O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2015 · Q98 Marks

A curve has equation y = 4x + 3 cos 2x. The normal to the curve at the point where x = π/4 meets the x- and y-axes at the points A and B respectively. Find the exact area of the triangle AOB, where O is the origin.

(a)A curve has equation y = 4x + 3 cos 2x. The normal to the curve at the point where x = π/4 meets the x- and y-axes at the points A and B respectively. Find the exact area of the triangle AOB, where O is the origin.[8]

Mark scheme

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

M1,A1 M1 for attempt to differentiate A1 for all correct
B1 for y
DM1 for substitution of x = π/4 into their dy/dx and use of 'm₁m₂ = −1', dependent on first M1
DM1 correct attempt to obtain the equation of the normal, dependent on previous DM mark
A1 must be terms of π
A1 must be terms of π
B1ft Follow through on their x and y intercepts; must be exact values

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.

Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, May/June 2015 Paper 1 Variant 2, question 9.

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