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Handling data: units, scales, rates and uncertainty questions
Units, prefixes and standard form; where significant figures come from; ratios and magnification; percentage change against percentage difference; rate as a gradient, including a tangent to a curve; logarithmic scales for population and pH; and uncertainty in a measurement and how it propagates through a calculation.
6 original questions · 19 marks · the handling data: units, scales, rates and uncertainty notes · Scientific method and quantitative biology
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A potato chip is weighed at 5.00 g, left in a sucrose solution for an hour and weighed again at 4.60 g, on a balance reading to plus or minus 0.01 g. Calculate the percentage change in mass, and calculate the percentage uncertainty in that percentage change.
Mark scheme
- M1 change in mass = 4.60 − 5.00 = −0.40 g, and because the two masses were subtracted the absolute uncertainties add to give plus or minus 0.02 g
- A1 percentage change = −0.40 ÷ 5.00 × 100 = −8.00 per cent, the sign showing that the chip lost mass
- M1 percentage uncertainty in the change = 0.02 ÷ 0.40 × 100 = 5.0 per cent, and in the initial mass = 0.01 ÷ 5.00 × 100 = 0.20 per cent
- A1 the two were divided, so the percentage uncertainties add: about 5.2 per cent
A bacterial culture is counted every hour for ten hours and the counts are plotted with the logarithm to base 10 of the count on the vertical axis. Explain why a logarithmic axis is used here, and explain what a straight line on such a plot tells you.
Mark scheme
- B1 a population that multiplies repeatedly spans several factors of ten, so on a linear axis the early counts lie flattened against the baseline where nothing can be read from them
- B1 on a logarithmic axis equal distances represent equal multiplications, so the steps 1, 10, 100 and 1000 are evenly spaced and every hour is as readable as every other
- B1 each hour multiplies the population by the same factor and therefore adds the same amount to the logarithm, so constant growth plots as a straight line
- B1 a straight line is therefore evidence that the growth factor never changed over that period, which is what exponential growth means, and a rise of 3 on the axis is a multiplication of the population by 1000
A student collects 24 cm³ of gas in 20.0 s and writes the rate as 1.2 cm³ s⁻¹. Explain why the answer is given to two significant figures, and explain why counting the decimal places in the measurements is the wrong guide.
Mark scheme
- B1 an answer carries the same number of significant figures as the least precise measurement that went into it, and the volume of 24 cm³ carries only two
- B1 significant figures record how finely the instrument measured, so writing more digits claims a precision the syringe never had
- B1 decimal places depend only on the unit chosen: 24 cm³ written as 0.024 dm³ has three decimal places and still two significant figures, because changing the unit cannot improve the measurement
A tangent is drawn at the origin of a curve of volume of oxygen collected against time. The tangent passes through the points (0 s, 2.0 cm³) and (30 s, 20.0 cm³). Calculate the initial rate of oxygen production and give its unit.
An osmosis investigation reports a percentage change in the mass of a potato chip carrying a percentage uncertainty of over 30 per cent, even though the balance reads to plus or minus 0.01 g. Suggest why the uncertainty is so large, and suggest one change to the method that would reduce it.
State what is meant by the resolution of a measuring instrument, and state the uncertainty carried by a single reading taken from a millimetre rule.
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