IGCSE 0625 / Section 1.1 / Extended
Supplement (Extended) content

Some quantities point somewhere.

A mass of 2 kg is just a number with a unit. A force of 2 N pushing east is something more: it has a direction, and pointing it the other way changes the physics entirely. That difference splits every physical quantity into two families.

The key idea

A scalar has magnitude (size) only. A vector has both magnitude and direction. Speed, distance, mass, time and energy are scalars; velocity, displacement, acceleration, force, weight and momentum are vectors.

Section 01

Turn the arrow, keep the number.

A vector is drawn as an arrow: its length shows the magnitude and the way it points shows the direction. Watch the orbit below. The speed (a scalar) never changes, but because the direction is constantly shifting, the velocity (a vector) is constantly changing.

Stage 1 · Learn

Check the idea the sim just showed

Four quick checks on the definitions and on what the orbit demonstrates. Each correct answer earns XP and lights this skill on your star map.

Quick check+10 XP

As the object moves around the circle at constant speed, its velocity...

Quick check+10 XP

A scalar quantity has...

Quick check+10 XP

Which of these is a vector quantity?

Quick check+10 XP

The orbit keeps a fixed speed but a changing velocity because...

Section 02

Which is which.

 Scalars (magnitude only)Vectors (magnitude and direction)
Examplesdistance, speed, time, mass, energy, temperaturedisplacement, velocity, acceleration, force, weight, momentum, gravitational field strength

Notice the pairs that are easy to confuse: distance (scalar) versus displacement (vector), and speed (scalar) versus velocity (vector). The vector version of each carries a direction; the scalar version does not.

Examiner trap

Because a vector has direction, the sign matters. A velocity of +5 m/s and one of −5 m/s have the same speed but opposite directions, and treating them as the same value is exactly the error that loses marks in momentum and force questions. Always decide which direction is positive before you start.

Worked example

Classify each of the following as a scalar or a vector: (i) the mass of a trolley, (ii) the velocity of a car, (iii) the distance walked, (iv) the weight of a book.

Step 1 · Ask: does it need a direction?A quantity is a vector only if a direction is needed to describe it fully.
Step 2 · Classify(i) mass needs no direction, so it is a scalar. (ii) velocity needs a direction, so it is a vector. (iii) distance needs no direction, so it is a scalar. (iv) weight is a force pulling downward, so it is a vector.
Step 3 · AnswerScalars: mass, distance. Vectors: velocity, weight.
Stage 2 · Exam

Exam-style questions

Unlocks once the four checks above are done. Worth more XP, written in the style of Paper 2.

Finish the four checks above to unlock the exam questions
Exam style+20 XP

Which list contains only vector quantities?

Exam style+20 XP

A car moves at +8 m/s, then travels at the same speed the opposite way, written as −8 m/s. These two values describe...

Exam style+20 XP

Distance is a scalar. Its vector counterpart, which also carries a direction, is...

Skill unlocked

Scalars and vectors, mastered.

This skill is now lit gold on your star map. Keep the chain going.

-Rank -Level -Score -Topics
Go deeper · practice
Six original Cambridge-style questions
The definitions, classifying quantities, the distance-versus-displacement pair, and why a vector's sign matters. Attempt each, then reveal the worked solution.
Stage 3 · master the unit
Motion, forces and energy challenge
Mixed questions across the whole unit, each one worth XP. Start this only when you feel confident across every topic in the unit, not just scalars and vectors.
Start the unit challenge →