• Calculations using experimental data — how to process raw readings (means, derived quantities like area, logs) before you can even plot anything.
• Plotting graphs — choosing scales, labelling axes correctly, drawing lines/curves of best fit, and reading off the y-intercept.
• Using units correctly — the 6 SI base units and how derived units (N, J, Pa) are built from them.
• Trends & patterns — recognising linear, directly proportional, inversely proportional, and rate-of-change relationships.
• Interpreting graphs — turning proportional relationships into equations, spotting inverse-square laws, and calculating gradients properly.
• Precision & accuracy — knowing the difference (this trips up almost everyone) plus sensitivity vs resolution.
• Reducing errors — parallax error, fiducial markers, zero errors, and how to fix each.
• Suggesting improvements — data loggers, cameras, computer modelling, and making a method reproducible.
• Uncertainties — absolute, fractional, percentage; how to find them for readings, measurements, repeated data, and digital displays.
• Combining uncertainties — the ADD rule for +/− and the ADD-percentages rule for ×/÷, plus the MULTIPLY rule for powers.

Collecting data is only half the practical. The moment you've got your raw readings, you need to process them — and crucially, you need to have planned your table so there's room to do this.

When you repeat a reading (say, three current readings for the same length of wire), you don't just pick one — you average them. But there's a subtlety examiners love to test:

• Ignore any anomalous readings when calculating the mean (a reading that's obviously way off due to a mistake, not natural variation).
• The mean must be given to the same number of significant figures as the readings that made it. If your readings were all to 3 s.f. (like 1.34, 1.35), your mean must also be 3 s.f. — don't suddenly give 5 decimal places just because your calculator did.

Sometimes the quantity you actually need for your graph isn't something you can point a ruler or ammeter at. You measure something else, then use an equation to get there. Two classic examples:

• Area of a wire: you can't measure area directly, so you measure the radius r with a micrometer, then calculate Area = πr² for each value of r.
• Extension in Hooke's Law: you can't measure "extension" with a ruler in one go — you measure the initial length and final length separately, then calculate Extension = Final length − Initial length.
• Logarithms: sometimes you need ln(value) or log(value) for a straight-line graph (see Topic 4). This always needs its own column in the table — one column for the raw reading, the next column for its log.

A graph is the visual "argument" for your results — a badly-scaled or badly-labelled graph can lose marks even if every data point is perfectly plotted. Three things matter: scale, labels, and the actual plotting.

• The scale must be big enough that your data uses at least half the grid in both the x and y direction. A tiny cluster of points in the corner of a huge grid is a common mark-loser.
• Use scales that are easy to read and plot on — multiples of 1, 2, 5, 10. Avoid multiples of 3 (try plotting 17 on a scale that goes up in 3s — it's a nightmare and leads to plotting errors).
• Scales increase outward and upward from the origin (bottom-left).

Every axis needs the quantity name and its unit, separated by a forward slash: e.g. F / N means "force, measured in Newtons".

• Independent variable (the one you choose/control) → x-axis.
• Dependent variable (the one you measure as a result) → y-axis.

• Points must be accurate to within half a small square — use a sharp pencil so the point is a fine, precise mark, not a fat blob that obscures its own position.
• You need at least 6 points on the graph, with any major outliers clearly identifiable.
• The line of best fit should have roughly equal numbers of points above and below it — it does NOT need to pass through the origin, and it should never be forced through it if the data doesn't support that.
• It should be a smooth, thin line/curve — never a jagged dot-to-dot "frequency polygon" style line.
• Any anomaly you spot (and can justify) should be ignored when drawing the line, because one wildly wrong point can drag your whole gradient off course.

Every quantity in physics is ultimately built from just 6 base units. Everything else — Newtons, Joules, Pascals — is "derived" by combining these mathematically.

To find the base units of a derived quantity, take the equation that defines it and substitute in base units:

Graphs let you see the relationship between two variables — but "the graph goes up" isn't enough for an exam answer. You need to describe the relationship precisely.

• Linear — any straight line (doesn't have to pass through the origin).
• Directly proportional (y ∝ x) — a straight line through the origin with a positive gradient. Double x, and y doubles too.
• Inversely proportional (y ∝ 1/x) — a curve with a decreasing gradient. Double x, and y halves.
• Rate of change — how quickly y is changing with x, shown by the steepness (gradient) of the graph at any point. An increasing gradient = increasing rate of change; a decreasing gradient = decreasing rate of change.

This is where trends become equations — and where gradients get turned into physical constants.

A "∝" sign becomes an "=" sign the moment you introduce a constant of proportionality, k:

Crucially — before declaring two variables "directly proportional" or "inversely proportional", you must check that every other variable in the equation is held constant. In F = ma, F and a are only directly proportional because m stays fixed. If m also changed, the relationship would break.

