2007 H2 Math Paper 2 Answers

Cyan: $3.50/L.
Magenta: $2.60/L.
Yellow: $4.90/L.
Total cost of producing Daisy: $7.65.

(b)

{1 - \frac{1}{ ( N + 1 )^2 }}

(c)

{N \to \infty,}

{\frac{1}{ ( N + 1 )^2 } \to 0}

{1 - \frac{1}{ ( N + 1 )^2 }\to1.}

Hence the series is convergent and the sum to infinity is

{1.}

(d)

{1 - \frac{1}{ N^2 }}

(a)

{1 + n x + \frac{n(n-1)}{2} x^2 + \frac{n(n-1)(n-2)}{6} x^3 + \ldots}

(b)

{8 - 3 x + \frac{387}{16} x^2 - \frac{1151}{128} x^3 + \ldots}

(c)

{- \frac{1}{2} \sqrt{2} < x < \frac{1}{2} \sqrt{2}.}

(a)

\int_0^{\frac{5}{3} \pi} \sin^2 x \, \mathrm{d}x = \frac{1}{8} \sqrt{3} + \frac{5}{6} \pi

\int_0^{\frac{5}{3} \pi} \cos^2 x \, \mathrm{d}x = - \frac{1}{8} \sqrt{3} + \frac{5}{6} \pi

(b)

(i)

{\left(\pi - 2\right) \textrm{ units}^2.}

(ii)

{5.391\textrm{ units}^3.}

—

(a)

0.933.

(b)

(i)

0.715.

(ii)

0.617.

(a)

{\overline{x} = 30.84, s^2 = 33.7.}

(b)

(i)

{p-\textrm{value} = 0.0382 \leq 0.05} \allowbreak \, \Rightarrow \, \allowbreak {H_0 \textrm{ rejected}.}

Hence there is sufficient evidence at the 5% level of significance to conclude that the population mean time for a student to prepare for the test exceeds 30 hours.

(ii)

No assumptions are needed about the population. This is because, as

{n=150}

is large, by the Central Limit Theorem,

{\overline{X}}

is normally distributed approximately so no further assumptions on the population are needed.

(a)

0.395.

(b)

0.160.

(c)

0.392.

(d)

The event in part (ii) is a subset of the event in part (iii).

(a)

(i)

479,001,600.

(ii)

46,080.

(b)

(i)

39,916,800.

(ii)

86,400.

(iii)

240.

(b)

{\frac{1}{64}.}

(c)

{\frac{21}{256}.}

(d)

{\frac{13}{17}.}

—