| Exam Board | OCR MEI |
|---|---|
| Module | Further Numerical Methods (Further Numerical Methods) |
| Year | 2020 |
| Session | November |
| Marks | 4 |
| 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 floating-point representation and rounding errors in numerical computing. While the topic (numerical error analysis) is A-level Further Maths content, the question requires only conceptual understanding rather than calculation. Part (a) is trivial notation conversion, parts (b) and (d) test awareness of precision limits and rounding errors (standard textbook concepts), and part (c) is straightforward reading comprehension. No complex problem-solving or novel insight required—just recall and application of basic numerical methods principles. |
| A | ||
| 1 | 1E-17 | |
| 2 | 1E-17 | |
| 3 | 1E-29 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | [1 ×] 10 ‒ 29 oe |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (b) | the numbers in cells A1 and A2 are different |
| Answer | Marks | Guidance |
|---|---|---|
| so their difference is non-zero) | B1 | 2.2a |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (c) | 1.000 000 000 001 × 10 ‒ 17 oe |
| [1] | 1.1 | |
| 1 | (d) | there could be more non-zero digits beyond |
| the limit of the accuracy of the display | B1 | 2.4 |
| Answer | Marks |
|---|---|
| 1 | 1.49697756786 |
Question 1:
1 | (a) | [1 ×] 10 ‒ 29 oe | B1 | 2.5
[1]
1 | (b) | the numbers in cells A1 and A2 are different
(although they are displayed as the same value
so their difference is non-zero) | B1 | 2.2a | do not allow eg they are
both approximations
[1]
1 | (c) | 1.000 000 000 001 × 10 ‒ 17 oe | B1
[1] | 1.1
1 | (d) | there could be more non-zero digits beyond
the limit of the accuracy of the display | B1 | 2.4 | or there may be more numbers after
the 29th decimal place
[1]
1 | 1.496977567861 Fig. 1 shows some spreadsheet output.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | c | l }
\hline
& A & \\
\hline
1 & 1E-17 & \\
\hline
2 & 1E-17 & \\
\hline
3 & 1E-29 & \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Write the value displayed in cell A3 in standard mathematical notation.
The formula in cell A3 is\\
$= \mathrm { A } 2 - \mathrm { A } 1$
\item Explain why the value displayed in cell A3 is non zero.
\item Write down the value of the number stored in cell A2 to the highest precision possible.
\item Explain why your answer to part (c) may be different to the actual value stored in cell A2.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Numerical Methods 2020 Q1 [4]}}