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Broad General Education

Senior Phase

Senior Phase · S5 / S6

Higher Applications of Mathematics

Data, finance and modelling – the maths of modern life.

  • SCQF Level 6
  • 4 units
  • 8 practice questions
  • 7 key dates
Start practising View key dates

Overview

About this course

Higher Applications of Mathematics is a modern, data-rich course that equips pupils with statistics, financial literacy, planning and mathematical modelling skills. Pupils learn to analyse real data sets using the programming language R, interpret results critically and communicate conclusions. It is accepted by a growing number of universities as a Level 6 maths qualification.

Course structure

What your child will learn

The course is organised into 4 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 Statistics & Probability7 topics
  • Sampling and study design
  • Summary statistics and data visualisation in R
  • Probability – conditional and independence
  • Normal distribution
  • Confidence intervals
  • Hypothesis testing – t-tests, chi-squared
  • Correlation and linear regression
2 Finance6 topics
  • Income tax, NI and student loans
  • Inflation and real terms
  • Savings – AER and compound interest
  • Loans, mortgages and APR
  • Pensions and annuities
  • Spreadsheet modelling
3 Planning & Decision Making5 topics
  • Project planning – activity networks, critical path
  • Gantt charts
  • Scheduling and resource allocation
  • Expected value and risk
  • Logic and decision trees
4 Mathematical Modelling4 topics
  • Formulating and refining models
  • Fermi estimation
  • Evaluating assumptions and limitations
  • Communicating results

Assessment

How the course is assessed

01

Question Paper

80 marks · 2 hours 40 minutes. Calculator and computer (R/RStudio) access for data analysis.

02

Project

30 marks. A statistical investigation of a provided data set, written up and externally marked by SQA.

03

Grading

Graded A–D on the combined total of 110 marks.

Assessment practice

Practise for forthcoming assessments

8 questions worth 19 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 · December

Statistics Assessment

4 questions · 9 marks

Print this set

  1. Q1

    Heights are normally distributed with mean 170 cm and SD 8 cm. Find the probability a person is taller than 182 cm.

    3 marks
    Show solution

    Solution

    z = (182 − 170)⁄8 = 1.5; P(Z > 1.5) = 0.0668.

  2. Q2

    A sample of 50 has mean 24.6 and SD 3.2. Calculate a 95% confidence interval for the population mean.

    3 marks
    Show solution

    Solution

    24.6 ± 1.96 × 3.2⁄√50 = 24.6 ± 0.887 → (23.7, 25.5).

  3. Q3

    Explain the difference between a Type I and a Type II error in hypothesis testing.

    2 marks
    Show solution

    Solution

    Type I: rejecting a true null hypothesis (false positive). Type II: failing to reject a false null hypothesis (false negative).

  4. Q4

    Write the R code to calculate the mean of a column named 'score' in a data frame called 'results'.

    1 mark
    Show solution

    Solution

    mean(results$score)

Set 2 · January

Prelim

4 questions · 10 marks

Print this set

  1. Q1

    £5 000 is invested at an AER of 3.4% for 6 years. Find the final value.

    2 marks
    Show solution

    Solution

    5 000 × 1.034⁶ = £6 110.47.

  2. Q2

    Inflation is 4% per year. A salary rises from £30 000 to £31 000. Has it risen in real terms?

    3 marks
    Show solution

    Solution

    £30 000 × 1.04 = £31 200 needed; £31 000 < £31 200, so it has fallen in real terms by ~£200.

  3. Q3

    A project has activities A(3 days), B(5 days, after A), C(2 days, after A), D(4 days, after B and C). Find the critical path and minimum duration.

    3 marks
    Show solution

    Solution

    A → B → D: 3 + 5 + 4 = 12 days. Critical path is A-B-D.

  4. Q4

    A game costs £2 to play. You win £10 with probability 0.15 and nothing otherwise. Find the expected profit per game.

    2 marks
    Show solution

    Solution

    E = 0.15 × 10 − 2 = −£0.50 (expected loss of 50p).

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

Thu 6 Nov 2025

S5/S6 Parents' Evening

Parents' Evening + cal

w/c 8 Dec 2025

Statistics class assessment

Assessment + cal

Thu 22 Jan 2026

Higher Applications Prelim

Prelim + cal

Feb – Mar 2026

Project completed under supervised conditions

Assessment

Tue 31 Mar 2026

Project submission deadline

Assessment + cal

May 2026

SQA Exam – Question Paper (date TBC)*

SQA Exam

Tue 4 Aug 2026

SQA results day

Information + cal

Progression

Where this course leads

University, college or employment. Pupils may also progress to Higher Mathematics.

More in the Senior Phase

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Have a question about Higher Applications?

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