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 Mathematics at every available level —National 4, National 5, Higher, and Advanced Higher.

Assessment

Course assessment is a mixture of demonstrating knowledge and understanding of mathematical operational skills, integrate mathematical skills developed throughout the course, demonstrate abstract mathematical reasoning and apply numerical calculation skills with and without the use of a calculator to demonstrate mathematical processes.

Within Mathematics, there is a specific focus on working with abstract algebraic concepts throughout each curricular level.

Each level will also have an non calculator element along with a calculator element with learners .

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

National 4

Internal Assessment

Four mandatory unit assessments:

Numeracy
Expressions & Formulae
Relationships
Added Value Unit.

External Assessment

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

To obtain a pass at National 4 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 either National 5 Applications of Mathematics or National 5 Mathematics.

National 5

External Assessment

The National 5 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):

40 marks

Time allowed - 1 hour

Paper 2 (Calculator):

50 marks

Time allowed - 1 hour 30 minutes

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

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

Higher

External Assessment

The Higher Mathematics grade, unlike most other Higher 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):

55 marks

Time allowed - 1 hour 15 minutes

Paper 2 (Calculator):

65 marks

Time allowed - 1 hour 30 minutes

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

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.

Advanced Higher

External Assessment

The Advanced Higher Mathematics grade, unlike most other Advanced Higher 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 - 1 hour

Paper 2 (Calculator):

80 marks

Time allowed - 2 hours 30 minutes

A pass at Advanced Higher Mathematics, is purely based on the final external assessment.

Advanced Higher Mathematics will provide learners with skills which will be vital to success within further education beyond Lanark Grammar School.

To prepare learners fully for the final exam, smaller class assessments will take place during October, December and April 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 Mathematics course would be best suited to a young person who is interested in developing skills in abstract algebra and gaining a knowledge and understanding of complex mathematical techniques to use in further study.

Success at Higher Mathematics and Advanced Higher Mathematics, relies on a strong understanding of skills taught within National 5 Mathematics and broadens & extends on the topics covered within this course.

Learners who have demonstrated a strong knowledge and understanding of Science based courses is preferable - specifically Physics and Chemistry.

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 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 Applications of Mathematics at all available levels - National 3, National 4, National 5 and Higher.

Further information on these courses can be found in the Applications of Mathematics tab or by clicking here.

National 5 Mathematics

What will you learn?

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

Algebraic Skills

Equation of a Straight Line
Solving Equations/Inequations
Simultaneous Equations
Expanding Brackets
Factorising
Completing the Square
Algebraic Fractions
Quadratic Graphs
Quadratic Equations

Geometric Skills

Pythagoras’ Theorem
Angles in Shapes
Similarity
Gradient of a Straight Line
Circle (Arcs and Sectors)
Volume
Vectors

Trigonometric Skills

Trigonometric Formulae
Trigonometric Graphs
Trigonometric Equations and Identities

Numerical Skills

Surds
Indices
Percentages
Fractions
Significant Figures
Scientific Notation

Statistical Skills

Statistics (Standard Deviation & IQR)
Comparing Datasets
Scattergraphs (Line of Best Fit)

Higher Mathematics

What will you learn?

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

Algebraic Skills

Sets & Functions
Polynomials
Quadratics
Recurrence Relations
Exponentials & Logarithms

Calculus Skills

Graphs of Functions
Differentiation
Integration
Further Calculus

Trigonometric Skills

Trigonometric Graphs and Equations
Addition Formulae
Wave Function

Geometric Skills

The Straight Line
Vectors
The Circle

Advanced Higher Mathematics

What will you learn?

Within Advanced Higher Mathematics, you will build upon skills taught within National 5 Mathematics & Higher Mathematics and focus on the following topics/skills:

Calculus