Easy -1.8 This is a pure recall question testing only whether students know the volume of revolution formula V = π∫y²dx. It requires no calculation, no problem-solving, and no integration—just recognition of the correct formula from four options. Even for Further Maths, this is trivial.
2 The function f is defined by
$$f ( x ) = 2 x + 3 \quad 0 \leq x \leq 5$$
The region \(R\) is enclosed by \(y = \mathrm { f } ( x ) , x = 5\), the \(x\)-axis and the \(y\)-axis.
The region \(R\) is rotated through \(2 \pi\) radians about the \(x\)-axis.
Give an expression for the volume of the solid formed.
Tick ( ✓ ) one box.
\(\pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) d x\)
\includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-02_113_108_1539_1000}
\(\pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) ^ { 2 } \mathrm {~d} x\)
\includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-02_115_108_1699_1000}
\(2 \pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) d x\) □
\(2 \pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) ^ { 2 } \mathrm {~d} x\) □
2 The function f is defined by
$$f ( x ) = 2 x + 3 \quad 0 \leq x \leq 5$$
The region $R$ is enclosed by $y = \mathrm { f } ( x ) , x = 5$, the $x$-axis and the $y$-axis.\\
The region $R$ is rotated through $2 \pi$ radians about the $x$-axis.\\
Give an expression for the volume of the solid formed.\\
Tick ( ✓ ) one box.\\
$\pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) d x$\\
\includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-02_113_108_1539_1000}\\
$\pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) ^ { 2 } \mathrm {~d} x$\\
\includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-02_115_108_1699_1000}\\
$2 \pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) d x$ □\\
$2 \pi \int _ { 0 } ^ { 5 } ( 2 x + 3 ) ^ { 2 } \mathrm {~d} x$ □
\hfill \mbox{\textit{AQA Further AS Paper 1 2024 Q2 [1]}}