Free Grade 3 Working with Vector Proof Essentials Flashcards
Free Grade 3 flashcards for Working with Vector Proof Essentials: 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
Core
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with vector proof essentials
Identify working with vector proof essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with vector proof essentials
Explain working with vector proof essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with vector proof essentials
Calculate working with vector proof essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with vector proof essentials
Compare working with vector proof essentials 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 Essentials 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, 1), b = (-1, 6). Find a + 2b.[1]
- 2.a = (5, -2), b = (-3, 3). Find a + 4b.[1]
- 3.a = (2, 4), b = (3, -6). Find a + 3b.[1]
- 4.a = (0, 2), b = (2, 3). Find a + 2b.[1]
- 5.a = (2, -1), b = (3, 1). Find a + 4b.[2]
- 6.a = (-5, -1), b = (0, 0). Find a + 3b.[2]
- 7.a = (-6, -1), b = (0, 4). Find a + 4b.[2]
- 8.a = (-5, -1), b = (3, 4). Find a + 4b.[2]
- 9.Find the magnitude of (-1, 6) to 2 d.p.[3]
- 10.Find the magnitude of (5, -4) to 2 d.p.[3]
- 11.Find the magnitude of (5, -1) to 2 d.p.[3]
- 12.Find the magnitude of (5, 1) to 2 d.p.[3]
Show answers and working
1. (-2, 13)
2b = (-2, 12). Add components: (0 + -2, 1 + 12).
2. (-7, 10)
4b = (-12, 12). Add components: (5 + -12, -2 + 12).
3. (11, -14)
3b = (9, -18). Add components: (2 + 9, 4 + -18).
4. (4, 8)
2b = (4, 6). Add components: (0 + 4, 2 + 6).
5. (14, 3)
4b = (12, 4). Add components: (2 + 12, -1 + 4).
6. (-5, -1)
3b = (0, 0). Add components: (-5 + 0, -1 + 0).
7. (-6, 15)
4b = (0, 16). Add components: (-6 + 0, -1 + 16).
8. (7, 15)
4b = (12, 16). Add components: (-5 + 12, -1 + 16).
9. 6.08
|v| = √(x² + y²) = √(1 + 36). = 6.08.
10. 6.4
|v| = √(x² + y²) = √(25 + 16). = 6.4.
11. 5.1
|v| = √(x² + y²) = √(25 + 1). = 5.1.
12. 5.1
|v| = √(x² + y²) = √(25 + 1). = 5.1.
Worked examples
a = (-3, 4), b = (-3, 1). Find a + 3b.
- 3b = (-9, 3).
- Add components: (-3 + -9, 4 + 3).
- Answer: (-12, 7)
a = (4, 3), b = (4, 2). Find a + 2b.
- 2b = (8, 4).
- Add components: (4 + 8, 3 + 4).
- Answer: (12, 7)
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 Working with Vector Proof Essentials flashcards really free?
- Yes. Every flashcards 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 Introducing Vector Proof. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards 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 Essentials?
- Move on to Working with Vector Proof Techniques, Working with Vector Proof Word Problems, Working with Vector Proof Common Errors, Introducing Vector Proof, which build directly on this idea.
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