Numerical Skills

Surds

Simplification with Surds

Rationalising Denominators

Laws of Indices

Laws of Indices

Scientific Notation

Writing in Scientific Notation

Calculations Using Scientific Notation

Rounding

Decimal Places & Significant Figures

Percentages

Reverse Percentages

Repeated Change

Appreciation & Depreciation

Fractions

Mixed Numbers & Improper Fractions

Addition & Subtraction with Fractions

Multiplication & Division with Fractions

Algebraic Skills

Expansion of Brackets

Single Brackets

Double Brackets

Factorisation

Common Factors

Difference of Two Squares

Factorising quadratics x²+bx+c

Factorising quadratics ax²+bx+c

Methods of Factorisation

Completing the Square

Completing the Square

Functions

Function Notation f(x)

Linear Equations & Inequations

Linear Equations

Linear Inequations

Equation of a Straight Line

Gradient of a Line

y-b=m(x-a)

Simultaneous Equations

Algebraic Solution to Simultaneous Equations

Graphical Solution to Simultaneous Equations

Construction of Simultaneous Equations

Algebraic Fractions

Simplest Form

Addition & Subtraction with Algebraic Fractions

Multiplication & Division with Algebraic Fractions

Solving Equations with Algebraic Fractions

Changing the Subject

Linear Formula

Formulae with Squares & Roots

Quadratic Equations & Roots

Factorising

Quadratic Formula

Discriminant

Quadratic Functions

Features of Quadratic Graphs

Equation of a Quadratic Graph

Sketching Quadratics

Geometric Skills

Circle Geometry

Arcs & Sectors

Problem Solving with Arcs & Sectors

Volume

Sphere, Cone & Pyramid

Composite Solids

Pythagoras' Theorem

Converse of Pythagoras' Theorem

Pythagoras' Theorem in 3D

Properties of Shapes & Angles

Triangles & Quadrilaterals

Polygons

Circles

Similarity

Similar Areas & Volumes

Vectors

Component Vectors in 2D and 3D

Vector Arithmetic

Magnitude of a Vector

Geometry of Vector Addition & Subtraction

Vector Pathways

Working with 3D coordinates

Trigonometric Skills

Graphs of Trigonometric Functions

Graphs of Basic Trigonometric Functions

Transformations of Trigonometric Graphs

Combinations of Transformations

Trigonometric Equations & Identities

Period & Related Angles

Trigonometric Equations

Trigonometric Identities

Trigonometry with Triangles

Sine Rule

Cosine Rule

Area of a Triangle

Bearings

Problem-Solving with Triangles

Statistical Skills

Data Sets

Mean & Standard Deviation

Median & Interquartile Range

Comparison of Data Sets

Scattergraphs & Linear Models

Line of Best Fit

Exam boards

• SQA National 5 Applications of Mathematics

Study tools

• SQA National 5 Maths · Past Papers

Related links

• National 5 Maths · Revision Notes
• National 5 Maths · Past Papers
• SQA National 5 Maths · Exam specification