Free Grade 3 Working with Vector Proof Techniques Quizzes
Free Grade 3 quizzes for Working with Vector Proof Techniques: 12 real questions with a full answer key and worked solutions. A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).
Free
Stretch
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with vector proof techniques
Identify working with vector proof techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with vector proof techniques
Explain working with vector proof techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with vector proof techniques
Calculate working with vector proof techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with vector proof techniques
Compare working with vector proof techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Vector Proof Techniques works
A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.a = (6, -4), b = (5, -3). Find a + 4b.[1]
- 2.a = (4, 1), b = (-6, -3). Find a + 3b.[1]
- 3.a = (-5, 4), b = (-5, 2). Find a + 4b.[1]
- 4.a = (4, -5), b = (0, -5). Find a + 2b.[1]
- 5.a = (4, 1), b = (0, 0). Find a + 3b.[2]
- 6.a = (-1, 0), b = (-6, 5). Find a + 2b.[2]
- 7.a = (0, -3), b = (-4, -3). Find a + 2b.[2]
- 8.a = (2, -4), b = (-4, 6). Find a + 3b.[2]
- 9.Find the magnitude of (3, -6) to 2 d.p.[3]
- 10.Find the magnitude of (3, 3) to 2 d.p.[3]
- 11.Find the magnitude of (4, -6) to 2 d.p.[3]
- 12.Find the magnitude of (-4, -1) to 2 d.p.[3]
Show answers and working
1. (26, -16)
4b = (20, -12). Add components: (6 + 20, -4 + -12).
2. (-14, -8)
3b = (-18, -9). Add components: (4 + -18, 1 + -9).
3. (-25, 12)
4b = (-20, 8). Add components: (-5 + -20, 4 + 8).
4. (4, -15)
2b = (0, -10). Add components: (4 + 0, -5 + -10).
5. (4, 1)
3b = (0, 0). Add components: (4 + 0, 1 + 0).
6. (-13, 10)
2b = (-12, 10). Add components: (-1 + -12, 0 + 10).
7. (-8, -9)
2b = (-8, -6). Add components: (0 + -8, -3 + -6).
8. (-10, 14)
3b = (-12, 18). Add components: (2 + -12, -4 + 18).
9. 6.71
|v| = √(x² + y²) = √(9 + 36). = 6.71.
10. 4.24
|v| = √(x² + y²) = √(9 + 9). = 4.24.
11. 7.21
|v| = √(x² + y²) = √(16 + 36). = 7.21.
12. 4.12
|v| = √(x² + y²) = √(16 + 1). = 4.12.
Worked examples
a = (5, -3), b = (3, -3). Find a + 3b.
- 3b = (9, -9).
- Add components: (5 + 9, -3 + -9).
- Answer: (14, -12)
a = (-2, 5), b = (-3, 4). Find a + 4b.
- 4b = (-12, 16).
- Add components: (-2 + -12, 5 + 16).
- Answer: (-14, 21)
Find the magnitude of (4, 6) to 2 d.p.
- |v| = √(x² + y²) = √(16 + 36).
- = 7.21.
- Answer: 7.21
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Adds x of one vector to y of the other.
Correction: Add x with x, y with y.
Forgets that a negative component means the opposite direction.
Correction: Draw the vector to check.
Teacher tips
- · Draw vectors on squared paper end to end.
Parent tips
- · Give directions as '3 steps right, 2 steps up'.
Real-life applications
- · Navigation, forces in physics, game movement.
Assessment objectives
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Frequently asked
- Is this Grade 3 Working with Vector Proof Techniques quiz really free?
- Yes. Every quizzes on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Working with Vector Proof Essentials, Introducing Vector Proof. Each one has its own free lesson, worksheet and quiz.
- How is the quiz sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Vector Proof Techniques?
- Move on to Working with Vector Proof Word Problems, Working with Vector Proof Common Errors, Introducing Vector Proof, Vector Proof in Context, which build directly on this idea.
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