◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2025 · Q126 Marks

A curve has equation y = e^(x²)/(x-2) for x < 2.

  1. (a)Find the value of dy/dx when x = 0.[4]
  2. (b)When x = 0, y is increasing at the rate of 0.5 units per second. Find the corresponding rate of change of x.[2]

Mark scheme

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

  1. [4] B1 for 2xe^(x²)
  2. M1 for differentiation of a quotient or equivalent correct product
  3. A1 all other terms correct
  4. A1 Must be from correct working, -1/4
  5. [2] M1 FT on 0.5 × 1 / their (-1/4)
  6. A1 Must be from correct working in part (a), -2

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 and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2025 Paper 1 Variant 2, question 12.

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

Related Additional Mathematics questions

Differentiation and integrationMay/June 20118m

A particle moves in a straight line so that, t s after passing through a fixed point O, its velocity, v ms⁻¹, is give…

Differentiation and integrationMay/June 20127m

Find the equation of the tangent to the curve y = x³ + 2x² – 3x + 4 at the point where the curve crosses the y-axis.

Differentiation and integrationMay/June 20129m

Variables x and y are such that y = e^(2x) + e^(-2x).

Equations, inequalities and graphsMay/June 20107m

Given that A = ( 4 3 / 1 2 ) and B = ( -2 0 / 1 4 ), find

Permutations and combinationsMay/June 20107m

A music student needs to select 7 pieces of music from 6 classical pieces and 4 modern pieces. Find the number of dif…

Permutations and combinationsMay/June 20105m

In a singing competition there are 8 contestants. Each contestant sings in the first round of this competition.

← Browse all past-paper questions

© 2026 Oracle Prep