Measurements and their errors questions

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• AQA 7408 · June 2025 · Paper 3A · Q1 · 8 marks

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  This question was about an investigation of how the frequency of a stationary wave on a string varied with tension. The main ideas tested were • identification of the control variables in required practical activity 1 (specification reference 3.7.5.5 and 8.3.2 PS2.4) • use of an oscilloscope as a voltmeter and as a clock (3.7.5.5) In part 01.1 what should have been a straightforward opening question proved tricky and only 17% obtained both marks. No credit was given for a careless annotation to Figure 1 to identify the length of string that should be controlled. In part 01.2 just under 50% correctly identified that m has a maximum range of 170 g. Part 01.3 was a bit mixed, although many could determine the peak voltage and divide by root 2. For the second mark we wanted a voltage between 13.0 and 13.2, so a 2-sf answer was not accepted. © 2025 AQA For part 01.4 nearly 70% correctly determined the period although a few thought that the time- base setting of 20 ms div−1 referred to minor divisions, thus getting about 530 ms. Here as elsewhere, some lost a mark, thinking they should round their 106 to 110 (mistakenly claiming this was 2 sf). A majority saw the intention of part 01.5 and made the expected quantitative comparison between the waveforms in Figure 2. The students who misinterpreted the time-base in the same way as above got about 375 ms and were not penalised. A few students took the novel approach of comparing the number of horizontal divisions for one cycle of each waveform. This was a valid idea and was not penalised.

  Text version

  This question is based on an investigation into how the frequency f of the first-harmonic stationary wave on a string varies with tension (required practical activity 1). A horizontal string runs from a vibration generator to a pulley, then vertically to a hanger carrying slotted masses of total mass m, so the tension is mg. A variable-frequency ac supply drives the vibration generator and an oscilloscope is connected across the supply. The frequency is varied until the first harmonic appears and the process is repeated for different m.

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• AQA 7408 · June 2025 · Paper 3A · Q4 · 12 marks

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  This question was about the vertical oscillations of a loaded test tube in a liquid. The main ideas tested were • use of vernier scales (8.1 ATe) • comment on experimental design (7.3.2 PS2.1) In 04.1 most correctly determined that there were 13 turns of the string between points P and Q but then could not make progress because they could not read the vernier scale. In 04.2 few took account of the thickness of the string in their calculation but over 50% obtained two marks for calculating an appropriate length for their number of turns. Some very good answers did use their string thickness but then did not record the length of string to the nearest mm. In 04.3 less than 50% correctly identified position B as the correct position for the fiducial mark. 04.4 was a simple problem and over 60% got fully correct answers. © 2025 AQA Part 04.5 presented a tricky problem. Many realised that to produce more oscillations the initial amplitude should be larger. However, the test tube was already in contact with the bottom of the beaker as it was released. This tempted some to suggest using a deeper beaker but that would not change the depth of the test tube when at rest. Others thought the beaker could be made narrower which would increase the depth at which the test tube floated, however that would increase the drag on the test tube due to the proximity of the walls. Therefore, to increase the initial amplitude the only available solution was to add more liquid. Many said that reducing drag would make the oscillations die away more slowly but there was very little they could say to explain how they would achieve this. Changes to the test tube or to the liquid would change the period and the question said that was not allowed.

  Text version

  Wire is wound tightly in 13 adjacent turns around a test tube. Points P and Q lie on the wire 13 turns apart. A travelling microscope reads 9.26 mm at P. At Q, the vernier zero lies between 24.7 and 24.8 mm on the fixed scale and the third vernier division aligns, giving a reading of 24.73 mm. The test tube external diameter is 18.0 mm.

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• AQA 7408 · June 2025 · Paper 3BD · Q1 · 16 marks

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  [01.1] Most students were able to gain at least one mark on this question, however very few were able to gain full marks. A significant minority did not appear familiar with the process of thermionic emission at all. Marks could be gained from the diagram or text. When drawing these diagrams students need to take care to label diagrams and make clear what lines are wires and which refer to the glass enclosure, as some diagrams were ambiguous. Most students were aware that a filament needed to be heated. However, a small minority did not realise that that was achieved with a power supply, with some students heating the filament with a heater or other source of heat: this did not gain a mark. Most students realised that a potential difference was required to accelerate the electrons, although some did not explicitly indicate that the anode required a hole to allow the electrons to pass through. Those who drew the power supply the wrong way round or drew incomplete circuits with only one side of the filament attached to the power supply, could not access this mark. Very few students realised that thermionic emission requires either a vacuum or a low pressure gas, with this mark being rarely awarded. Only a few students fully attempted the question and provided values for the potential differences; of these, most did not give suitable values. Many thought the low pd accelerated the electrons while a high pd was required to heat the metal, while others attempted to use just one pd to both heat the filament and accelerate the electrons. 01.2-01.5 Students had to determine a value for the specific charge, using Thomson’s original approach which involved measuring the deflection angle of the electron beam. It was not expected that all students would have seen Thomson’s approach before; however, it was expected that students would be able to apply their knowledge of fields and their understanding of measuring the specific charge to this technique. The question explicitly told students that in this determination of 𝑒𝑒 𝑚𝑚 it was not appropriate to use the values of 𝑒𝑒 and 𝑚𝑚 from the formulae booklet, so the many attempts which did use these values scored 0 for the part of the question where these values were used. However, this did not prevent other parts from scoring. Questions 01.2 to 01.4 were “show that” questions where students are expected to provide the equations used as they appear on the formulae sheet, a substitution, a rearrangement (if required) and the answer to at least one more significant figure that the approximate value given in the question. While most students appeared to follow this, some lost marks by missing out some of these steps, most commonly only quoting the answer as the approximate value given in the question. Most students found 01.2 accessible and were able to gain full marks. 01.3 was reasonably accessible with around two thirds realising that they could use trigonometry with their previous answer to get the mark. 01.4 proved more challenging, with the most common © 2025 AQA approach being to use 𝑚𝑚𝑚𝑚= 𝑄𝑄𝑄𝑄 𝑑𝑑 with the values from the formulae sheet, which scored zero. Unfortunately, most of those students did not realise they could use this approach in 01.5 where it provided the correct route to the answer. In 01.4 the correct approach was to use the horizontal motion to determine a time and then an equation of motion to determine the vertical acceleration. Of those that used this approach, around half correctly used 𝑣𝑣ℎ= 𝑎𝑎𝑎𝑎 with their answer to 01.3. However, the other half used 𝑣𝑣2 = 2𝑎𝑎𝑎𝑎, either using 2.5 cm as 𝑠𝑠 or estimating a value smaller than this, as they realised the beam did not reach the top plate. These students were awarded 1 mark. Very few were able to determine the specific charge using 𝑚𝑚𝑚𝑚= 𝑄𝑄𝑄𝑄 𝑑𝑑 in 01.5. Most students either used 𝑒𝑒 and 𝑚𝑚 from the formulae booklet or mixed up the accelerating pd with the pd across the plates. A small number of students attempted to use the vertical deflection with the magnetic field.

