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P1 Position and Direction Paper 3 (challenge)
P1 Position and Direction Paper 3 (challenge)
Ten challenge items on comparing grid positions, multi-step routes, lift floors and shortest routes.
Direct answers Q1 3 north, Q2 north-east, Q3 3 squares, Q4 number 10, Q5 4, Q6 3 east and 2 north in 9 squares, Q7 10 squares, Q8 floor 5, Q9 8 squares, Q10 6 people.
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: P1 Position and Direction |
| Level | P1 |
02 Questions (10 items)
- FoundationA is at (2, 3) and B is at (2, 6). Where is B from A, and how far?
- FoundationA post office is east of a school and a hospital is north of the post office. Where is the hospital from the school?
- FoundationA row of squares is numbered 1 to 9 from the left. How many squares lie between number 4 and number 8?
- IntermediateA queue has 15 people and Ming is 6th from the front. What is his position from the back?
- IntermediateIn a 3 by 3 array, how many squares touch the centre square on a side?
- IntermediateFrom A walk 4 east, 3 north, 1 west and 1 south. How far east and north of A, and how far in all?
- ChallengeTwo people start from the same point; one walks 6 squares east and the other 4 squares west. How far apart are they?
- ChallengeThe ground floor of a building is floor 0. A lift goes up 4 floors, down 2 floors, then up 3 floors. Which floor is it on?
- ChallengeOn a 5 by 5 grid, walk from the top left corner to the bottom right using only east and south moves. What is the shortest number of squares?
- Error redoMing is 3rd from the front and 4th from the back, so the whole queue has 7 people. Is this correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3 squares north of A | The sideways count is the same, and the upright count rises by 3. |
| 2 | to the north-east | East then north combines into the north-east. |
| 3 | 3 squares | The squares between them are 5, 6 and 7. |
| 4 | number 10 | 15 – 6 + 1 = 10 from the back. |
| 5 | 4 | One above, one below, one on each side; the corners do not touch. |
| 6 | 3 east, 2 north, 9 squares in all | East and west leave 3, north and south leave 2, and the walk totals 9 squares. |
| 7 | 10 squares | Opposite directions, so add: 6 + 4 = 10. |
| 8 | floor 5 | Work in order: 0 + 4 = 4, 4 – 2 = 2, 2 + 3 = 5. |
| 9 | 8 squares | Four squares across plus four down gives 8. |
| 10 | No, there are 6 people in all | Ming was counted twice: 3 + 4 – 1 = 6. |
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.
Check every answer, then draw each route on squared paper to confirm.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.