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same thing happened to me with maths 99/100 exam 95/100 internal was ranked first..

i always seem to overcomplicate things although, integrating t from 0 to 4 seems not enough for 2 marks (especially Q9)

i'm pretty sure part (i) was a hint for: 2 + \frac{t^2}{t+1} = 1 + \frac{1}{t+1} + t which can now be integrated

yeah

omg i thought i was the only one who noticed lol

P(x_{1}, \ y_{1}) \ \ S(0, \ a) \ \ Q \left ( \frac{2ay_{1}}{x_{1}} , \ 0 \right ) \ \ R(0 , \ -y_{1}) d) \begin{align*} m_{SQ}&=\frac{0-a}{\frac{2ay_{1}}{x_{1}}-0}\\ &=\frac{-a\times x_{1}}{2ay_{1}}\\ &=-\frac{x_{1}}{2y_{1}}\\\\ m_{PQ}&=\frac{y_{1}-0}{x_{1}-\frac{2ay_{1}}{x_{1}}}\\...

\begin{align*} \frac{\mathrm{d} V}{\mathrm{d} t}&=10\\ V&=10t+c\\ \textup{when }t=0&, \ V=0 \ \ \therefore c=0\\ V&=10t\\ \textup{but } V&=\frac{\pi x^{3}}{12}\\\\ \therefore 10t&=\frac{\pi x^{3}}{12}\\ x^{3}&=\frac{120t}{\pi}\\ \textup{when } t=2&, \\ x^{3}&=\frac{240}{\pi}\\ x^{2}&=\left...

\begin{align*} 2\cos(x)&-\sin(x)=0\\ 2\cos(x)&=\sin(x)\\ 2&=\frac{\sin(x)}{\cos(x)}\textup{ \space\space (}\cos(x)\neq 0\textup{ )}\\ \therefore \tan(x)&=2 \\\\ x&=\tan^{-1}(2), 180^{\circ}+\tan^{-1}(2) \end{align*}

\begin{align*} m_{p}&=p,\ m_{q}=q\\ m_{p} &\perp m_{q}\\ \therefore pq&=-1 \end{align*} \\ \begin{cases} y&=px-ap^2\\ y&=qx-aq^2\\ \end{cases}\\ \begin{align*} \therefore px-ap^2&=qx-aq^2\\ x(p-q)&=a(p+q)(p-q)\\ x&=a(p+q) \\\\ y&=p\left [ a(p+q) \right ]-ap^2\\ &=ap^2+apq-ap^2\\ &=apq\\ &=-a...

x=t^2, \ y=-2t \\ \begin{align*} \therefore x&=\left ( -\frac{y}{2} \right )^{2} \\ y^{2}&=4x, \end{align*} \\ \textup{Focal length}: a=1 \\ \textup{Vertex}: (0,0) \\ \textup{Focus}: (1,0) \\ \\ \begin{align*} \therefore \frac{-4-0}{4 - 1}&=\frac{y-0}{x-1} \\ -4(x-1)&=3y \\-4x+4&=3y \\\therefore...

Re: James ruse 2011 trial papers? try this

Re: 2 Unit Revising Marathon HSC '10 \begin{align*} \frac{\mathrm{d} }{\mathrm{d} x}(a^{f(x)})=a^{f(x)} \times \log_{e}(a)\times f'(x) \\ \therefore \int a^{f(x)} \times \log_{e}(a)\times f'(x) \ dx &= a^{f(x)} \\ \textrm{because} \log_{e}(a) \textrm{ is constant:} \\ \log_{e}(a) \int f'(x)...

Re: 2 Unit Revising Marathon HSC '10 new question: find \frac{\mathrm{d} }{\mathrm{d} x}\left ( x^x \right ) that'll test if you understand

Re: 2 Unit Revising Marathon HSC '10 \begin{align*} a^x &= e^{\log_{e}(a^{x})} \\ &=e^{x.\log_{e}(a)} \\ \frac{\mathrm{d} }{\mathrm{d} x}(a^x) &= \frac{\mathrm{d} }{\mathrm{d} x}(x.\log_{e}(a)) \times e^{x.\log_{e}(a)} \\ &=e^{x.\log_{e}(a)} \ \log_{e}(a) \\ &=e^{\log_{e}(a^x)} \ \log_{e}(a)...