| Exam Board | OCR MEI |
|---|---|
| Module | Further Numerical Methods (Further Numerical Methods) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule applied to real-world data |
| Difficulty | Standard +0.8 This question requires understanding of ill-conditioning and error propagation in linear systems, going beyond routine solving to analyze numerical reliability. While the algebra is straightforward, recognizing that small coefficient changes cause large solution changes requires insight into numerical analysis concepts not typically emphasized in standard A-level content. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (i) | x = 101 |
| y = −100 | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (ii) | Substitution of 0.985 and 0.995 to obtain |
| Answer | Marks |
|---|---|
| numbers | B1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| I | N |
| Answer | Marks |
|---|---|
| dramatically | Or maximum possible error is |
Question 1:
1 | (i) | x = 101
y = −100 | B1
B1
[2] | 1.1
1.1
1 | (ii) | Substitution of 0.985 and 0.995 to obtain
−200 < y < − 66.67
67.67 < x < 201
E.g. calculation involves subtraction of nearly equal
numbers | B1
B1
E1
[3] | 1.1
1.1
2.4
I | N
For either condition
E
For either condition
M
E.g. equations represent lines
which are almost parallel, so a
small change in gradient affects
the point of intersection
dramatically | Or maximum possible error is
100%
Or full argument based on
determinants or gradients
Do not allow general statements
such as “the problem is ill-
conditioned”1 (i) Solve the following simultaneous equations.
$$\begin{aligned}
& x + \quad y = 1 \\
& x + 0.99 y = 2
\end{aligned}$$
(ii) The coefficient 0.99 is correct to two decimal places. All other coefficients in the equations are exact. With the aid of suitable calculations, explain why your answer to part (i) is unreliable.
\hfill \mbox{\textit{OCR MEI Further Numerical Methods Q1 [5]}}