| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2012 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Complete table then apply trapezium rule |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring only calculator work to complete a table and then direct application of the trapezium rule formula. No conceptual understanding or problem-solving is needed—just mechanical execution of standard procedures taught in C2. |
| Spec | 1.09f Trapezium rule: numerical integration |
| \(x\) | 0 | 0.25 | 0.5 | 0.75 | 1 |
| \(y\) | 1 | 1.251 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(x\): 0, 0.25, 0.5, 0.75, 1; \(y\): 1, 1.251, 1.494, 1.741, 2 | B1, B1 | First B1 for 1.494, second B1 for 1.741 (1.740 is B0). Wrong accuracy e.g. 1.49, 1.74 is B1B0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{1}{2} \times 0.25,\ \{(1+2) + 2(1.251 + 1.494 + 1.741)\}\) | B1, M1, A1ft | B1: Need \(\frac{1}{2}\) of 0.25 or 0.125. M1: first bracket must contain first plus last values and second bracket must include no additional values from the three in the table |
| \(= 1.4965\) | A1 | Accept 1.4965, 1.497, or 1.50 only after correct work |
## Question 7:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $x$: 0, 0.25, 0.5, **0.75**, 1; $y$: 1, 1.251, **1.494**, **1.741**, 2 | B1, B1 | First B1 for 1.494, second B1 for 1.741 (1.740 is B0). Wrong accuracy e.g. 1.49, 1.74 is B1B0 |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{1}{2} \times 0.25,\ \{(1+2) + 2(1.251 + 1.494 + 1.741)\}$ | B1, M1, A1ft | B1: Need $\frac{1}{2}$ of 0.25 or 0.125. M1: first bracket must contain first plus last values **and** second bracket must include no additional values from the three in the table |
| $= 1.4965$ | A1 | Accept 1.4965, 1.497, or 1.50 only after correct work |
---7.
$$y = \sqrt { } \left( 3 ^ { x } + x \right)$$
\begin{enumerate}[label=(\alph*)]
\item Complete the table below, giving the values of $y$ to 3 decimal places.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & 0 & 0.25 & 0.5 & 0.75 & 1 \\
\hline
$y$ & 1 & 1.251 & & & 2 \\
\hline
\end{tabular}
\end{center}
\item Use the trapezium rule with all the values of $y$ from your table to find an approximation for the value of $\int _ { 0 } ^ { 1 } \sqrt { } \left( 3 ^ { x } + x \right) \mathrm { d } x$
You must show clearly how you obtained your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2012 Q7 [6]}}