What does Mathematics cover in IB Physics?

This topic covers the fundamental mathematical skills for solving physics problems and interpreting data. Perform basic arithmetic, algebraic manipulations, and trigonometric calculations. Use scientific notation, calculate mean, range, and rates of change.

Is Mathematics SL or HL?

Both. SL and HL students study Mathematics to the same depth.

How does FourtyFive help me practise Mathematics?

FourtyFive has 6 Mathematics questions. Every answer you write is marked mark by mark, IB-style, and you see where each mark was won or lost. Every part has a hint, the AI tutor helps you through the step you are stuck on, and your Study Profile picks what to practise next.

Is FourtyFive free for Mathematics practice?

Yes. A free account gives you 50 marked answers a month, and you do not need a card to sign up.

Can I handwrite Mathematics answers on an iPad?

Yes. In the FourtyFive iPad app you write your working by hand with Apple Pencil, the way you would on paper, and it is marked the same way.

Topic T.3 · SL and HL

Mathematics: notes and practice questions

Q: How do I revise Mathematics for IB Physics?

Start from the core idea: this topic covers the fundamental mathematical skills for solving physics problems and interpreting data. In the exam: paper 1B is built on this subtopic, and it leaks into Paper 2 constantly. Real May 2025 evidence: Uncertainty propagation. Then practise exam-style questions, easiest first, writing out every step of your working before you check it.

4 min read Jump to 6 practice questions

Summary

This topic covers the fundamental mathematical skills for solving physics problems and interpreting data.
Perform basic arithmetic, algebraic manipulations, and trigonometric calculations.
Use scientific notation, calculate mean, range, and rates of change.
Understand direct and inverse proportionality.
Identify scalar and vector quantities, and perform vector addition, subtraction, and resolution.
Calculate and interpret percentage change and percentage uncertainty.
Use radian measurement and convert between degrees and radians.

How it is examined

Paper 1B is built on this subtopic, and it leaks into Paper 2 constantly. Real May 2025 evidence:

Uncertainty propagation. Paper 1B TZ1 question 1(b)(i), 2 marks: calculate a density and its absolute uncertainty from (10.6 ± 0.2) cm³ and (10.82 ± 0.01) g. The mark scheme allowed the mass uncertainty to be neglected provided the candidate said so, and instructed "DO NOT penalize for SF". - Precision and unit conversion. Question 1(b)(ii), 1 mark, was purely "State your answers in kg m⁻³ and with correct precision", answer 1020 ± 20. Here precision is the mark, and the notes required 3 significant figures with matching precision in the uncertainty. - Gradient from a best-fit line. Question 2(c)(i), 2 marks, required the candidate to use two points spanning more than half the line, with the note "Look for Δx ≥ 0.3". - Maximum-gradient line. Question 2(c)(ii), 1 mark, "draw max from lower end of lower error bar to upper end of upper error bar". - Uncertainty in a gradient. Question 2(c)(iii), 2 marks, accepted a range: "Look for working leading to 0.1 ≤ Δn ≤ 0.2". - Fundamental units. Paper 2 TZ1 question 1(b), both levels, ended with "State the fundamental SI unit for your answer", answer kg m⁻¹. Note the two rules pulling in opposite directions. Instruction 13 in every mark scheme says do not penalize errors in units or significant figures unless the Notes say otherwise. But the Notes say otherwise often, and in Paper 1B they say it about precision specifically. The default is lenient; the exceptions are where the skill is the point of the question.

Given in the booklet

The data booklet carries the SI prefixes, the fundamental and derived units, the unit conversions and the constants. It does not carry the uncertainty propagation rules, so the student must know that fractional uncertainties add for a product or quotient, that absolute uncertainties add for a sum or difference, and that a power multiplies the fractional uncertainty.

Key ideas

Use basic arithmetic and algebraic calculations to solve problems.
Calculate areas and volumes for simple shapes.
Carry out calculations involving decimals, fractions, percentages, ratios, reciprocals, exponents and trigonometric ratios.
Carry out calculations involving logarithmic and exponential functions.

Not assessed

The formal process of dimensional analysis will not be assessed, although checking an expression using units is expected.

