| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core (Further Pure Core) |
| Year | 2019 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Volume with trigonometric functions |
| Difficulty | Challenging +1.2 This is a straightforward volumes of revolution question requiring integration of sec²(x/2), which is a standard result. While it involves trigonometric functions and requires careful substitution (u = x/2), the method is routine for Further Maths students and the integration is a known formula. The 'show detailed reasoning' requirement and exact form answer add minor complexity but this remains a standard textbook exercise. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs4.08d Volumes of revolution: about x and y axes |
| Answer | Marks |
|---|---|
| 4 | DR |
| Answer | Marks |
|---|---|
| = (2tan ¼ π 0) = 2 | B1 |
| Answer | Marks |
|---|---|
| [3] | 1.1b |
| Answer | Marks |
|---|---|
| 1.1b | correct integral and limits |
| Answer | Marks |
|---|---|
| unsupported B0 | condone π missing |
Question 4:
4 | DR
1
V 2sec2 xdx
0 2
1 2
2tan x
2
0
= (2tan ¼ π 0) = 2 | B1
B1
B1cao
[3] | 1.1b
1.1b
1.1b | correct integral and limits
1
2tan x
2
unsupported B0 | condone π missing4 In this question you must show detailed reasoning.
Fig. 4 shows the region bounded by the curve $y = \sec \frac { 1 } { 2 } x$, the $x$-axis, the $y$-axis and the line $x = \frac { 1 } { 2 } \pi$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{01a574f1-f6f6-40f5-baa5-535c36269731-2_501_670_1329_242}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{center}
\end{figure}
This region is rotated through $2 \pi$ radians about the $x$-axis.\\
Find, in exact form, the volume of the solid of revolution generated.
\hfill \mbox{\textit{OCR MEI Further Pure Core 2019 Q4 [3]}}