◈ Oracle PrepSign Up Free
A-LevelMathematicsCoordinate geometry9709/12 · May/June 2013 · Q35 Marks

The straight line y = mx + 14 is a tangent to the curve y = 12/x + 2 at the point P. Find the value of the constant m and the coordinates of P.

  1. (a)Find the value of the constant m and the coordinates of P.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

  1. [1] M1 Eliminates x (or y) to form a quadratic equation (e.g. mx² + 12x - 12 = 0)
  2. [1] M1 Uses the discriminant b² - 4ac = 0 for tangency
  3. [1] A1 Correct value for m = -3
  4. [1] DM1 Solves for x (or y) using the found value of m (e.g. -3x² + 12x - 12 = 0 → x = 2)
  5. [1] A1 Correct coordinates of P (2, 8)

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
Coordinate geometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2013 Paper 1 Variant 2, question 3.

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

Coordinate geometryFeb/Mar 20217m

The points A (7, 1), B (7, 9) and C (1, 9) are on the circumference of a circle.

Coordinate geometryFeb/Mar 20236m

Points A (7, 12) and B lie on a circle with centre (–2, 5). The line AB has equation y = −2x + 26. Find the coordinat…

Coordinate geometryMay/June 20117m

The line L₁ passes through the points A (2, 5) and B (10, 9). The line L₂ is parallel to L₁ and passes through the or…

AlgebraFeb/Mar 20206m

Find the quotient when 4x³ + 17x² + 9x is divided by x² + 5x + 6, and show that the remainder is 18.

IntegrationFeb/Mar 20206m

It is given that ∫⁽³ᵃ⁾ₐ (2/(2x-5)) dx = ln(7/2). Find the value of the positive constant a.

DifferentiationFeb/Mar 20206m

A curve has equation 3x² - y² – 4 ln(2y + 3) = 26. Find the equation of the tangent to the curve at the point (3, −1).

← Browse all past-paper questions

© 2026 Oracle Prep