2025 NASS PRELIMS P1 Q6

2025 NASS PRELIMS P1 Q6

Secondary 4
8 marks
2025 Ngee Ann Secondary School Prelims A Math Paper 1
  1. It is given that \(\sin A=-\frac{1}{\sqrt{5}}\) and \(\tan B=-\frac{3}{4}\), where \(A\) and \(B\) are in the same quadrant. Without using a calculator, find the exact value of
    1. \(\tan(-A)\),[2]
    2. \(\sin(A+B)\),[2]
    3. \(\cos\frac{B}{2}.\)[2]
  2. Given that \(\sin A=q\), where \(A\) is an obtuse angle, express \(\tan^2 A\) in terms of \(q\).[2]

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Answer:\(\text{(a)(i)}\hspace{0.5em}\frac12,\quad\text{(ii)}\hspace{0.5em}-\frac{2}{\sqrt5},\quad\text{(iii)}\hspace{0.5em}-\frac3{\sqrt{10}},\quad\text{(b)}\hspace{0.5em}\frac{q^2}{1-q^2}\)

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