| Exam Board | OCR MEI |
|---|---|
| Module | Further Numerical Methods (Further Numerical Methods) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule applied to real-world data |
| Difficulty | Standard +0.3 This question tests understanding of relative error calculation and floating-point representation in spreadsheets. Part (a) involves straightforward application of the relative error formula, while part (b) requires explaining that spreadsheet display vs. stored values differ due to rounding. The conceptual insight needed is modest—recognizing that C1 stores the exact value 2 (from SQRT then squaring) rather than the displayed approximation. This is slightly easier than average as it's primarily about careful reasoning rather than complex calculation or novel problem-solving. |
| A | B | C | ||
| 1 | 2 | 1.414214 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | i |
| Answer | Marks |
|---|---|
| 0.000000618898 isw | M1 |
| Answer | Marks |
|---|---|
| A1 | 1.1a |
| Answer | Marks |
|---|---|
| 1.1 | ignore modulus signs |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | ii |
| error oe | B1 | 2.2a |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (b) | Ben is wrong because the spreadsheet stores |
| Answer | Marks | Guidance |
|---|---|---|
| calculated, 2 is returned) isw | B1 | 2.4 |
Question 1:
1 | (a) | i | or oe soi
2
1.414214−√2 1.414214 −2
0.00√02000309449 is2w
0.000000618898 isw | M1
A1
A1 | 1.1a
1.1
1.1 | ignore modulus signs
to 2 sf or more
to 2 sf or more
[3]
1 | (a) | ii | the second relative error is double the first relative
error oe | B1 | 2.2a
[1]
1 | (b) | Ben is wrong because the spreadsheet stores
1.414214 to a higher precision than is displayed
(and so when the square of this number is
calculated, 2 is returned) isw | B1 | 2.4 | or 1.414214 is an approximation to
so 1.4142142 ≠ 2 oe
√2
[1]
11
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Determine the relative error when
\begin{itemize}
\item 1.414214 is used to approximate $\sqrt { 2 }$,
\item $1.414214 ^ { 2 }$ is used to approximate 2.
\item Write down the relationship between your answers to part (a)(i).
\item Fig. 1 shows some spreadsheet output.
\end{itemize}
\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
& A & B & C & \\
\hline
1 & 2 & 1.414214 & 2 & \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{table}
The formula in cell B1 is = SQRT (A1)\\
and the formula in cell C 1 is $\quad = \mathrm { B } 1 \wedge 2$.\\
Ben evaluates $1.414214 ^ { 2 }$ on his calculator and obtains 2.000001238 . He states that this shows that the value displayed in cell C1 is wrong.
Explain whether Ben is correct.
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Numerical Methods 2021 Q1 [5]}}