Maths Core WMA01/WMA02: PARTIAL FRACTIONS Topical Past Paper Questions

Given that $$ \frac{3x^{2}+4x-7}{\left(x+1\right)\left(x-3\right)}\equiv A+\frac{B}{x+1}+\frac{C}{x-3} $$ (a) find the values of the constants A, B and C. (4) (b) Hence, or otherwise, find the series expansion of $$ \frac{3x^{2}+4x-7}{(x+1)(x-3)}\quad\left|x\right| (6)

$$ \frac{6-5x-4x^{2}}{(2-x)(1+2x)}\equiv A+\frac{B}{(2-x)}+\frac{C}{(1+2x)} $$ (a) Find the values of the constants $A, B$ and $C$. (4) $$ \mathrm{f}(x)=\frac{6-5x-4x^{2}}{(2-x)(1+2x)}\qquad x>2 $$ (b) Using part (a), find $ f'(x) $. (3) (c) Prove that $f(x)$ is a decreasing func…

Figure 4 Figure 4 shows a hemispherical bowl containing some water. At $t$ seconds, the height of the water is $h$ cm and the volume of the water is $V$ cm$^{3}$, where $$ V=\frac{1}{3}\pi h^{2}(30-h),\qquad0 (5) (b) Write $ \frac{30(20-h)}{h(30-h)} $ in partial fraction form. (3…