National 4 Maths focuses on building secure numeracy and problem-solving skills, while developing confidence with algebra, geometry and data handling. The course is assessed internally and does not include a final exam. Students must pass all units and complete an Added Value Unit.

Assessment

• Numeracy Unit (internal assessment)
• Expressions and Formulae Unit (internal assessment)
• Relationships Unit (internal assessment)
• Added Value Unit – Application of Maths (problem-solving task)

Key Areas of the Course

• Fractions, decimals, percentages and ratio
• Negative numbers, rounding and significant figures
• Money and finance (including tax, hire purchase and foreign exchange)
• Measurement, unit conversions and practical numeracy
• Data handling and interpretation
• Algebraic expressions and simplifying
• Substitution into formulae and changing the subject
• Solving equations
• Expanding brackets
• Working with straight line graphs
• Angles and geometric properties
• Coordinates, gradients and straight lines
• Pythagoras and basic trigonometry
• Area, volume and scale drawing
• Sequences and number patterns

Added Value Unit

• Extended problem-solving task
• Application of skills from across the course
• Multi-step reasoning and interpretation

Students often need support with:

• Building confidence with core numeracy skills
• Translating worded problems into clear mathematical steps
• Working accurately without losing marks through small errors
• Understanding algebra rather than memorising procedures
• Interpreting graphs and data correctly
• Applying skills across different topics in the Added Value Unit

Students working towards National 4 often develop at different speeds. In some cases, learners may complete aspects of National 5 content alongside National 4, particularly where they are close to the National 5 standard.

National 5 Mathematics tutoring focuses on strengthening core algebraic and numerical skills while developing confidence with multi-step problem solving. Lessons are adapted to the student’s current level, whether they need targeted support with specific topics or structured revision across the full course.

Topics covered include:

• Algebraic fractions and expanding brackets
• Factorising and completing the square
• Equations, inequalities and simultaneous equations
• Changing the subject of a formula
• Indices and surds
• Quadratics, parabolas and the quadratic formula
• Functions and straight line graphs
• Trigonometry, sine and cosine rules
• Trigonometric equations, graphs and identities
• Vectors
• Percentages and fractions
• Scientific notation
• Pythagoras and similar shapes
• Arcs, sectors and shapes within circles
• Bearings, triangle area and Volume
• Statistics

Students often need support with:

• Selecting appropriate methods rather than attempting trial-and-error approaches.
• Interpreting worded problems and translating them into correct mathematical models.
• Managing accuracy and avoiding small errors that cost marks.
• Applying trigonometry, quadratics, circle geometry and bearings confidently in unfamiliar problem contexts.
• Linking algebraic methods to graphical representations, particularly with straight lines, functions and parabolas.
• Structuring multi-step reasoning clearly in non-calculator and problem-solving questions.

Higher Mathematics demands greater fluency in algebra and calculus, along with the ability to apply methods accurately in unfamiliar and multi-step contexts. Lessons focus on developing confidence with abstract reasoning, structured working and exam-level problem solving, not just procedural competence.

Topics commonly covered include:

• Polynomials and quadratics
• Functions and graphs of functions
• Straight lines
• Circles
• Exponential and logarithmic functions
• Trigonometric formulae and equations
• Vectors
• Recurrence relations
• Differentiation (including optimisation and rates of change)
• Integration and area under a curve
• Further calculus techniques
• Wave function

Students often need support with:

• Linking algebraic processes to graphical behaviour, particularly with functions and transformations.
• Understanding differentiation conceptually rather than treating it as a memorised rule set.
• Applying integration correctly and interpreting areas in context.
• Handling multi-step calculus problems such as optimisation.
• Working confidently with logarithms and exponentials without procedural confusion.
• Managing algebraic complexity in recurrence relations, trig identities and polynomial manipulation.

Advanced Higher Mathematics demands confident algebraic control and the ability to think logically across extended, multi-step problems. The course moves beyond standard techniques and focuses on proof, structured reasoning and combining ideas from different areas of mathematics within a single question. Lessons emphasise clarity of argument, precision of working and genuine conceptual understanding.

Topics commonly covered include:

• Properties of functions and advanced graph analysis
• Differentiation and further differentiation
• Integration and further integration
• Differential equations
• Sequences and series, including further series methods
• Binomial theorem
• Partial fractions
• Complex numbers
• Matrices and systems of equations
• Vectors
• Further number theory
• Methods of proof

Students often need support with:

• Constructing clear and logically sound proofs rather than relying on memorised methods.
• Managing algebraic complexity across multi-stage calculus and differential equation problems.
• Working confidently with formal notation in sequences, series and functions, particularly when generalising or proving results.
• Working confidently with complex numbers in both algebraic and geometric form.
• Interpreting questions involving functions, derivatives and integrals in extended, unfamiliar problems.
• Maintaining precision in extended solutions where small logical gaps can cost marks.