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

A curve is such that its gradient at the point (x, y) is given by (5x-2)³ᐟ². The curve passes through the point (2, 32/5). Find the coordinates of the stationary point on the curve.

  1. Find the coordinates of the stationary point on the curve.[6]

Mark scheme

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

  1. [B1] When dy/dx=0, x=2/5 (Must come from first derivative and not the second derivative)
  2. [M1] (5x-2)⁵ᐟ² term (from integral of (5x-2)³ᐟ²)
  3. [A1] Coefficient (2/5) for y = (2/5)(5x-2)⁵ᐟ² + c
  4. [M1] Substitute point (2, 32/5) into y expression: 32/5 = (2/5)(5(2)-2)⁵ᐟ² + c (Dep for attempt to find c using their k(5x-2)⁵ᐟ²)
  5. [A1] Calculate c: c=4 (Allow an unsimplified fraction)
  6. [B1] Stationary point (2/5, 4) (Dep on first B mark)

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, May/June 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 20108m

Variables x and y are related by the equation y = 5x + 2 – 4e⁻ˣ. Find dy/dx

Differentiation and integrationMay/June 201011m

Answer only one of the following two alternatives. EITHER A curve has equation y = ln x / x², where x > 0.

Differentiation and integrationMay/June 201011m

OR A curve is such that dy/dx = 6 cos(2x + π/2) for -π/4 <= x <= 5π/4. The curve passes through the point (π/4, 5).

Factors of polynomialsMay/June 20106m

Solve the equation 2x³ - 3x² - 11x + 6 = 0.

Equations, inequalities and graphsMay/June 20107m

Sketch the graph of y = |3x + 9| for -5 < x < 2, showing the coordinates of the points where the graph meets the axes.

SeriesMay/June 20108m

Write down the first 4 terms, in ascending powers of x, of the expansion of (1 – 3x)⁷.

← Browse all past-paper questions

© 2026 Oracle Prep