◈ Oracle Prep Sign Up Free

A-LevelMathematicsSeries9709/33 · May/June 2017 · Q24 Marks

Expand (3 + 2x)⁻³ in ascending powers of x up to and including the term in x², simplifying the coefficients.

(a)Expand (3 + 2x)⁻³ in ascending powers of x up to and including the term in x², simplifying the coefficients.[4]

Mark scheme

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

[M1] EITHER: State a correct unsimplified version of the x or x² term in the expansion of (1+x)⁻³ or (3+2x)⁻³. OR: Differentiate expression and evaluate f(0) and f'(0), where f'(x)=k(3+2x)⁻⁴
[B1] State correct first term 1/27
[A1] Obtain term -2/27 x
[A1] Obtain term 8/81 x²

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, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2017 Paper 3 Variant 3, question 2.

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

Related Mathematics questions

SeriesFeb/Mar 20184m

Expand ∛(1 – 4x) in ascending powers of x, up to and including the term in x³, simplifying the coefficients.

SeriesFeb/Mar 20197m

The first and second terms of a geometric progression are p and 2p respectively, where p is a positive constant. The …

SeriesFeb/Mar 20205m

The coefficient of 1/x in the expansion of (2x + a/x²)⁵ is 720.

AlgebraFeb/Mar 20247m

The polynomial p(x) is defined by p(x) = 6x³ + ax²+3x-10, where a is a constant. It is given that (2x – 1) is a facto…

TrigonometryFeb/Mar 202410m

Prove that sin 2θ(a cotθ+b tan θ) ≡ a+b+ (a−b) cos 2θ, where a and b are constants.

AlgebraFeb/Mar 20243m

Find the quotient and remainder when x⁴ - 3x³ + 9x² - 12x + 27 is divided by x² + 5.

← Browse all past-paper questions