Physics Exemplars
AS 90252 (Physics 2.1) version 2.
Take measurements of physical quantities and analyse data graphically to determine a relationship
Level 2, 4 credits.
The following extracts from student work are intended to exemplify the boundaries between Achieved, Merit and Excellence for this achievement standard. While a particular grade would not be awarded on the basis of a single aspect of a student’s work, these exemplars are designed to show features typical of work that level.
See also
- 2008 National Moderator’s Report [
- 2007 National Moderator’s Report [
- 2006 National Moderator’s Report [
Explanatory Note 4 of the standard providesguidance on the typical level of performanceexpected for Achieved, Merit, and Excellence grades:
Measuring instruments
For Achievement, instruments are set up and connected or operated in orderto take a measurement. A unit is recorded along with the measurement.
For achievement with Merit, techniques that improve accuracy ofmeasurements could include - the observer and/or the instrument placement,zero error correction, averaging repeated measurements, number of repeatedreadings sufficient for purpose. Techniques could be observed, stated orobvious from the data measurements. Appropriate use of significant figures isdemonstrated in the measured value.
For achievement with Excellence, justification of each technique shouldinvolve a rationale for using the technique involved in the context of themeasurements being made.
Graphical Techniques
For Achievement, graphical techniques could include - data plotted correctly,choice of appropriate axes and scales, axes labelled with quantities and units,a line of best fit. The shape of the graph is used to suggest the type ofrelationship.
For achievement with Merit, data is plotted. A gradient, and where relevantan intercept, is calculated and a mathematical relationship between the twovariables is stated. A physical quantity, with its unit, is determined from thegradient or intercept.
For achievement with Excellence, the data from a non-linear graph isprocessed to enable a linear graph to be constructed. A gradient, and whererelevant an intercept, is calculated and a mathematical relationship betweenthe two variables is stated. From this linear graph a physical quantity, with itsunit, is determined from the gradient.
Measurement
For Achievement, students must use instruments to take measurements of physical quantities.
For a typical assessment activity with fivemeasurement opportunities, any three correct measurements, with units, would provide sufficiency.
Student / Grade / Student Response / Moderator Commentary1 / Not Achieved / Time = 1.7
Volume = 12 mL3
Weight = 150 grams / Correct units must be given with the measurement value.
2 / Achieved / Time = 1.7 s
Time = 1.7 (± 0.1) s
Volume = 12 mL
Weight = 1.5 N / Uncertainties may be given, but are not required.
Significant figures
For Merit, appropriate use of significant figures isdemonstrated in the measured value.
Student / Grade / Student Response / Moderator Commentary3 / Achieved, Not Merit / Volume (mL)
12
12
13
Average: 12.33
/ At Merit or Excellence level, evidence of correct use of significant figures is required
4 / Merit / Excellence / Trial / Height of bounce (cm)
1 / 32
2 / 35
3 / 34
Average / 33.666
Answer = 34 cm / Final answer has appropriate use of significant figures. There is no distinction between Merit and Excellence for use of significant figures. The final grade would depend on other aspects of the task.
5 / Merit / Excellence / Thickness of 10 pages = 2 mm. Therefore thickness of 1 page = 0.20 mm / Appropriate use of significant figures.
Accuracy-increasing techniques
For Merit, techniques that increase accuracy must be used.
For a typical assessment activity with fivemeasurement opportunities, use of any three techniques, along with appropriate use of significant figures, provides sufficiency.
Student / Grade / Student Response / Moderator Commentary6 / Achieved
Not Merit / The needle kept moving so it was impossible to get an accurate result. / No specific technique employed.
I measured carefully to get as accurate a result as I could. / No specific technique employed. “Measuring carefully” is merely normal experimental practice.
Because the voltmeter did not start at zero I measured three times and took the average. / The technique must be valid. A systematic error (such as zero-error) is not reduced by repeating and averaging.
I checked to see that the voltmeter was pointing to zero before I turned on the switch. / Not Merit: Unless there was zero error that was corrected or allowed for, merely checking is not an accuracy-increasing technique. Explanatory Note 2 specifies that the assessment will include use of an instrument that requires zero error correction or reading.)
7 / Merit / I measured 10 swings then divided by 10. / Multiples
The time for 10 swings = 17 s…. the period is 1.7 s / It may be apparent in their data that they have measured the time for ten swings and divided by ten, even if they do not explicitly refer to this as an accuracy-increasing technique in their discussion.
I lined up my eye at the same level as the measuring cylinder’s scale. / Eye position (parallax reduction)
The voltmeter was pointing to 0.2 volts when the voltage was zero, so I subtracted 0.2 V from all my readings. / Zero-error correction
I measured the height of the bounce 5 times and took the average. / Repeat and average
I was careful not to splash any water when I lowered the rock gently into the measuring cylinder. / Technique specific to the task
I used a mark on the bench to line up the pendulum against so I hit the stopwatch button at exactly the same point in each swing. / Use of a fiducial mark
Justification of accuracy-increasing techniques
For Excellence, students must justify the techniques used.
For a typical assessment activity with fivemeasurement opportunities, any three techniques, justified, would provide sufficiency.
Student / Grade / Student Response / Moderator commentary8 / Merit, not Excellence / I measured 10 swings then divided by 10 to get a more accurate result. / It does not say why the technique is necessary or why the result will be more accurate.
I measured the height of the bounce 5 times, and took the average because this averages out any errors. / It does not say why a single measurement might be inaccurate.
I measured the height of the bounce 5 times, and took the average because there is a systematic error in starting and stopping the stopwatch. / Repeating and averaging do not reduce a systematic error.
