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.

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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

ItemInformation
Basic pay£420.00
Overtime7 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 marks

1.2. Calculate the employee's net pay after all supplied deductions.

4 marks

1.3. After the travel budget is paid, how much net income remains?

3 marks

1.4. The employee wants to save £320 this month. Is that possible after the travel budget? Justify.

3 marks

1.5. A trip needs €360. The supplied exchange rate is £1 = €1.20. How many pounds are needed before fees?

3 marks

1.6. Provider A charges 2% of £300. Provider B charges a flat £8 fee. Which fee is lower, and by how much?

2 marks

Case study 2: Community project

Use the precedence plan and supplied measurements throughout.

Project precedence plan

TaskDuration (days)Must follow
Survey2None
Design3Survey
Order2Design
Prepare4Survey
Install3Order, Prepare

2.1. Find the earliest project completion time when independent tasks run in parallel.

4 marks

2.2. A 24 m route is drawn at 1 cm represents 2 m. Find its drawing length.

2 marks

2.3. 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 marks

2.4. Items sized 7, 6, 5, 4, 3, 3, 2 must go into containers of capacity 10. Find the minimum container count.

4 marks

2.5. 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 marks

2.6. 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 marks

Case study 3: Venue design and visitor data

Use the venue model and visitor information to make calculations and conclusions.

3.1. Find the total volume of the two non-overlapping cuboids.

4 marks

3.2. 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 marks

3.3. 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 marks

3.4. A ramp runs from (2, 3) to (8, 6). Find its gradient.

2 marks

3.5. A survey estimates probability 0.35 that a visitor cycles. Find the expected number from 240 visitors.

2 marks

3.6. An online survey was shared only with cycling-club members. Explain one likely source of bias.

2 marks