Additional Mathematics 4037: Simultaneous equations Topical Past Paper Questions

The line $y = 3x + 4$ meets the curve $y = 2x^{2} + 8x + 1$ at two points $A$ and $B$. Find the equation of the perpendicular bisector of AB, giving your answer in the form $ax+by+c=0$, where $a, b$ and $c$ are integers. [9]

(a) Find $ \int\frac{1}{\sqrt{3x+2}}dx $. [2] (b) Find, in terms of a, $ \int_{0.5}^{a}e^{(1-2x)}dx $. [3]

(a) Solve the following simultaneous equations. $$ \begin{aligned}&3\log_{2}x+2\log_{2}y=24\\&5\log_{2}x-3\log_{2}y=2\\ \end{aligned} $$ (b) Solve the equation $ \frac{2^{t+4}}{2^{1-2t}}=512 $. [5]