Standard +0.8 This is a straightforward application of Simpson's rule to find a volume of revolution. While it involves the inverse cosine function and requires careful arithmetic with five ordinates, it's a standard technique with no conceptual challengesโstudents follow a memorized formula. The 5-mark allocation reflects computational work rather than problem-solving difficulty, placing it moderately above average but well within typical A-level Further Maths scope.
The diagram shows part of the graph of \(y = \cos^{-1} x\)
\includegraphics{figure_7}
The finite region enclosed by the graph of \(y = \cos^{-1} x\), the \(y\)-axis, the \(x\)-axis and the line \(x = 0.8\) is rotated by \(2\pi\) radians about the \(x\)-axis.
Use Simpson's rule with five ordinates to estimate the volume of the solid formed. Give your answer to four decimal places.
[5 marks]
The diagram shows part of the graph of $y = \cos^{-1} x$
\includegraphics{figure_7}
The finite region enclosed by the graph of $y = \cos^{-1} x$, the $y$-axis, the $x$-axis and the line $x = 0.8$ is rotated by $2\pi$ radians about the $x$-axis.
Use Simpson's rule with five ordinates to estimate the volume of the solid formed. Give your answer to four decimal places.
[5 marks]
\hfill \mbox{\textit{AQA Further Paper 2 2020 Q7 [5]}}