◈ Oracle PrepSign Up Free
A-LevelMathematicsIntegration9709/12 · Oct/Nov 2021 · Q44 Marks

A curve is such that dy/dx = 8 / (3x + 2)². The curve passes through the point (2, 5²/₃). Find the equation of the curve.

  1. A curve is such that dy/dx = 8 / (3x + 2)². The curve passes through the point (2, 5²/₃). Find the equation of the curve.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [*B1] For (3x+2)⁻¹
  2. [DB1] For -8/3
  3. [M1] Substituting (2, 5²/₃) into their integrated expression defined by power = -1, or dividing by their power. + c needed
  4. [A1] y = -8/(3(3x+2)) + 6 OE e.g. y = -8(3x+2)⁻¹/3 + 6

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 Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, Oct/Nov 2021 Paper 1 Variant 2, question 4.

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

IntegrationFeb/Mar 20195m

A curve with equation y = f(x) passes through the points (0, 2) and (3, -1). It is given that f'(x) = kx² – 2x, where…

IntegrationFeb/Mar 201911m

Show that ∫⁴₁ (2/x + 2/(2x+1)) dx = ln 48.

IntegrationFeb/Mar 20195m

Show that ∫₁⁴ x^(-1/2) ln x dx = 2 – ln 4.

Probability and statisticsFeb/Mar 20208m

An ordinary fair die is thrown repeatedly until a 1 or a 6 is obtained.

Probability and statisticsFeb/Mar 20207m

The weights of apples of a certain variety are normally distributed with mean 82 grams. 22% of these apples have a we…

Probability and statisticsFeb/Mar 20206m

Richard has 3 blue candles, 2 red candles and 6 green candles. The candles are identical apart from their colours. He…

← Browse all past-paper questions

© 2026 Oracle Prep