Q1
Answer
Solve $2\sin (2x) = 3\cos(2x)$ in the range $0 < x \leq 360^{\circ}$.
$28, 118, 208, 298$
Q2
Answer
Solve $2\sin^2 x + 3\cos x = 0$ in the range $0 < x \leq 360^{\circ}$.
$120, 240$
Q3
Answer
The population of a town, $p$, can be modelled by the equation $p = ab^t$, where $t$ is the time in years after the year 2000, and $a$ and $b$ are constants.
  1. Show that a plot of $\log_{10} p$ against $t$ produces a straight line graph.
  2. A straight line graph of $\log_{10} p$ against $t$ was plotted. The gradient was found to be $0.3$ and the $\log_{10} p$ intercept was found to be $3$. Find the value of the constants $a$ and $b$.
  3. What is the meaning of the constant $a$ in this model?
  4. Suggest one limitation of this model.
  1. $\log_{10} p = \log_{10} a + t\log_{10} b$
  2. $a = 100$ and $b = 10^{0.3} = 2.00$
  3. Population in the year 2000
  4. Population cannot grow infinitely which this model predicts