| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule with stated number of strips |
| Difficulty | Easy -1.2 This is a straightforward application of the trapezium rule with clearly specified intervals and a simple function to evaluate. Students only need to substitute x-values into 2^x and apply the standard trapezium rule formula—pure procedural execution with no problem-solving or conceptual challenges beyond basic recall. |
| Spec | 1.09f Trapezium rule: numerical integration |
| Answer | Marks | Guidance |
|---|---|---|
| Table with \(x\): \(-2, -1, 0, 1, 2\); \(2^x\): \(\frac{1}{4}, \frac{1}{2}, 1, 2, 4\) | B1 | |
| \(\text{area} = \frac{1}{2} \times 1 \times [\frac{1}{4} + 4 + 2(\frac{1}{2} + 1 + 2)]\) | B1 M1 A1 | |
| \(= 5\frac{5}{8} \text{ or } 5.63 \text{ (3sf)}\) | A1 | (5) |
Table with $x$: $-2, -1, 0, 1, 2$; $2^x$: $\frac{1}{4}, \frac{1}{2}, 1, 2, 4$ | B1 |
$\text{area} = \frac{1}{2} \times 1 \times [\frac{1}{4} + 4 + 2(\frac{1}{2} + 1 + 2)]$ | B1 M1 A1 |
$= 5\frac{5}{8} \text{ or } 5.63 \text{ (3sf)}$ | A1 | (5)2.
\begin{figure}[h]
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\includegraphics[alt={},max width=\textwidth]{c7c8cf84-06ac-4059-b8f0-d68b6d1d8dcc-2_613_911_692_376}
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\caption{Figure 1}
\end{center}
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Figure 1 shows the curve with equation $y = 2 ^ { x }$.\\
Use the trapezium rule with four intervals of equal width to estimate the area of the shaded region bounded by the curve, the $x$-axis and the lines $x = - 2$ and $x = 2$.\\
\hfill \mbox{\textit{Edexcel C2 Q2 [5]}}