IB Physics: Vectors & Scalars — Complete FAQ

A scalar has magnitude only (mass, speed, energy); a vector has magnitude and direction (displacement, velocity, force). In the current IB Physics guide (first exams 2025), this sits in Topic A1 and is examined through Paper 1 multiple-choice, Paper 2 calculation questions, and vector diagrams in Paper 3 data-based questions.

A vector needs both size and direction to be fully described — force, displacement, momentum. A scalar only needs a number and a unit — distance, time, energy, temperature. Mixing them up is the single most common Paper 1 error I see: writing 'speed = 5 m/s north' treats a scalar as if it had direction.

You add vectors either graphically (tip-to-tail, then measure the resultant) or algebraically by resolving each vector into perpendicular components, adding the components separately, then recombining with Pythagoras and trigonometry. HL students are expected to do this fluently with three-dimensional problems too.

Split any vector into horizontal and vertical (or x and y) parts using $F_x=F\cos \theta$ and $F_y=F\sin \theta$, where $\theta$ is measured from the horizontal. This is essential for projectile motion, inclined-plane forces, and any question involving forces at an angle — which appears in nearly every mechanics exam series.

Vectors and scalars are formally introduced in Topic A1 (Space, Time and Motion) of the current IB Physics guide, with first exams in 2025 for both SL and HL. But the skill isn't confined to one topic — it resurfaces in forces (A2), fields (D-topics), and momentum questions throughout both years.

The core concept — magnitude versus direction — is identical at SL and HL. What changes is application: HL students handle vector problems in three dimensions, more complex circular motion and magnetic field questions, and denser Paper 2 calculations that stack several vector steps together.

No — the IB Physics data booklet and exam papers don't require formal i-j-k unit vector notation. You're expected to resolve vectors into components using angles and trigonometry, and to represent them with labelled arrows in diagrams, not abstract vector algebra notation.

The top three: forgetting direction when stating a vector answer, adding vector magnitudes directly instead of resolving into components first, and confusing displacement with distance (or velocity with speed) under exam pressure. All three cost easy marks that have nothing to do with difficult physics.

Start with the data booklet — identify every vector quantity listed, then practise resolving forces and velocities at different angles until the trig becomes automatic, not something you have to think through. Past paper Paper 1 questions are the fastest way to test whether you truly know vector from scalar under time pressure.

Projectile motion, relative velocity (boats/planes in currents or wind), resolving forces on inclined planes, resultant momentum in collisions, and magnetic force on a moving charge (HL) all rely directly on vector skills. If a question mentions direction, angle, or 'resultant', vectors are almost certainly involved.

Yes — vectors and scalars are a universal physics foundation, so the core concept your child learns in IB Physics matches what's taught in A-Level, AP Physics, or first-year university mechanics. The IB's emphasis on applying vectors to real experimental data (Paper 3) is where it differs most from exam-only systems.

Self-study resources — revision notes, topical worksheets, and mock papers — typically run from free past papers up to a modest annual subscription for a structured platform, far cheaper than private tutoring which can run into hundreds per month. For a foundational skill like vectors, targeted worksheets are usually all a student needs.