Vectors
Cambridge IGCSE Mathematics (0580) · Unit 7: Transformations and vectors · 10 flashcards
Vectors is topic 7.2 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 7 — Transformations and vectors , alongside Transformations. In one line: A vector is a quantity with both magnitude (size) and direction. A scalar, like temperature or mass, only has magnitude.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator. It is a Supplement (Extended-tier) topic, so it appears only on the Extended-tier papers.
The deck below contains 10 flashcards — 3 definitions and 3 key concepts — covering the precise wording mark schemes reward. Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
The term 'vector' and differentiate it from a scalar
A vector is a quantity with both magnitude (size) and direction. A scalar, like temperature or mass, only has magnitude.
Questions this Vectors deck will help you answer
- › Vectors p and q are parallel. If p = (2, -3), give a possible vector for q and explain your reasoning.
- › Describe how to perform vector subtraction, a - b, geometrically.
- › Explain what a 'negative vector' is, using vector a = (4,1) as an example.
Represent the displacement from point A(1, 2) to point B(4, 6) as a column vector.
A column vector represents displacement. Subtract the coordinates of A from B: (4-1, 6-2) = (3, 4). Therefore, the column vector is (3, 4).
Define the term 'vector' and differentiate it from a scalar.
A vector is a quantity with both magnitude (size) and direction. A scalar, like temperature or mass, only has magnitude.
Calculate the magnitude of the vector v = (5, -12).
The magnitude of a vector (x, y) is √(x² + y²). For v = (5, -12), the magnitude is √(5² + (-12)²) = √(25 + 144) = √169 = 13.
If vector a = (2, -1) and vector b = (-3, 4), find the resultant vector a + b.
To add vectors, add their corresponding components. a + b = (2 + (-3), -1 + 4) = (-1, 3).
Explain the concept of a 'position vector'.
A position vector describes the location of a point relative to the origin (0,0).
Vectors p and q are parallel. If p = (2, -3), give a possible vector for q and explain your reasoning.
Parallel vectors are scalar multiples of each other. q could be (4, -6) because q = 2 * p. Both vectors have the same direction.
Describe how to perform vector subtraction, a - b, geometrically.
Geometrically, a - b is equivalent to a + (-b). You reverse the direction of vector b and then add it to vector a using the parallelogram or triangle rule.
Vector 'r' is the scalar multiple 3 * (1, -2). Determine vector r.
To find the scalar multiple, multiply each component of the vector by the scalar. r = (3*1, 3*-2) = (3, -6).
What does it mean for two vectors to be 'equal'?
Two vectors are equal if and only if they have the same magnitude and the same direction (or, equivalently, the same components).
Explain what a 'negative vector' is, using vector a = (4,1) as an example.
A negative vector has the same magnitude but the opposite direction. The negative vector of a = (4, 1) is -a = (-4, -1).
Key Questions: Vectors
Define the term 'vector' and differentiate it from a scalar.
A vector is a quantity with both magnitude (size) and direction. A scalar, like temperature or mass, only has magnitude.
Explain the concept of a 'position vector'.
A position vector describes the location of a point relative to the origin (0,0).
What does it mean for two vectors to be 'equal'?
Two vectors are equal if and only if they have the same magnitude and the same direction (or, equivalently, the same components).
Tips to avoid common mistakes in Vectors
- ● Label every intermediate vector you derive (e.g., write 'AK = ...' on its own line before substituting values for a and b) so the marker can follow your chain of reasoning step by step.
- ● Practice vector problems and work neatly; careful organisation will help you avoid simple sign errors.
- ● When determining a vector like AB, make sure you're calculating the difference between point B and point A (B - A).
- ● Always draw your route; then each vector will be clear on your diagram.
More topics in Unit 7 — Transformations and vectors
Vectors sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Vectors deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
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