Free Grade 3 Working with Adding Vectors Techniques Quizzes
Free Grade 3 quizzes for Working with Adding Vectors 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
Higher
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with adding vectors techniques
Explain working with adding vectors techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with adding vectors techniques
Calculate working with adding vectors techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with adding vectors techniques
Compare working with adding vectors techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with adding vectors techniques
Justify working with adding vectors 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 Adding Vectors 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 = (2, -4), b = (1, -4). Find a + 3b.[1]
- 2.a = (1, -5), b = (-6, -6). Find a + 4b.[1]
- 3.a = (-1, 2), b = (1, 6). Find a + 3b.[1]
- 4.a = (3, -1), b = (-5, -2). Find a + 3b.[1]
- 5.a = (-5, -6), b = (-2, -2). Find a + 2b.[2]
- 6.a = (-3, 5), b = (4, 1). Find a + 3b.[2]
- 7.a = (0, -1), b = (1, -4). Find a + 2b.[2]
- 8.a = (-4, 5), b = (4, 2). Find a + 4b.[2]
- 9.Find the magnitude of (3, -6) to 2 d.p.[3]
- 10.Find the magnitude of (-4, 6) to 2 d.p.[3]
- 11.Find the magnitude of (-6, 1) to 2 d.p.[3]
- 12.Find the magnitude of (-6, -2) to 2 d.p.[3]
Show answers and working
1. (5, -16)
3b = (3, -12). Add components: (2 + 3, -4 + -12).
2. (-23, -29)
4b = (-24, -24). Add components: (1 + -24, -5 + -24).
3. (2, 20)
3b = (3, 18). Add components: (-1 + 3, 2 + 18).
4. (-12, -7)
3b = (-15, -6). Add components: (3 + -15, -1 + -6).
5. (-9, -10)
2b = (-4, -4). Add components: (-5 + -4, -6 + -4).
6. (9, 8)
3b = (12, 3). Add components: (-3 + 12, 5 + 3).
7. (2, -9)
2b = (2, -8). Add components: (0 + 2, -1 + -8).
8. (12, 13)
4b = (16, 8). Add components: (-4 + 16, 5 + 8).
9. 6.71
|v| = √(x² + y²) = √(9 + 36). = 6.71.
10. 7.21
|v| = √(x² + y²) = √(16 + 36). = 7.21.
11. 6.08
|v| = √(x² + y²) = √(36 + 1). = 6.08.
12. 6.32
|v| = √(x² + y²) = √(36 + 4). = 6.32.
Worked examples
a = (6, -3), b = (-6, -1). Find a + 3b.
- 3b = (-18, -3).
- Add components: (6 + -18, -3 + -3).
- Answer: (-12, -6)
a = (-1, -4), b = (-1, 4). Find a + 4b.
- 4b = (-4, 16).
- Add components: (-1 + -4, -4 + 16).
- Answer: (-5, 12)
Find the magnitude of (-3, -1) to 2 d.p.
- |v| = √(x² + y²) = √(9 + 1).
- = 3.16.
- Answer: 3.16
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 Adding Vectors 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 Adding Vectors Essentials, Introducing Adding Vectors. 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 Adding Vectors Techniques?
- Move on to Working with Adding Vectors Word Problems, Working with Adding Vectors Common Errors, Introducing Adding Vectors, Adding Vectors in Context, which build directly on this idea.
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