Mastering Mathematics Smartly by Wee Wen Shih

Answers to 2008 H2 maths exam

The full worked solutions will be available in my upcoming book by Dyna Publisher scheduled to be released in early 2009. Here is a sneak preview.

Paper 1

Q1 a = 2.73

Q3 (i)    (ii)    (iii)

Q4 (i)    (ii)
      (iii) The gradient tends to become parallel to the x-axis.

Q5 (i)    (ii)

Q6 (a) a = 2, b = 3/4   (b) f(0) = 1, f'(0) = 4, f''(0) = 16,

Q7 x = 6.09, y = 12.6

Q8 (i) -8   (ii) a = -3, b = 6

Q9 (ii) The graph is a horizontal line parallel to the x-axis.

Q10 (i) 1 October 2011   (ii)(a) $6.08   (b) $310   (c) 81

Q11    (i)

        (ii) = -22, = 17
        (iii) = -22,  is a real number except 17
        (iv) -3x + y + 2z = 2

Paper 2

Q1 (ii)    (iv) -1.96 < x < 1.56

Q2 (i) 0.999   (ii)   (iii)

Q3 (a) |p| = 1, arg(p) = ,
      (b)(ii) Least = 0.058, Greatest = 1.229

Q4 (ii) , Domain = (1, $\infty$ )
      (iv) y = x,

Q6 Use t-test with $\nu = 14$ . Insufficient evidence, at the 5% significance level, that the mean mass has changed.

Q7 (i) 0.5   (ii) 0.512   (iii)

Q8 (i) 0.970   (iii) P is the point (4.8, 7.6)
      (iv) a = 1.42, b = 4.40   (v) 8.3

Q9 0.109, 0.192, 0.134

Q10 (i) 120   (ii) 9   (iii) 210   (iv) 485

Q11 (i) 0.0385   (ii) 0.0924
        E(Y) = 110, Var(Y) = 576, a = 3, b = -40

Answers to 2008 H1 maths exam

The full worked solutions will be published in my upcoming book by Dyna Publisher Pte Ltd. Here is a sneak preview for the keen learner.

Q1 (i) $c$    (ii) $-c$ ,   $x = \pi + \alpha$

Q2 $x = 10 + 5\sqrt{2}, y = 10 - 5\sqrt{2}$

Q3 $\frac{4}{3}k^3$

Q4 (ii) Greatest $a = 0$ ,   domain of $f^{-1}$ is $[-1, \infty)$ ,   $f^{-1}(x) = -\sqrt{x + 1}$

Q5 (ii) $t = 11.7\text{s}$

Q6 $x$ -coordinate of N is $1 + \frac{1}{3}\text{ln}\:6$ ,   area $=\frac{5}{3}(\text{ln}\:6)^2$

Q7 $0.747$

Q8 $0.276$ ,   $0.927$ ,   $\sigma = 0.137$

Q9 (ii) $\frac{5}{8}$ ,   (iii) $\frac{21}{64}$ ,   (iv) $\frac{3}{7}$

Q10 $p-\text{value}=0.0975$
        There is sufficient evidence, at the 10% significance level, that $\mu < 150$ .

Q11 (ii) $\overline{x} = 17, \overline{y} = 343.75$    (iii) $y = 17.1x + 53.3$    (iv) $r = 0.969$    (v) $y = 395$

Q12 $0.296$ ,   $0.926$ ,   $0.908$