  Text version

  This question concerns Thomson's determination of the electron's specific charge e/m. Do not use the electron charge, mass or specific charge from the data booklet. In the apparatus, a horizontal electron beam passes between two horizontal parallel plates and then strikes a fluorescent screen carrying an angular scale.

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• AQA 7408 · June 2024 · Paper 3A · Q1 · 15 marks

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  We expect students to have used a micrometer screw gauge and in 01.2 87% correctly indicated that the reading shown was 6.72 mm. In 01.3 they were told to state and explain how the micrometer should be closed; many could ‘state’ what they should do but then overlooked the ‘explain’ part. In 01.4 the working could be hard to follow but usually saw one of several acceptable approaches, including some novel potential-divider solutions. Having been required to show that R was about 0.5 Ω, a 2 sf final answer 0.51 would have been fine, otherwise only 0.512 and 0.5117 were accepted. Over 70% scored both marks. Parts 01.5 and 01.6 proved very accessible. A clear majority correctly identified nichrome by matching up their 01.5 result with a value of resistance per metre from Table 1, deducing the wire diameter and completing the resistivity calculation successfully. Some imported a power of ten error from their 01.5 calculation which led to them identifying copper. Others simply ignored powers of ten altogether and just tried matching up numbers so a resistance per metre of 1.68 became 0.168 and led to alumel. Part 01.7 was not well answered. We wanted students to compare the L bars and the R bars separately. A simple statement that the L bars were the same was accepted but we wanted a quantitative comparison of the R bars. Some ignored the L bars and others penalised themselves by not mentioning error bars at all. A few compared the bars at the first point with those at the fourth point (and not the fifth point as specified). Most knew how to determine the uncertainty in a gradient but the use of error bars in drawing the lines of maximum or minimum gradient was poorly explained. Although we expected students to explain how to determine the absolute uncertainty, we allowed them to give correct expressions for fractional or percentage uncertainty.

  Text version

  A student investigates the resistivity of a wire. The wire diameter is measured with a micrometer. A circuit contains a 1.2 ohm fixed resistor in series with the test wire and a dc supply; voltmeters measure the potential differences across the fixed resistor and across the test wire. The student measures the resistance R for several lengths L of wire.

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• AQA 7408 · June 2024 · Paper 3A · Q2 · 15 marks

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  In 02.1 most wrote something sensible about the display, as the question said they should, although a few said that the selector switch in Figure 6 was shown set to range C. In 02.2 65% got both marks and only a few did not use logs to base 10 or substitute 2840 correctly. However, some solutions were overlong, extending beyond the usual answer space. In 02.3 many said they would obtain EV and x data from Figure 7 and show that these gave similar values of EV × x2. We wanted these data to be from more than two points but only a few thought to mention this detail. We didn’t allow the use of ‘multiple points’. An alternative approach was to plot EV against x2 or plot log EV against log x and this could get full credit as long as the expected outcome was explained for each graph. The idea behind 02.3 was developed in 02.4 and many calculated a suitable value of x when EV = 130 lx. Some penalised themselves by rounding their final answer to 630 or 640 mm. In 02.5 most correctly supplied 1645 and 1.73 then used information from their completed Table 3 to justify why range B should be used to determine R. Some tried the idea that resolution of range B was superior but were unsure whether they should say that the resolution was ‘smaller’, ‘greater’ (we accepted either) or ‘better’ (we rejected this). Students are well aware of what a control variable is, but they are not always able to identify suitable examples. In 02.6 they often made generic suggestions such as temperature or the length of the connecting wires, but we wanted things that, if changed, would have a more obvious impact such as background illumination, lamp brightness or slide thickness. Most students can find the unknowns in decay problems. In 02.7 about half knew that µ would be found by calculating the negative reciprocal of the gradient of an ln EV against N graph. A handful correctly explained how to obtain µ using a log EV against N graph. In 02.8, once again about half correctly deduced that eight slides would be the minimum needed to reduce EV by 50%. Some tried trial and improvement, but credit depended on showing that N = 7 did not work while N = 8 did. A common error was to use EV = 0.5 which led to N = 74.3 but we allowed one mark if this was then rounded to 75.

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  A student investigates an LDR illuminated by a lamp. An ohmmeter connected to the LDR displays 02.84. Its selectable ranges are: A, 000.1 to 199.9 ohm; B, 0001 to 1999 ohm; C, 00.01 to 19.99 kohm; D, 000.1 to 199.9 kohm; E, 0.001 to 1.999 Mohm. The lamp-LDR separation is x and the illuminance at the LDR is EV.

