Q1
Answer
  1. Sketch on the same set of axes the graphs of $y=3\sin x$ and $y = 1+\mathrm{cosec}\ x$ for $-180^{\circ} < x < 180^{\circ}$.
  2. Find the $x$ coordinate of each point where the curves intersect in this interval, giving your answers to 1 decimal place.
  1. Sketches
  2. $50.1, 129.9, -25.7, -153.3$
Q2
Answer
The figure below shows a circular sector $ABC$ of radius $r$ cm subtending an angle $ heta$ radians at $C$. The length of the arc $AB$ is $\dfrac{2}{9}$ of the perimeter of the sector. Show that $\theta=\dfrac{4}{7}$ radians.
Use arc: $r\theta$ and perimeter: $r\theta + 2r = r(\theta + 2)$
Q3
Answer
Evaluate $\displaystyle\int_1^2\dfrac{3x^3+1}{2x^2}\ \mathrm{d}x$.
$2.5$