Practical Investigation
Internal 4 credits Method Linearising UncertaintyYou design and carry out an investigation to find a relationship between two variables, then process the data, usually by linearising and taking a gradient. Excellence is about a valid method and a well-justified conclusion with uncertainty.
1 Reading the notation
The practical standard has its own vocabulary for measurement and error. These are the terms the marking schedule uses.📖 Symbols and terms in practical work
10 termsCover the right column and check you can say what each one means.
- Independent variable
- The one you deliberately change. Goes on the x-axis.
- Dependent variable
- The one you measure in response. Goes on the y-axis.
- Controlled variable
- Everything you deliberately hold constant so the comparison is fair.
- ± (absolute uncertainty)
- The range within which the true value lies. Usually half the smallest scale division for a single reading. A burette reading involves TWO readings, so its uncertainty doubles.
- % uncertainty
- Absolute uncertainty ÷ measured value × 100. Add percentage uncertainties when quantities are multiplied or divided.
- Gradient
- The slope of a straight-line graph, rise ÷ run. Its units are y-units ÷ x-units, and it usually IS the quantity you are after.
- Intercept
- Where the line crosses an axis. An unexpected non-zero intercept is evidence of a systematic error.
- Linearisation
- Rearranging a relationship so a graph comes out straight: e.g. plotting T² against L when T ∝ √L. A straight line is the only shape the eye judges reliably, which is why this is worth doing.
- Random vs systematic
- Random scatters points either side of the line and IS reduced by repeating. Systematic shifts every point the same way and is NOT.
- ∝ (proportional to)
- “Varies directly with.” y ∝ x means y = kx for some constant k.
Which error does repeating fix?
Only random error. If your evaluation proposes “repeat more times” for a systematic offset, that is wrong. The fix is calibration or a change of method.2 Designing the investigation
A sound method
- Identify the independent, dependent and controlled variables clearly.
- Choose a sensible range and enough values (≥ 6–8 points) with repeats.
- Control variables to keep the test fair; describe how.
- Reduce uncertainty: measure larger quantities, repeat, use appropriate instruments.
3 Linearising data
Most relationships are turned into a straight line y = mx + c so the gradient gives the physics. Plot the quantity that makes it linear.| Suspected relation | Plot y vs x | Gradient gives |
|---|---|---|
| T = 2π√(L/g) | T² vs L | 4π²/g → g |
| T = 2π√(m/k) | T² vs m | 4π²/k → k |
| v² = u² + 2as | v² vs s | 2a → a |
| y = k/x (inverse) | y vs 1/x | k |
Straight line = confirmed relationship
If plotting the linearised variables gives a straight line (through the expected intercept), that supports the relationship. Read the gradient with a best-fit line, not just two points.4 Uncertainty & conclusion
Uncertainty rules you will actually use
Reading uncertainty ± half the smallest scale division (analogue) · ± the last digit (digital) Timing by hand is dominated by reaction time, ~±0.2 s: much larger than the stopwatch resolution. Percentage uncertainty \%\ \text{uncertainty}=\frac{\text{absolute uncertainty}}{\text{measured value}}\times100 Adding / subtracting ADD the absolute uncertainties Multiplying / dividing ADD the percentage uncertainties Raising to a power n MULTIPLY the percentage uncertainty by n So squaring a quantity doubles its % uncertainty: worth choosing what you measure carefully. Gradient uncertainty (steepest gradient − shallowest gradient) ÷ 2 Worked example From gradient to g, with uncertainty A T² vs L graph has gradient 4.10 ± 0.15 s² m⁻¹. Find g and its uncertainty. T² = (4π²/g)L, so gradient = 4π²/g ⟹ g = 4π²/gradient. g = 4π² / 4.10 = 39.48 / 4.10 = 9.63 m s⁻². % uncertainty in gradient = (0.15/4.10) × 100 = 3.7%. g depends on gradient to the power −1, so g carries the same 3.7%: 0.037 × 9.63 = 0.36. Compare with the accepted 9.81: the difference (0.18) is smaller than the uncertainty (0.36). ✓ g = 9.6 ± 0.4 m s⁻², which agrees with the accepted value of 9.81 m s⁻² within experimental uncertainty.For Merit / Excellence
- Draw best-fit and worst-fit (max/min gradient) lines to estimate the uncertainty in the gradient.
- Quote the final result as value ± uncertainty, with sensible significant figures and units.
- Evaluate: largest error source, systematic vs random, and how the method could be improved.
- State a clear conclusion that answers the original question and references the data.
Practice
Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.
Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.
Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.
Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.