National 5 Applications of Mathematics
Paper 1 — non-calculator practice
An original 35-mark, 50-minute practice paper. It follows the current assessment structure but is not an official Qualifications Scotland paper.
Paper 1 — non-calculator practice
35 marks · 50 minutes · Calculator prohibited
2. A data set has lower quartile 16 and upper quartile 24. Calculate the interquartile range.
2 marks3. A bag has 3 blue and 2 yellow counters. Two counters are selected without replacement. Find the probability both are blue.
3 marksCounter bag
| Colour | Starting count |
|---|---|
| Blue | 3 |
| Yellow | 2 |
| Replacement | No |
4. A salesperson receives £380.00 basic weekly pay plus 2% commission on sales of £2400.00. Calculate gross pay.
3 marks5. A triangular prism has triangular cross-section base 10 cm and height 5 cm. Its length is 18 cm. Calculate its volume.
3 marks6. Use the three bearings and leg lengths in the shown navigation course. In which direction is Finish from Start?
2 marksThree-leg navigation course
- Leg 1: 045°, 6 km
- Leg 2: 120°, 5 km
- Leg 3: 210°, 4 km
7. Which task order satisfies every dependency in the precedence table?
2 marksEvent setup plan
| Task | Duration (days) | Must follow |
|---|---|---|
| Survey | 2 | None |
| Design | 3 | Survey |
| Order | 1 | Design |
| Prepare | 2 | Survey |
| Build | 4 | Order, Prepare |
8. Using the precedence table, find the earliest completion time if independent tasks start together.
4 marksProject tasks
| Task | Duration (hours) | Must follow |
|---|---|---|
| A | 3 | None |
| B | 5 | None |
| C | 4 | A |
| D | 2 | B |
| E | 3 | C, D |
9. A straight slope passes through (2, 4) and (8, 16). Calculate its gradient.
2 marks10. A compound garden is made from a rectangle 11 m by 4 m and a triangle with base 4 m and height 6 m. Calculate the total area.
3 marksCompound shape
11. Pack items taking 3, 2, 6, 2, 4, 4, 3, 6 litres of space into uniform containers of capacity 10 litres. What is the minimum number of containers?
4 marksMinimum-container packing
Capacity 10; item sizes:
12. A school asks only pupils leaving the sports centre whether more PE should be offered. What is the main concern?
2 marks13. Choose an option with price at most £18.00, waiting time at most 3 days, and accessibility available.
3 marksService comparison
| Option | Distance km | Price | Capacity | Wait days | Accessible |
|---|---|---|---|---|---|
| A | 12 | £18 | 40 | 2 | Yes |
| B | 18 | £16 | 30 | 4 | No |
| C | 15 | £20 | 50 | 3 | Yes |