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Date May 2014 Marks available 2 Reference code 14M.2.sl.TZ2.3
Level SL only Paper 2 Time zone TZ2
Command term Write down 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 \(b\).

[2]
a(i).

Explain what the gradient \(a\) represents.

[1]
a(ii).

Use the model to estimate the amount of fuel the car would use if it is driven \(110\) km.

[2]
b.

Markscheme

\(a = 0.0823604{\text{, }}b = 0.306186\)

\(a = 0.0824{\text{, }}b = 0.306\)     A1A1     N2

[2 marks]

a(i).

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]

a(ii).

valid approach     (M1)

eg     \(y = 0.0824(110) + 0.306\), sketch

\(9.36583\)

\(9.37\) (litres)     A1 N2

[2 marks]

b.

Examiners report

[N/A]
a(i).
[N/A]
a(ii).
[N/A]
b.

Syllabus sections

Topic 5 - Statistics and probability » 5.4 » Linear correlation of bivariate data.
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