(a) Draw the graph of \(\quad y = 3.6x \quad\) for values of \(x\) from 0 to 20 [2 marks]
In the formula \(\quad y = 3.6x\)
\(y\) is speed in kilometres per hour (km/h) \(x\) is speed in metres per second (m/s)
(b) Convert 50 km/h to m/s
Give your answer to the nearest whole number. [1 mark]
(c) Convert 30 m/s to miles per hour.
Use 1 mile per hour \(=\) 1.61 km/h [3 marks]
Mark scheme (a)
Answer
Mark
Comments
Correct ruled straight line through (0, 0) and (20, 72)
B2
\(\pm\dfrac{1}{2}\) square B1 any one correct coordinate plotted or seen in a table of values with \(1 \leqslant x \leqslant 20\) eg (1, 3.6) (2, 7.2) (3, 10.8) (4, 14.4) (5, 18) (10, 36) (15, 54) or (20, 72)
Additional guidance
Ignore lines beyond (0, 0) to (20, 72)
Ignore incorrect points plotted
To award B1, points plotted cannot be implied by an incorrect line, there must be a coordinate plotted or values in a table
Correct ruled line but too short
B1
Mark scheme (b)
Answer
Mark
Comments
14
B1ft
ft from their graph in part (a) \(\pm\dfrac{1}{2}\) square
Additional guidance
Answer must be a whole number
Mark scheme (c)
Answer
Mark
Comments
Alternative method 1 (using formula and conversion factor)
\(30 \times 3.6\) or 108 or \(30 \div 1.61\) or [18.6, 18.64] or \(3.6 \div 1.61\) or [2.2, 2.24] or \(1.61 \div 3.6\) or [0.4, 0.45]
M1
oe working in metres eg \(30 \times 60 \times 60\) or 108 000
their \(108 \div 1.61\) or their \([18.6, 18.64] \times 3.6\) or their \([2.2, 2.24] \times 30\) or \(30 \div\) their [0.4, 0.45]
M1dep
oe working in metres eg \(108\,000 \div 1610\)
[67, 67.1]
A1
[67, 67.1]
Alternative method 2 (using graph and conversion factor)
Uses their graph to convert 30 m/s to km/h or 108
M1
eg \(3 \times\) (their \(y\) at \(x = 10\)) or (their \(y\) at \(x = 10\)) + (their \(y\) at \(x = 20\)) \(\pm\dfrac{1}{2}\) square
their \(108 \div 1.61\)
M1dep
[67, 67.1]
A1ft
ft from their graph in part (a) and M2
Additional guidance
Alt 2 For A1ft answers may be rounded to the nearest integer or rounded to 1 decimal place eg their graph used correctly gives 114 km/h \(114 \div 1.61\) [70.8, 71]
