| Date | May 2014 | Marks available | 5 | Reference code | 14M.2.SL.TZ1.1 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 1 |
| Command term | Comment, Determine, Draw, Outline, and State | Question number | 1 | Adapted from | N/A |
Question
Data analysis question.
Connie and Sophie investigate the effect of colour on heat absorption. They make grey paint by mixing black and white paint in different ratios. Five identical tin cans are painted in five different shades of grey.
Connie and Sophie put an equal amount of water at the same initial temperature into each can. They leave the cans under a heat lamp at equal distances from the lamp. They measure the temperature increase of the water, T, in each can after one hour.
Connie suggests that T is proportional to B, where B is the percentage of black in the paint. To test this hypothesis, she plots a graph of T against B, as shown on the axes below. The uncertainty in T is shown and the uncertainty in B is negligible.
(i) State the value of the absolute uncertainty in T.
(ii) Comment on the fractional uncertainty for the measurement of T for B=10 and the measurement of T for B=90.
(iii) On the graph opposite, draw a best-fit line for the data.
(iv) Outline why the data do not support the hypothesis that T is proportional to B.
Sophie suggests that the relationship between T and B is of the form
\[T = k{B^{\frac{1}{2}}} + c\]
where k and c are constants.
To test whether or not the data support this relationship, a graph of T against \({B^{\frac{1}{2}}}\) is plotted as shown below. The uncertainty in T is shown and the uncertainty in \({B^{\frac{1}{2}}}\) is negligible.
(i) Use the graph to determine the value of c with its uncertainty.
(ii) State the unit of k.
Markscheme
(i) (±) 1 ( °C );
(ii) absolute uncertainty is the same for the two points;
since T is higher at B = 90 (stated or shown), relative uncertainty is smaller;
or
fractional uncertainties are 0.07/\(\frac{1}{{14}}\) /7% for B=10 and 0.03/\(\frac{1}{{33}}\)/3% for B=90;
fractional uncertainty is smaller for B=90;
(iii) smooth curve passing through all error bars;
Do not allow thick or hairy or doubled lines, or lines where the curvature changes abruptly.
it does not pass through the origin/(0, 0)/zero;
(i) 
intercept read as 4.7; (ignore significant figures, allow range of 4.5 to 4.9)
two worst fit lines drawn through extremes of error bars;
uncertainty found from worst fit lines;
uncertainty rounded to 1 significant digit expressed in the form as ± (value)
and intercept rounded to same precision;
Award [4] for a statement of 5±2 and lines drawn.
(ii) °C ;
Examiners report
ai) Most candidates could accurately read the absolute uncertainty from an error bar. The only mistake made was by those who wrote ± 2.
aii) Most were able to calculate the fractional uncertainties, but too often the figures were not compared.
aiii) This was mainly answered well, with few straight lines.
aiv) Most recognized the shape of the line required for proportionality.
bi) Few candidates appreciated the importance of using the best and worst fit lines in finding an uncertainty from the line of best-fit. Many candidates could not state the uncertainty and value to an appropriate precision.
bii) Most candidates successfully identified the unit.
