Mathematics B (MEI) H630: ALGEBRA Topical Past Paper Questions

In this question you must show detailed reasoning. Express $ \frac{1+4\sqrt{3}}{2+\sqrt{3}} $ in the form $ a+b\sqrt{3} $, where a and b are integers to be determined. [3]

A family is planning a holiday in Europe. They need to buy some euros before they go. The exchange rate, y, is the number of euros they can buy per pound. They believe that the exchange rate may be modelled by the formula $$ y=a t^{2}+b t+c, $$ where t is the time in days from wh…

In this question you must show detailed reasoning. You are given that $ f(x) = 4x^{3} - 3x + 1 $. (i) Use the factor theorem to show that $ (x+1) $ is a factor of $ f(x) $. [2] (ii) Solve the equation $ f(x)=0 $. [3]