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• AQA 7408 · June 2024 · Paper 3A · Q3 · 15 marks

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  03.1 is a type of question that students with limited practical experience struggle with. Once again, we have to point out that clamp stand rods may not be used as a vertical datum, but benches can be assumed to be horizontal. The question said a metre ruler must be involved in establishing that the rod was horizontal. Some used the ruler to measure between bench and rod at different points and check that the heights were the same. When this idea was combined with an appropriate use of a set-square to make the ruler vertical, usually explained by annotation to Figure 10, all three marks were awarded. Others placed the set square where the vertical ruler met the rod. We did not allow this because a set square is too short to accurately judge whether the rod is horizontal. Good sketches saved those who struggled to explain their methods, but poor sketches condemned others who showed gaps between their set squares and the bench. Most knew what was behind 03.2 but only the better ones were able to identify the direction of the force on the rod. Some good answers went through the action-reaction idea in great detail to make sure the examiner knew what they were thinking. Others just referred to ‘the force’ and assumed it was upwards because the balance reading had decreased when there was a current in the rod. We gave no credit for current ‘from positive to negative’. Those who did not mention a current direction could only get one mark. However, most could predict a suitable magnetic field direction having identified directions for their force and current although we wanted to see the left-hand rule mentioned in justification. The solution to 03.3 was, first, to produce a homogeneous expression involving k, flux density, current and mass; second, to eliminate flux density using force, current and length, then to eliminate force using mass, length and time. We allowed working in which quantities and units were mixed, but many failed to connect the parts of their solutions using equals signs, making the work difficult to assess. 17% reached the correct solution of s2 in a few lines and earned all three marks. Others slipped up at the last stage of re-arrangement to get s−2 which cost one mark. Some deduced a homogeneous expression with non- base units, usually k = kg T−1 A−1 which got one mark. We also saw much ‘kg = kTA + kg + kg’ which the student then tried to simplify by cancelling kg as if performing conventional algebra. Over 60% made some progress and use of F = BIL and N = kg m s−2 were often seen. The use of simultaneous equations to determine Y in 03.4 was widespread. Predictably, the use of the wrong scale to determine the M2 intercept was also common. The M1 and M2 intercepts were usually recorded to 2 decimal places as we required and 16% gave completely correct solutions for three marks. Those reading off M2 incorrectly as 135.35 could still get two marks. Some thought that reading off M1 and M2 intercepts at a particular non-zero current, usually 5.2 A, would allow them to find Y. The majority of these attempts failed because the student did not appreciate that B was different for each of the simultaneous equations so they could not cancel the kB terms. A very small number did recognise that problem and worked out both gradients to arrive at a completely correct value for Y. As in 03.2, the writing in 03.5 often betrayed a poor understanding of how the physics of the current balance worked. Several referred to flux cutting or alluded to induction in other ways. However, the general trend was to spot that B would be smaller so the gradient would be less steep, and the intercept stayed the same. Some saw that the gradient was kB so a smaller B meant a smaller gradient while others saw that the intercept was 2Z + Y and hence independent of B. However, very few rarely put the whole thing together, so we saw lots of two-mark answers but very few with all three. We expected students to know that the field between the magnets was uniform, but it did not end abruptly at the top edges of the yoke, yet some said that B at the rod was undetectable. They concluded that the gradient would be zero and the intercept was unchanged. We allowed one mark for this idea.

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  A horizontal current-carrying rod lies in a magnetic field and rests on a balance. A yoke holds removable magnets above and below the rod. The rod current is horizontal and the measured balance reading M changes linearly with current I. The model is M = kBI + nZ + Y, where B is magnetic flux density, n is the number of magnets, Z is the mass of one magnet and Y is the yoke mass.

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• AQA 7408 · June 2024 · Paper 3BD · Q2 · 12 marks

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  Question 2 was about Millikan’s experiment to determine the charge on the electron.

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  Millikan observes a charged oil droplet through a microscope between horizontal parallel plates X and Y separated by 6.0 mm. A variable voltage supply and voltmeter are connected across the plates through a switch. Opening the switch removes the electric field; closing it allows the potential difference to be adjusted. Millikan first determines the droplet radius.

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• AQA 7408 · June 2023 · Paper 3A · Q1 · 13 marks

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  [01.6] Comparatively few added suitable annotation to Figure 3. Rather than take the expected route of dividing the distance by their 01.5 result, some used 2 2 1 at s = with s = 495 mm and g = 9.79 m s−2 but apart from those who forgot to multiply their t by 2 or who failed to cope with the mixed units, this approach worked well. Some credit was given for determining the time by estimating a non- integer number of intervals between the contacts.

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  A stroboscope has maximum flash duration T1 = 300 microseconds and maximum flash frequency 150 Hz. The time from the start of one flash to the start of the next is T2, and duty cycle is T1/T2. In a later experiment a ball is photographed while bouncing under 31.0 Hz stroboscopic illumination; vertical height h is measured from the floor, the initial height is H = 1.550 m, and image number n starts at zero.

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• AQA 7408 · June 2023 · Paper 3A · Q2 · 16 marks

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  [02.3] This part was well answered and many recognised that they should calculate the minimum current or the minimum potential difference when X was set to maximum resistance. Better-performing students often went on to compare these results with relevant data in Figure 4 to justify their rejection of circuit 1. A few proved circuit 1 was unsuitable by comparing 2.3  with the resistance calculated using the first or second points on Figure 4. We wanted them to say that the potential divider could vary the pd from 0 to 12 V so circuit 2 could produce the data in Figure 4, but this detail eluded most. Some tried to calculate the maximum current in X for circuit 1 but mistakenly used 2.3  in their calculation. 02.4 and 02.5 Although most found 02.4 and 02.5 straightforward, some penalised themselves in 02.4 by inconsistent s.f. in the data or, in 02.5, by failing to recognise the non-linear trend in their plotted points. It was surprising to find how many did not draw any best-fit line.

