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VECTORS · LESSON 12

Vectors Final Checkpoint

Complete an exam-style assessment across the full topic.

⏱️ 45–55 min 📘 Checkpoint➶ Diagrams included

Final Checkpoint

Section A: Foundations

  1. Distinguish a scalar from a vector.
  2. State what makes two vectors equal.
  3. Write the negative of (5,−2).
  4. Find PQ⃗ for P(1,−3), Q(6,4).

Section B: Operations

  1. Calculate (4,7)+(−2,3).
  2. Calculate 3(−1,5)−(2,4).
  3. Find the magnitude of (−9,12).
  4. Solve x+(3,−2)=(8,6).

Section C: Geometry

  1. OA⃗=a, OB⃗=b. Express BA⃗.
  2. ABCD is a parallelogram with AB⃗=p, AD⃗=q. Express AC⃗ and DC⃗.
  3. Show that (6,−9) is parallel to (−2,3).
  4. A=(2,4), B=(10,8). Find midpoint M.

🏁 Interactive Final Checkpoint

Complete the six questions without notes, then check your score.

1. Which is a vector quantity?

2. (2,3)+(4,−1)=

3. 3(−2,5)=

4. |(5,12)|=

5. A(−1,2), B(4,−3): AB=

6. Equal vectors have the same...

Score: 0/6

✅ Check Your Work

Show answers and working
  1. A scalar has magnitude only; a vector has magnitude and direction.
  2. Same magnitude and same direction.
  3. (−5,2).
  4. (6−1,4−(−3))=(5,7).
  5. (2,10).
  6. 3(−1,5)=(−3,15); subtract (2,4) to get (−5,11).
  7. √(81+144)=15.
  8. x=(8,6)−(3,−2)=(5,8).
  9. BA⃗=a−b.
  10. AC⃗=p+q; DC⃗=p.
  11. (6,−9)=−3(−2,3), so the vectors are scalar multiples.
  12. M=((2+10)/2,(4+8)/2)=(6,6).

📘 Remember

Vectors carry both magnitude and direction. Work with horizontal and vertical components separately, and keep signs consistent.

⚠️ Common Mistakes

Do not confuse a point with its position vector. For AB, always calculate B − A, not A − B.

⭐ Exam Tips

Sketch arrows, label directions clearly, show component working and check whether the final direction agrees with the diagram.

🌍 Did You Know?

Vectors are used in navigation, animation, engineering, robotics, weather modelling and computer games.

Revision Guidance and Readiness