Download C3 homework 13 24/11/2016 10:48:38 Text File 866.09 KB

C3 – Homework 13 – (33 marks)
Q1.
A cuboid has a rectangular cross-section where the length of the rectangle is equal to twice
its width, x cm, as shown in Figure 2.
The volume of the cuboid is 81 cubic centimetres.
(a) Show that the total length, L cm, of the twelve edges of the cuboid is given by
(3)
(b) Use calculus to find the minimum value of L.
(6)
(c) Justify, by further differentiation, that the value of L that you have found is a minimum.
(2)
(Total 11 marks)
Q2.
The curve C has equation y =12√ (x) − x − 10,
x>0
(a) Use calculus to find the coordinates of the turning point on C.
(7)
(b) Find
.
(2)
(c) State the nature of the turning point.
(1)
(Total 10 marks)
Q3.
(a) Use the identity cos(A + B) = cos A cos B − sin Asin B, to show that
cos 2A = 1 − 2 sin2A
(2)
The curves C1 and C2 have equations
(b) Show that the x-coordinates of the points where C1 and C2 intersect satisfy the equation
(3)
(c) Express 4cos 2x + 3sin 2x in the form R cos (2x − α), where R > 0 and 0 < α < 90°, giving the value of α to 2
decimal places.
(3)
(d) Hence find, for 0 ≤ x < 180°, all the solutions of
giving your answers to 1 decimal place.
(4)
(Total 12 marks)