Cambridge Maths Academy

수학 모음 (Maths collection) 전체보기 This question comes from a test paper for A-level maths for Michaelmas Term at Eton College. Q16. (a) Solve the equation $$ \begin{align} \log_{10}\left(3^x-5^{2-x}\right)=2+\log_{10}(2)-x\log_{10}(5), \end{align} $$ giving your answer as exact. [3 marks] (b) Solve the equation $$ \begin{align} \left(5\sqrt{5}\right)^{3x}-31=30\left(\frac1{\sqrt[4]{5}}\right)^{9x}, ..

수학 모음 (Maths collection) 전체보기 This question comes from a test paper for A-level maths for Michaelmas Term at Eton College. Q15. (a) Express $\cos(2\theta)+\sin(2\theta)$ in the form $R\sin(2\theta+\alpha)$ where $R>0$ and $0 < \alpha < \frac{\pi}{2}$. [3 marks] (b) Hence show that $$ \begin{align} \frac{1-\sqrt{2}}{2}\le \cos\theta(\cos\theta+\sin\theta) \le\frac{1+\sqrt{2}}{2} \end{align} $$ fo..

수학 모음 (Maths collection) 전체보기 This question comes from a test paper for A-level maths for Michaelmas Term at Eton College. Q14. At time $t$ secons after the start of an experiment, the temperature of a cooling liquid is proportional to $\textrm{e}^{-kt}$. (a) Given that the liquid's initial temperature was $80^\circ$C, find a formula for $T$ in terms of $t$ and $k$. [1 mark] (b) Given also that ..