2011 H2 Math Solutions

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We have digitized the answers and solutions from 2007 to 2022 at
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In particular, you can start navigating the 2011 answers and full worked solutions from
2011P1Q1.

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$-2 < x < 1$
(i) $f(x) = 0.215x^2 – 0.490x + 3.281$
(ii) $(1.14, \infty)$
(i) $y=\displaystyle – \frac{1}{p^3} x + \frac{3}{p}$.
(ii) $Q(3p^2, 0)$, $R \displaystyle \left( 0, \frac{3}{p} \right)$.
(iii) $\displaystyle y^2 = \frac{27}{8x}$.
(i) $1-3x^2 + 4x^4 + \ldots$
(iia) $a-a^3+\displaystyle \frac{4}{5}a^5$, 0.540.
(iib) 0.475.
(ii) $[0, 2]$.
(iii) $a = 2 + \sqrt{5}$.
$\displaystyle \sum_{r=1}^n \cos r\theta = \frac{1}{2\sin {\textstyle\frac{1}{2} \theta} } \left( \sin ({\textstyle n + \frac{1}{2}}) \theta – \sin {\textstyle \frac{1}{2}\theta }\right)$.

(ai) $\displaystyle \frac{1}{4} – \left( \frac{1}{2}n^2 + \frac{1}{2} n + \frac{1}{4} \right) \mathrm{e}^{-2n}$
(aii) $\displaystyle \frac{1}{4}$
(b) $(2 \pi^2 – 4 \pi)$