Practice questions

6 questions · 1 easy · 3 medium · 2 hard

Showing 6 of 6

Question 1

EasyPaper 1A · calculator1 mark

A student measures the mass of a metal block as $(250 \pm 5)$ g and its volume as $(50 \pm 2)$ cm $^3$ . What is the fractional uncertainty in the calculated density of the block?

A. 0.02

B. 0.04

C. 0.06

D. 0.08

Question 2

MediumPaper 2 · calculator2 marks

(a) A large wind turbine generates electrical power at a rate of $1.5 \text{ MW}$ when its blades are rotating at $120 \text{ revolutions per minute (rpm)}$ . Calculate the magnitude of the torque exerted by the wind on the turbine shaft.

Question 3

HardPaper 1A · calculator1 mark

The characteristic impedance of free space, $Z_0$ , is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. It is given by the expression $Z_0 = \sqrt{\frac{\mu_0}{\epsilon_0}}$ . What are the fundamental SI units of $Z_0$ ?

A. $\text{kg m}^2 \text{A}^{-2} \text{s}^{-3}$

B. $\text{kg}^{-1} \text{m}^{-2} \text{A}^{2} \text{s}^{3}$

C. $\text{kg}^2 \text{m}^4 \text{A}^{-4} \text{s}^{-6}$

D. $\text{m}^{-2} \text{s}^2$

Question 4

MediumPaper 2 · calculator7 marks

(a)

A student performs an experiment to determine the resistivity of a metal wire. The resistance $R$ , length $L$ , and diameter $d$ of the wire are measured.

(a) The diameter is measured with a micrometer screw gauge. State one experimental precaution that should be taken to ensure this measurement is accurate.

[1]

(b)

(b) The following data are collected:

Resistance $R = (5.2 \pm 0.1) \, \Omega$

Length $L = (1.50 \pm 0.01) \, \text{m}$

Diameter $d = (0.45 \pm 0.02) \, \text{mm}$

Calculate the resistivity of the wire and its absolute uncertainty.

[3]

(c)

[1]

(d)

(d) The accepted value for the resistivity of nichrome at the experimental temperature is $1.10 \times 10^{-6} \, \Omega \text{ m}$ . Deduce, using your answer from (c), whether the wire is likely to be made of nichrome.

[2]

Question 5

HardPaper 1A · calculator1 mark

In a photoelectric effect experiment, a graph of stopping potential $V_s$ is plotted against the wavelength $\lambda$ of the incident light for a particular metal surface. What is the magnitude of the gradient of the graph at wavelength $\lambda$ ?

A. $\frac{h}{e}$

B. $\frac{hc}{e}$

C. $\frac{hc}{e\lambda^2}$

D. $\frac{h}{e\lambda}$

Question 6

MediumPaper 2 · calculator13 marks

(a)(i)

A small spherical steel ball is released from rest at the surface of a tall column of glycerin.

The following data are available:

radius of the steel ball = $2.0\text{ mm}$

density of steel = $7850\text{ kg m}^{-3}$

density of glycerin = $1260\text{ kg m}^{-3}$

viscosity of glycerin = $1.4\text{ Pa s}$

acceleration due to gravity $g = 9.81\text{ m s}^{-2}$

(a) (i) Calculate the volume of the steel ball.

[2]

(a)(ii)

(a) (ii) Calculate the initial acceleration of the steel ball.

[4]

(b)

(b) Describe how the acceleration of the steel ball changes as it falls through the glycerin.

[2]

(c)(i)

[2]

(c)(ii)

[3]

Every Mathematics question, marked for you

Every answer is marked mark by mark, IB-style, and the AI tutor helps when you are stuck.

Where marks are lost

Stopping one step short of the conclusion. Two numbers and no sentence is two marks out of three.
Answering a procedure question with a platitude.
Losing precision in Paper 1B. Uniquely to this paper, quoting the right number badly loses marks.

Mathematics: notes and practice questions

How it is examined

Practice questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Every Mathematics question, marked for you

Where marks are lost

Practise this topic as a session

Questions,
answered.

Start with the IB question
bank built for you.

How it is examined

Practice questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Every Mathematics question, marked for you

Where marks are lost

Questions,answered.

Start with the IB questionbank built for you.

Questions,
answered.

Start with the IB question
bank built for you.