SPS SPS SM 2021 November — Question 7 5 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2021
SessionNovember
Marks5
TopicAreas by integration
TypeArea under polynomial curve
DifficultyStandard +0.3 This is a straightforward integration problem requiring finding roots of a quartic (which factors nicely as a difference of squares), then applying the definite integral formula. The algebraic manipulation is routine and the integration of (2x-5)^4 is a standard chain rule application, making it slightly easier than average.
Spec1.08e Area between curve and x-axis: using definite integrals

The diagram below represents the graph of the function \(y = (2x - 5)^4 - 1\) \includegraphics{figure_7}
  1. Find the intersections of this graph with the \(x\) axis. [1]
  2. Hence find the exact value of the area bounded by the curve and the \(x\) axis. [4]

The diagram below represents the graph of the function $y = (2x - 5)^4 - 1$

\includegraphics{figure_7}

\begin{enumerate}[label=(\alph*)]
\item Find the intersections of this graph with the $x$ axis. [1]

\item Hence find the exact value of the area bounded by the curve and the $x$ axis. [4]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS SM 2021 Q7 [5]}}