AQA C3 June 2014 Unofficial Mark Scheme

[br]\begin{enumerate}[br]\item \int = 2.449 \hfill \textbf{\underline{[4]}} \\[br]\end{enumerate}[br]

[br]\begin{enumerate}[br]\setcounter{enumi}{1}[br]\item[br]\begin{enumerate}[br]\item \dfrac{dy}{dx} = \dfrac{-2}{2e - x} \hfill \textbf{\underline{[2]}} \\[br]\item \text{Equation of Normal} = y-2=\dfrac{e}{2}(x-e) \hfill \textbf{\underline{[4]}} \\[br]\item [br]\begin{enumerate}[br]\item \text{Show} 1 \textless \alpha \textless 3 \hfill \textbf{\underline{[2]}} \\[br]\item x_2 = 2.980, x_3 = 1.798 \hfill \textbf{\underline{[2]}} \\[br]\item \text{Draw cobweb diagram} \hfill \textbf{\underline{[2]}} \\[br]\end{enumerate}[br]\end{enumerate}[br]\end{enumerate}[br]

[br]\begin{enumerate}[br]\setcounter{enumi}{2}[br]\item[br]\begin{enumerate}[br]\item [br]\begin{enumerate}[br]\item \dfrac{d}{dx}[(x^{2}+1)^{\dfrac{5}{2}}] = 5x(x^{2}+1)^{\dfrac{3}{2}} \hfill \textbf{\underline{[2]}} \\[br]\item f'(0) = 2 \hfill \textbf{\underline{[3]}} \\[br]\end{enumerate}[br]\item \text{x-coordinates} = \dfrac{-1}{2}, 2 \hfill \textbf{\underline{[5]}} \\[br]\end{enumerate}[br]\end{enumerate}[br]

[br]\begin{enumerate}[br]\setcounter{enumi}{3}[br]\item[br]\begin{enumerate}[br]\item \text{Sketch graph of} y=-\abs{f(x)} \hfill \textbf{\underline{[3]}} \\[br]\item \text{Sketch graph of} y=f(\abs{2x}) \hfill \textbf{\underline{[2]}} \\[br]\item[br]\begin{enumerate}[br]\item \text{Stretch, x-direction, sf} \dfrac{1}{2}, \text{Translate}[\dfrac{-1}{0}] \hfill \textbf{\underline{[4]}} \\[br]\item P'(1,-3) \hfill \textbf{\underline{[2]}} \\[br]\end{enumerate}[br]\end{enumerate}[br]\end{enumerate}[br]

[br]\begin{enumerate}[br]\setcounter{enumi}{4}[br]\item[br]\begin{enumerate}[br]\item f(x) \geq -4 \hfill \textbf{\underline{[2]}} \\[br]\item f^{-1}(x) = 3+\sqrt{x+4} \hfill \textbf{\underline{[4]}} \\[br]\item[br]\begin{enumerate}[br]\item gf(x) = \abs{x^2 - 6x - 1} \hfill \textbf{\underline{[1]}} \\[br]\item x = 5, 7 \hfill \textbf{\underline{[4]}} \\[br]\end{enumerate}[br]\end{enumerate}[br]\end{enumerate}[br]

[br]\begin{enumerate}[br]\setcounter{enumi}{5}[br]\item[br]\begin{enumerate}[br]\item \int = \dfrac{-x^{2}cos{2x}}{2} + \dfrac{xsin{2x}}{2} + \dfrac{cos{2x}}{4} + c \hfill \textbf{\underline{[6]}} \\[br]\item \text{Volume of revolution} = \pi(\dfrac{\pi^2}{8} - \dfrac{1}{2}) \hfill \textbf{\underline{[3]}} \\[br]\end{enumerate}[br]\end{enumerate}[br]

[br]\begin{enumerate}[br]\setcounter{enumi}{6}[br]\item \dfrac{-1}{3} + ln{\dfrac{3}{2}} \hfill \textbf{\underline{[6]}} \\[br]\end{enumerate}[br]

[br]\begin{enumerate}[br]\setcounter{enumi}{7}[br]\item[br]\begin{enumerate}[br]\item \text{Show expression can be written as} 2secx \hfill \textbf{\underline{[4]}} \\[br]\item x = 71, 180, 289 \hfill \textbf{\underline{[6]}} \\[br]\item \theta = 51, 105, 160 \hfill \textbf{\underline{[2]}} \\[br]\end{enumerate}[br]\end{enumerate}[br]