A-LevelMathematicsSeries9709/32 · May/June 2025 · Q25 Marks

Expand (6-x)(1-2x)¯½ in ascending powers of x, up to and including the term in x², simplifying the coefficients.

(a)Expand (6-x)(1-2x)¯½ in ascending powers of x, up to and including the term in x², simplifying the coefficients.[4]
(b)State the set of values of x for which the expansion is valid.[1]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[B1] Find the first two terms of the expansion of (1-2x)^(-3/2)
[B1] Obtain correct third term (-3/2)(-1/2)/2! (-2x)^2 or (-3/2)(-1/2)/2! (2x)^2 Ignore extra terms.
[M1] Multiply their 3 term expansion a+bx+cx^2 by (6 – x) obtaining all necessary terms 6+18x+45x^2-x-3x^2.... Ignore extra terms.
[A1] 6 + 17x + 42x^2 Ignore extra terms. Allow with the terms in any order.
[B1] |x| <= 1/2 or -1/2 < x < 1/2 or (-0.5, 0.5) or ]-0.5, 0.5[ OE BO for an ambiguous statement. Must be strict inequality.

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: Series, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, May/June 2025 Paper 3 Variant 2, 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