Paper 3 Variant 1, question 7.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Mathematics questions

DifferentiationFeb/Mar 20195m

The variables x and y satisfy the relation sin y = tan x, where –½π < y < ½π. Show that dy/dx = 1 / (cos x √(cos 2x)).

DifferentiationFeb/Mar 20203m

The function f is defined by f(x) = 1 3x + 2 + x² for x < -1.

DifferentiationFeb/Mar 20204m

A curve has equation y = x² – 2x – 3. A point is moving along the curve in such a way that at P the y-coordinate is i…

AlgebraFeb/Mar 20188m

The polynomial p(x) is defined by p(x) = 4x³ + 4x² – 29x – 15.

Numerical methodsFeb/Mar 20189m

It is given that ∫₋ₐ²ᵃ 4e⁻²ˣ dx = 25, where a is a positive constant.

TrigonometryFeb/Mar 20189m

Show that cosec 2x + cot 2x = cotx.

← Browse all past-paper questions

© 2026 Oracle Prep