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.
IB-style question — judging a method
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.
Solution
- (a) Control variable. Anything else that could change the depth must be held constant — e.g. the same block of clay (same density/hardness), or the same pellet mass. Name one and say it is kept constant:
- (b) Why one reading is poor. A single reading carries the full random uncertainty — you cannot tell a good reading from an anomaly, and you cannot average out the scatter.
- So you would repeat each pressure several times and take the mean, discarding any anomaly first.
Final answer
(a) keep the clay block (and pellet) the same; (b) one reading can't be checked or averaged — repeats let random scatter cancel and reveal anomalies.
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, - or 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 |
[Diagram: phys-best-fit] - Available in full study mode
Here is the headline skill: balancing units to find unknown exponents.
IB-style question — find the exponents from the units
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.
Solution
- Write the units of each side. Depth d has units of metres:
- The right side is the units of k times the units of pˣ:
- Collect the powers of each base unit. Match kg first (left side has none, power 0):
- Check it works for m (left side has power 1):
- And for s (left side has power 0):
Final answer
x = 0.5, i.e. d = k·√p — depth is proportional to the square root of pressure.
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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.
[Diagram: phys-best-fit] - Available in full study mode
IB-style question — (a) state the units of the gradient
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. State the SI units of the gradient constant k.
Solution
- The gradient is the y-axis quantity ÷ the x-axis quantity:
- Replace the newton with its fundamental units, N = kg m s⁻²:
- Cancel the metres and tidy up:
Final answer
k has units kg⁻¹ s² (equivalently m N⁻¹).
IB-style question — (b) why repeat each reading?
Same experiment. The student measured each extension only once. Suggest one improvement to make the gradient more reliable.
Solution
- A single reading carries the full random uncertainty and can't be checked against an anomaly.
- Repeat each force several times and take the mean extension (discarding any clear anomaly) — the random scatter then partly cancels, so each plotted point, and the gradient, is more reliable.
Final answer
Repeat each force and average the extension (after discarding anomalies) to reduce random uncertainty in each point and so in the gradient.