Free Grade 3 Introducing Vector Proof Common Errors Flashcards
Free Grade 3 flashcards for Introducing Vector Proof 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).
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35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing vector proof common errors
Identify introducing vector proof common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing vector proof common errors
Explain introducing vector proof common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing vector proof common errors
Calculate introducing vector proof common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing vector proof common errors
Compare introducing vector proof 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 Introducing Vector Proof 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 = (-1, -4), b = (1, -2). Find a + 3b.[1]
- 2.a = (-2, -5), b = (0, 0). Find a + 4b.[1]
- 3.a = (-4, -5), b = (3, -4). Find a + 4b.[1]
- 4.a = (2, 3), b = (1, -1). Find a + 4b.[1]
- 5.a = (-5, -5), b = (-1, 4). Find a + 3b.[2]
- 6.a = (-5, 6), b = (-3, 3). Find a + 4b.[2]
- 7.a = (1, 5), b = (3, -5). Find a + 3b.[2]
- 8.a = (-3, -4), b = (4, -4). Find a + 4b.[2]
- 9.Find the magnitude of (6, -6) to 2 d.p.[3]
- 10.Find the magnitude of (2, 3) to 2 d.p.[3]
- 11.Find the magnitude of (0, -3) to 2 d.p.[3]
- 12.Find the magnitude of (2, 1) to 2 d.p.[3]
Show answers and working
1. (2, -10)
3b = (3, -6). Add components: (-1 + 3, -4 + -6).
2. (-2, -5)
4b = (0, 0). Add components: (-2 + 0, -5 + 0).
3. (8, -21)
4b = (12, -16). Add components: (-4 + 12, -5 + -16).
4. (6, -1)
4b = (4, -4). Add components: (2 + 4, 3 + -4).
5. (-8, 7)
3b = (-3, 12). Add components: (-5 + -3, -5 + 12).
6. (-17, 18)
4b = (-12, 12). Add components: (-5 + -12, 6 + 12).
7. (10, -10)
3b = (9, -15). Add components: (1 + 9, 5 + -15).
8. (13, -20)
4b = (16, -16). Add components: (-3 + 16, -4 + -16).
9. 8.49
|v| = √(x² + y²) = √(36 + 36). = 8.49.
10. 3.61
|v| = √(x² + y²) = √(4 + 9). = 3.61.
11. 3
|v| = √(x² + y²) = √(0 + 9). = 3.
12. 2.24
|v| = √(x² + y²) = √(4 + 1). = 2.24.
Worked examples
a = (5, -6), b = (-6, -2). Find a + 3b.
- 3b = (-18, -6).
- Add components: (5 + -18, -6 + -6).
- Answer: (-13, -12)
a = (2, 5), b = (5, -5). Find a + 2b.
- 2b = (10, -10).
- Add components: (2 + 10, 5 + -10).
- Answer: (12, -5)
Find the magnitude of (-6, 3) to 2 d.p.
- |v| = √(x² + y²) = √(36 + 9).
- = 6.71.
- Answer: 6.71
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 Introducing Vector Proof Common Errors 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 Word Problems, Introducing Vector Proof Techniques, Collinearity. 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 Introducing Vector Proof Common Errors?
- Move on to Working with Vector Proof, Vector Proof in Context, which build directly on this idea.
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