AQA GCSE Combined Science (8464), Higher tier · Physics › Forces › Forces and their interactions
Practise Scalar and vector quantities. 13 exam-style questions on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Scalar quantities have size (magnitude) only; vector quantities have size and direction. You need to sort quantities into the two groups and show vectors as arrows. It is usually tested with short recall and tick-box questions, and it underpins the rest of the Forces topic.
Grade by grade
What you need to be able to do, from the first marks up to the top grade.
3
Define scalar and vector quantitiesA scalar has magnitude only; a vector has magnitude and an associated direction.
4
Sort common quantities into scalars and vectorsDistance, speed, mass, time, energy and temperature are scalars; displacement, velocity, acceleration, force and momentum are vectors.
5
Represent a vector with an arrowThe length of the arrow shows the magnitude and the way it points shows the direction.
6
Use a scale to draw or read vector arrowsWith a scale of 1 cm = 5 N, a 4.0 cm arrow represents a 20 N force.
7
Explain scalar–vector pairs such as speed and velocityTwo objects can have the same speed but different velocities if they move in different directions.
Notes
Scalars and vectors
A scalar quantity has magnitude (size) only.
A vector quantity has magnitude and an associated direction.
Scalars: distance, speed, mass, time, energy, temperature, power, density.
Vectors: displacement, velocity, acceleration, force (every force, including weight and friction) and momentum.
Pairs to know
Distance (scalar) and displacement (vector): displacement is the straight-line distance from start to finish, with a direction.
Speed (scalar) and velocity (vector): velocity is speed in a given direction.
Mass (scalar, in kg) and weight (vector, in N): weight is a force, so it has a direction, towards the centre of the Earth.
Drawing vectors as arrows
A vector quantity can be shown by an arrow.
The length of the arrow shows the magnitude, drawn to a scale.
The direction of the arrow shows the direction of the vector quantity.
Two arrows of the same length pointing opposite ways show vectors of the same size in opposite directions.
For motion along a line, you can show direction with a sign: choose one direction as positive, so the opposite direction is negative (e.g. +8 m/s and −8 m/s). grade 6+
Cheatsheet
Scalar = magnitude only
Vector = magnitude and direction
Scalars: distance, speed, mass, time, energy, temperature
Vector arrow: length = magnitude, arrow direction = direction of the quantity
Mass is a scalar (kg); weight is a force, so it is a vector (N)
How to answer each type of question
Tick-box: identify scalar or vector quantities
1 to 2 marks3
Ask: does this quantity need a direction to describe it fully?
If yes, it is a vector; if no, it is a scalar.
Tick exactly the number of boxes asked for.
Example. Which two of these are vector quantities? energy / force / mass / speed / velocity
Show the model answer
force (1) velocity (1)
Describe the difference between a scalar and a vector
2 marks4
Write one sentence about the scalar: magnitude only.
Write one sentence about the vector: magnitude and direction.
Example. Speed is a scalar quantity. Velocity is a vector quantity. Describe the difference between speed and velocity.
Show the model answer
Speed has magnitude (size) only (1). Velocity has magnitude and direction: it is speed in a given direction (1).
Read or draw a vector arrow to scale
1 to 2 marks5
Use the scale to convert between length and magnitude.
Length = magnitude ÷ value of 1 cm; magnitude = length × value of 1 cm.
Example. A force diagram uses a scale of 1 cm = 10 N. (a) What length of arrow represents a force of 45 N? (b) An arrow on the diagram is 2.5 cm long. What force does it represent?
Show the model answer
(a) 45 ÷ 10 = 4.5 cm (1) (b) 2.5 × 10 = 25 N (1)
Explain using the idea of a vector
2 marks6
Say that the quantity is a vector, so direction matters.
Apply this to the situation: same size but different direction means a different vector.
Example. Two cars pass each other on a straight road. Each car is travelling at 20 m/s. A student says the cars have the same velocity. Explain why the student is wrong.
Show the model answer
Velocity is a vector, so it includes direction (1). The cars have the same speed but move in opposite directions, so their velocities are different (e.g. +20 m/s and −20 m/s) (1).
Shortcuts and memory tricks
Direction test: if it makes sense to add 'to the left' or 'northwards', the quantity is a vector.
Learn the pairs scalar-first: distance/displacement, speed/velocity, mass/weight. The second word in each pair is the vector.
Every force is a vector, so weight, friction, tension, drag and upthrust are all vectors.
Energy is never a vector: it has no direction, even though it is transferred from place to place.
Where marks are lost
Calling mass a vector or weight a scalar. Weight is a force, so it is a vector.
Writing 'a vector has direction' without saying it also has magnitude. You need both for the mark.
Thinking acceleration is a scalar. Acceleration is a change in velocity, so it has a direction.
Thinking energy is a vector because it is 'transferred'. Energy is a scalar.
Drawing force arrows that are not to a consistent scale, so a bigger force has a shorter arrow.
Exam technique
For 'describe the difference', write one clear sentence about each type of quantity.
In tick-box questions, ticking more boxes than asked for usually scores zero for that part.
Whenever you compare speed with velocity, or distance with displacement, mention direction.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
Sort the quantities in the list into scalar quantities and vector quantities.