| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2018 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Find stationary points coordinates |
| Difficulty | Standard +0.3 This is a straightforward C2 question requiring standard techniques: differentiate using product/chain rule, find stationary point by setting derivative to zero, find x-intercept by solving algebraic equation, and integrate using power rule. All steps are routine applications of core techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.08e Area between curve and x-axis: using definite integrals |
| END |
9.
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\caption{Figure 3}
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Figure 3 shows a sketch of part of the curve with equation
$$y = 7 x ^ { 2 } ( 5 - 2 \sqrt { x } ) , \quad x \geqslant 0$$
The curve has a turning point at the point $A$, where $x > 0$, as shown in Figure 3.
\begin{enumerate}[label=(\alph*)]
\item Using calculus, find the coordinates of the point $A$.
The curve crosses the $x$-axis at the point $B$, as shown in Figure 3.
\item Use algebra to find the $x$ coordinate of the point $B$.
The finite region $R$, shown shaded in Figure 3, is bounded by the curve, the line through $A$ parallel to the $x$-axis and the line through $B$ parallel to the $y$-axis.
\item Use integration to find the area of the region $R$, giving your answer to 2 decimal places.\\
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END & \\
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\hfill \mbox{\textit{Edexcel C2 2018 Q9 [12]}}