◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsLogarithmic and exponential functions4037/11 · May/June 2015 · Q811 Marks

It is given that f(x) = 3e²ˣ for x ≥ 0, g(x) = (x + 2)² + 5 for x ≥ 0.

  1. (i)Write down the range of f and of g.[2]
  2. (ii)Find g⁻¹, stating its domain.[3]
  3. (iii)Find the exact solution of gf(x) = 41.[4]
  4. (iv)Evaluate f'(ln4).[2]

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

  1. [B1] Range for f: y ≥ 3
  2. [B1] Range for g: y ≥ 9
  3. [M1] attempt to obtain the inverse function
  4. [A1] Must be correct form
  5. [B1] for domain
  6. [M1] correct order
  7. [DM1] correct attempt to solve the equation
  8. [M1] dealing with the exponential correctly in order to reach a solution for x
  9. [A1] Allow equivalent logarithmic forms
  10. [B1] g'(x) = 6e2x
  11. [B1] g'(ln 4) = 96

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
Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 11 marks.
Source
O-Level Additional Mathematics, May/June 2015 Paper 1 Variant 1, question 8.

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

Logarithmic and exponential functionsMay/June 20125m

Using the substitution u = 2ˣ, find the values of x such that 2²ˣ⁺² = 5 (2ˣ) – 1 .

Logarithmic and exponential functionsMay/June 20128m

Variables N and x are such that N = 200 + 50e^(x/100).

Logarithmic and exponential functionsMay/June 20126m

Solve the equation 3²ˣ = 1000, giving your answer to 2 decimal places.

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…

Vectors in two dimensionsMay/June 20108m

In this question, (1 / 0) is a unit vector due east and (0 / 1) is a unit vector due north. A lighthouse has position…

Differentiation and integrationMay/June 20103m

Find ∫ (2+5x - 1/(x-2)²) dx.

← Browse all past-paper questions

© 2026 Oracle Prep