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AS & A Level · AS/A Level

Mathematics

Trigonometry

Name: ____________________Date: October 10, 2026
  1. 1.

    Solve 2 sin x = 1 for 0 <= x <= 2 pi, giving your answers in terms of pi.

    [3 marks] · no calculator
  2. 2.

    Show that tan x + cot x = 2/sin 2x.

    [3 marks] · no calculator
  3. 3.

    Express 3 sin x + 4 cos x in the form R sin(x + alpha), where R > 0 and 0 < alpha < pi/2. Hence state the maximum value and the smallest positive x at which it occurs.

    [4 marks]
  4. 4.

    Solve 2cos^2 x + sin x - 1 = 0 for 0 <= x < 2 pi, giving exact answers.

    [4 marks] · no calculator
  5. 5.

    A sector of a circle of radius r cm has perimeter 24 cm. Show that its area is A = 12r - r^2 cm^2, and find the maximum area and the angle of the sector at that point.

    [5 marks] · no calculator
  6. 6.

    Solve tan 2x = 3 tan x for 0 degrees <= x <= 180 degrees.

    [6 marks] · no calculator

Original, unofficial practice questions from SubjectScout — not official past-paper questions.

Marking points are indicative, not an official mark scheme. Accept equivalent valid methods and supported interpretations that address the task; award each mark once without requiring the model wording.