2013 A-level H2 Mathematics (9740) Suggested Solutions

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: (- \frac{38}{3}, - \frac{119}{3}, - \frac{25}{3}); No solutions, triangular prism.
Question 2: \{ y: y \in \mathbb{R}, y \le 3 - 2\sqrt{3} \text{~or~} y \ge 3 + 2 \sqrt{3}\}

Question 3: x < 0.5 \text{~or~} x > 2
Question 4:  -11 - 2i;~a= 27, b = 295;~ 1 + 2i, 1 -2i, -\frac{59}{27}
Question 5: \frac{a \pi}{12}
Question 6: \vec{ON} = \frac{4 \textbf{a} +. 3\textbf{c}}{7};~ \lambda = \frac{8\mu}{7}
Question 7: A = 1, B = 6, C = -1, D =1;~12
Question 8: 2r, \theta - \frac{\pi}{3};~\frac{\pi}{24}
Question 9: a = 6;~ \frac{n}{6}(2n+1)(n+1);~\frac{n}{2}(n+1)(n^2 +n + 1) + \frac{n}{2}(2n+1)(n+1) + 24n
Question 10: z = \frac{3}{2} -  Ae^{-2x};~ y = \frac{3}{2}x - \frac{A}{2}e^{-2x} + D;~a=-2, b =3;~y = \frac{3}{2}x, y = \frac{3}{2}x +1
Question 11: y = tx - t^3;~ M(\frac{3}{2},  \frac{1}{\sqrt{2}});~ \frac{2\sqrt{2}}{15}

Paper 2

Numerical Answers (click the questions for workings/explanation)
Question 1: a = 4
Question 2: V = \frac{a^3}{54}
Question 3: 0, 2, -4, 14, f(x) = 2x - 2x^2 +\frac{7}{3}x^3 + \ldots;~ a=-1, n = 2, - \frac{1}{x}x^3
Question 4: 40.4^{\circ };~c = -49 \text{~or~} \frac{35}{13}
Question 5:
Question 6: k=1.29
Question 7: 0.377;~ 0.185
Question 8: 0.24;~0.06;~0.26
Question 9: 12.8, 2.31;~ p = 0.052397
Question 10: r = -0.939;~ y=190 - 0.00462x^2 ,134
Question 11: 0.789;~\frac{4}{9};~ 0.197;~0.186
Question 12: 4;~ 0.397;~0.848

Relevant materials

MF15

KS Comments:

This paper is not that difficult. I think the hardest question will be the permutation question.

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