WJEC Unit 3 2023 June — Question 3 11 marks

Exam BoardWJEC
ModuleUnit 3 (Unit 3)
Year2023
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicGeneralised Binomial Theorem and Partial Fractions
TypePartial fractions with validity range
DifficultyStandard +0.3 This is a standard two-part question combining partial fractions with binomial expansion. Part (a) is routine A-level technique with a repeated linear factor. Part (b) requires expanding three binomial terms and collecting coefficients, which is methodical but straightforward. The 11 marks reflect length rather than conceptual difficulty—this is slightly above average due to the algebraic manipulation required, but remains a textbook-style question testing standard techniques.
Spec1.02y Partial fractions: decompose rational functions

  1. Express \(\frac{9}{(1-x)(1+2x)^2}\) in terms of partial fractions. [4]
  2. Using your answer from part (a), find the expansion of \(\frac{9}{(1-x)(1+2x)^2}\) in ascending powers of \(x\) as far as the term in \(x^2\). State the values of \(x\) for which the expansion is valid. [7]

\begin{enumerate}[label=(\alph*)]
\item Express $\frac{9}{(1-x)(1+2x)^2}$ in terms of partial fractions. [4]

\item Using your answer from part (a), find the expansion of $\frac{9}{(1-x)(1+2x)^2}$ in ascending powers of $x$ as far as the term in $x^2$. State the values of $x$ for which the expansion is valid. [7]
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 3 2023 Q3 [11]}}