The big idea: Paper 1B doesn't just ask you to crunch numbers — it asks you to judge an experiment.
Three questions come up again and again
- Which variable must you control (keep the same) so the test is fair?
- Why repeat a reading and average it? To cut down random uncertainty.
- Is a method any good — and how would you improve it?
Two words to get right first: Control variable — a quantity you deliberately keep constant so it can't affect the result.
Anomaly — a reading that is clearly out of line with the others (a mistake), so you leave it out before averaging.
Why repeats + averaging help
- Random uncertainty scatters readings up and down by chance (reaction time, last-digit estimation).
- Averaging several repeats lets the high and low scatter cancel out, so the mean is more reliable.
- Spotting an anomaly and discarding it stops one bad reading from dragging the mean off.
- Repeats do not fix a systematic error (a zero-offset, a mis-calibrated meter) — that shifts every reading the same way.
Random uncertainty
- Scatters readings randomly up and down
- Caused by chance: reaction time, reading the last digit
- Reduced by repeating and averaging
Systematic error
- Shifts every reading the same way
- Caused by a fault: zero-offset, mis-calibration, parallax done the same way each time
- Not reduced by averaging — fix the instrument or method
How this is tested: Paper 1B almost always has a short 'suggest an improvement' or 'state the controlled variable' part worth 1–2 marks.
Typical asks: name the variable to keep constant · explain why a length was measured in several places · why taking one reading per setting is poor · suggest a better instrument or repeat scheme.
A student measures how far an air-gun pellet sinks into a block of modelling clay for different firing pressures, to test how depth d depends on pressure p. They take one depth reading at each pressure. (a) State one variable they must control. (b) Suggest why taking only one reading per pressure is a poor method.
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A systematic error shifts every reading by the same amount or in the same proportion. On a graph it shows up as an intercept where the law predicts none.
Accurate or precise?: Precise: readings close together (small uncertainty). Accurate: close to the accepted value.
Compare: if the accepted value lies inside value ± uncertainty, the result is consistent with it (accurate). If it lies outside, the method has a systematic error or a flawed assumption.
Assumptions and limitations: Every method rests on assumptions: friction or air resistance negligible, a small angle, a load shared evenly, no heat lost. Say which assumption a step needs and how the set-up makes it true (a long thread keeps the angle small).
Realistic improvements
- A wider range of the independent variable, and more values in it
- Evenly spaced readings (choose the intervals, not the clock)
- Repeats to reduce random error; a calibrated or zeroed instrument for systematic error
- A sensor or light gate instead of hand timing
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A separate skill — checking units: Dimensional analysis means balancing the fundamental SI units on both sides of an equation. The four you need are kg (mass), m (length), s (time) and A (current).
Use it two ways
- Find an unknown power in a relationship.
- State the units of a constant read off a gradient.
The one rule: Whatever units are on the left must equal the units on the right.
Match the power of each base unit (the kg's, the m's, the s's) separately — that gives you one equation per base unit.
| Quantity | Symbol | Fundamental SI units |
|---|---|---|
| force | F | kg m s⁻² |
| energy / work | E | kg m² s⁻² |
| pressure | p | kg m⁻¹ s⁻² |
| speed | v | m s⁻¹ |
| charge | q | A s |
A Paper-1B graph: depth d against root-pressure is a straight line through the origin, so d = k·sqrt(p). The gradient is the constant k — and we can work out its units.
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Here is the headline skill: balancing units to find unknown exponents.
The depth d (in metres) that a pellet sinks is modelled as d = k·pˣ, where p is the pressure (units kg m⁻¹ s⁻²) and k is a constant with SI units m¹·⁵ kg⁻⁰·⁵ s. Use dimensional analysis to find the exponent x.
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.
How this is tested: A common Paper-1B pattern: you plot data, draw a best-fit line, read a gradient, and then state the units of the constant that gradient represents — pure dimensional analysis.
Classic trap: Giving the gradient a number but no units, or guessing the units instead of dividing the y-axis units by the x-axis units.
Units of a gradient: A gradient is rise ÷ run, so its units are the y-axis units ÷ the x-axis units.
Write both axis units, divide, simplify — that is the constant's unit.
Extension x (cm) against applied force F (N): a straight line through the origin. The gradient is a constant; the steeper and shallower lines through the error bars show where its uncertainty comes from.
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A spring's extension x (in metres) is plotted against the applied force F (in newtons). The points lie on a straight line through the origin, so x = k·F. (a) State the SI units of the gradient constant k. (b) The student measured each extension only once — suggest one improvement to make the gradient more reliable.
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.