These Ten-Year-Series (TYS) worked solutions with video explanations for 1998 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
(a)
Given that $x$ is real, prove that ${{x}^{2}}-4x+9$ is always positive.
Solve the inequality $\frac{{{x}^{3}}+2{{x}^{2}}+x+14}{{{x}^{2}}+5}>x+1$.
(a) Given that $x$ is real, prove that ${{x}^{2}}-4x+9$ is always positive.
Solve the inequality $\frac{{{x}^{3}}+2{{x}^{2}}+x+14}{{{x}^{2}}+5}>x+1$.
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(b)
The complex number $q$ is given by $q=\frac{{{e}^{i\theta }}}{1-{{e}^{i\theta }}}$, where $0<\theta \le 2\pi $.
In either order,
The complex number $q$ is given by $q=\frac{{{e}^{i\theta }}}{1-{{e}^{i\theta }}}$, where $0<\theta \le 2\pi $.
In either order,
(i) find the real part of $q$,
(i) find the real part of $q$,
(ii) show that the imaginary part of $q$ is $\frac{1}{2}\cot \left( \frac{1}{2}\theta \right)$.
(ii) show that the imaginary part of $q$ is $\frac{1}{2}\cot \left( \frac{1}{2}\theta \right)$.
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