Outline Why Equations of Planes Are a Core Topic in AS Level Further Mathematics (9231) Three Main Forms of a Plane Equation Cartesian Form: ax + by + cz = d Vector Form: r · n = p Parametric Form: …
Outline Why Area of a Sector (½ r²θ) Is a High-Scoring Concept in AS Level Further Mathematics (9231) Derivation and Meaning of the Formula ½ r²θ Importance of Radian Measure in Sector Area Questions Conditions for Using the Integration-Free Method …
Outline Why Sketching Polar Curves Is a High-Scoring Topic in AS Level Further Mathematics (9231) Core Forms of Polar Equations Frequently Tested Understanding Symmetry in Polar Curves Testing for Symmetry About the Initial Line Testing for Symmetry About θ = …
Outline Why Cartesian–Polar Conversion Is a Core Topic in AS Level Further Mathematics (9231) Fundamental Relationships Between Cartesian and Polar Coordinates Converting Points Between Cartesian and Polar Forms Converting Equations from Cartesian to Polar Form Converting Equations from Polar to …
Outline Why Invariant Points & Invariant Lines Are High-Level Matrix Concepts in AS Level Further Mathematics (9231) Meaning of Invariant Points Under a Linear Transformation Invariant Lines and Invariant Directions Explained Link Between Invariant Directions and Eigenvectors Eigenvalues and Their …
Outline Why Area Scale Factor & Determinants Are Examiner-Favourite in AS Level Further Mathematics (9231) Determinant as a Geometric Interpretation Absolute Value of Determinant and Area Change Orientation Change and Negative Determinant Area Transformation Under a 2×2 Matrix Step-by-Step Method …
Outline Why Geometric Transformations Using 2×2 Matrices Are Core in AS Level Further Mathematics (9231) Representing Points as Column Vectors General Structure of a 2×2 Transformation Matrix Rotation Matrices – Anticlockwise and Clockwise Reflection Matrices in Coordinate Axes Reflection in …
Outline Why (AB)⁻¹ = B⁻¹A⁻¹ Is a Core Identity in AS Level Further Mathematics (9231) Understanding the Order Reversal in Matrix Inverses Proof of (AB)⁻¹ = B⁻¹A⁻¹ Using Identity Matrix Logic Conditions Required for Multi-Matrix Inverses Step-by-Step Exam Technique for …
Outline Why Determinants & Inverses Are High-Weight Topics in AS Level Further Mathematics (9231) Definition of Determinant for 2×2 Matrices Condition for a Non-Singular Matrix Inverse of a 2×2 Matrix – Adjoint Method Determinant of a 3×3 Matrix – Cofactor …
Outline Importance of Matrix Operations in AS Level Further Mathematics (9231) Matrix Order and Compatibility Rules Matrix Addition – Rules and Structured Application Scalar Multiplication and Distribution Accuracy Matrix Multiplication – Fundamental Logic Non-Commutativity of Matrix Multiplication Identity Matrix – …