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  A data logger records the current-voltage characteristic of filament lamp L at 2.5 samples per second while V increases steadily. Representative data include (V, I): (3.30 V, 1.07 A), (5.17 V, 1.32 A), (7.69 V, 1.59 A), (9.58 V, 1.77 A), (11.47 V, 1.94 A). The first plotted current is about 0.36 A, and the characteristic extends smoothly to about I = 1.98 A at 12 V.

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• AQA 7408 · June 2023 · Paper 3A · Q3 · 16 marks

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  [03.2] Many recognised that cos 25 was involved in the calculation but to get credit we needed to see this used in a valid percentage-difference calculation. About a third of the students gave fully correct solutions.

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  A vertical circular coil of radius r carries constant direct current. Q is its centre and PR is the horizontal axis through Q. A sensor measures the horizontal flux density B_H along this axis; Earth's field is negligible. Later, two identical coaxial coils are separated by r and each carries 225 mA.

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• AQA 7408 · June 2022 · Paper 3A · Q1 · 8 marks

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  This question tested students’ understanding of the use of a CRO as a clock. In 01.1, nearly two-thirds correctly identified Y-shift. For full credit in 01.2, examiners wanted to see use of time contact rod of length 2 speed × = . Some students missed the factor of 2 or assumed that the time-base setting referred to minor divisions. It was disappointing that more than half of the students could not score. In 01.3 there was strong representation at each mark. Better students took note that they should add quantitative detail. Once it was clear that the new waveform would have twice the number of cycles and would therefore no longer be fully visible, most could correctly identify that the time- base should be adjusted. ‘X-gain’ was accepted for time-base and many correctly suggested changing the setting to 0.1 ms div−1. Some wrote that, when a rod of twice the length was used, the period / wavelength / frequency / speed of the waves would change.

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  Figure 1 shows apparatus used to measure the speed of sound in a steel rod. Figure 1 The steel rod is suspended from a beam using rubber bands. When the hammer is in contact with the end L of the steel rod, a circuit is completed and the signal generator is connected to the oscilloscope. Figure 2 shows the waveform then displayed on the oscilloscope. Figure 2

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• AQA 7408 · June 2022 · Paper 3A · Q3 · 11 marks

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  This question was about finding the resistivity of conductive putty and addressed ideas behind required practical activity 5. In 03.1, about two-thirds of students identified that use of callipers could deform the putty or cause the diameter reading to be reduced. Although a ‘show that’ question, 03.2 was very similar to 03.3 in November 2021. More than half earned both marks by producing an answer that rounded to 2.37%. Nearly 30% scored full credit in 03.3. Some penalised themselves by not combining the percentage uncertainties correctly, but could still get credit for determining a recognisable volume or for substituting their values into a calculation of the uncertainty in the volume. There were isolated cases where maximum and minimum volumes were calculated based on the extreme values of d and L. This proved to be a viable alternative to the anticipated method and could earn full credit. In 03.4 students were back on familiar territory and (mostly) drew an acceptable line, measured the gradient, and did the required calculation to find the resistivity. A common error was to miss the multiplier with the label on the L2 axis leading to 10−5 on the answer line. The margin of error with the numerical value was small so truncation to 2 sf was ill-advised. Over half of the students scored at least 3 marks.

  Text version

  Conductive putty can easily be formed into different shapes to investigate the effect of shape on electrical resistance.

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• AQA 7408 · June 2022 · Paper 3A · Q4 · 19 marks

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  This question was about methods to confirm Boyle’s Law (required practical activity 8). The method described in parts 04.1 to 04.3 was for a loaded gas syringe. In parts 04.4 to 04.7 the method was the familiar version in which pressure is applied to air trapped above a column of oil. 04.1 is a similar question to 01.3 in November 2021. While half could perform calculations that could lead to a conclusion, nearly all then stated that their ‘M  y values were different.’ Random error will inevitably affect real data so students were required to make a reasoned comment about the extent of the discrepancy. Some seemed to think they were being asked to test for an exponential relationship while others, sowing the seeds of the downfall in 04.3, said the points in Figure 10 lay on a straight line. In 04.2 students needed to explain how the pressure inside the cylinder changed as P moved downwards, how this led to P coming to rest and why P fell out of the cylinder when the valve was opened. Misconceptions seen included saying that P came to rest when the internal and external pressures were the same. Some thought pressure could be equated with force or suggested that there was a ‘suction’ effect on P. Others said that, when the valve was opened, air rushed into the cylinder and pushed P downwards. Many struggled to make progress and 60% were unable to score. The instruction in 04.3 to ‘Draw a best fit line on Figure 10’ seems to have persuaded many to draw a straight line. Only a quarter of students drew a smooth curve following the obvious trend of the points. Many realised they should extrapolate their line to deduce y for the inverted cylinder but nearly all read off at M = −0.35. Since M did not include the mass of P, the y read-off should have been made at M = −0.70. Meniscus is a term for the curved surface of a liquid. In 04.4 many used the term appropriately in explaining the error made by the student. Others earned this mark with a sketch. The alternative suggestion that the student thought the sub-divisions were at 0.1 cm3 intervals was accepted. At least a quarter failed to record 35.8 as the correct reading. In 04.5 students were asked to explain why the gradient in Figure 13 confirmed Boyle’s Law. A calculation to show the gradient was approximately −1 and relevant algebra to explain the y = mx + c form of Figure 13 were expected. Some did not use the blank space provided for a calculation and just said the line had a negative slope. In 04.6 students were required to make use of a point on the line in Figure 13 in their solution. Gradient calculations were not accepted as part of the working here. Many decided to substitute their data into the equation for the line in Figure 13. This required a calculation of the intercept but many claimed the value to be 1.685. Others ignored the intercept altogether and stated that log V = the gradient  log 0.34. It was possible to solve this problem in two or three lines but keeping more complex working error- free was often an insurmountable problem. Students found 04.5 and 04.6 to be very challenging and only a third of them were able to make progress in either part. In 04.7 keeping temperature constant was correctly identified by over 80%. About half of these added the second mark by saying they would change the pressure slowly, showing good recall of the required practical. Examiners did not allow ‘carry out the experiment at room temperature’.

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  Air is trapped by a frictionless piston P in a vertical cylinder with a closed valve. Added mass M moves P down and distance y measures trapped-air volume. The six (M/kg, y/mm) points are (0.50,89), (1.00,82), (1.50,76), (2.00,71), (2.50,66.5), (3.00,62.5). In a later log-log plot, the best-fit line for log(V/cm^3) against log(p/MPa) passes approximately through (-1.10,1.69) and (-0.60,1.17).

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• AQA 7408 · November 2021 · Paper 3A · Q1 · 16 marks

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  The question was set in the context of Required Practical Activity 12. The demand of question 01.2 was not much beyond GCSE so it was unsurprising that the mean mark (75% of the maximum) was much higher than for any other part. In question 01.3 we asked students to explain whether the data indicate an inverse-square relationship. It was encouraging that 75% could suggest calculations that would lead to a conclusion. However, in rejecting the prediction, only 6% of students earned full credit by providing more than the obvious comment that their ‘RC  d2 values are different.’ In the 2019 paper the students were told that the sealed source depicted emitted three types of radiation. This meant that for α and β radiation the source could be thought of as directional. Later in that question, an aluminium absorber was placed in front of the open end of the source so that only γ radiation could be detected. However this radiation is emitted in all directions regardless of which way the open end of the source is pointing. It seemed that in the 2021 paper many students overlooked this when answering question 01.4. We expected them to state that the detector would be moved towards the source (about 40% did), but less than 15% explained that this maximised the distance between themselves and the source. This question discriminated in favour of those with direct experience of using a sealed source. In question 01.6, only 30% of students gave the analysis (log RC = −2 log d + log k) that was the gateway to further progress in this straightforward question. In question 01.8, about 40% referred to the random nature of radioactive decay, scoring the first mark, although some thought that the question concerned exponential decay. Some of the attempts to explain why all 100 photons would not be detected were tortuous to read.

  Text version

  A sealed gamma source has its open end 138 mm above a bench. A detector is clamped vertically above it to test the inverse-square law.

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• AQA 7408 · November 2021 · Paper 3A · Q2 · 10 marks

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  This question was about the light emitted from different LEDs but included general ideas about the use of diffraction gratings, as used in Required Practical Activity 2. In question 02.1 students had to make an easy read-off from Figure 3 and then apply an equation available in the Formulae and Data booklet. Despite the low demand of the question, fewer than a third of the students were able to obtain full credit. Question 02.2 is one of several in the paper where those suggesting simple practically-based explanations were most likely to score. About 40% of students mentioned some relevant characteristic of the 5th maximum to score the available mark. It was clear that some did not understand what we wanted them to do in question 02.3 and many showed no evidence of working on Figure 4. In question 02.4 only 3% of the students successfully used data about both LEDs; some engineered an answer that duplicated the value in the Formulae and Data booklet. All students realised that c is the speed of light but not all recognised that e is the electronic charge and used 2.718 in their calculation. Question 02.5 was the least accessible part and only 10% of students used Figure 4 to determine the voltage drop across the LED before going on to deduce the minimum value of R.

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  Green LED LG and red LED LR have equal peak intensity. Their spectral peaks are about 565 nm and 635 nm. Extrapolated activation voltage for LG is 2.00 V; the LR current-voltage graph has a linear high-current section and at 21.0 mA its forward voltage is 2.01 V.

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• AQA 7408 · November 2021 · Paper 3A · Q3 · 19 marks

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  This question was set in the context of Required Practical Activity 9. In question 03.1 more students chose the distractor 13.5 than the correct value of 2.7, suggesting that many did not appreciate the distinction between ‘more sensitive’ and ‘less sensitive’. Question 03.2 is a question used in an earlier series. Some students improvised answers such as ‘the mirror was used to illuminate the scale to eliminate human error’. Only 10% could supply a completely correct answer. Question 03.3 was poorly answered in comparison with similar examples in previous papers, with many failing to halve the range before calculating the percentage uncertainty. In question 03.5 most found that the space provided was adequate for them to complete their answer; those who needed supplementary pages usually included information already provided in the question. Many could suggest something sensible about meter protection, checking that C was discharged being the most popular idea. Some recognised the advantage of timing for longer but suggested impractical ideas such as ‘measure the time for C to fully discharge’ or ‘add a resistor to the circuit’. Few could state how they would test for any relationship between range and time constant. Weaker students wrote that they would check whether the half life was 2.5 s. More than half were able to score one mark in question 03.6 by making at least one relevant observation about the values of V in Table 2, although finding an explanation to back up their observation was a harder proposition. In question 03.7 at least 30% knew how to find the voltmeter resistance (as per page 116 of the physics practical handbook). However, half of the students, despite often obtaining relevant data from Figure 8, then failed to make enough progress to score. In question 03.8 it was surprising to find that many, having correctly read relevant information from Figure 8, then attempted to calculate the current using 3 10 10 16 ln × V . Concluding Remarks The demands of this paper were no greater than in 2019. Besides demonstrating knowledge and understanding of the required practical activities, students must show that they can apply their core understanding of practical work in new and unfamiliar contexts. Some will not have seen an analogue meter and we would not expect any to have heard about the dead time of a radiation detector, but this would not have affected their ability to tackle the questions we set. Question 1 revisited Required Practical Activity 12 which featured in 2019 and this will have benefited those who looked at past papers and schemes. Specification coverage of theory leading up to Required Practical Activities 12 and 9 (see question 3) would normally take place later in the course, so both of these should have been fresh in students’ memory. However this assumes that students will have had uninterrupted study and this clearly will not be true in every case. The impression gained was that students felt more comfortable writing about capacitor discharge than about the inverse-square law. Where possible they should be given direct experience of using equipment relevant in each of the practical activities, including the safe manipulation of a sealed radioactive source. As might be expected, work at grade A was in very short supply, but a handful of capable students submitted answers and some of them found innovative variations on the expected approaches to question 03.7. At the other end of the spectrum we saw evidence of calculators set to read angles in radians (in question 02.1) and misguided attempts to use the Boltzmann constant (in question 01.3). Aside from questions 01.2, 01.3, 02.1 and 03.3, students at about the E boundary found marks difficult to obtain. Some of the work seen in questions 01.1 and 03.2 show that, while students know about parallax error, they are not always aware of techniques used to limit its effect. This is an area we will continue to test and the best way to acquire knowledge of such techniques is by direct practical experience. Work seen in question 01.4 suggests that some students wrongly assume that sealed sources emit γ radiation only through the open end of the source. Students should be made aware of the expectations behind the different command words used in the questions. When we use ‘Explain’ we expect a reasoned justification to be included and when, as in question 01.3, they are basing a decision based on a numerical outcome, the justification should be quantitative, eg a percentage-difference calculation. There is always scope in this paper to test the Maths Skills listed in section 6 of the specification. Question 01.6 exposed weak understanding about the use of logarithmic plots to test power law variations (MS3.11). Relevant opportunities for skills development are identified in the main body of the specification.

  Text version

  A dual-range analogue voltmeter has 3 V and 15 V ranges. On the 3 V scale its uncorrected zero is +0.3 V. A mirror runs along the scale. After zero correction, an unknown capacitor discharges through the meter. For the later 820 microF discharge, Figure 8 is a straight best-fit plot of ln(V / 1 V) against t passing approximately through (0 s,2.64) and (28 s,0.50).

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• AQA 7408 · November 2020 · Paper 3A · Q1 · 15 marks

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  This question expanded on the ideas behind assessed practical 7. About half the students knew the mark should be at the equilibrium position in 01.1, but disappointingly few of them could explain why this was so. In 01.2, some thought they were measuring the period and not the amplitude. Too many described trigonometric methods based on an angle measurement. To determine the percentage increase in 01.3, some tried a mathematical approach based on the average rate of increase shown in Figure 3. We expected students to extrapolate the curve and those that did could usually proceed smoothly. Over half scored at least 2 out of 3 marks. The key in 01.4 was to calculate the average having rejected the anomalous data, then determine the uncertainty from half the resulting range. About a third of the students were able to follow one or both of these steps. It was hard to find many solutions to 01.5 and 01.6 that indicated work of A-grade standard and even the correct completion of Table 2 proved beyond nearly 10% of the cohort. Both in data tabulation and in the labels marked on graph axes, we expect consistency in decimal places. We saw far too many reversed scales that produced upwards-sloping lines and compressed scales that produced shallow lines. Less than 20% of students produced completely correct solutions to this routine problem. 01.7 discriminated well in favour of the stronger students who manipulated the equation to produce an expression of the form y = mx + c and went on to deduce that δ = e−gradient. A novel approach seen was to deduce A0 from the intercept and then obtain a value of An from a convenient point on the line, e.g. at n = 2. Going on to explain that n A A0 = δ earned full credit.

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  A simple pendulum is investigated to measure its period, the limit of small-amplitude behaviour and its damping.

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• AQA 7408 · November 2020 · Paper 3A · Q2 · 13 marks

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  This question was about the bending of a beam and tested ideas about different types of error, orders of magnitude, and the interpretation of log-log graphs. In 02.1 a popular distractor for the vernier reading was 45.8. Nearly 60% gave the correct answer of 37.8. The word ‘random’ was supplied by 40% to earn the mark in 02.2, although just as many preferred ‘systematic’. ‘Human error’ is not a term examiners allow or expect students to use. About 70% of students obtained a mark in 02.3 for stating that the thinner beam would deflect more. Some went on to identify correctly that this would reduce the percentage uncertainty in s. The third mark could be earned in a variety of ways, e.g. suggesting that the beam could become permanently deformed. We expected students to understand the distinction between elastic limit and limit of proportionality. Many knew the meaning of the Giga prefix in the value of Young modulus in 02.4 and could then combine this with data obtained from Figure 8. A common error was failing to notice that s was in millimetres. Many students still do not understand what is required when we ask them to make an order-of-magnitude calculation (specification objective MS 1.4), the majority leaving their raw values for η on the answer line. Only 15% supplied the expected answer 8 or 108; we did not accept 1  108. A worrying number seemed confused by the unit on the answer line and spoiled a perfectly acceptable result by carrying out some additional mathematical operation. Question 02.5 addressed specification objective MS 3.11 which identifies that logarithmic plots are used ‘to test power-law variations’. This was the least accessible question on the paper, many claiming that Figure 9 showed an exponential relationship. This question exposed lack of knowledge in the same way as did the question about logarithmic scales from 2019. Successful students, of which there were less than 5%, suggested a mathematical expression such as s = kLn, k being identified as a constant. In 02.6, about 75% got as far as identifying log L = −0.097 but some failed to see the next step and used Figure 9 incorrectly. Question 02.7 discriminated well in favour of the stronger students, but over 20% did not attempt this part.

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  A horizontal beam is supported 0.80 m apart and loaded at its midpoint. A travelling microscope measures midpoint deflection s while mass m is loaded and unloaded. For the original beam, a best-fit graph of s against m has gradient about 0.102 m kg^-1 and s=eta m/E, where E=1.14 GPa. A second log-log graph uses a fixed central mass while varying support spacing L.

