A compact navigation directory for the BTT Additional Mathematics Synthesis Guide series. The guides connect algebra, functions, trigonometry, geometry, calculus, modelling, proof, verification and examination transfer.
52 published guides are indexed here as of 25 September 2026. This page is a routing directory; the individual guides remain the topic owners.
Guides 1–10
- Additional Mathematics Synthesis Guide 1: Quadratics, Coordinate Geometry and Tangency
- Additional Mathematics Synthesis Guide 2: Exponentials, Logarithms, Linear Law and Modelling
- Additional Mathematics Synthesis Guide 3: Trigonometric Functions, Identities, Equations and Geometry
- Additional Mathematics Synthesis Guide 4: Calculus, Algebra and Kinematics
- Additional Mathematics Synthesis Guide 5: Functions, Inverses, Compositions and Graph Transformations
- Additional Mathematics Synthesis Guide 6: Polynomials, Factor and Remainder Theorem, Partial Fractions and Binomial Expansion
- Additional Mathematics Synthesis Guide 7: Surds, Indices, Inequalities and Exact Algebra
- Additional Mathematics Synthesis Guide 8: Equations, Parameters and Algebraic Proof
- Additional Mathematics Synthesis Guide 9: Plane Geometry, Coordinate Geometry, Trigonometry and Proof
- Additional Mathematics Synthesis Guide 10: Tangents, Normals, Stationary Points and Optimisation
Guides 11–20
- Additional Mathematics Synthesis Guide 11: Definite Integrals, Area, Accumulation and Motion
- Additional Mathematics Synthesis Guide 12: Mixed-Topic Recognition, Method Selection, Verification and Transfer
- Additional Mathematics Synthesis Guide 13: Radians, Arc Length, Sector Area and Trigonometric Modelling
- Additional Mathematics Synthesis Guide 14: Rational Functions, Algebraic Fractions, Asymptotes and Domain Control
- Additional Mathematics Synthesis Guide 15: Exponential and Logarithmic Change, Differentiation, Growth and Decay
- Additional Mathematics Synthesis Guide 16: Hidden Quadratics, Substitution, