National 5 Applications of Mathematics
Full 90-mark mock practice
Complete Paper 1 and Paper 2 as separate sections. All questions and case-study sources are original and generated by CfE Maths Hub.
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 |
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 | 8 hours at £18.00 |
| Income tax | £62.40 |
| National Insurance | £31.20 |
| Pension | £21.00 |
| Travel budget | £86.00 |
1.1. Calculate the employee's gross pay.
3 marks1.2. 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
3.1. Find the total volume of the two non-overlapping cuboids.
4 marks3.2. A floor is a 16 m by 10 m rectangle plus a semicircle of diameter 10 m. Find its area to 1 decimal place.
4 marks3.3. A 6 m by 8 m diagonal is used as one side of a second right triangle with other side 24 m. Find the final diagonal.
5 marks3.4. A ramp runs from (2, 3) to (8, 6). Find its gradient.
2 marks3.5. A survey estimates probability 0.35 that a visitor cycles. Find the expected number from 240 visitors.
2 marks3.6. An online survey was shared only with cycling-club members. Explain one likely source of bias.
2 marksFull mock total: 90 marks