| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule applied to real-world data |
| Difficulty | Easy -1.2 This is a straightforward application of the trapezium rule with all values provided in a table. Students simply substitute into the formula with h=1.5 and add the given depths according to the standard trapezium rule pattern. No problem-solving, interpretation challenges, or multi-step reasoning required—purely mechanical calculation. |
| Spec | 1.09f Trapezium rule: numerical integration |
| Distance across river \(( \mathrm { m } )\) | 0 | 1.5 | 3 | 4.5 | 6 | 7.5 |
| Depth of river \(( \mathrm { m } )\) | 0.6 | 2.3 | 3.1 | 2.8 | 1.8 | 0.7 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{1}{2} \times 1.5 \times (0.6 + 0.7 + 2(2.3+3.1+2.8+1.8))\) | M2 | M1 if one error; or M2 for sum of 5 unsimplified individual trapezia: 2.175, 4.05, 4.425, 3.45, 1.875 |
| \(= 15.975\) rounded to 2 s.f. or more | A1 |
**Question 3:**
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{1}{2} \times 1.5 \times (0.6 + 0.7 + 2(2.3+3.1+2.8+1.8))$ | **M2** | **M1** if one error; or **M2** for sum of 5 unsimplified individual trapezia: 2.175, 4.05, 4.425, 3.45, 1.875 | Basic shape of formula must be correct. Must be 5 strips. **M0** if pair of brackets omitted or $h=7.5$ or 1. Allow recovery of brackets omitted to obtain correct answer. **M0** for other than 5 trapezia |
| $= 15.975$ rounded to 2 s.f. or more | **A1** | | isw only if 15.975 clearly identified as cross-sectional area |
---3 At a place where a river is 7.5 m wide, its depth is measured every 1.5 m across the river. The table shows the results.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Distance across river $( \mathrm { m } )$ & 0 & 1.5 & 3 & 4.5 & 6 & 7.5 \\
\hline
Depth of river $( \mathrm { m } )$ & 0.6 & 2.3 & 3.1 & 2.8 & 1.8 & 0.7 \\
\hline
\end{tabular}
\end{center}
Use the trapezium rule with 5 strips to estimate the area of cross-section of the river.
\hfill \mbox{\textit{OCR MEI C2 2011 Q3 [3]}}