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S5 Maths: Vectors – Error Clinic (Paper 4)
S5 Maths: Vectors – Error Clinic (Paper 4)
Targets the common slips of negative lengths, swapped parallel and perpendicular tests, and wrong section ratios.
Direct answers Each item matches one common slip and its answer carries a one-line correction.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S5 Maths: Vectors |
| Level | Error replay |
02 Questions (10 items)
- FoundationFind |(-5, 12)|.
- FoundationGiven a = (-2, 3), find 4a.
- FoundationGiven a = (1, 3) and b = (5, 2), find a dot b.
- IntermediateFind the unit vector of (8, -6).
- IntermediateGiven (k, 6) parallel to (4, 3), find k.
- IntermediateGiven (2, k) perpendicular to (3, -4), find k.
- ChallengeGiven |a| = 1, |b| = 2 and a dot b = 1, find |a + b| and the angle.
- ChallengeGiven A(2, 3) and B(6, 11), find the length and midpoint of AB.
- ChallengeGiven A(0, 0) and B(6, 9), P on AB with AP to PB as 2 to 1, find P.
- Error redoA student writes |a| = -7 and says a length can be negative. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 13 | 25 plus 144 is 169 and its square root is 13; a length is never negative. |
| 2 | (-8, 12) | Multiply each component by 4 and keep the negative sign. |
| 3 | 11 | 1 times 5 plus 3 times 2 gives 11. |
| 4 | (0.8, -0.6) | The length is 10, so divide both components by 10. |
| 5 | k = 8 | Proportional components give 3k equal to 24. |
| 6 | k = 1.5 | The dot product 6 minus 4k is zero, so k is 1.5. |
| 7 | |a + b| about 2.65 (root 7), angle 60 degrees | The squares add to 1 plus 4 plus 2, and the cosine is 1 over 2. |
| 8 | Length about 8.94 (root 80), midpoint (4, 7) | AB is (4, 8) with length root 80, and the midpoint averages the coordinates. |
| 9 | (4, 6) | P covers two thirds of the segment, so 6 and 9 are each scaled by two thirds. |
| 10 | A length is a square root of a sum of squares, so it is never negative | Length is a distance: only the zero vector has length zero and everything else is positive. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Write one line per slip, such as treating perpendicular as parallel.Tutor Registration →
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