What maths skills do you need for IB Physics?

IB Physics requires fluency in: significant figures and rounding; standard form and powers of ten; unit conversions (eV to J, nm to m, °C to K, and others); algebra and rearranging equations; trigonometry and vector resolution; reading gradients and areas from graphs; uncertainty calculations (absolute, percentage, and how uncertainties combine); logarithms for linearising exponential data; and proportionality reasoning for sketch graph questions. These skills are tested across all three papers, but are most heavily examined in Paper 1B.

Do you need to be good at maths to pass IB Physics?

You do not need to be exceptional at maths, but you do need to be reliable with a specific set of mathematical skills. The maths in IB Physics is not advanced by the standards of HL Maths, but it is applied under time pressure to unfamiliar physical contexts. Students who lose marks to maths errors rather than physics misunderstandings are almost always making mistakes with significant figures, unit conversions, or uncertainty calculations. These are learnable and worth drilling deliberately.

How do you calculate uncertainty in IB Physics?

Absolute uncertainty is the ± value on a measurement, typically half the resolution of the instrument. Percentage uncertainty is (absolute uncertainty divided by the measured value) multiplied by 100. When combining uncertainties: add absolute uncertainties for addition and subtraction; add percentage uncertainties for multiplication and division; multiply the percentage uncertainty by the power when raising to a power. For example, if T has a 2% uncertainty, T² has a 4% uncertainty. The uncertainty in a gradient is found by drawing the steepest and shallowest plausible lines through data points and taking half the difference between their gradients.

How are logarithms used in IB Physics?

The IB Physics syllabus explicitly requires carrying out calculations involving logarithmic and exponential functions and constructing graphs using logarithmic scales. In practice the main application is linearising exponential relationships: radioactive decay follows N = N₀e^(-λt), and taking the natural log of both sides gives ln(N) = ln(N₀) - λt, a straight line with gradient -λ. A common Paper 2 question asks you to plot ln(N) against t, find the gradient, and extract the decay constant λ. The same approach applies wherever an exponential relationship appears in the course.

What is the small angle approximation in IB Physics?

The small angle approximation states that for small angles measured in radians, sin θ ≈ tan θ ≈ θ. This simplification is used in IB Physics in simple harmonic motion (to show that a pendulum undergoes SHM), in single slit and double slit diffraction (to derive fringe spacing equations), and in some optics questions. The approximation is valid when θ is less than about 10 degrees (0.17 radians). IB Physics exam questions that use it will typically state that the angle is small.

Maths Skills for IB Physics: Everything You Need to Know

IB Physics is not just a physics course. It is also a maths course, and the maths skills it tests are not always the ones students expect.

Some of them are things you probably learned in GCSE or middle school and have not thought about since. Others are more nuanced, and the way the IB applies them in exam questions is specific enough that getting them wrong costs marks even when your physics is correct.

This post covers every maths skill you need for IB Physics, what the exam actually asks you to do with each one, and where students most often drop marks.

One thing worth saying upfront: there is no calculus in IB Physics, at SL or HL. There are parts of the course where calculus fits naturally (simple harmonic motion, equations of motion) but the syllabus does not require it and the exams do not test it. If that has been a worry, you can put it aside.

Your physics can be perfect and your maths can still lose you marks. These skills are worth an hour of your time.

Significant figures

This comes up in almost every calculation in every paper.

The rule for IB Physics is straightforward: your answer should be given to the same number of significant figures as the least precise value in the question. If the question gives you data to 3 significant figures, your answer should be to 3 significant figures.

Where students lose marks:

Rounding too early in a multi-step calculation. Keep at least one extra significant figure in intermediate steps, and only round at the final answer.
Giving too many significant figures on a “show that” question. If the question asks you to show that a value is approximately 9.8, writing 9.823 without rounding is technically incorrect.
Forgetting that trailing zeros after a decimal point are significant. 4.50 has three significant figures. 4.5 has two.

Standard form and powers of ten

You need to be completely fluent with this. IB Physics deals with quantities ranging from the radius of a proton (~10⁻¹⁵ m) to the distance to a galaxy (~10²⁵ m). Clumsy handling of powers of ten is one of the most common sources of arithmetic errors.

Specific things to practise:

Multiplying and dividing numbers in standard form without a calculator (Paper 1A is non-calculator).
Converting between units that involve powers of ten: nm to m, MeV to J, mA to A.
Estimating orders of magnitude for Paper 1B unfamiliar context questions.

Units and unit conversions

Every numerical answer in IB Physics requires correct units. Missing or incorrect units costs marks even when the number is right.

The conversions that appear most frequently in past papers:

Energy: eV to J (multiply by 1.6 × 10⁻¹⁹)
Wavelength: nm to m (multiply by 10⁻⁹)
Temperature: °C to K (add 273)
Pressure: kPa to Pa (multiply by 10³)
Mass: u to kg (1 u = 1.66 × 10⁻²⁷ kg)
Angular quantities: rpm to rad s⁻¹ (for HL circular motion and rotational mechanics)

A useful habit: write the units of every quantity at every step of a calculation. If the units do not cancel or combine to give what you expect, your method is wrong before you have even found the answer.

