| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 1 (Further AS Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola area calculations |
| Difficulty | Standard +0.3 This is a straightforward volumes of revolution question requiring integration of y² = 4x rotated about the x-axis, then solving for d given V = 1000. The setup is standard (π∫y²dx = π∫4x dx = 2πx²), requiring only basic integration and algebraic manipulation. While it's Further Maths content, it's a routine application of a core technique with no conceptual challenges or novel insights needed. |
| Spec | 4.08d Volumes of revolution: about x and y axes |
| Answer | Marks | Guidance |
|---|---|---|
| 9(a) | Sketches correct parabola | 1.2 |
| Answer | Marks | Guidance |
|---|---|---|
| 9(b)(i) | OLibmtaitisn sn o 𝜋𝜋t r�eq4u𝑥𝑥ir 𝑑𝑑e𝑥𝑥d for this mark. | |
| Condone missing | 3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2𝑥𝑥 𝑑𝑑 | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Using 1000000 mm3 leads to a correct answer of 399 mm for 4/4. | 3.2a | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 9(b)(ii) | States appropriate assumption | 3.5b |
| Total | 6 | |
| Q | Marking instructions | AO |
Question 9:
--- 9(a) ---
9(a) | Sketches correct parabola | 1.2 | B1
--- 9(b)(i) ---
9(b)(i) | OLibmtaitisn sn o 𝜋𝜋t r�eq4u𝑥𝑥ir 𝑑𝑑e𝑥𝑥d for this mark.
Condone missing | 3.3 | M1 | 𝑑𝑑
2
volume=𝜋𝜋�𝑦𝑦 𝑑𝑑𝑥𝑥
0
𝑑𝑑
∴ 1000=𝜋𝜋�4𝑥𝑥 𝑑𝑑𝑥𝑥
0
2 𝑑𝑑
1000 4𝑥𝑥
=� �
𝜋𝜋 2 0
1000 2
=2𝑑𝑑 −0
𝜋𝜋
2
2𝜋𝜋𝑑𝑑 =1000
500
𝑑𝑑de=pt � h = 12.6 cm
𝜋𝜋
𝑑𝑑𝑥𝑥
Obtains and uses limits of and 0 (oe).
2
2𝑥𝑥 𝑑𝑑 | 1.1b | B1
Forms an equation of the form ( oe)
2 | 3.4 | M1
𝑘𝑘𝑑𝑑 = volume
Correct depth to nearest millimetre.
Condone 126 or 12.6 without units.
NMS: 126 or 12.6 scores 4/4.
Using 1000000 mm3 leads to a correct answer of 399 mm for 4/4. | 3.2a | A1
--- 9(b)(ii) ---
9(b)(ii) | States appropriate assumption | 3.5b | B1 | The thickness of the plastic is negligible
Total | 6
Q | Marking instructions | AO | Mark | Typical solution\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y^2 = 4x$
[1 mark]
\includegraphics{figure_9a}
\item Ben is using a 3D printer to make a plastic bowl which holds exactly $1000\text{cm}^3$ of water.
Ben models the bowl as a region which is rotated through $2\pi$ radians about the $x$-axis.
He uses the finite region enclosed by the lines $x = d$ and $y = 0$ and the curve with equation $y^2 = 4x$ for $y \geq 0$
\begin{enumerate}[label=(\roman*)]
\item Find the depth of the bowl to the nearest millimetre.
[4 marks]
\item What assumption has Ben made about the bowl?
[1 mark]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 1 2018 Q9 [6]}}