# 2018 H2 Math

## Paper 1

1. (i) $1-\frac{1-\ln x}{x^2}$.
(ii) $1-\frac{2}{\mathrm{e}}$.
2. (i) $\frac{1}{2}$ and $3$.
(ii) $\frac{125\pi}{6} \textrm{ units}^3$.
3. (i) $f(x) = -\frac{6}{x^3}$.
(ii) $y=3-x^2$.
4. (i) $x=-1-\sqrt{3}, -1, 0$ or $-1+\sqrt{3}$.
(ii) $-1-\sqrt{3} < x <-1$ or $0 < x <-1+\sqrt{3}$.
5. $b=-1$.
$f^{-1}(x) = \frac{x+a}{x-1}$.
6. (ii) $\pm 2 \sqrt{31}$.
7. (ii) $N \left (-\frac{1}{17},0\right )$.
8. (i) $A=5, u_3=40$.
(ii) $a=\frac{15}{2}, b=-5, c=-5$.
(iii) $15(2^n-1) – \frac{5n}{2} (n + 3)$.
9. (ii) $x=2\alpha$.
(iii) $8$ units.
10. (i) Conditions on $V$: $V$ is a constant.
(iii) $I = \frac{3A}{2\mathrm{e}}$.
11. (i)(a) $102.43. (i)(b)$1215.71.
(i)(c) First day of June 2018.