Paper 1B — Data Analysis

Enter your text Twenty marks. The same twenty at SL and at HL, sat in the same session as Paper 1A, and worth roughly 16% of your final grade at SL and 12% at HL. That is more than most single themes.

It is also the only part of the exam you cannot revise by learning content. You will be given an experiment you have never seen, and the physics in it is usually straightforward — the marks are for what you do with the data. Because the skills involved used to be a topic of their own and are now scattered through the course, most students never deliberately practise them at all. That is the whole opportunity here.here...

What the paper actually asks

The scenario changes every year; the question types barely do. Expect to be asked to:

  • calculate an absolute, fractional or percentage uncertainty
  • complete a table, or plot the remaining points on a graph
  • draw a best-fit line through plotted points with error bars
  • determine a gradient, with units
  • determine the uncertainty in that gradient
  • say what the intercept means physically, or what a non-zero intercept implies
  • state whether the data supports a proposed relationship
  • suggest an improvement to the experiment

Every one of those is a technique, not a fact. They can all be practised.

Linearisation — the single most valuable skill

The IB almost always wants a straight line, because a gradient and an intercept are unambiguous to extract and to mark. So the recurring question is: what should be plotted to produce a straight line?

The method is always the same. Rearrange the proposed relationship until it has the shape y = mx + c, then read off what belongs on each axis and what the gradient represents.

Error bars and the best-fit line

An error bar extends one absolute uncertainty either side of the point. If the uncertainty is too small to draw at the scale you are using, write that down rather than leaving the point bare — it is often worth a mark.

A best-fit line should pass through or close to the error bars, with roughly as many points above it as below. Two things it does not have to do: pass through the origin, or touch every point. And it is a line — never join the dots.

Uncertainty in the gradient — the max/min method

This is where the most marks are dropped, and it is entirely mechanical once you have done it three times.

  1. Draw the best-fit line and find its gradient, m.
  2. Draw the steepest line that still passes through the error bars — this gives mmax.
  3. Draw the shallowest such line — this gives mmin.
  4. Take half the difference.

Δm = (mmax − mmin) / 2
quote as: m ± Δm, with units

Two habits that protect these marks. Take your two points for the gradient from far apart on the line, never from the plotted data — the line is your best estimate, the points are not. And do not forget to halve the difference; leaving it as (mmax − mmin) is the single most common slip in this question.

The same construction gives the uncertainty in the intercept, if the question asks for it.

Reading the intercept

Two versions of this question come up repeatedly.

The intercept should be zero and is not. That is a systematic error, and the mark is for naming a plausible source of one: a zero error on the instrument, a background count that was never subtracted, friction that was ignored, the mass of the holder left out of the load.

The intercept has physical meaning. In v² = u² + 2as, plotting v² against s gives an intercept of u² — the square of the initial velocity. Say what it is, not just that it exists.

"Does the data support the relationship?"

Answer this with a structure rather than an impression. Four sentences will collect the marks:

  1. State what the linearised graph should look like if the relationship holds — a straight line, and whether it should pass through the origin.
  2. State what it actually looks like.
  3. Say whether a straight line can be drawn that passes through all the error bars.
  4. Conclude — and if it does not hold, offer a reason.

Point 3 is the one students skip, and it is usually where the mark is. The error bars are what turn "it looks roughly straight" into an actual argument.

Suggesting an improvement

Never leave this blank — it is one or two nearly free marks. What loses them is vagueness. "Be more careful" and "avoid human error" earn nothing.

Instead of Write
"use a better thermometer" "use a thermometer with a resolution of 0.1 °C"
"repeat the experiment" "repeat each reading three times and take a mean, to reduce random error"
"be more accurate" "use light gates rather than a stopwatch, to remove reaction-time error"
"control the variables" "keep the length constant at 1.00 m throughout"

The pattern is: name the instrument or the action, and name the error it removes.

How to spend the time

Paper 1A and 1B are sat together — 1 hour 30 minutes at SL, 2 hours at HL — with no break and no instruction about how to divide them. That is a trap, because Paper 1A is multiple choice and will absorb as much time as you let it.

Decide in advance how long you will give 1A, and stop when you reach it. Twenty marks of data analysis at roughly a minute and a half per mark needs about thirty minutes, and unlike the multiple choice, every one of those marks is available to a student who has practised the technique. Graph work is slow but it is reliable — it is the last place you want to be rushing.

You are allowed a calculator and the data booklet in this paper. Know where the equations you need actually sit in the booklet before exam day; hunting for one costs more time than most people expect.

Where marks are actually lost

  • A gradient quoted with no units, or with the units of the raw quantity rather than the plotted one.
  • Calculating the gradient from two data points instead of two points on the line.
  • Forgetting to halve (mmax − mmin).
  • Joining the dots instead of drawing a best-fit line.
  • Forcing the line through the origin when the data does not support it.
  • Answering "does the data support it" without referring to the error bars.
  • Vague improvements that name neither an instrument nor an error.
  • Leaving the last question blank because time ran out in Paper 1A.

Practice

Reading through this can make it feel clear; working through the questions is what tells you whether it really is.

The skills this paper is built on

Uncertainties and error analysis ➡️  

Vectors: components and resolving ➡️

Teaching IB Physics one to one is what I do full time, and I take a small number of online students. → See how tutoring works