Free Grade 3 Vector Proof in Context Techniques Worksheets
Free Grade 3 worksheets for Vector Proof in Context 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify vector proof in context techniques
Identify vector proof in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain vector proof in context techniques
Explain vector proof in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate vector proof in context techniques
Calculate vector proof in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare vector proof in context techniques
Compare vector proof in context 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 Vector Proof in Context 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, 1), b = (-3, 6). Find a + 4b.[1]
- 2.a = (-2, -5), b = (-6, 0). Find a + 4b.[1]
- 3.a = (6, -2), b = (1, -2). Find a + 2b.[1]
- 4.a = (-5, 0), b = (-5, 2). Find a + 2b.[1]
- 5.a = (6, 5), b = (3, -6). Find a + 4b.[2]
- 6.a = (6, 1), b = (4, 4). Find a + 4b.[2]
- 7.a = (1, 5), b = (5, 2). Find a + 3b.[2]
- 8.a = (0, 3), b = (6, 0). Find a + 2b.[2]
- 9.Find the magnitude of (2, -5) to 2 d.p.[3]
- 10.Find the magnitude of (-5, -3) to 2 d.p.[3]
- 11.Find the magnitude of (-2, 0) to 2 d.p.[3]
- 12.Find the magnitude of (1, -1) to 2 d.p.[3]
Show answers and working
1. (-18, 25)
4b = (-12, 24). Add components: (-6 + -12, 1 + 24).
2. (-26, -5)
4b = (-24, 0). Add components: (-2 + -24, -5 + 0).
3. (8, -6)
2b = (2, -4). Add components: (6 + 2, -2 + -4).
4. (-15, 4)
2b = (-10, 4). Add components: (-5 + -10, 0 + 4).
5. (18, -19)
4b = (12, -24). Add components: (6 + 12, 5 + -24).
6. (22, 17)
4b = (16, 16). Add components: (6 + 16, 1 + 16).
7. (16, 11)
3b = (15, 6). Add components: (1 + 15, 5 + 6).
8. (12, 3)
2b = (12, 0). Add components: (0 + 12, 3 + 0).
9. 5.39
|v| = √(x² + y²) = √(4 + 25). = 5.39.
10. 5.83
|v| = √(x² + y²) = √(25 + 9). = 5.83.
11. 2
|v| = √(x² + y²) = √(4 + 0). = 2.
12. 1.41
|v| = √(x² + y²) = √(1 + 1). = 1.41.
Worked examples
a = (-3, -2), b = (-6, 1). Find a + 2b.
- 2b = (-12, 2).
- Add components: (-3 + -12, -2 + 2).
- Answer: (-15, 0)
a = (6, 4), b = (6, 1). Find a + 3b.
- 3b = (18, 3).
- Add components: (6 + 18, 4 + 3).
- Answer: (24, 7)
Find the magnitude of (-1, -6) to 2 d.p.
- |v| = √(x² + y²) = √(1 + 36).
- = 6.08.
- Answer: 6.08
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
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Vector Proof in Context Techniques worksheet really free?
- Yes. Every worksheets 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 Vector Proof in Context Essentials, Working with Vector Proof. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Vector Proof in Context Techniques?
- Move on to Vector Proof in Context Word Problems, Vector Proof in Context Common Errors, Introducing Vector Proof, Working with Vector Proof, which build directly on this idea.
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