|v| = √(x² + y²): Problem Solving & Reasoning
Mathematics
Grade 6
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on calculating the magnitude of vectors using |v| = √(x² + y²). This includes procedural practice, reasoning, real-world applications, and challenging extension problems suitable for Grade 6 students.
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|v| = √(x² + y²): Problem Solving & Reasoning
Subject: MathematicsGrade: Grade 6
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Date:
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Untitled Worksheet
Grade Grade 6
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the magnitude |v| for a vector with components x=3 and y=4.
[2 marks]2.
Find the magnitude |v| when x = -6 and y = 8.
[2 marks]3.
A vector has components x = 5 and y = 12. What is |v|?
[2 marks]B
Targeted Practice
Answer all questions. Show your working clearly.
1.
Calculate the magnitude |v| for x=9 and y=12.
[2 marks]2.
A vector has x = -8 and y = -15. Find |v|.
[2 marks]3.
Determine |v| when x=0 and y=7.
[2 marks]4.
Calculate |v| when x=1 and y=1.
[2 marks]C
Real-world Applications
Answer all questions. Show your reasoning.
1.
A drone moves 6 units east and 8 units north. What is the straight-line distance from its starting point?
[3 marks]2.
A hiker walks 9 km south and then 12 km west. What is her straight-line distance from her starting point?
[3 marks]D
Challenge & Extension
Answer all questions. Use your reasoning skills.
1.
A vector has components x = 20 and y = 21. Calculate |v|. Is it closer to 29 or 30?
[3 marks]2.
If a vector's magnitude is 13 and y=5, find possible x-component(s).
[3 marks]E
Mixed Review
Answer all questions. Review your answers carefully.
1.
Calculate |v| for x=0 and y=0.
[1 mark]2.
A vector has components x=7 and y=24. What is |v|?
[2 marks]3.
If x=–9 and y=–12, find |v|.
[2 marks]F
Error Analysis
Review each mistake and correct it. Explain what was wrong.
1.
A student calculated |v| as 25 when x=7 and y=24. Identify and explain the mistake, then find the correct answer.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet