How do I choose a good IA2 research question?

Three tests for a good question. First, the underlying relationship must be one Unit 3 equation, not a chain of two or three (which makes uncertainty propagation impractical). Second, the IV must be controllable to at least five distinct values within laboratory time and equipment limits. Third, the DV must be measurable to better than 5 percent precision with the school's instruments. Projectile range vs angle, pendulum period vs length, induced EMF vs magnet speed, and transformer voltage ratio vs turns ratio all pass these tests.

How many trials and IV values do I need?

QCAA criteria reward 'sufficient and relevant data'. The practical floor for a Band 5-6 IA2 is five IV values across the planned range, with three trials per IV value, giving fifteen data points before processing. More is fine if time permits, but only if uncertainty handling keeps pace; ten IV values without uncertainty bars is weaker than five IV values with full propagation.

What is linearisation and why does it matter?

Linearisation transforms a non-linear theoretical relationship into a straight line, so that the gradient and intercept have a known physical meaning and gradient uncertainty can be extracted via the min/max slope method. Pendulum period $T = 2\pi\sqrt{L/g}$ becomes $T^2 = (4\pi^2/g) L$, plotting $T^2$ against $L$ with gradient $4\pi^2/g$. Linearisation is expected on every IA2 where the theoretical relationship is non-linear.

How do I propagate uncertainty?

For sums and differences, add absolute uncertainties. For products and quotients, add fractional uncertainties (then convert back). For powers, multiply the fractional uncertainty by the power. For gradient from a graph, use the min/max slope method: draw the steepest and shallowest lines that still fit through the error bars, then take half the difference in slopes as the gradient uncertainty.

What lifts the IA2 discussion from Band 4 to Band 6?

Specificity. Band 4 discussions list generic uncertainty sources (parallax, friction, air resistance). Band 6 discussions identify the specific experimental step where each uncertainty entered, quantify its contribution where possible, and propose a specific improvement tied to that step. 'Stopwatch reaction time of approximately 0.2 s contributed up to 4 percent to the period measurement at L = 0.25 m, which would be addressed by using a photogate' is Band 6 reasoning.

How long should the IA2 report be?

QCAA sets a 1500 to 2000-word limit (excluding appendices, references, raw data tables and figures). Going under 1500 words almost always reflects under-developed methodology or discussion. Going over 2000 words risks being cut by markers at the limit. Word budgets typically split as: introduction 300, methodology 350, results and analysis 400, discussion 600, conclusion 150.

QLDPhysics

QCE Physics IA2 experiment design and report writing: the 2026 guide

How to design and write the QCE Physics IA2 student experiment. Choosing a research question, justifying the methodology, propagating uncertainty, linearising the data, and writing the discussion in a way that hits every QCAA criterion.

Generated by Claude Opus 4.817 min readQCAA-PHYS-IA2Updated 2026-06-20

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this guide is for
Choosing the research question
Justifying the methodology
Data collection and uncertainty
Linearisation
The discussion
The conclusion
Check your knowledge

What this guide is for

The QCE Physics IA2 is the Student Experiment, worth 20 percent of the subject result. It is a student-designed and student-conducted Unit 3 experiment, reported as a 1500 to 2000-word scientific report. The published companion guide on this site covers report structure and common contexts. This guide is the design and writing playbook: how to choose a research question, justify the methodology, propagate uncertainty, linearise, and write a discussion that hits every QCAA criterion.

The IA2 is graded against published QCAA criteria covering research and planning, analysis of evidence, interpretation and evaluation, and conclusion. Top band requires evidence of excellence in all four.

Choosing the research question

A good IA2 research question is narrow, controllable and tied to one Unit 3 equation. Three tests.

First. The underlying theoretical relationship is one named equation, not a chain. Pendulum period from length is one equation ( $T = 2\pi\sqrt{L/g}$ ). Range of a projectile from launch angle is one equation ( $R = v^2 \sin(2\theta)/g$ ). Transformer voltage ratio from turns ratio is one equation ( $V_s/V_p = N_s/N_p$ ). All three are tractable.

Second. The IV is controllable to at least five distinct values within laboratory time. Pendulum length from 0.25 m to 1.25 m in 0.25 m increments is straightforward. Projectile launch angle from 15 to 75 degrees in 10-degree increments is straightforward, assuming a fixed-velocity launcher.

Third. The DV is measurable to better than 5 percent precision with school instruments. A period of 1.0 s measured with a stopwatch carries about 0.2 s reaction time uncertainty, so a single trial gives 20 percent uncertainty. Three trials drop this to about 12 percent. Photogates drop it to under 1 percent. The choice of instrument is part of the design.

A weak research question fails one of these tests. "How does air resistance affect a falling object" fails the first test (no single Unit 3 equation governs it). "How does temperature affect electrical resistance" fails the syllabus mapping (this is not Unit 3). "How does the launch velocity of a marble affect range" fails the third test at most schools, because the launch velocity is hard to measure accurately.

Justifying the methodology

The QCAA research-and-planning criterion rewards explicit justification of design choices. Every choice gets a sentence.

Why these IV values. "Five values from 0.25 m to 1.25 m were chosen to span a factor of five in length, giving a clear gradient on the linearised graph while staying within the school pendulum stand's vertical clearance of 1.5 m."

Why this many trials. "Three trials per IV value were conducted, with the mean reported and the half-range used as the random uncertainty. This is sufficient for stopwatch-precision data; a fourth trial would not meaningfully reduce uncertainty."

Why these controlled variables. "The bob mass was held at 50.0 plus/minus 0.1 g across all trials, because $T = 2\pi\sqrt{L/g}$ predicts no mass dependence; varying mass would test that prediction and was beyond the scope of this question."

Why this instrument. "Period was measured with a stopwatch (resolution 0.01 s, reaction time approximately 0.2 s). A photogate would have given better precision but was not available; the trade-off was managed by timing ten oscillations and dividing by ten."

The marker is looking for evidence that you made these choices deliberately, not by accident.

The standard QCE IA2 magnet-drop rig: release height sets the entry speed via energy conservation, photogates measure it, and the datalogger records the induced EMF for the application criterion.

Data collection and uncertainty

Raw data goes in a table with units in the column headers. Every measured value carries its absolute uncertainty (from the instrument resolution and, where relevant, reaction-time or parallax estimates).

Processed data goes in a second table. Means, derived quantities, propagated uncertainties.

For sums and differences. Add absolute uncertainties.

For products and quotients. Add fractional uncertainties, then convert back to absolute.

For powers. Multiply the fractional uncertainty by the power. For $T^2$ where $T$ has 5 percent uncertainty, $T^2$ has 10 percent uncertainty.

For means. The half-range across trials is the practical uncertainty estimator at IA2 level. Standard deviation is acceptable but the half-range is what most QCAA exemplars use.

Linearisation

Most Unit 3 relationships are non-linear. Linearisation transforms them so that a straight-line graph extracts a physically meaningful gradient.

Pendulum. $T = 2\pi\sqrt{L/g}$ becomes $T^2 = (4\pi^2/g) L$ . Plot $T^2$ (vertical) against $L$ (horizontal). The gradient is $4\pi^2/g$ , so $g = 4\pi^2 / \text{gradient}$ .

Projectile range. $R = v^2 \sin(2\theta)/g$ becomes $R = (v^2/g) \sin(2\theta)$ . Plot $R$ against $\sin(2\theta)$ . The gradient is $v^2/g$ .

Induced EMF. For a magnet moving at speed $v$ through a coil, $\varepsilon \propto v$ at fixed geometry. Plot $\varepsilon$ against $v$ directly; the relationship is already linear.

Draw the best-fit line by eye, then the steepest and shallowest lines that still pass through every error bar. Half the difference in their slopes is the gradient uncertainty.

The processed table's two key columns map directly onto the linearised graph's axes; the gradient then becomes the experimental value that evaluates the model under the judgement criterion.

The discussion

Band 6 discussions are specific. For every uncertainty source, name the experimental step, quantify the contribution if possible, and propose a specific improvement.

Generic. "Parallax error may have affected the readings."

Specific. "Parallax error in reading the protractor scale to set the launch angle contributed up to approximately 2 degrees of uncertainty at high angles, which propagates to about 8 percent uncertainty in $\sin(2\theta)$ near 75 degrees. A digital inclinometer would resolve this to better than 0.5 degree."

Generic. "Air resistance was not accounted for."

Specific. "Air resistance on the marble (drag coefficient approximately 0.4, mass 5 g, peak velocity 5 m/s) is estimated as about 1 percent of the gravitational force, so its effect on the trajectory is within the experimental uncertainty bars and does not affect the conclusion."

The discussion also addresses limitations of the experimental design (range, scope, controlled variables that were assumed but not tested) and proposes improvements.

The conclusion

A direct answer to the research question. State the experimental value with its uncertainty. Compare to theoretical or accepted value. State whether the hypothesis is supported within experimental uncertainty.

"The measured value of $g$ was 9.7 plus/minus 0.4 m/s $^2$ , which agrees with the accepted value of 9.81 m/s $^2$ to within experimental uncertainty. The hypothesis is supported."

Check your knowledge

Six student-experiment process questions for IA2. These rehearse the moves a marker rewards across research-question design, methodology justification, uncertainty propagation, and evaluation. ISMG criteria are signposted in the solutions. Three significant figures, units throughout.

A student proposes the research question "How does mass affect the period of a pendulum?" Identify three flaws against IA2 top-band specificity and rewrite the question to address each, naming a single Unit 3 equation. (4 marks)
A projectile-range experiment uses a spring-loaded launcher firing a 20 g steel ball at fixed initial speed onto a marked floor at five launch angles (15, 30, 45, 60, 75 degrees, $\pm$ 0.5 degrees). List five controlled variables the student must hold constant and for each justify why with reference to the projectile range equation $R = u^2 \sin(2 \theta)/g$ . (5 marks)
The student measures induced EMF $\varepsilon$ as a function of magnet drop speed $v$ through a coil. Five paired values: 0.50 m s $^{-1}$ $\rightarrow$ 0.10 V; 1.00 $\rightarrow$ 0.21 V; 1.50 $\rightarrow$ 0.30 V; 2.00 $\rightarrow$ 0.42 V; 2.50 $\rightarrow$ 0.51 V. Voltage read-off uncertainty is $\pm$ 0.01 V and speed uncertainty is $\pm$ 0.05 m s $^{-1}$ . (a) State the theoretical relationship and predict the gradient given a coil constant of $N A B / L = 0.20 \ \text{V s m}^{-1}$ . (b) Calculate the gradient using the first and last data points with min/max line method, reporting uncertainty. (c) Compare with prediction and identify the dominant uncertainty source. (7 marks)
The student's evaluation reads: "The major source of error was human error in timing." Identify three weaknesses in this evaluation, and rewrite a one-paragraph evaluation that addresses all three for a pendulum experiment measuring $g$ . (5 marks)
A linearisation is required to test $T = 2\pi \sqrt{m/k}$ for a vertical mass-spring oscillator at five masses. Five paired values: $m$ (kg): 0.100, 0.200, 0.300, 0.400, 0.500; $T$ (s): 0.50, 0.71, 0.87, 1.00, 1.12. (a) Linearise the equation and state what should be plotted on each axis. (b) Calculate the gradient using the first and last linearised points, and from it determine $k$ . (c) Identify one source of systematic error that would shift the apparent $k$ from its true value. (6 marks)
A transformer ratio experiment measures $V_s/V_p$ at five turns ratios $N_s/N_p$ : 0.10, 0.25, 0.50, 1.00, 2.00; observed $V_s/V_p$ : 0.094, 0.236, 0.475, 0.948, 1.892. (a) Calculate the percent deviation of each point from the ideal-transformer prediction $V_s/V_p = N_s/N_p$ . (b) State the pattern in the deviations. (c) Propose a physical explanation, identify the dominant non-ideal effect, and suggest one modification to reduce it. (6 marks)

Solutions

Q1: Three flaws: (1) "How does X affect Y" is qualitative; IA2 requires "What is the relationship between" with specific units and ranges. (2) "Mass" must be specified as IV with discrete values, range, and precision (the QCAA expects at least five). (3) No reference to the underlying physics or equation - the student must show that mass does not appear in $T = 2\pi \sqrt{L/g}$ for the small-angle pendulum, which is part of the result rather than a confound. Rewrite: "What is the relationship between the period $T$ of a simple pendulum (small angle, less than 10 degrees) and the bob mass ( $m$ = 0.020, 0.050, 0.100, 0.200, 0.500 kg, $\pm$ 0.001 kg) at fixed length $L$ = 1.000 $\pm$ 0.002 m, measured as the mean time for 20 oscillations divided by 20?" This question rewards knowledge of IA2 research-question conventions (knowledge and analysis criterion).
The rewrite names IV range and precision, fixes $L$ explicitly, defines DV measurement protocol, and references $T = 2\pi\sqrt{L/g}$ .
Q2: Five controlled variables: (1) Initial speed $u$ - the range equation has $u^2$ dependence, so any drift in spring compression between trials produces a quadratic bias in $R$ ; the spring must be fully compressed each time and re-checked. (2) Projectile mass - drag depends on mass-to-area ratio, so using a consistent ball ensures the no-air-resistance idealisation is equally good at each angle. (3) Launch height - $R = u^2 \sin(2\theta)/g$ assumes launch from ground level; any variation in launcher height between angles biases the measurement systematically. (4) Air conditions - draught from doors or HVAC produces variable drag asymmetrically with launch angle; conduct trials in a still room. (5) Surface flatness - the landing surface must be horizontal because the projectile-range equation assumes the projectile lands at the same height it was launched. This question rewards application of the projectile-range equation (application criterion) and judgement of which variables matter most (judgement criterion).
Five controlled variables - initial speed, projectile mass, launch height, air conditions, and surface flatness - each tied to a term in $R = u^2 \sin(2\theta)/g$ .
Q3: (a) Theoretical: $\varepsilon = N A B v / L$ (Faraday's law for a magnet falling through a coil of length $L$ ), so $\varepsilon$ is linear in $v$ with gradient $N A B / L = 0.20 \ \text{V s m}^{-1}$ . (b) Gradient from first and last: $(0.51 - 0.10)/(2.50 - 0.50) = 0.41/2.00 = 0.205 \ \text{V s m}^{-1}$ . Min/max bounds using error bars ( $\pm$ 0.01 V on each $\varepsilon$ and $\pm$ 0.05 m s $^{-1}$ on each $v$ ): max gradient $= (0.52 - 0.09)/(2.45 - 0.55) = 0.43/1.90 = 0.226$ ; min gradient $= (0.50 - 0.11)/(2.55 - 0.45) = 0.39/2.10 = 0.186$ . Half-range $= (0.226 - 0.186)/2 = 0.020$ . Gradient $= 0.205 \pm 0.020 \ \text{V s m}^{-1}$ , which encompasses the prediction. (c) Percent error from prediction $= (0.205 - 0.200)/0.200 \times 100 = 2.5$ percent, well within the 10 percent uncertainty interval. Dominant uncertainty source: speed measurement at the moment the magnet passes through the coil - a photogate triggered by the magnet's leading edge gives speed at one instant, but the EMF is generated over the full magnet length, so the relevant speed is the average over that interval. Modification: use two photogates at the coil's top and bottom and average the speeds; alternatively use a high-speed camera. This question rewards application of Faraday's law (application criterion), uncertainty propagation, and judgement of error sources (judgement and communication criteria).
Gradient $0.205 \pm 0.020 \ \text{V s m}^{-1}$ agrees with prediction 0.20 within 2.5 percent; photogate timing of the magnet through the coil is the dominant uncertainty.
Q4: Three weaknesses: (1) "Human error" is too vague to be marked - QCAA top band requires a specific source named with its quantified contribution. (2) "Error" conflates accuracy and precision; the statement gives no indication of whether the result is consistent with the accepted value. (3) No modification is proposed. Rewrite: "The mean experimental $g$ was 9.74 $\pm$ 0.08 m s $^{-2}$ (RSD 0.8 percent over five replicates), consistent with the accepted value 9.80 m s $^{-2}$ within the propagated uncertainty interval (9.66 to 9.82). The dominant random source was timing uncertainty in identifying the start and end of a single oscillation by eye, estimated at $\pm$ 0.03 s per cycle from inter-trial scatter; this propagates to roughly $\pm$ 0.5 percent in $g$ when 20 cycles are averaged. A small systematic shift of $-0.06$ m s $^{-2}$ is consistent with a finite-amplitude correction (the experiment used 5 degree amplitude, where the small-angle approximation $\sin\theta \approx \theta$ introduces a $-0.4$ percent bias in $T^2$ versus $L$ , equivalent to $-0.04$ m s $^{-2}$ in $g$ ). The modification with highest impact would replace eye-timing with a photogate at the lowest point of swing, eliminating reaction-time bias and reducing the per-cycle uncertainty to under $\pm$ 0.001 s." This question rewards judgement (judgement criterion) and communication of structured evaluation (communication criterion).
The original evaluation names no specific source, no quantification, and no modification; the rewrite addresses all three with photogate timing as the targeted improvement.
Q5: (a) $T = 2\pi \sqrt{m/k}$ gives $T^2 = (4 \pi^2 / k) m$ , so plot $T^2$ versus $m$ ; gradient $= 4 \pi^2 / k$ . (b) $T^2$ values: 0.250, 0.504, 0.757, 1.000, 1.254. Gradient $= (1.254 - 0.250)/(0.500 - 0.100) = 1.004/0.400 = 2.51 \ \text{s}^2 \text{kg}^{-1}$ . $k = 4 \pi^2 / 2.51 = 39.48/2.51 = 15.7 \ \text{N m}^{-1}$ . (c) Systematic source: the spring has finite mass $m_s$ , but the formula treats it as massless; the effective oscillating mass is $m + m_s/3$ , so the apparent $k$ from the gradient is biased low (the gradient is steeper than predicted) unless the spring mass is subtracted. A 50 g spring would shift the apparent $k$ by around 5 percent. This question rewards application of linearisation (application criterion) and judgement of systematic source (judgement criterion).
Gradient $2.51 \ \text{s}^2 \text{kg}^{-1}$ gives $k = 15.7 \ \text{N m}^{-1}$ ; finite spring mass biases $k$ low and needs the $m_s/3$ correction.
Q6: (a) Predicted $V_s/V_p = N_s/N_p$ : 0.100, 0.250, 0.500, 1.000, 2.000. Percent deviation $= (V_s/V_p - N_s/N_p)/(N_s/N_p) \times 100$ : $-6.0$ percent, $-5.6$ percent, $-5.0$ percent, $-5.2$ percent, $-5.4$ percent. (b) Deviations are uniformly around $-5$ to $-6$ percent across all turns ratios, not growing with turns ratio. (c) Physical explanation: the transformer is not ideal because (i) flux leakage from the primary that does not link the secondary, (ii) winding resistance dropping a small voltage across the primary winding before the magnetic coupling, and (iii) hysteresis and eddy currents in the core dissipating energy. A roughly 5 percent uniform shortfall is characteristic of an air-cored or low-permeability transformer at this frequency; the deviation does not grow with turns ratio because it is dominated by leakage and resistive losses rather than ratio-dependent core saturation. Modification: replace the air core with a high-permeability laminated iron core to reduce flux leakage, and use heavier-gauge windings to reduce resistive losses; the modified transformer should approach $V_s/V_p$ within 1 to 2 percent of the ideal prediction. This question rewards application of transformer theory (application criterion), judgement of non-ideal effects (judgement criterion), and communication of modification (communication criterion).
Deviations cluster around $-5$ to $-6$ percent across all ratios from flux leakage and resistive losses; laminated iron core is the targeted modification.