Curves are hard to extract precise numbers from. So physicists often use logarithms to turn an exponential relationship into a straight line — because straight lines give you a clean gradient and y-intercept.

Take radioactive decay: N = N₀e^(−λt). Taking natural logs of both sides:

Now plotting ln(N) on the y-axis against t on the x-axis gives a straight line where:

• Gradient, m = −λ (so λ = −gradient)
• y-intercept = ln(N₀)

• Draw a triangle that takes up more than half the line — tiny triangles risk losing marks even with the correct final answer.
• Only use points that lie on the line of best fit — never use your raw data points if they sit off the line.
• Always double-check the axis scale/powers of ten before reading off values (e.g. "Force × 10³ / N" means a reading of "5" is actually 5000 N).

These two words get used interchangeably in everyday speech — but in physics, mixing them up is one of the most commonly-penalised mistakes in the whole practical paper.

Think of a dartboard: hitting the same spot every time (tightly clustered) but missing the bullseye = precise but not accurate. Hitting scattered points that average out around the bullseye = accurate but not precise. You want both — tightly clustered and centred on the bullseye.

• Resolution = the smallest change an instrument can display/observe (e.g. the smallest marked division on a ruler).
• Sensitivity = the smallest change an instrument can actually detect — i.e. how much the output changes for a given change in the input.

Example: an analogue thermometer might only be sensitive to 1 °C changes, while a digital probe thermometer is sensitive down to 0.1 °C — meaning the digital one will give more accurate results if you're working with very small temperature changes.

Random errors can never be fully removed — but you can shrink their effect. Here's the toolkit examiners expect you to know and apply:

When timing a pendulum, the bob moves fastest at the bottom of its swing and slowest at the top. If you time it at the top (where it briefly pauses), tiny timing errors have a huge effect on the period. A fiducial marker — a fixed reference point placed at the centre of the oscillation — lets you time the pendulum as it whips past at top speed, where your reaction-time error matters far less relative to the total swing time.

Exam questions love asking "how could this experiment be improved?" — and the best answers go beyond "take more readings" (which is true but generic) and mention specific technology or reproducibility improvements.

• Data loggers — connect sensors that automatically record variables (temperature, voltage, pressure) over time, feeding straight into a computer. They're faster, more accurate, and remove human reaction-time error entirely.
• Cameras — useful when an experiment happens too fast to read a scale in real time (e.g. a fast-moving object). A photo burst captures the scale reading at each instant, which can be read afterwards; if the frame rate is known, you can even calculate velocity from consecutive frames.
• Spreadsheet software (e.g. Excel) — processes large datasets, generates graphs, and calculates gradients/averages far more precisely and quickly than doing it by hand.

• Higher accuracy (no human reaction time delay).
• Can log readings continuously over very long periods (e.g. hourly readings for days) — impractical for a human.
• Can log readings over very short periods (millisecond-scale) — too fast for a human to see.
• Removes safety risk in extreme conditions (e.g. measuring boiling water temperature without a person having to stand right next to it).

A "reproducible" method is one that other scientists (or you, with different materials) can repeat and still trust the result. For example, if you measure the resistivity of constantan wire, you could test whether the same method gives an accurate resistivity for copper or aluminium too — if it does, your method is properly reproducible, not just a one-off fluke that worked for one material.

No measurement is ever perfectly exact — uncertainty is your honest estimate of "how far off could this reasonably be from the true value?" There are three ways to express it:

Once you start combining measurements in calculations (adding, dividing, raising to a power), the uncertainties combine too — and there's a specific rule for each type of operation.

Add the absolute uncertainties together (even when subtracting the values themselves!).

Add the percentage (or fractional) uncertainties.

Multiply the percentage uncertainty by the power.

This is probably the single most commonly-penalised confusion in this whole topic. Precise = repeatable/consistent. Accurate = close to the true value. A set of tightly-clustered readings can still be wrong (precise but inaccurate) if there's a systematic error.

Even with the mathematically correct final answer, examiners want to see a triangle that spans more than half the line — small triangles amplify reading errors and are penalised even when the arithmetic is right.

Never force a line through (0,0) unless the data genuinely supports it. Doing this artificially "fixes" your y-intercept and can badly distort your calculated gradient.

Students often think "if I divide by something, its uncertainty should reduce the total." It doesn't! For multiplication AND division, you always add percentage uncertainties — never subtract.

State your uncertainty to a similar number of significant figures as your value — not more, not less. "12.0 ± 1.204" should become "12.0 ± 1.2".

• Full working shown for gradient/uncertainty calculations — not just a final answer.
• Specific, named improvements (e.g. "use a data logger with light gates") rather than generic ones ("be more careful", "use better equipment").
• Correct units at every stage — including on gradients (units of y ÷ units of x).
• Consistent significant figures across a whole table of calculated values.