| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| 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 C2 question requiring basic substitution into a given function and application of the trapezium rule formula. Both parts are routine calculations with no problem-solving or conceptual challenges—simpler than the average A-level question. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.09f Trapezium rule: numerical integration |
| \(x\) | - 2 | 2 | 6 | 10 |
| \(y\) | 0 | \(6 \sqrt { } 3\) |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Answer/Working | Marks |
| (a) | At \(x=2\), \(y=2\) and at \(x=6\), \(y=4\sqrt{2}\) or \(2\sqrt{8}\) or awrt 5.7 | B1 cao |
| (b) | \(\frac{1}{2} \times 4\); or \(h=4\) | B1 oe |
| \(\{0 + 6\sqrt{3} + 2(their2 + their4\sqrt{2})\}\) | M1A1ft | M1: requires correct \(\{...\}\) bracket structure. It needs first bracket to contain first \(y\) value (as this is zero it may be omitted) plus last \(y\) value and second bracket to be multiplied by 2 and to be summation of remaining \(y\) values in table with no additional values. If only mistake is copying error or is to omit one value from bracket this may be regarded as slip and M mark can be allowed (An extra repeated term forfeits M mark however). M0 if values used in brackets are \(x\) values instead of \(y\) values |
| \(\frac{1}{2} \times 4\{0 + 6\sqrt{3} + 2(2 + 4\sqrt{2})\} = 2(25.706) = 51.412...\) = awrt 51.412 | A1 | A1ft: for correct bracket following through candidate's \(y\) values found in part (a). A1: for answer which rounds to 51.412 then isw |
| (4) | ||
| (5 marks) |
| **Part** | **Answer/Working** | **Marks** | **Notes** |
|---|---|---|---|
| (a) | At $x=2$, $y=2$ and at $x=6$, $y=4\sqrt{2}$ or $2\sqrt{8}$ or awrt 5.7 | B1 cao | B1: 2 and $4\sqrt{2}$ or $2\sqrt{8}$ or awrt 5.7 (or any correct unsimplified surd equivalent given as final answer). These may be stated as final answer and not appear in table, or may appear in table. If correct surd appears in working (unsimplified) and is then simplified to give incorrect answer to (a) which is used in table and in part (b) then this is B0. |
| (b) | $\frac{1}{2} \times 4$; or $h=4$ | B1 oe | B1: for using $\frac{1}{2} \times 4$ or 2 or equivalent or for stating $h$ |
| | $\{0 + 6\sqrt{3} + 2(their2 + their4\sqrt{2})\}$ | M1A1ft | M1: requires correct $\{...\}$ bracket structure. It needs first bracket to contain first $y$ value (as this is zero it may be omitted) plus last $y$ value and second bracket to be multiplied by 2 and to be summation of remaining $y$ values in table with no additional values. If only mistake is copying error or is to omit one value from bracket this may be regarded as slip and M mark can be allowed (An extra repeated term forfeits M mark however). M0 if values used in brackets are $x$ values instead of $y$ values |
| | $\frac{1}{2} \times 4\{0 + 6\sqrt{3} + 2(2 + 4\sqrt{2})\} = 2(25.706) = 51.412...$ = awrt 51.412 | A1 | A1ft: for correct bracket following through candidate's $y$ values found in part (a). A1: for answer which rounds to 51.412 then isw |
| | | **(4)** | |
| | | **(5 marks)** | |
**Special case:** Bracketing mistake $2 \times (0 + 6\sqrt{3}) + 2(2 + 4\sqrt{2})$ scores B1 M1 A0 A0 unless final answer implies calculation has been done correctly (then full marks can be given). An answer of 36.098 usually indicates this error.
---1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{8daf56fa-bfce-454e-bbb8-fecd8170d77e-02_575_812_214_566}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation
$$y = \frac { ( x + 2 ) ^ { \frac { 3 } { 2 } } } { 4 } , \quad x \geqslant - 2$$
The finite region $R$, shown shaded in Figure 1, is bounded by the curve, the $x$-axis and the line with equation $x = 10$
The table below shows corresponding values of $x$ and $y$ for $y = \frac { ( x + 2 ) ^ { \frac { 3 } { 2 } } } { 4 }$
\begin{enumerate}[label=(\alph*)]
\item Complete the table, giving values of $y$ corresponding to $x = 2$ and $x = 6$
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$x$ & - 2 & 2 & 6 & 10 \\
\hline
$y$ & 0 & & & $6 \sqrt { } 3$ \\
\hline
\end{tabular}
\end{center}
\item Use the trapezium rule, with all the values of $y$ from the completed table, to find an approximate value for the area of $R$, giving your answer to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2018 Q1 [5]}}