A-LevelMathematicsSeries9709/33 · Oct/Nov 2024 · Q88 Marks

Let f(x) = 7a² / ((a-2x)(3a+x)), where a is a positive constant.

(a)Express f(x) in partial fractions.[3]
(b)Hence obtain the expansion of f(x) in ascending powers of x, up to and including the term in x².[4]
(c)State the set of values of x for which the expansion in part (b) is valid.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

[M1] (a) State or imply the form A/(a-2x) + B/(3a+x) and use a correct method to find a constant.
[A1] (a) Obtain A=2a or B = a.
[A1] (a) Obtain A=2a and B = a.
[M1] (b) Use a correct method to obtain the first two terms of the expansion of (a-2x)⁻¹ or (1-2x/a)⁻¹ or (3a+x)⁻¹ or (1+x/3a)⁻¹.
[A1ft] (b) Obtain 2(1 + 2x/a + 4x²/a²) + 1/3(1 - x/3a + x²/9a²) + ... (Follow their A, B for an expansion involving a).
[A1] (b) Obtain 7/3 + 35x/(9a) + 217x²/(27a²). Or simplified equivalent. Final answer.
[B1] (c) |x| < a/2. Or -a/2 < x < a/2.

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, 8 marks.
Source: A-Level Mathematics, Oct/Nov 2024 Paper 3 Variant 3, question 8.

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