National 5 Applications of Mathematics
Paper 2 — case-study practice
A 55-mark, 1-hour-40-minute calculator practice paper with linked source material. This is original exam-style practice, not an official paper.
Paper 2 — case-study practice
55 marks · 100 minutes · Calculator permitted
Case study 1: Employment and travel
Use the payslip and travel information for all six questions.
Monthly pay and travel information
| Item | Information |
|---|---|
| Basic pay | £420.00 |
| Overtime | 7 hours at £18.00 |
| Income tax | £62.40 |
| National Insurance | £31.20 |
| Pension | £21.00 |
| Travel budget | £86.00 |
1.2. Calculate the employee's net pay after all supplied deductions.
4 marks1.3. After the travel budget is paid, how much net income remains?
3 marks1.4. The employee wants to save £320 this month. Is that possible after the travel budget? Justify.
3 marks1.5. A trip needs €360. The supplied exchange rate is £1 = €1.20. How many pounds are needed before fees?
3 marks1.6. Provider A charges 2% of £300. Provider B charges a flat £8 fee. Which fee is lower, and by how much?
2 marksCase study 2: Community project
Use the precedence plan and supplied measurements throughout.
Project precedence plan
| Task | Duration (days) | Must follow |
|---|---|---|
| Survey | 2 | None |
| Design | 3 | Survey |
| Order | 2 | Design |
| Prepare | 4 | Survey |
| Install | 3 | Order, Prepare |
2.1. Find the earliest project completion time when independent tasks run in parallel.
4 marks2.2. A 24 m route is drawn at 1 cm represents 2 m. Find its drawing length.
2 marks2.3. Using the scale 1 cm represents 1 km, describe the correct construction for the two route legs 060° for 6 km and 145° for 5 km.
2 marksScaled route construction
Scale: 1 cm represents 1 km.
- Leg 1: 060°, 6 km
- Leg 2: 145°, 5 km
2.4. Items sized 7, 6, 5, 4, 3, 3, 2 must go into containers of capacity 10. Find the minimum container count.
4 marks2.5. A meeting starts at 15:30 in London (UTC+0). The partner is at UTC+5. What local time is it for the partner?
2 marks2.6. A shaft can be 19.96–20.04 mm and a hole can be 20.05–20.11 mm. Will every acceptable shaft fit? Explain.
4 marksCase study 3: Venue design and visitor data
Use the venue model and visitor information to make calculations and conclusions.
Venue storage model