# 2011 H2 Math Solutions

## Math Repository

We have digitized the answers and solutions from 2007 to 2022 at
Math Repo.

In particular, you can start navigating the 2011 answers and full worked solutions from
2011P1Q1.

They are designed to be digital and mobile friendly: we hope you will have a good experience there.

## Math Pro

Done with your TYS but Prelims still too difficult? Try out the questions
at Math Pro where we tweak the past TYS questions.

We are still under construction, but 6 pure math topics have been completed so far, with more to come!

## Paper 2

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

## Paper 2

1. (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) $(2 \pi^2 – 4 \pi)$