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• AQA 7408 · November 2020 · Paper 3A · Q3 · 17 marks

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  This question was about assessed practical 6. Physics errors seen in the diagrams for 03.1 included some that were below the level of a good GCSE student. Some were drawn freehand or contained gaps. Only 40% obtained the mark for this part. In 03.2, credit for describing the procedure was withheld when the voltmeter was connected across P or there was a suggestion that Q had been calibrated. Descriptions of the processing were generally consistent with the version in the physics handbook and about 30% were able to get full credit. However, it was disappointing that 25% scored zero and a further 11% did not attempt this very accessible question. It was rare to find completely successful answers to the sequence from 03.3 to 03.5. In the first part we hoped to see (22  the result of a gradient calculation) but full credit could be earned by outlining a simultaneous-equation approach. The only way to show that the current was about 0.25 A was by recognising that n = 4 and then using Figure 12. In 03.5, students could often deduce the e.m.f. and the internal resistance but less than 10% scored all 4 marks. The rubric states that answers to 1 sf will not (normally) be acceptable but it was common to find the internal resistance given as 0.9 Ω. In 03.6, it seemed that many did not recognise the impossibility of distributing data evenly across the gap between n = 1 and n = 14. Presumably this was why so many suggested the combination of n = 4, 7 and 10. Others suggested using non-integer values for n. In 03.7, about 30% scored 1 mark, usually by deducing that the use of 27 Ω resistors would decrease the gradient. Only about 5% recognised that this would require both points to move to the right of the graph. Concluding Remarks Each marking point proved accessible except 02.5 and the third mark in 03.7. Despite having similar demands to the 2019 edition, the 2020 paper proved less discriminating, probably because stronger students were under-represented. Students generally engaged with the command word although there is still a reluctance to ‘annotate’, e.g. where we ask them to put detail on a printed Figure. They did not always pay attention to the entirety of the command sentence, e.g. in 02.6 and 03.4 some clearly missed the instruction to use a particular Figure to make their deduction. The mathematical skills employed by the students were usually sound and at least as good as in a typical series. Most recognise and can exploit the y = mx + c idea. Working was usually transparent and faulty manipulation was rare. There is evidence that teachers are not examining the ‘dark corners’ of Section 6 of the specification. Many students have a blind spot with log-log plots and with order of magnitude calculations. Candidates are sometimes unsuccessful even with AO1 questions. Review of previous mark schemes would remedy many of these shortcomings. Questions testing the AO2 criteria are also a mixed bag: in 01.4 the uncertainty calculations were often done well but the graph scaling/plotting in 01.6 was patchy. When the information is out in the open and the context is familiar as in 03.5, students can make progress with AO3 questions, but the novel scenarios such as in 03.6 defeat most.

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  Experiments determine the emf epsilon and internal resistance r of a power supply. One method varies external resistance and measures terminal pd V and current I. Another connects n identical 22 ohm resistors in parallel, for which 22/n = epsilon/I - r, and plots reciprocal variables.

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• AQA 7408 · June 2018 · Paper 2 · Q5 · 6 marks

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  [05.2] It was clear that over 90% of students were not aware of how materials can become radioactive. There were extremely few references to nuclei. Students mainly wrote that the induced radioactivity was “too small to be of harm” or “has a short half-life” or “is only ionised a bit, so can be ignored”.

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  Metal surgical instruments are radiation-sterilised. A G-M source experiment gives background-corrected counts/min9013,1395,242 at distances0.20,0.50,1.00m.

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• AQA 7408 · June 2018 · Paper 3A · Q1 · 19 marks

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  [01.4] The first row of Table 1 attracted the most correct responses and thereafter things got patchier. Examiners needed to see correct responses in both row 3 and row 4 to earn the third marking point; this proved beyond all but the most able, with only 11.4% obtaining full credit.

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  A practical uses a metre ruler pivoted at1.0 cm and supported by a prism on a zeroed balance at30.0 cm; with the horizontal ruler alone the balance reads214.66 g. In the side-view diagram, terminal P is at the left end and Q at the right end of a wire along the ruler. The supply makes conventional current flow P-to-Q, rightwards across a5.0 cm horizontal magnetic-field region at the85-90 cm marks. The straight M-against-I graph has gradient -0.28 g A^-1.

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• AQA 7408 · June 2018 · Paper 3A · Q3 · 14 marks

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  [03.2] Many answers suggested that Charles’s Law was even less well understood than Boyle’s Law. Only the better students realised that they were being asked to give two conditions that should be met if Charles’s Law is to apply. While some correctly stated that pressure must remain the same, only 7% added that the mass of gas must be constant.

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  To estimate absolute zero, air is trapped in a flask at 86 degC, then cooled to 19 degC. The inverted flask valve is opened under water, then its depth is adjusted until inside and outside water levels match. Measured water volumes are V1=48 cm^3 and flask volume V2=255 cm^3.

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• AQA 7408 · June 2018 · Paper 3BD · Q1 · 9 marks

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  [01.3] Students needed to show all data substituted to gain full marks. Most appreciated that the answer needed to be given to two significant figures for consistency with the significant figures in the data used. 58.8% of students were awarded both marks.

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  Electrons thermionically emitted from a filament accelerate through V then follow radius r perpendicular to magnetic flux density B. Data: V=320 V,r=4.0 cm,B=1.5 mT.

