Higher November 2018 Paper 1 Q19

(a) Simplify \(\dfrac{3}{\sqrt{3}}\). [1]

(b) Write \(\sqrt{63} + \sqrt{175}\) in the form \(k\sqrt{7}\), where \(k\) is an integer. [2]

(c) Expand and simplify \(\left(4 - 2\sqrt{5}\right)\left(2 + \sqrt{5}\right)\). [2]

(d) Complete the following identity. [1]\[x^2 - 3 \equiv (x - \ldots\ldots)(x + \ldots\ldots)\]