Mastering Mathematics Smartly
by Wee Wen Shih

A unique self-help website that provides comprehensive coverage of mathematics at A-level & beyond, written in a student-friendly style.

Answers to 2007 exam

H2 Mathematics was assessed for the first time in 2007.

This document analyses the questions in depth and it contains answers to all questions. Interested students may refer to the full worked solutions in my book by "Dyna Publisher", which is available at Popular bookshops.

Syllabus 9233 & 9234

Note: Questions from syllabus 9233 and 9233 exam papers 2007 will be included in the 2009 edition of H2 mathematics ten-year-series (by Dyna Publisher) which will be out in early 2009.

Answers to 9233 Paper 1 (2007 Exam):

Q2 -\frac{405}{1024}

Q3 \frac{\pi^2}{24}

Q4 (i) 18   (ii) 81

Q7 P (-5, 6, 0),   AP = 7

Q8 0.312

Q9 z = -3i or 3i

Q10 4\sqrt[]{2}

Q11 -ln 8

Q13 \frac{1}{2}x^2 + \frac{1}{12}x^4 + ...

Answers to 9233 Paper 2 (2007 Exam):

Q1 \frac{27}{2}(3^{2n} - 1)

Q2 (i) \bold r = \begin{pmatrix} {4}\\ {1}\\ {3} \end{pmatrix} + \lambda \begin{pmatrix} {1}\\ {1}\\ {0} \end{pmatrix}, \lambda \in \mathbb{R}   (ii) \begin{pmatrix} {1}\\ {-2}\\ {3} \end{pmatrix}

Q3 x = 0.631 or -2

Q4 (i) y = 4, x = 3   (iii) f^{-1}(x) = \frac{13}{x-4} + 3, D_{f^{-1}} = \mathbb{R}-\{4\}

Q5 1 + (2 + \sqrt{3})i

Q23 0.890

Q25 (i) \frac{5}{13}   (ii) \frac{1}{2}   (iii) \frac{18}{25}
        W and B are not independent.
        M and C are not independent.

Q26 (i) 0.440   (ii) 0.123

Q27 0.778,   0.157

Answers to 9234 Paper 1 (2007 Exam):

Q2 \frac{1}{3} - \frac{1}{3^{N+1}(N+1)},   \frac{1}{3}


Q5 -4,   32

Q6 \begin{pmatrix} {6}\\ {4}\\ {3} \end{pmatrix},   16.1^{\circ}

Q9 z = e^{(\frac{2k\pi}{5})i}, k = 0, 1, ..., 4
      \frac{2\pi}{5}, \frac{3\pi}{5}

Q12 (i) a = 2, b = 3   (ii) c = -2   (iii) \{y : -25 < y < -1\}

Answers to 9234 Paper 2 (2007 Exam):

Q8 (i) 0.945   (ii) 14.8

Q10 Use t-test with \nu = 11. p-value = 0.0467 < 0.05.
        There is sufficient evidence, at 5% significance level, that the mean IQ of comedians exceed 128.