2025 Ahmad Ibrahim Secondary School Prelims A Math Paper 2
Without using a calculator, solve the equation \(x\sqrt{15}+\sqrt{5}=x\sqrt{2}+\sqrt{6}\). Leave your answer in the form \(p\sqrt{10}+q\sqrt{3}\), where \(p\) and \(q\) are fractions.[4]
Without using a calculator, solve the equation \(\log_2 x-\log_x 16=0\).[4]
Solve the equation \(3^{x+2}-2\left(3^{-x}\right)=17\).[4]
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Answer:(a) \(x=\dfrac{2}{13}\sqrt{10}-\dfrac{3}{13}\sqrt3\) (b) \(x=4\) or \(x=\dfrac14\) (c) \(x=\dfrac{\ln2}{\ln3}=0.631\)