Mathematics Pure WMA11: Proof Topical Past Paper Questions

(a) Factorise $ x^{2}-4y^{2} $ (1) (b) Use proof by contradiction to prove that there are no positive integers x and y such that $$ x^{2}-4y^{2}=27 $$

Use proof by contradiction to show that for all angles $x$, where $90^{\circ}<x<180^{\circ}$ $$ \left|\frac{\cos2x}{\cos x-\sin x}\right|<1 $$

$$ \mathrm{f}(x)=(8-3x)^{\frac{4}{3}}\quad0 (4) (b) Use proof by contradiction to prove that the curve with equation $$ y=8+8x-\frac{15}{2}x^{2} $$ does not intersect the curve with equation $$ y=A-8x+\frac{x^{2}}{2}+Bx^{3}\quad0 (4)