◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · May/June 2012 · Q78 Marks

The table shows experimental values of variables x and y. X | 5 | 30 | 150 | 400 y | 8.9 | 21.9 | 48.9 | 80.6

  1. (i)By plotting a suitable straight line graph, show that y and x are related by the equation y = axᵇ, where a and b are constants.[4]
  2. (ii)Use your graph to estimate the value of a and of b.[2]
  3. (iii)Estimate the value of y when x = 100.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

  1. [B1] (i) ln y = ln a+b ln x OR lg y = lg a + b lg x may be implied
  2. [M1] (i) Plot ln y / lg y against ln x / lg x with attempt at linear scale
  3. [A2, 1, 0] (i) (Marks for points and line on graph NOT for table)
  4. [M1] (ii) Calculates gradient of straight line log graph
  5. [A1] (ii) b = 0.5±0.03
  6. [M1] (ii) Intercept is ln a or lg a on straight line log graph
  7. [A1] (ii) a = 4±0.3
  8. [M1] (iii) Uses suitable graph or formula
  9. [A1] (iii) 32 to 49

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, 8 marks.
Source
O-Level Additional Mathematics, May/June 2012 Paper 2 Variant 2, question 7.

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 20109m

Given that logₚ X = 6 and logₚ Y = 4, find the value of

Logarithmic and exponential functionsMay/June 20113m

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

Logarithmic and exponential functionsMay/June 20118m

The temperature, T° Celsius, of an object, t minutes after it is removed from a heat source, is given by T = 55e⁻⁰·¹ᵗ…

Factors of polynomialsMay/June 20116m

Show that 2x – 1 is a factor of 2x³ – 5x² + 10x – 4.

Permutations and combinationsMay/June 20117m

A team of 6 members is to be selected from 6 women and 8 men.

Vectors in two dimensionsMay/June 20117m

Relative to an origin O, points A and B have position vectors (5 -6) and (29 -13) respectively.

← Browse all past-paper questions

© 2026 Oracle Prep