can be written in the form (1 – 5 cos 2x) sin 2x = 0
(b) Hence solve, for 0° ≤ x < 180°, tan 2x = 5 sin 2x
giving your answers to 1 decimal place where appropriate.
You must show clearly how you obtained your answers.
(a) Complete the table below, giving the values of y to 3 decimal places
(b) Use the trapezium rule with all the values of y from your table to find an approximation
You must show clearly how you obtained your answer.
Given that the volume of each tablet has to be 60 mm3
(a) express h in terms of x,
(b) show that the surface area, A mm2, of a tablet is given by A = 2πx2 + 120/x
The manufacturer needs to minimise the surface area A mm2
(c) Use calculus to find the value of x for which A is a minimum.
(d) Calculate the minimum value of A, giving your answer to the nearest integer.
(e) Show that this value of A is a minimum.
A geometric series is a + ar + ar2 + ...
(a) Prove that the sum of the first n terms of this series is given by
The third and fifth terms of a geometric series are 5.4 and 1.944 respectively and all the terms in the series are positive.
For this series find,
(b) the common ratio,
(c) the first term,
(d) the sum to infinity.
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