From Paper 1: Pure Mathematics
(a) Show that cos(x + 60°) + cos(x - 60°) ≡ cos x.
(b) Solve 2sin xtan x = 3 for 0° ≤ x < 360°.
From Paper 2: Pure Mathematics and Statistics
A sector of a circle has area 24 cm2 and perimeter 20 cm. Find the two possible pairs of values of the radius r cm and the angle θ radians.
From Paper 3: Pure Mathematics and Mechanics
(a) Show that, for small θ measured in radians, (1 - cos 2θ)/(θtan θ) ≈ 2.
(b) Show that sec θ ≈ 1 + 1/2θ2 for small θ.
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This paper is written by Plasmo in the style of the OCR A-Level Maths exam. It is not a past paper and is not produced or endorsed by the exam board.