| Date | May 2014 | Marks available | 2 | Reference code | 14M.2.sl.TZ2.3 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Estimate | Question number | 3 | Adapted from | N/A |
Question
The following table shows the amount of fuel (\(y\) litres) used by a car to travel certain distances (\(x\) km).
| Distance (x km) | 40 | 75 | 120 | 150 | 195 |
| Amount of fuel (y litres) | 3.6 | 6.5 | 9.9 | 13.1 | 16.2 |
This data can be modelled by the regression line with equation \(y = ax + b\).
Write down the value of \(a\) and of \(b\).
Explain what the gradient \(a\) represents.
Use the model to estimate the amount of fuel the car would use if it is driven \(110\) km.
Markscheme
\(a = 0.0823604{\text{, }}b = 0.306186\)
\(a = 0.0824{\text{, }}b = 0.306\) A1A1 N2
[2 marks]
correct explanation with reference to number of litres
required for \(1\) km A1 N1
eg \(a\) represents the (average) amount of fuel (litres) required to drive \(1\) km, (average) litres per kilometre, (average) rate of change in fuel used for each km travelled
[1 marks]
valid approach (M1)
eg \(y = 0.0824(110) + 0.306\), sketch
\(9.36583\)
\(9.37\) (litres) A1 N2
[2 marks]
