Free Grade 3 Vector Proof in Context Common Errors Quizzes
Free Grade 3 quizzes for Vector Proof in Context Common Errors: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify vector proof in context common errors
Identify vector proof in context common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain vector proof in context common errors
Explain vector proof in context common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate vector proof in context common errors
Calculate vector proof in context common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare vector proof in context common errors
Compare vector proof in context common errors 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 Common Errors 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 = (0, 0), b = (-4, -3). Find a + 3b.[1]
- 2.a = (0, -6), b = (-5, -4). Find a + 3b.[1]
- 3.a = (-4, 6), b = (-4, -1). Find a + 4b.[1]
- 4.a = (-2, -2), b = (1, 1). Find a + 2b.[1]
- 5.a = (0, 3), b = (-3, -4). Find a + 2b.[2]
- 6.a = (1, 2), b = (3, -4). Find a + 4b.[2]
- 7.a = (4, 2), b = (-6, -4). Find a + 2b.[2]
- 8.a = (6, 5), b = (-3, -5). Find a + 3b.[2]
- 9.Find the magnitude of (5, -4) to 2 d.p.[3]
- 10.Find the magnitude of (-1, -6) to 2 d.p.[3]
- 11.Find the magnitude of (1, -6) to 2 d.p.[3]
- 12.Find the magnitude of (-6, 4) to 2 d.p.[3]
Show answers and working
1. (-12, -9)
3b = (-12, -9). Add components: (0 + -12, 0 + -9).
2. (-15, -18)
3b = (-15, -12). Add components: (0 + -15, -6 + -12).
3. (-20, 2)
4b = (-16, -4). Add components: (-4 + -16, 6 + -4).
4. (0, 0)
2b = (2, 2). Add components: (-2 + 2, -2 + 2).
5. (-6, -5)
2b = (-6, -8). Add components: (0 + -6, 3 + -8).
6. (13, -14)
4b = (12, -16). Add components: (1 + 12, 2 + -16).
7. (-8, -6)
2b = (-12, -8). Add components: (4 + -12, 2 + -8).
8. (-3, -10)
3b = (-9, -15). Add components: (6 + -9, 5 + -15).
9. 6.4
|v| = √(x² + y²) = √(25 + 16). = 6.4.
10. 6.08
|v| = √(x² + y²) = √(1 + 36). = 6.08.
11. 6.08
|v| = √(x² + y²) = √(1 + 36). = 6.08.
12. 7.21
|v| = √(x² + y²) = √(36 + 16). = 7.21.
Worked examples
a = (6, 0), b = (-3, 6). Find a + 3b.
- 3b = (-9, 18).
- Add components: (6 + -9, 0 + 18).
- Answer: (-3, 18)
a = (5, 6), b = (-1, -3). Find a + 3b.
- 3b = (-3, -9).
- Add components: (5 + -3, 6 + -9).
- Answer: (2, -3)
Find the magnitude of (-4, -4) to 2 d.p.
- |v| = √(x² + y²) = √(16 + 16).
- = 5.66.
- Answer: 5.66
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 Common Errors 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 Vector Proof in Context Word Problems, Vector Proof in Context Techniques, Working with 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 Vector Proof in Context Common Errors?
- Move on to Introducing Vector Proof, Working with Vector Proof, which build directly on this idea.
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