2014 A-level H2 Mathematics (9740) Suggested Solutions

By KS Teng

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

Please kindly comment at the specific questions should you have any questions.

Paper 1

Numerical Answers (click the questions for workings/explanation)
Question 1: f^2(x) = f^{-1}(x);~ f^3(x) = x
Question 2: (-3, -3)

Question 3: \hat{n}= \frac{1}{\sqrt{1+2^{2}+2^{2}}}\begin{pmatrix}1\\2\\-2\end{pmatrix};~ \frac{2}{3}
Question 4:
Question 5: -\frac{11}{125}+\frac{2}{125}i; q = -250p
Question 6: \frac{7}{3}n - \frac{4}{9}(4^n -1);~ 1;~\frac{n}{(n+1)!}
Question 7: \beta = \sqrt{3};~ -0.597;~ \frac{54}{35}\sqrt{3};~ \pm a \pm bi
Question 8: \text{sin}^{-1} \frac{x}{3} + c;~ \frac{1}{3}+\frac{x^{2}}{54}+\frac{x^{4}}{648}+\frac{5x^{6}}{34992}+ \ldots ;~ \frac{x}{3}+\frac{x^{3}}{162}+\frac{x^{5}}{3240}+\frac{5x^{7}}{244944}
Question 9: x- 2y - z = 0;~ \textbf{r}= \begin{pmatrix}6\\3\\0\end{pmatrix} + \lambda \begin{pmatrix}4\\1\\2\end{pmatrix}, \lambda \in \mathbb{R};~({\frac{18}{7}},{\frac{15}{7}},{\frac{-12}{7}})
Question 10: k = -0.2;~ t = {\sqrt{5}} \mathrm{ln} \frac {\sqrt{5}-2x+1}{\sqrt{5}+2x-1};~{\sqrt{5}} \mathrm{ln} \frac {2\sqrt{5}+1}{2\sqrt{5}-1};~2.152;~x = \frac{1}{2} \bigg[1 + \frac{\sqrt{5}-\sqrt{5} e^{\frac{t}{\sqrt{5}}}}{(1 + e^{\frac{t}{\sqrt{5}}})}\bigg]
Question 11: r = 1.207, r = 3.951;~ h = 0.625

Paper 2

Numerical Answers (click the questions for workings/explanation)
Question 1: t = 2.5;~ 27x = 2y^{2}
Question 2: A = 3, B = 3, C = 8;~ a = \frac{3}{2}, b = \frac{13}{45}, c = \frac{8}{3}, d = \frac{2}{3}

Question 3: 35;~ 1816
Question 4: 5, 11, 17
Question 5:
Question 6: 31500;~16800;~8820
Question 7: 0.155;~0.273;~0.350
Question 8: \text{Model~}B;~P=33700\text{ln}m+196000;~64000
Question 9: \bar{t}>3.48;~ 0 < k^{2} \le 0.423
Question 10: 0.002;~0.352;~0.058;~\frac{71}{306}
Question 11: 0.768;~0.675;~5;~0.821

Relevant materials

MF15

KS Comments

I find this paper really interesting. It is slightly harder than the 2013 paper. There are several new things and trends that this paper has brought to the table as I had analysed with my classes.

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