|v| = √(x² + y²): Real-world Applications
Mathematics
Year 9
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the magnitude of vectors using |v| = √(x² + y²) through real-world contexts, practice, and extension questions.
Worksheet Preview
Full preview • 15 questions
|v| = √(x² + y²): Real-world Applications
Subject: MathematicsGrade: Year 9
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz
Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the magnitude of the vector with components x = 3 and y = 4.
[2 marks]2.
A vector has components x = -6 and y = 8. Find its magnitude |v|.
[2 marks]3.
Calculate |v| when x = 0 and y = -9.
[2 marks]4.
Find the magnitude of a vector with x = 12 and y = 5.
[2 marks]B
Problem Solving & Reasoning
Answer these multi-step questions showing your reasoning.
1.
A drone flies 6 km east and then 8 km north. Calculate its straight-line distance from the starting point using the magnitude formula.
[3 marks]2.
A boat travels 9 km west and then 12 km south. Find the direct distance from the starting point.
[3 marks]3.
A hiker moves 7 km northwest (assume x and y components are equal in magnitude). If the components are x = y, find the magnitude of her displacement.
[3 marks]C
Real-world Applications
Solve these contextual problems related to vectors.
1.
A car moves 50 km east and then 30 km north. Calculate the magnitude of its displacement from the starting point.
[3 marks]2.
A delivery person walks 8 km south and then 6 km east. Determine the straight-line distance back to the start.
[3 marks]D
Challenge & Extension
Attempt these more advanced problems for extension.
1.
A vector has components x = 15 and y = -8. Calculate its magnitude and describe its position relative to the origin.
[4 marks]2.
A hiker’s displacement vector has components x = -9 and y = -12. Find the magnitude and interpret what this indicates about their movement.
[4 marks]E
Mixed Review
Answer these questions that test different aspects of |v| = √(x² + y²).
1.
If a vector has magnitude 13 and x component 5, find the y component.
[4 marks]2.
A vector with components x = -7 and y = ? has a magnitude of 10. Find y.
[3 marks]F
Error Analysis
Identify and correct the common mistake in each question.
1.
A student calculates |v| as x + y instead of √(x² + y²). Explain why this is incorrect and provide the correct method.
[3 marks]2.
A student forgets to take the square root and reports |v| = x² + y². Describe the mistake and how to fix it.
[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