◈ Oracle PrepSign Up Free
A-LevelFurther MathematicsIntegration9231/12 · Oct/Nov 2013 · Q15 Marks

The curve C has polar equation r = 2e^θ, for π/6 < θ < π/3. Find

  1. (i)the area of the region bounded by the half-lines θ = π/6, θ = π/3 and C,[2]
  2. (ii)the length of C.[3]

Mark scheme

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

  1. [M1] (i) Uses area formula.
  2. [A1] Obtains result. = e^(2π/3) - e^(π/3) (= 20.3)
  3. [M1A1] (ii) Uses arc length formula.
  4. [A1] Obtains result. = 2√2 [e^θ] (from π/6 to π/3) = 2√2(e^(π/3) - e^(π/6)) (= 8.83)

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
Integration, A-Level Further Mathematics (syllabus 9231). Structured question, 5 marks.
Source
A-Level Further Mathematics, Oct/Nov 2013 Paper 1 Variant 2, question 1.

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

Related Further Mathematics questions

IntegrationMay/June 20107m

At any point (x, y) on the curve C, dx/dt = t(t²+4) and dy/dt = -t√(4-t²), where the parameter t is such that 0 ≤ t ≤ 2.

IntegrationMay/June 20109m

Let I_n = ∫_1^e x(lnx)ⁿ dx, where n ≥ 1.

IntegrationMay/June 201112m

The curve C has equation \( y = x^{3/2} \).

Proof by inductionMay/June 20166m

Prove by mathematical induction that, for all positive integers n, 10ⁿ + 3 × 4ⁿ⁺² + 5 is divisible by 9.

Complex numbersMay/June 20169m

Use de Moivre's theorem to express cot 7θ in terms of cot θ. Use the equation cot 7θ = 0 to show that the roots of th…

VectorsMay/June 201611m

Find a cartesian equation of the plane Π₁ passing through the points with coordinates (2, −1, 3), (4, 2, -5) and (−1,…

← Browse all past-paper questions

© 2026 Oracle Prep