◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2017 · Q118 Marks

The curve y = f(x) passes through the point (1/2, 7/2) and is such that f'(x) = e^(2x-1).

  1. (i)Find the equation of the curve.[4]
  2. (ii)Find the value of x for which f''(x) = 4, giving your answer in the form a + b ln √2, where a and b are constants.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [M1] me^(2x-1) where m is numeric constant
  2. [A1] f(x) = (1/2)e^(2x-1) (+c)
  3. [DM1] correct attempt to find arbitrary constant
  4. [A1] must be an equation f(x) = (1/2)e^(2x-1) + 3
  5. [M1] ke^(2x-1) where k is a numeric constant
  6. [A1] f''(x) = 2e^(2x-1)
  7. [DM1] attempt to equate to 4 and use logarithms
  8. [A1] x = 1/2 + ln√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, 8 marks.
Source
O-Level Additional Mathematics, May/June 2017 Paper 1 Variant 2, question 11.

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 20107m

Given that a curve has equation y = x² + 64√x, find the coordinates of the point on the curve where d²y/dx² = 0.

Differentiation and integrationMay/June 20108m

A particle starts from rest and moves in a straight line so that, t seconds after leaving a fixed point O, its veloci…

Differentiation and integrationMay/June 20103m

Find ∫ (2+5x - 1/(x-2)²) dx.

FunctionsMay/June 201010m

Answer only one of the following two alternatives. EITHER It is given that f(x) = 4x² + kx + k.

TrigonometryMay/June 20113m

Show that (1 / (1 - cosθ)) + (1 / (1 + cosθ)) = 2cosec²θ.

Logarithmic and exponential functionsMay/June 20113m

Express lga + 3lgb – 3 as a single logarithm.

← Browse all past-paper questions

© 2026 Oracle Prep