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Broad General Education

Senior Phase

Senior Phase · S4 / S5

National 5 Applications of Mathematics

Practical, powerful maths for the real world.

  • SCQF Level 5
  • 3 units
  • 8 practice questions
  • 7 key dates
Start practising View key dates

Overview

About this course

National 5 Applications of Mathematics develops the skills to reason with numbers, money, measurement and data in realistic situations. Assessed by two external SQA exam papers, it is widely accepted as a Level 5 maths qualification for college courses, apprenticeships and many university entry requirements, including primary teaching and nursing.

Course structure

What your child will learn

The course is organised into 3 units. Topics are usually taught in the order shown, though teachers may adapt the sequence for their class. Select a unit to see its topics.

1 Numeracy5 topics
  • Rounding and estimation
  • Fractions, decimals and percentages
  • Ratio and proportion
  • Interpreting graphs, charts and diagrams
  • Making and justifying decisions
2 Finance & Statistics7 topics
  • Income – wages, salaries, commission
  • Deductions – tax, NI, pensions
  • Budgeting and spreadsheets
  • Savings, loans and credit – APR
  • Foreign exchange
  • Mean, median, mode, range, standard deviation
  • Box plots, scatter graphs, pie charts
3 Geometry & Measures6 topics
  • Pythagoras and trigonometry in context
  • Perimeter, area and volume (incl. composite)
  • Scale drawings, bearings and navigation
  • Time management and timetables
  • Tolerance and precision
  • Container packing and Gantt-style planning

Assessment

How the course is assessed

01

Paper 1 (Non-calculator)

35 marks · 50 minutes.

02

Paper 2 (Calculator)

55 marks · 1 hour 40 minutes. Extended, real-life problems; a formulae sheet is provided.

03

Grading

Graded A–D on the combined total of 90 marks.

Assessment practice

Practise for forthcoming assessments

8 questions worth 21 marks, matched to the assessments on this course. Try each question on paper first, then select it to reveal the worked solution. You can also print a blank set for revision.

Set 1 · January

Prelim – Paper 1 (Non-calculator)

4 questions · 7 marks

Print this set

  1. Q1

    Find 17.5% of £240.

    2 marks
    Show solution

    Solution

    10% = £24, 5% = £12, 2.5% = £6; total £42.

  2. Q2

    A pie chart shows 90° for 'walk'. 120 pupils were surveyed. How many walk?

    2 marks
    Show solution

    Solution

    90⁄360 × 120 = 30 pupils.

  3. Q3

    Share £560 in the ratio 2 : 5.

    2 marks
    Show solution

    Solution

    £80 per share → £160 : £400.

  4. Q4

    Estimate 4.9 × 61.2 by rounding each number to 1 significant figure.

    1 mark
    Show solution

    Solution

    5 × 60 = 300.

Set 2 · January

Prelim – Paper 2 (Calculator)

4 questions · 14 marks

Print this set

  1. Q1

    Jo's annual salary is £28 600. Her personal allowance is £12 570 and tax is 20% on the rest. Calculate her monthly tax.

    4 marks
    Show solution

    Solution

    Taxable: £16 030; tax = £3 206 per year = £267.17 per month.

  2. Q2

    A cylindrical tank has radius 0.6 m and height 1.5 m. Calculate its volume in litres.

    3 marks
    Show solution

    Solution

    V = π × 0.6² × 1.5 = 1.696 m³ = 1 696 litres.

  3. Q3

    The heights (cm) of six plants are 12, 15, 15, 18, 20, 22. Find the mean and standard deviation.

    4 marks
    Show solution

    Solution

    Mean = 17; s = √(74⁄5) = 3.85.

  4. Q4

    A car hire company charges £35 per day plus 12p per mile. Calculate the cost of a 3-day hire covering 420 miles.

    3 marks
    Show solution

    Solution

    105 + 50.40 = £155.40.

Key dates

Important dates for this course

Session 2025–26. Dates marked * are indicative pending the official SQA timetable; items marked TBC will be updated as soon as they are confirmed. Select “+ cal” on any date to add it to your own calendar.

  • Prelim
  • SQA Exam
  • Parents' Evening
  • Assessment
  • Information

w/c 13 Oct 2025

Numeracy class assessment

Assessment + cal

Thu 27 Nov 2025

S4 Parents' Evening

Parents' Evening + cal

w/c 15 Dec 2025

Finance & Statistics assessment

Assessment + cal

Fri 23 Jan 2026

National 5 Applications Prelim

Prelim + cal

Mar 2026

Easter revision school (dates TBC)

Information

May 2026

SQA Exam – Papers 1 & 2 (date TBC)*

SQA Exam

Tue 4 Aug 2026

SQA results day

Information + cal

Progression

Where this course leads

Higher Applications of Mathematics in S5/S6, or National 5 Mathematics for pupils who wish to access Higher Mathematics.

More in the Senior Phase

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Have a question about National 5 Applications?

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