OCR C2 — Question 6

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
TopicTrig Equations

  1. \(f ( x ) = \cos 2 x , 0 \leq x \leq \pi\).
    1. Sketch the curve \(y = \mathrm { f } ( x )\).
    2. Write down the coordinates of any points where the curve \(y = \mathrm { f } ( x )\) meets the coordinate axes.
    3. Solve the equation \(\mathrm { f } ( x ) = 0.5\), giving your answers in terms of \(\pi\).
    4. (i) Find
    $$\int \left( x + 5 + \frac { 3 } { \sqrt { x } } \right) \mathrm { d } x$$
  2. Evaluate $$\int _ { - 2 } ^ { 0 } ( 3 x - 1 ) ^ { 2 } d x$$