Further Mathematics 7366: Further Algebra and Functions Topical Past Paper Questions

Use Maclaurin's series expansion for $ \ln(1 + x) $ to show that the first three terms of the Maclaurin's series expansion of $ \ln(1 + 3x) $ are $$ 3x-\frac{9}{2}x^{2}+9x^{3} $$ [1 mark] (b) Julia attempts to use the series expansion found in part (a) to find an approximation fo…

The inequality $$ (x^{2}-5x-24)(x^{2}+7x+a)<0 $$ has the solution set $$ \{x:-9<x<-3\}\cup\{x:2<x<b\} $$ Find the values of integers $a$ and $b$ [4 marks]

A curve $ C_{1} $ has equation $$ y=\frac{2x+7}{3x+5} $$ Write down the equations of the asymptotes of curve $C_{1}$ [2 marks] (b) On the axes below, sketch the graph of curve $C_{1}$ Indicate the values of the intercepts of the curve with the axes. [3 marks] (c) Hence, or otherw…