Two discs, one of radius 8 cm and one of radius 5 cm, are placed such that they touch each other. A piece of string is wrapped around the discs. This is shown in the diagram below.

Calculate the length of string needed to go around the discs.

\({\text{AC}} = {\text{BD}} = \sqrt {{{13}^2} - {3^2}}  = 12.64...\)     (A1)

\(\cos \alpha  = \frac{3}{{13}} \Rightarrow \alpha  = 1.337...(76.65...^\circ .)\)     (M1)(A1)

attempt to find either arc length AB or arc length CD     (M1)

\({\text{arc length AB}} = 5(\pi  - 2 \times 0.232...){\text{ }}( = 13.37...)\)     (A1)

\({\text{arc length CD}} = 8(\pi  + 2 \times 0.232...){\text{ }}( = 28.85...)\)     (A1)

length of string = 13.37... + 28.85... + 2(12.64...)     (M1)

= 67.5 (cm)     A1

[8 marks]

Given that this was the last question in section A it was pleasing to see a good number of candidates make a start on the question. As would be expected from a question at this stage of the paper, more limited numbers of candidates gained full marks. A number of candidates made the question very difficult by unnecessarily splitting the angles required to find the final answer into combinations of smaller angles, all of which required a lot of work and time.