| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 8 |
| Topic | Indefinite & Definite Integrals |
| Type | Pure definite integration |
| Difficulty | Standard +0.3 This question tests understanding of definite integrals from graphs and basic transformations. Part (a) requires reading areas from a graph (straightforward). Part (b) involves recognizing that horizontal translations and vertical shifts affect integral values in predictable ways—standard A-level techniques requiring minimal problem-solving beyond pattern recognition. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.08e Area between curve and x-axis: using definite integrals |
1.
The graph of $y = \mathrm { f } ( x )$ is shown below for $0 \leq x \leq 6$\\
\includegraphics[max width=\textwidth, alt={}, center]{a1b449df-1096-4b3a-8306-fca410a7e530-04_499_551_331_877}
\begin{enumerate}[label=(\alph*)]
\item Evaluate $\int _ { 0 } ^ { 6 } \mathrm { f } ( x ) \mathrm { d } x$\\[0pt]
[2 marks]
\item Deduce values for each of the following, giving reasons for your answers.\\
(b) (i) $\int _ { 1 } ^ { 7 } \mathrm { f } ( x - 1 ) \mathrm { d } x$\\
(b) (ii) $\int _ { 0 } ^ { 6 } ( \mathrm { f } ( x ) - 1 ) \mathrm { d } x$
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q1 [8]}}