SPS SPS SM Pure 2020 October — Question 6 5 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2020
SessionOctober
Marks5
TopicPartial Fractions
TypePartial fractions with linear factors – decompose and integrate (indefinite)
DifficultyModerate -0.8 This is a straightforward two-part question testing standard partial fractions technique followed by direct integration. Part (i) is routine algebraic manipulation with linear factors, and part (ii) requires only recognizing that partial fractions integrate to logarithms. Both are textbook exercises with no problem-solving or insight required, making this easier than average but not trivial since it does require correct algebraic technique.
Spec1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions

  1. Express \(\frac{x}{(x + 1)(x + 2)}\) in partial fractions. [3]
  2. Hence find \(\int \frac{x}{(x + 1)(x + 2)} dx\). [2]

\begin{enumerate}[label=(\roman*)]
\item Express $\frac{x}{(x + 1)(x + 2)}$ in partial fractions.
[3]

\item Hence find $\int \frac{x}{(x + 1)(x + 2)} dx$.
[2]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS SM Pure 2020 Q6 [5]}}