◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsSeries4037/12 · May/June 2017 · Q45 Marks

The first 3 terms in the expansion of (3 - x/6)^n are 81 + ax + bx². Find the value of each of the constants n, a and b.

  1. The first 3 terms in the expansion of (3 - x/6)^n are 81 + ax + bx². Find the value of each of the constants n, a and b.[5]

Mark scheme

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

  1. [B1] 3^n = 81, so n=4
  2. [M1] for -n3^(n-1)(x/6), "C13^(n-1)(x/6)" with/without their n
  3. [A1] using their n and equating to a to obtain a=-18
  4. [M1] for n(n-1)/2 * 3^(n-2) * (x/6)², "C23^(n-2)(x/6)²" with/without their n
  5. [A1] using their n and equating to b to obtain b=3/2

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
Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2017 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 Additional Mathematics questions

SeriesMay/June 20146m

Find and simplify the first three terms of the expansion, in ascending powers of x, of (1 – 4x)5.

SeriesMay/June 20156m

Find the first 4 terms in the expansion of (2 + x²)⁶ in ascending powers of x.

SeriesMay/June 20165m

The first 3 terms in the expansion of (2 - 1/(4x))^5 are a + b/x + c/x². Find the value of each of the integers a, b …

Differentiation and integrationMay/June 20146m

Given that y = e^(x²), find dy/dx.

Simultaneous equationsMay/June 20147m

Matrices A and B are such that A = (-1 4; 7 6) and B = (2 1; 3 5)

Differentiation and integrationMay/June 20148m

A curve is such that dy/dx = 4x + 1/(x+1)² for x > 0. The curve passes through the point (1/2, 5/6).

← Browse all past-paper questions

© 2026 Oracle Prep