Algebra and rearranging equations

The data booklet gives you most equations in one form. The exam will regularly ask you to use a different form. You need to be able to rearrange fluently.

Common rearrangements that catch students out:

Rearranging equations involving squares and square roots: from E_k = ½mv² to v = √(2E_k/m)
Rearranging equations involving reciprocals: from 1/f = 1/u + 1/v to find v
Rearranging simultaneous equations, particularly in Topic D fields questions

Geometry and trigonometry

You need to know:

sin, cos, tan and when to use each
The small angle approximation: sin θ ≈ tan θ ≈ θ (in radians) for small angles. This appears in SHM, optics, and diffraction questions.
Pythagoras for vector components and resultant magnitudes
Area of a circle (πr²), area of a sphere (4πr²), volume of a sphere (4/3 πr³). These appear in radiation, gravitational fields, and nuclear physics questions. They are in the data booklet.

Vectors

Vectors appear throughout IB Physics. You need to be able to:

Resolve a vector into perpendicular components: Fx = F cos θ, Fy = F sin θ
Add vectors by resolving into components and recombining
Draw vector diagrams accurately and to scale
Identify when a quantity is a vector and when it is a scalar (velocity vs speed, displacement vs distance, force vs energy)

The most common error is using the wrong angle in a trigonometry calculation: measuring θ from the wrong reference direction. Always draw a diagram and label the angle clearly before substituting.

Gradients and areas under graphs

Graph questions appear in Paper 1B and Paper 2, and they almost always ask either for the gradient or the area under the curve.

Gradients you need to know:

Gradient of a displacement-time graph = velocity
Gradient of a velocity-time graph = acceleration
Gradient of a force-extension graph = spring constant
Gradient of a V-I graph = resistance (or 1/resistance depending on axes)
Gradient of a ln(N) vs t graph = -λ (decay constant)

Areas you need to know:

Area under a force-time graph = impulse (= change in momentum)
Area under a velocity-time graph = displacement
Area under a pressure-volume graph = work done

For estimating areas under curves, the trapezium method (or counting grid squares) is acceptable in IB Physics. State your method clearly.

Uncertainty and error analysis

This is the maths skill most closely tied to Paper 1B, and the one students are most likely to be underprepared for. For a full breakdown of what Paper 1B tests and how to prepare, read the IB Physics Paper 1B guide.

The rules you need:

Absolute uncertainty is the ± value associated with a measurement. It is typically half the resolution of the measuring instrument.

Percentage uncertainty = (absolute uncertainty / measured value) × 100%

Combining uncertainties:

Adding or subtracting quantities: add the absolute uncertainties
Multiplying or dividing quantities: add the percentage uncertainties
Raising to a power: multiply the percentage uncertainty by the power

For example, if T has a 2% uncertainty and you calculate T², the uncertainty in T² is 4%.

Uncertainty in a gradient: draw the steepest and shallowest plausible lines through the data points (not just the best-fit line). The uncertainty in the gradient is half the difference between these two gradients.

Logarithms

The IB Physics syllabus explicitly requires you to carry out calculations involving logarithmic and exponential functions, and to construct and interpret graphs using logarithmic scales.

In practice this means one main skill: linearising exponential relationships. Radioactive decay follows N = N₀e^(-λt). Taking the natural log of both sides gives ln(N) = ln(N₀) - λt, which is a straight line with gradient -λ. This is a common Paper 2 question: plot ln(N) vs t, find the gradient, and extract λ. You need to be able to do this and explain why plotting ln(N) against t is more useful than plotting N against t.

The same technique applies anywhere an exponential relationship appears. Recognising when to take logs, doing so correctly, and interpreting the resulting straight line are the core skills.

The log rules you need:

log(ab) = log(a) + log(b)
log(a/b) = log(a) − log(b)
log(aⁿ) = n log(a)
ln(eˣ) = x

Proportionality and inverse proportionality

Many IB Physics questions ask you to predict what happens to one quantity when another changes, without doing a full calculation.

You need to be able to work with:

Direct proportion: if F = ma and m doubles, F doubles (for constant a)
Inverse proportion: if F = GMm/r² and r doubles, F decreases by a factor of 4
Square root relationships: if E_k = ½mv², doubling E_k increases v by a factor of √2

Sketch graph questions in Paper 2 frequently test this. Drawing the correct shape of curve (linear, 1/x, √x, x²) and labelling axes with the correct quantities is a skill in itself.

What to do with this list

Work through each skill category and honestly assess which ones feel uncertain. The uncertainty and logarithms sections are the ones most students need to spend time on. The significant figures and unit conversion sections are the ones most students underestimate.

The GradePod Exam Pack includes a complete maths skills checklist, the Paper 1B question bank, and all the topic-by-topic practice you need to turn these skills into automatic habits before exam day.

Get the GradePod Exam Pack for £39 →

Sally Weatherly is a Fellow of the Institute of Physics, author of 4 IB Physics books (two hit #1 on Amazon), and has been teaching IB Physics since 2004. GradePod has helped 30,000+ students since 2020.