Applications of Mathematics

Faculty of Mathematics & Numeracy

Further information on the LGS Mathematics Department can also be found on our departmental website and X accounts:

LGS Maths Website: https://sites.google.com/sl.glow.scot/lgsmaths/

LGS Maths X Account: https://x.com/lgs_maths

Mathematics is rich and stimulating. It engages and fascinates learners of all ages, interests and abilities.

Learning mathematics develops logical reasoning, analysis, problem-solving skills, creativity, and the ability to think in abstract ways. It uses a universal language of numbers and symbols, which allows us to communicate ideas in a concise, unambiguous and rigorous way.

Using mathematics enables us to model real-life situations and make connections and informed predictions. It equips us with the skills we need to interpret and analyse information, simplify and solve problems, assess risk and make informed decisions.

Most importantly, Mathematics equips us with many of the skills required for life, learning and work. Understanding the part that mathematics plays in almost all aspects of life is crucial. This reinforces the need for mathematics to play an integral part in lifelong learning and be appreciated for the richness it brings.

At Lanark Grammar School, we teach Applications of Mathematics at every available level — National 3, National 4, National 5 and Higher.

Assessment

The purpose of the National 5 Applications of Mathematics course is to motivate and challenge candidates by enabling them to think through real-life situations involving mathematics and to form a plan of action based on logic. The mathematical skills within this course are underpinned by numeracy, and designed to develop candidates’ mathematical reasoning skills in areas relevant to learning, life and work.

A summary of the assessment at each level is shown below for information:

National 3 Applications

Internal Assessment

Three mandatory unit assessments:

Numeracy
Manage, Money & Data
Shape, Space & Measures

External Assessment

There is no external exam for the National 3 Applications Mathematics course.

To obtain a pass at National 3 Mathematics, learners must pass all mandatory units of the course.

The entirety of the National 3 Applications of Mathematics course is calculator based, however learners may be asked to completed non-calculator work as extension to National 4 Applications of Mathematics.

Successful completion of this course enables learners to progress to National 4 Applications of Mathematics.

National 4 Applications

Internal Assessment

Four mandatory unit assessments:

Numeracy
Finance & Statistics
Geometry & Measures
Added Value Unit.

External Assessment

There is no external exam for the National 4 Applications of Mathematics course.

To obtain a pass at National 4 Applications of Mathematics, learners must pass all mandatory units of the course.

The Added Value Unit will contain a Non-calculator and Calculator element.

Successful completion of this course enables learners to progress to National 5 Applications of Mathematics.

National 5 Applications

External Assessment

The National 5 Applications Mathematics grade, unlike most other National 5 courses, is awarded purely based on the total number of marks achieved across both papers of the course assessment (final external exam).

Learners will complete a final external exam which will be completed under exam conditions and sent to the SQA for marking.

The final exam will consist of two components:

Paper 1 (Non-calculator):

35 marks

Time allowed - 50 minutes

Paper 2 (Calculator):

55 marks

Time allowed - 1 hour 40 minutes

A pass at National 5 Applications of Mathematics is purely based on the final external assessment and successful completion of this course enables learners to progress to either National 5 Mathematics or Higher Applications of Mathematics.

To prepare learners fully for the final exam, smaller class assessments will take place during September, November and March of the academic year, alongside a prelim assessment in January.

Higher Applications

External Assessment

The Higher Applications Mathematics grade, unlike other Mathematics courses, is based on the marks achieved across the final external exam and a statistical research based project.

Learners will complete a final external exam which will be completed under exam conditions and sent to the SQA for marking. This exam accounts for 73% of a candidates final grade.

The final exam will consist of one component:

Question Paper (Calculator):

65 marks

Time allowed - 2 hour 05 minutes

The project consists of individual research and is submitted to the SQA for marking. This accounts for 27% of the final course award.

Project:

30 marks

Time allowed in class - 8 hours

To prepare learners fully for the final exam, smaller class assessments will take place during October, December and March of the academic year, alongside a prelim assessment in January.

Ideal Candidates

For S1 to S4, Mathematics is a mandatory subject as part of the Scottish Curriculum.

In S3, you will be placed into either an Applications of Mathematics or Mathematics class based on discussions with class teachers as well as performance in the Mathematics and Numeracy work carried out in S1 and S2.

The Applications of Mathematics course would be best suited to a young person who is interested in developing skills in real world and everyday Mathematics; if you've ever asked "when am I actually going to use this?", the answer for Application of Mathematics is everyday!

Unlike Mathematics, Applications of Mathematics courses provide a particular understanding of Finance and Statistics which lend themselves well to those interested in pursuing a career in areas such as Business, Research, and Sports Science.

Success at Higher Applications of Mathematics relies on a strong understanding of the Finance, Probability, Problem Solving and Statistics skills taught within National 5 Applications of Mathematics and broadens & extends on the topics covered within this course. The Higher Applications course also introduces a computing element to Mathematics, providing learners with skills and experience in Excel and RStudio.