I measured ten paper clips, and then divided by ten because it is hard to weigh a single paper clip. / It does not say why the single measurement could be inaccurate or why the accuracy has been improved.
I lined up my eye to the height where the ball bounced to in order to eliminate parallax error. / It does not say why parallax will occur or why this technique will reduce the problem.
I checked that the ammeter pointed to zero before the battery was connected, in order to eliminate zero error. / As the needle apparently did not need zero error correction, the accuracy was not improved over what would have occurred if the technique had not been used.
The ruler scale did not start at the end of the ruler so I had to correct for zero error. / It does not say what correction was applied, so it cannot be judged whether the technique was valid.
The ruler scale started 4 mm from the end of the ruler so I had to correct for this 4 mm zero error. / It does not say whether 4 mm was added or subtracted from the measurement, unless this is made clear within the recorded data.
I chose the measuring cylinder calibrated in 1 mL scale divisions instead of the one with 10 mL divisions because it gave me a more accurate result. / It does not say why the result was more accurate.
Student / Grade / Student Response / Moderator Commentary
9 / Excellence / I measured 10 swings then divided by 10 because then the judgement error of starting and stopping the stopwatch is spread over ten swings. / Describes the source of uncertainty and how it is reduced by this technique.
I measured the height of the bounce 5 times, and found the average because there might be random error when I start and stop the stopwatch, and by taking the average this is reduced. / Describes the source of uncertainty and how it is reduced by this technique.
I measured ten paper clips, and then divided by ten because the balance only had a 0.1 g scale division. By dividing the measurement by ten I could get the result for a single paper clip to 0.01 g accuracy. / Describes the source of uncertainty and how it is reduced by this technique.
I lined up my eye and the ruler at the height of the bounce because parallax could occur if my eye was not at the same height because the ruler was some distance behind the ball. / Describes the source of uncertainty in terms of the specific measurement task and how it is minimised.
I lined up the voltmeter needle so I could not see its reflection in the mirror on the scale. This eliminated parallax which could occur as the needle is some distance away from the scale. / Describes the source of uncertainty in terms of the specific measurement task and how it is minimised.
I had to add 5 mm to the height of all the bounces because the ruler scale started 5 mm up from bench height. / Explains why zero-error was a problem and how it was reduced.
I used the millimetre scale rather than the centimetre scale as it gave me a measurement to 2 significant figures instead of 1 sf. / Describes how the choice of scale results in a more accurate result.
Graphical Techniques
For Achieved, graphical techniques could include: data plotted correctly,choice of appropriate axes and scales, axes labelled with quantities and units,a line of best fit. The shape of the graph is used to suggest the type ofrelationship.
Student / Grade / Moderator Commentary10 / Not Achieved / No line of best fit drawn. Not an appropriate graph for relating continuous-variable data.
(See below)
11 / Not Achieved / Point-to-point connection rather than a (straight) line of best-fit.
(See below)
12 / Achieved / A reasonable line of best fit.
(See below)
Mathematical Relationship
For Merit, data is plotted. A gradient, and where relevantan intercept, is calculated and a mathematical relationship between the twovariables is stated. A physical quantity, with its unit, is determined from thegradient or intercept.
Student / Grade / Student Response / Moderator Response13 / Not Achieved / The relationship is: as time increases, distance increases. / The description does not necessarily refer to a relationship that is linear.
14 / Achieved / The relationship is: y is proportional to x. / This can be accepted, as only the type of relationship is required for Achievement, not the specific mathematical relationship between d and t.
The relationship is: d is proportional to t. / The type of relationship is described
The relationship is a linear relationship. / The type of relationship is described
The relationship is: d = mt + c / The type of relationship is described
A gradient, and where relevant an intercept, is calculated:
Student / Grade / Student Response / Moderator Response15 / Not Merit / Gradient = 17 / 10 = 1.7 m/s / If the gradient has been calculated using the coordinates of a particular data point, but the graph line does not pass through this point, the result is not valid. This might happen if students used data from the table rather than using the graph line. (If, however, the graph line did pass through that data point, then the result can be accepted for Merit.)
(See below)
16 / Merit / Gradient = 17.5 / 10 = 1.75 m/s / Gradient calculated using the coordinates of the graph line.
(See below)
A mathematical relationship between the two variables is stated:
Student / Grade / Student Response / Moderator Response17 / Achieved, not Merit / The mathematical relationship is:
y = mx + c / The student has just given the general equation form and has not defined y, x, or calculated the value of m.
The mathematical relationship is:
y = 6.2x / Not Merit if student has not defined y, x elsewhere, and they are not the normal symbols for the dependent and independent variables.
18 / Merit / The mathematical relationship is:
F = kx (value of k given elsewhere). / Merit if they have calculated the value of k elsewhere, and F, x have their common physics meanings (Force, extension).
The mathematical relationship is:
F = 17x / The expected form.
Non-linear Relationship
For Excellence, the data from a non-linear graph isprocessed to enable a linear graph to be constructed. A gradient, and whererelevant an intercept, is calculated and a mathematical relationship betweenthe two variables is stated. From this linear graph a physical quantity, with itsunit, is determined from the gradient.
Student / Grade / Student Response / Moderator Response19 / Merit, not Excellence / The relationship is a parabolic relationship. / The equation of the relationship is needed.
20 / Excellence / Gradient = 4 / 20
= 0.2s2/m
t2 = 0.2 d
t2 = 0.2 d,
so 0.2 = t2 / d,
and since d = ½ a t2 (from supplied equation),
½ a = 1/ 0.2
and a = 10 m/s2. / Gradient found
Mathematical relationship stated
A physical quantity, with its unit, is determined from the gradient.
(See below)