Date | May 2021 | Marks available | 2 | Reference code | 21M.1.SL.TZ1.4 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 1 |
Command term | Find | Question number | 4 | Adapted from | N/A |
Question
The price of gas at Leon’s gas station is $1.50 per litre. If a customer buys a minimum of 10 litres, a discount of $5 is applied.
This can be modelled by the following function, L, which gives the total cost when buying a minimum of 10 litres at Leon’s gas station.
L(x)=1.50x-5, x≥10
where x is the number of litres of gas that a customer buys.
Find the total cost of buying 40 litres of gas at Leon’s gas station.
Find L-1(70).
The price of gas at Erica’s gas station is $1.30 per litre. A customer must buy a minimum of 10 litres of gas. The total cost at Erica’s gas station is cheaper than Leon’s gas station when x>k.
Find the minimum value of k.
Markscheme
L(40)=1.50×40-5 (M1)
=$55 A1
[2 marks]
70=1.50x-5 (M1)
(x=) 50 litres A1
[2 marks]
1.30x (A1)
1.30x<1.50x-5 (M1)
Note: Award M1 for a graph showing two intersecting linear functions, provided one function has a y-intercept of 0 and the other function has a negative y-intercept.
(minimum value of k=) 25 A1
Note: Accept x>25.
[3 marks]