Higher June 2018 Paper 2 Q14
14. Lewis is organising a music festival for up to 200 people.
He has investigated the charges for booking bands.
The band Rightjet gives its charges using a graph, as shown below.
(a) Find the gradient of the graph and state the units of your answer. [2]
(b)
(i) The band Draigetal charges a fee of £60 and an additional £3 per person.
On the same axes as Rightjet, draw a graph to show Draigetal’s total charges for up to 200 people. [2]
On the same axes as Rightjet, draw a graph to show Draigetal’s total charges for up to 200 people. [2]
(ii) Let \(t\) represent the total charge, in pounds, and \(p\) represent the number of people.
Hence, write down the equation of the line you have drawn in part (b)(i). [1]
Hence, write down the equation of the line you have drawn in part (b)(i). [1]
(c) Lewis wonders,
‘If ………………… people attend, the charge would be the same for having the band Rightjet or the band Draigetal. This charge would be £ …………………’ [2]
Will Rightjet’s charge ever be the
same as Draigetal’s charge?
‘If ………………… people attend, the charge would be the same for having the band Rightjet or the band Draigetal. This charge would be £ …………………’ [2]
| Scheme | Marks | Comments |
|---|---|---|
| 2 | B1 | Accept answers in the range 1.9 to 2.1 |
| £(s)/person | U1 | Allow £(s) per person or pounds per person Do not accept £/people (singular is needed for people), or charge per person |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) Correct graph with points connected, for 0 people £60 to 200 people £660 | B2 | B1 for 0 people costing £60 shown OR B1 for a straight line with a gradient of 3 |
| (b)(ii) \(t = 3(\times)p + 60\) | B1 | CAO, not FT |
| Scheme | Marks | Comments |
|---|---|---|
| 20 (people) | B1 | Allow tolerance of ½ small square FT from ‘their line’ |
| (£) 120 | B1 | FT from ‘their line’ |
| (7) |