| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| 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 need to recall and apply the formula with h=1.5 and sum the given depths. No problem-solving, interpretation challenges, or algebraic manipulation required—purely mechanical calculation, making it easier than average. |
| 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/Working | Mark | Guidance |
| \(\frac{1}{2} \times 1.5 \times (0.6 + 0.7 + 2(2.3+3.1+2.8+1.8))\) | M2 | 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. 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 | isw only if \(15.975\) clearly identified as cross-sectional area |
## Question 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{1}{2} \times 1.5 \times (0.6 + 0.7 + 2(2.3+3.1+2.8+1.8))$ | M2 | 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. 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 | isw only if $15.975$ clearly identified as cross-sectional area |
---2 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 Q2 [3]}}