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• AQA 7408 · June 2017 · Paper 3A · Q2 · 14 marks

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  This question addressed the ideas behind assessed practical activity 9. Students who had seen the second set of specimen questions should have been well prepared for the parts relating to the use of the oscilloscope. It was clear from the descriptive parts of this question, however, that many students had not had direct experience of using an oscilloscope, as shown by the lack of much, if any, use of correct terminology to describe the controls. Even if some students thought the waveform shown in Figure 8 showed an ac signal, the instruction to determine the peak to peak voltage should have made question 02.1 straightforward. However, a disappointing number of students found a variety of ways to get this wrong and were similarly unsuccessful with question 02.2. Those students who obtained 6.3 V and 250 Hz were well-placed to score in question 02.3 and a popular and successful approach was to use RC t e V V ∆ − = 0 ; a transparent, viable attempt along these lines could earn a mark, even if the final answer fell outside the required range. Others read off the time interval for V to fall to 37% when the capacitor was discharging, but poor communication often made it harder to give any credit, if the final result obtained by this method was unsuccessful. Those using the idea that the capacitor would completely discharge in five time constants were almost invariably unsuccessful due to difficulty in accurately pinpointing the time for 5RC from Figure 10. In question 02.4, most students knew what would happen to the waveform displayed in the oscilloscope when the time-base was adjusted, but often struggled to give a convincing explanation. Stating that the ‘waveform would not fit’ left examiners looking for further evidence to decide whether the student was referring to vertical or horizontal direction. Some students referred to the ‘wavelength increasing’, or equivocated by suggested that the waveform ‘might not fit’. While better answers suggested that either the charging or discharging parts (but not both) would now be displayed, very few students took a quantitative approach, e.g. that the discharge curve would now be 2.5 times wider. Here and elsewhere in the paper, some students explained that uncertainty would be reduced, but without supporting reasoning this gained no credit. Question 02.5 discriminated well, with better students stating that the resistance, and hence the time constant, is halved, and spotted the opportunity to give the quantitative detail suggested by the information in the question. The sketches on Figure 11 showed that some students thought that adding the extra resistor would change the amplitude or the period of the waveform; relatively few students supplied the sketch examiners were looking for. In the sketch for question 02.6, examiners wanted to see a complete half cycle while the signal generator output was V, and a complete half cycle when the output was zero. Students were generally more successful with the latter, but often failed to consider how Figures 12a and 12b could be used in combination to deduce the other part of the waveform. In question 02.7, “reduce Y-gain”, or “increase volt per division” could score but an equivocal “change the Y-gain” could not. Once again, extra credit was available for quantitative detail such as “set the gain to 2 V per division”. Some students clearly failed to appreciate that Figure 12c showed a graph and was not the way the waveform would appear on the oscilloscope; these students stated that the waveform was already fully visible, so no changes were necessary.

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  A signal generator produces a square wave. The oscilloscope settings are 1 V division^-1 and 0.5 ms division^-1. The trace spans 6.3 vertical divisions peak-to-peak and one period spans 8 horizontal divisions. With a series R-C circuit and the oscilloscope across C, each transition is exponential between +3.15 V and -3.15 V; after a step, the trace crosses 0 V about 0.175 ms later.

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• AQA 7408 · June 2017 · Paper 3A · Q3 · 13 marks

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  Those students who did not fall back on a generic response in question 03.6 gained a significant advantage. The numerical and graphical parts of question 3 were generally done well. Questions 03.1 and 03.2 were quite accessible for those students who took in all the information from Figures 13, 14 and 15. The data students added to Table 2 should give the p and x data to a consistent and appropriate number of decimal places. Thus, for n = 13 examiners wanted to see x = 30.0; a mark was withheld from the many students who missed this point. In question 03.3, most students earned a mark for working out the ln (x/cm) values correctly, and recording these in a consistent fashion to at least 2 decimal places. The second marking point was much more discriminating, and was forfeited by many students who included the origin, thus compromising the vertical scale. Others did not show the bracket around the axis label correctly, or spaced their values too widely along the axis. The point plotting was generally fine, but some students lost the mark by using ‘blobs’ rather than clearly-defined points, or by drawing a thick or non-ruled line. Those producing a curve could not score here. In question 03.4, examiners wanted students to point out that their graph was a straight line, and that it had a negative gradient. It was clear that large numbers of students seemed to think that any straight line graph represents direct or inverse proportion. Examiners insisted on seeing ‘linear’ or ‘straight line’, and any mention of proportion (of any sort) was rejected. Once back to numerical work in question 03.5, students were on surer ground and most measured a gradient before successfully going on to find x when n = 20. Students who feel that this type of question is testing maths and not physics should acquaint themselves with section 6 of the specification. Question 03.6 highlighted once again how ill-equipped some students were when it came to writing with authority about practical procedures to reduce uncertainty. Some immediately seized on the idea that (percentage) uncertainty could be reduced by either increasing the raw measurements, or by reducing the intervals between the markings on a scale. Neither of these things made any sense in the context of the question, so suggestions such as “increase the length of the air track”, and “use a vernier scale”, gained no credit. Some students failed to gain credit here because they suggested the use of lasers or computers to measure distances, or simply gave vague statements about some procedure which ‘will reduce uncertainty’. Students who stuck with what, in the circumstances, would be an obvious and effective strategy, such as repeating and averaging to reduce the impact of random error, were on the safest ground. Whenever data-logging is suggested, examiners expect to see an appropriate sensor identified. In the context of this experiment a motion sensor would be fine, but a light gate would not. The use of video cameras, used increasingly in schools and colleges, to pinpoint p as the glider comes to rest, was accepted either as a means to reduce the impact of random error, or to avoid parallax error. Use of statistics Statistics used in this report may be taken from incomplete processing data. However, this data still gives a true account on how students have performed for each question.

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  A glider rebounds repeatedly on an inclined linear air track. The fixed scale zero is at the lower end. The glider's reference edge at the bumper is 23.8 cm; in the initial-position diagram it aligns with 198.4 cm. Highest positions after rebounds are: (n, p/cm)=(2, 157.0), (4, 125.4), (6, 101.3), (9, 75.4), (13, 53.8). For each rebound the distance travelled from the lower reference is x=p-23.8 cm.

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