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Extended · Practice questions · Scalars and vectors

Number, or number plus direction.

Six original Cambridge-style Extended questions on the definitions, classifying quantities, the distance-versus-displacement trap, and why a vector's sign carries real meaning.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
The test to apply

Does it need a direction?

01
[2 marks]

Define a scalar quantity and a vector quantity.

  • A scalar has magnitude (size) only. ✓
  • A vector has both magnitude and direction. ✓
02
[2 marks]

Give one example of a scalar quantity and one example of a vector quantity (other than speed or velocity).

  • Scalar: mass (or distance, time, energy, temperature). ✓
  • Vector: force (or displacement, acceleration, weight, momentum). ✓
03
[3 marks]

State whether each of the following is a scalar or a vector: temperature, acceleration, time, force, distance, momentum.

  • Scalars: temperature, time, distance. ✓
  • Vectors: acceleration, force, momentum. ✓
04
Analysis
[3 marks]

A runner completes exactly one lap of a 400 m circular track, finishing at the same point where they started.

(a)State the distance travelled. (b)State the magnitude of the displacement, and explain your answer.
  • (a) Distance = 400 m (the total path length). ✓
  • (b) Displacement = 0 m. ✓
  • The finish point is the same as the start, so there is no overall change in position. ✓
05
Analysis
[2 marks]

Explain why weight is treated as a vector but mass is treated as a scalar.

  • Weight is a force and acts in a definite direction (downward, toward the Earth), so it has direction as well as size, making it a vector. ✓
  • Mass is just a quantity of matter with no direction, so it is a scalar. ✓
06
Analysis
[2 marks]

A ball moves to the right at 6 m/s, hits a wall, and rebounds to the left at 6 m/s. Explain why its velocity has changed even though its speed has not.

  • Speed is a scalar (size only), and the size is 6 m/s both before and after, so the speed is unchanged. ✓
  • Velocity is a vector; the direction has reversed (for example from +6 m/s to −6 m/s), so the velocity has changed. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.