For Higher Applications, learners who have demonstrated a strong knowledge and understanding of Business & IT based courses is preferable - specifically experience with coding languages and/or Excel from courses such as Admin & Accounting or Business & IT.

Mathematics

vs

Applications of Mathematics

In S3, you will be placed into a class working either on an Applications of Mathematics route or a Mathematics route.

Applications of Mathematics is now a highly respected qualification which will also open up many career opportunities.

The Applications of Mathematics course route removes the abstract algebra element found in Mathematics and instead explores the application of mathematical techniques and skills in everyday situations, including financial matters, statistical analysis, modelling, planning and measurement and is recognised throughout many further education establishments as an alternative Mathematics qualification. Part of the Higher Applications of Mathematics course also places significant emphasis on the use of Excel and R Studio Coding based software to demonstrate how mathematical skills will be applied in real life.

At Lanark Grammar School, we also offer Mathematics at all available levels - National 4, National 5, Higher and Advanced Higher.

Further information on these courses can be found by clicking here.

National 4 Applications of Mathematics

What will you learn?

Within National 4 Applications of Mathematics, you will build upon skills taught within National 3 Applications of Mathematics & BGE Mathematics and focus on the following topics/skills:

Numeracy

Measures & Scale
Percentages
Fractions
Graphs, Charts & Tables
Arithmetic
Probability
Ratio & Proportion

Finance & Statistics

Budgeting
Income
Best Deals
Foreign Currency Exchange
Savings & Loans
Statistics
Drawing & Interpreting Graphs Charts & Tables
Comparing Data Sets
Scattergraphs

Geometry & Measures

Time Management
Scale Drawings
Navigation & Bearings
Container Packing Problems
Tolerance
Gradient
Area & Perimeter
Volume
Pythagoras
Distance, Speed, Time

National 5 Applications of Mathematics

What will you learn?

Within National 5 Applications of Mathematics, you will build upon skills taught within National 4 Applications of Maths and focus on the following topics/skills:

Numeracy

Number Work & Rounding
Percentages
Fractions
Ratio & Proportion
Graphs, Charts, Tables
Distance, Speed, Time
Probability

Finance & Statistics

Income
Money Matters
Best Deals
Budgeting
Averages & Range
Standard Deviation
Boxplots & Inter-Quartile Range
Statistical Comparisons
Scattergraphs & Correlation

Geometry & Measures

Tolerance
Rules & Formulae
Scale Drawing & Bearings
Pythagoras Theorem
Gradients
Area & Perimeter
Volume
Container Packing
Precedence Tables

Higher Applications of Mathematics

What will you learn?

Within Higher Mathematics, you will build upon skills taught within National 5 Applications of Mathematics and gain experience working with computing programs Excel and RStudio.

Excel is used in the majority of workplaces to manage a variety of resources.

RStudio is a statistical coding language used within universities and companies such as the NHS for research and reporting.

You will focus on the following topics/skills in Higher Applications of Mathematics:

Probability & Statistics

Venn Diagrams
Probability Trees
Data Types & Sampling
RStudio - Graphs, Charts & Tables
RStudio - Distributions
RStudio - Descriptive Statistics
RStudio - Scatterplots & Correlations
RStudio - Linear Regression
RStudio - Hypothesis Testing
Errors in Statistical Testing

Planning & Decision Making

PERT & Gantt Charts
Cost Benefit Analysis
Risks & Decision Making

Finance

Capital & Interest Rates
Present & Future Values
Savings Products
Credit Cards & Loan Repayment Plans
Excel - Savings & Pensions
Excel - Loan Repayments
Insurance
National Insurance & Income Tax

Mathematical Modelling

Fermi Estimation
Types of Mathematical Models - Linear, Quadratic, Exponential, Recurrence)
Excel - Mathematical Modelling
Errors & Tolerance

Career Pathways

Demonstrated attainment in Mathematics will allow a young person to access further education or training in many different fields including:

Accounting
Actuarial Science
Administration
Allied Health Professions
Architecture
Armed Forces
Banking
Business Management
Civil Service
Clerical Work
Construction
Coding
Data Analyst
Economics
Environmental Management
Finance
Geographical Surveyor
Health Sciences
Hospitality Management
Industrial Design & Manufacture
Marketing
Meteorologist
Network Management
Nursing
Operations Management
Project Management
Researcher
Resource Management
Retail & Sales Analyst
Social Work
Software Development
Sound Technology
Statistician
Stockbroking
Surveying
Transport & Logistics
Travel & Tourism
Teaching

plus many more!

Skills Developed

Through the study of Applications of Mathematics young people will develop skills in but not exclusive to the following areas:

Interpersonal

Develop and Maintain Relationships
Respect

Employability

Thinking Critically and Creatively
Solving Problems
Working with Others
Communicating

Innovation

Problem Solving
Critical Thinking
Forward Planning

Communication

Giving and Receiving Information

Skills for Learning

Higher Order Thinking
Literacy and Numeracy

Digital Technology

Recognising Reliable Sources of Information
Communicating using ICT

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