(a) Show that (sin 2θ)/(1 + cos 2θ) ≡ tan θ.
(b) Hence solve (sin 2θ)/(1 + cos 2θ) = √3 for 0 ≤ θ < 2π.
From Paper 1: Pure Mathematics
1610 marks
(a) Express 3sin x + 4cos x in the form Rsin(x + α), where R > 0 and 0 < α < π/2. Give α to 4 decimal places.
(b) Find the maximum value of 3sin x + 4cos x and the smallest positive value of x at which it occurs.
(c) Solve 3sin x + 4cos x = 2.5 for 0 ≤ x < 2π. Give your answers to 3 significant figures.
From Paper 2: Pure and Mechanics
21 mark
For small θ measured in radians, which is the best approximation for cos θ?
From Paper 2: Pure and Mechanics
67 marks
Solve the equation 3sec2 x - 4tan x - 4 = 0 for 0° ≤ x < 360°. Give your answers to 1 decimal place.
From Paper 3: Pure and Statistics
11 mark
Find the exact value of sin π/3 cos π/6.
From Paper 3: Pure and Statistics
55 marks
A sector OAB of a circle has radius 8 cm and angle 1.2 radians.
(a) Find the arc length AB and the area of the sector.
(b) Find the area of the segment between the chord AB and the arc AB.
Score 0 / 30 · 0 of 6 marked
This paper is written by Plasmo in the style of the AQA A-Level Maths exam. It is not a past paper and is not produced or endorsed by the exam board.