| Exam Board | OCR MEI |
|---|---|
| Module | Further Numerical Methods (Further Numerical Methods) |
| Year | 2020 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule applied to real-world data |
| Difficulty | Moderate -0.3 This question tests understanding of rounding vs truncation errors with straightforward calculations. Part (a) and (b) require applying standard error formulas (±0.05 and -0.1 respectively per item, multiplied by 154). Part (c) involves comparing calculated bounds to actual data. While it requires careful reasoning about error accumulation, the mathematics is elementary arithmetic with no complex problem-solving or novel insight required. |
| Weight (kg) |
| 17.2 |
| 19.9 |
| 22.3 |
| 20.1 |
| 21.5 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | [±] 7.7 kg |
| [±] 0.05 ×154 | M1 | |
| A1 | 3.3 | |
| 3.4 | use of 0.05 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (b) | kg |
| 0.1 ×154 | M1 | |
| A1 | 3.3 | |
| 1.1 | use of 0.1 | |
| 15.4 | [2] | |
| 3 | (c) | 3080.2 + 7.7 = 3087.9 < 3089.44 soi |
| Answer | Marks |
|---|---|
| so the only viable model is Piotre’s | B1FT |
| Answer | Marks |
|---|---|
| B1FT | 3.4 |
| Answer | Marks |
|---|---|
| 3.5a | or 7.7 < 9.42 |
| Answer | Marks |
|---|---|
| 3 | 1.49682595579 |
Question 3:
3 | (a) | [±] 7.7 kg
[±] 0.05 ×154 | M1
A1 | 3.3
3.4 | use of 0.05
[2]
3 | (b) | kg
0.1 ×154 | M1
A1 | 3.3
1.1 | use of 0.1
15.4 | [2]
3 | (c) | 3080.2 + 7.7 = 3087.9 < 3089.44 soi
3080.2 + 15.4 = 3095.6 kg > 3089.44 soi
so the only viable model is Piotre’s | B1FT
B1FT
B1FT | 3.4
3.3
3.5a | or 7.7 < 9.42
or 15.4 > 9.42
[3]
3 | 1.496825955793 At Heathwick airport each passenger's luggage is weighed before being loaded into the hold of the aeroplane. Each weight is displayed digitally in kg to 1 decimal place. Some examples are given in Fig. 3.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | }
\hline
Weight (kg) \\
\hline
17.2 \\
\hline
19.9 \\
\hline
22.3 \\
\hline
20.1 \\
\hline
21.5 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{center}
\end{table}
On each flight, the total weight of luggage is calculated to ensure compliance with health and safety regulations.
Winston models this situation by assuming that the displayed weights are rounded to 1 decimal place, and that the total weight of luggage is calculated using the displayed values.
On a flight to Athens, there are 154 items of passengers' luggage.
\begin{enumerate}[label=(\alph*)]
\item Determine the maximum possible error, according to Winston's model, when the total weight of luggage is calculated for the flight to Athens.
Piotre models this situation by assuming that the displayed weights are chopped to 1 decimal place, and that the total weight of luggage is calculated using the displayed values.
\item Determine the maximum possible error, according to Piotre's model, when the total weight of luggage is calculated for the flight to Athens.
A health and safety inspector notes that the total of the displayed weights is 3080.2 kg . However, when the luggage is all weighed together in the loading bay, the total weight is found to be 3089.44 kg .
\item Determine whether Winston's model or Piotre's model is a better fit for the data.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Numerical Methods 2020 Q3 [7]}}