Read directed segments and column-vector components
Read an arrow in its stated direction · Interpret horizontal then vertical components · Distinguish a movement vector from a point location
Section Paper 4 · Historical Extended · calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Signed coordinates
- Horizontal and vertical movement
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Read an arrow in its stated direction
- Interpret horizontal then vertical components
- Distinguish a movement vector from a point location
An arrow specifies a movement
The directed segment →AB starts at A and ends at B. A column vector puts the horizontal component above the vertical component. Here [a; b] is compact text notation for that column, with a on top and b below. Positive components mean right and up; negative components mean left and down.
For →AB = [3; 2], move three units right and two up. A vector describes the movement, not where its arrow is drawn. Two arrows at different starting positions can represent the same vector if their movement agrees.
Point and vector notation
A point (x,y) specifies a position relative to coordinate axes. A vector column [a; b] specifies displacement. A zero column [0; 0] means no movement; there is no non-zero arrow direction to read. Extended lessons introduce vector letters, magnitude symbols and arithmetic separately.
Sources for this lesson
Pause and explain
What movement does [3; −2] represent?
Worked example
Read the column vector [−4; 3] and the direction of →AB.
Show the worked solution
- The top component gives four units left.
- The bottom component gives three up; the arrow runs from A to B.
Answer Four left, three up; start A, end B.
Try a topic test
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Describe [4; −1] in words.
Give me a hint
Read the top then lower component.
Compare my reasoning
- 4 means four right.
- −1 means one down.
Four right and one down.
Look for these in your work
- Read components in order
- Interpret both signs
Two arrows each move two left and five up, but start at different points. Write their common column vector and explain whether it is the same movement.
Give me a hint
Ignore the starting positions when comparing displacement.
Compare my reasoning
- The components are −2 horizontally and 5 vertically.
- Both arrows represent that same displacement.
Both represent [−2; 5], the same movement.
Look for these in your work
- Separate location from displacement
- Use one consistent component order
A student reads →AB as beginning at B, and [0; 0] as moving along the x-axis. Correct both interpretations.
Give me a hint
Use the arrow's ordered endpoints and the zero components.
Compare my reasoning
- →AB begins at A and ends at B.
- [0; 0] gives no movement and no non-zero direction.
Start A and end B; [0; 0] is no movement.
Look for these in your work
- Read the directed notation
- Handle the zero case
Common mistakes
- Read horizontal before vertical.
- An arrow's starting location is not its vector component.
What can you explain now?
What movement does [3; −2] represent?
Compare with the explanation
Three right and two down.
The top component is horizontal and the lower one is vertical.
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Make it stick
What movement does [3; −2] represent?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.