2012 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: 7.65; 9.85; 8.52
Question 2: \frac{1}{4}\ln (1+ x^4) + c;~ \frac{1}{2} \tan^{-1}x^2 + c;~ 0.186
Question 3: u_2 = \frac{5}{6},~u_3 = \frac{1}{4}:~ l = - \frac{1}{3}
Question 4: a = 1,~ b =1.5
Question 5: \mu = 6;~C(5, 7, 1), ( \frac{17}{3}, \frac{19}{3}, \frac{5}{3})
Question 6: 1 - 3c² + (3c-c^3)i;~ z = 1 \pm \sqrt{3} i;~ n = 10, \vert z^{10} \vert = 1024, \text{arg~} ( z^{10} ) = \frac{2\pi}{3}
Question 7: y =x
Question 8: Maximum
Question 9: \textbf{r} = \begin{pmatrix}7\\8\\9\end{pmatrix} + \lambda \begin{pmatrix}1\\2\\1\end{pmatrix}, \lambda \in \mathbb{R};~ \vec{ON} = \begin{pmatrix}5\\4\\7\end{pmatrix};~1:3;~ x- 7 = \frac{y-8}{-4} = z-9
Question 10: r = h = \big( \frac{3k}{5\pi} \big)^{1/3};~ r = 3.04, h = 4.88
Question 11: 3\pi

Paper 2

Numerical Answers (click the questions for workings/explanation)
Question 1: y = 8x^2 - \frac{3}{4} x^4 + Cx + D;~ t = \frac{1}{24} \ln \bigg| \frac{4+3u}{7(4-3u)} \bigg|
Question 2: \sqrt{58} - 4;~ 7 - \frac{28}{\sqrt{58}} - i ( 3 - \frac{12}{\sqrt{58}}) ;~-0.9579
Question 3: x=2;~x=-1;~x=-2, 0, 1, 2
Question 4: 1.8\%
Question 5: 0.00599;~0.166;~ p = 0.999666
Question 6: H_0: \mu =14, ~\mu \neq 14;~ \{ x: x \in \mathbb{R}, 12.3 < \bar{x} < 15.7\};~ H_0 will be rejected.
Question 7: \frac{2}{15};~ \frac{34}{35};~ \frac{2}{455};~ \frac{43}{273};~ \frac{1}{7}
Question 8: L= 91,~ r = 0.929744;~ L=92; ~13
Question 9: 0.373;~ p = 0.39
Question 10: 0.0474;~ x = 0.324; ~0.144; ~0.245; ~0.912

Relevant materials

MF15

KS Comments:

Overall, this paper was okay in my opinion. The student’s handwork will be rewarded through this paper.

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    2012 A-level H2 Mathematics (9740) Paper 1 Question 10 Suggested SolutionsJC Mathematics
    2012 A-level H2 Mathematics (9740) Paper 2 Question 1 Suggested SolutionsJC Mathematics