Vectors Revision Notes for IGCSE Maths
These comprehensive revision notes cover everything you need to know about vectors for the Cambridge IGCSE Mathematics 0580 examination. Written by Teacher Rig, each section includes key concepts, essential formulas, and practical exam tips to help you achieve your best grade.
Vector Basics
A vector has both magnitude (size) and direction. Vectors can be written as column vectors, as bold letters (a), or with arrows above (AB with arrow). Two vectors are equal if they have the same magnitude and direction. The negative of a vector has the same magnitude but opposite direction. Column vectors are written as (x, y) where x is the horizontal component and y is the vertical component.
Key Formulas
- |a| = sqrt(x squared + y squared)
- -a has opposite direction to a
Exam Tips
- Underline vector letters when handwriting (since you cannot write bold)
- The magnitude is always positive
- Parallel vectors are scalar multiples of each other
Vector Addition and Subtraction
Vectors are added by placing them end to end (triangle law) or by adding components. The resultant vector goes from the start of the first to the end of the last. Subtraction means adding the negative: a - b = a + (-b). With column vectors, add or subtract corresponding components.
Key Formulas
- (a, b) + (c, d) = (a+c, b+d)
- a - b = a + (-b)
Exam Tips
- When finding a path between two points, always go via a known route using vectors you know
- AB = -BA (reversing direction negates the vector)
- Draw diagrams to visualise the vector paths
Scalar Multiplication
Multiplying a vector by a scalar changes its magnitude but keeps (or reverses) its direction. If k > 0, the direction stays the same. If k < 0, the direction reverses. If k = 0, the result is the zero vector.
Key Formulas
- k(a, b) = (ka, kb)
- If b = ka for some scalar k, then a and b are parallel
Exam Tips
- A scalar multiple means the vectors are parallel
- Scale factor 2 means twice as long in the same direction
- Scale factor -1/2 means half the length in the opposite direction
Vector Proofs
Common proof tasks include showing that points are collinear (lie on a straight line) and showing that lines are parallel. For collinearity, show that AB = k times AC for some scalar k, and note that A is a common point. For parallelism, show that one vector is a scalar multiple of the other.
Exam Tips
- For collinearity: find two vectors from a common point, show one is a scalar multiple of the other, then state the conclusion clearly
- For parallelism: show PQ = k times RS for some scalar k
- Always state your conclusion in words for full marks
Revision Checklist
- I understand all key concepts in vectors
- I have memorised the essential vectors formulas
- I can apply these concepts to exam-style questions
- I have practised past paper questions on vectors
- I know the common mistakes to avoid in vectors questions
Frequently Asked Questions
What vectors topics are covered in IGCSE Maths?
The IGCSE 0580 syllabus covers vectors across both Core and Extended tiers. Key areas include vector basics. Key areas include vector addition and subtraction. Key areas include scalar multiplication.
How important is vectors in the IGCSE exam?
Vectors is a significant part of the IGCSE Mathematics exam, typically appearing in Paper 2 (non-calculator) and Paper 4 (calculator). Questions range from straightforward calculations to multi-step problems that combine vectors with other topics.
What are the most common mistakes in vectors?
Common mistakes include not showing full working, forgetting to state units, misreading the question, and rushing through calculations. For vectors specifically, make sure you understand the underlying concepts rather than just memorising procedures.
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