| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 4 |
| 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 formula with clearly specified ordinates and interval. It requires only substitution of values into a standard formula with no conceptual challenges or problem-solving—purely procedural calculation that is easier than average A-level questions. |
| Spec | 1.09f Trapezium rule: numerical integration |
| Answer | Marks | Guidance |
|---|---|---|
| x | 1 | 1.5 |
| \(\sqrt{4x-1}\) | \(\sqrt{3}\) | \(\sqrt{5}\) |
| area \(\approx \frac{1}{2} \times 0.5 \times [\sqrt{3} + \sqrt{11} + 2(\sqrt{5} + \sqrt{7} + 3)]\) | B1 M1 | |
| \(= 5.20 (3sf)\) | A1 | (4) |
| x | 1 | 1.5 | 2 | 2.5 | 3 |
|---|---|-----|---|-----|---|
| $\sqrt{4x-1}$ | $\sqrt{3}$ | $\sqrt{5}$ | $\sqrt{7}$ | 3 | $\sqrt{11}$ |
area $\approx \frac{1}{2} \times 0.5 \times [\sqrt{3} + \sqrt{11} + 2(\sqrt{5} + \sqrt{7} + 3)]$ | B1 M1 |
$= 5.20 (3sf)$ | A1 | **(4)**2.
\begin{figure}[h]
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\includegraphics[alt={},max width=\textwidth]{05006f1f-ebf0-4d70-9dbb-68221c09043e-2_510_842_534_513}
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\caption{Figure 1}
\end{center}
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Figure 1 shows the curve with equation $y = \sqrt { 4 x - 1 }$.
Use the trapezium rule with five equally-spaced ordinates to estimate the area of the shaded region bounded by the curve, the $x$-axis and the lines $x = 1$ and $x = 3$.\\
\hfill \mbox{\textit{Edexcel C2 Q2 [4]}}