Exercise 1 — Cambridge IGCSE 0580 Mar 2025 Paper 42 Q21
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Cambridge IGCSE·Mathematics 0580·Extended
Further Vectors Vector Combinations
Key knowledge — Vectors
Formulas & equations
Magnitude of vector (a, b): |v| = √(a² + b²)Unit vector: v̂ = v ÷ |v|If M is the midpoint of AB: OM = ½(OA + OB)Column vector addition: (a,b) + (c,d) = (a+c, b+d)Scalar multiplication: k(a,b) = (ka, kb)
Key facts & rules
- Vectors have magnitude AND direction; scalars have magnitude only.
- AB = OB − OA (go from A to B via origin).
- Parallel vectors: one is a scalar multiple of the other.
- Collinear points: AB and AC are parallel (and share point A).
- To prove a quadrilateral is a parallelogram: show two pairs of opposite sides are equal vectors.
IGCSE Vectors — Further vectors (vector combinations) Practice Extended
7 Cambridge IGCSE 0580 questions on further vectors (vector combinations) at the Extended tier — each with its full mark scheme. For the Core tier on the same skill, click here.
How to approach further vectors (vector combinations) — open the study guide
Further vectors (vector combinations) on IGCSE 0580
Practice with past paper questions on further vectors (vector combinations) at the Extended tier.
Practice exercises
Exercise 2 — Cambridge IGCSE 0580 Jun 2024 Paper 22 Q24
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Exercise 3 — Cambridge IGCSE 0580 Jun 2024 Paper 23 Q26
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Exercise 4 — Cambridge IGCSE 0580 Jun 2025 Paper 21 Q21
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Exercise 5 — Cambridge IGCSE 0580 Jun 2025 Paper 22 Q23
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Exercise 6 — Cambridge IGCSE 0580 Jun 2025 Paper 43 Q26
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Exercise 7 — Cambridge IGCSE 0580 Nov 2024 Paper 42 Q6
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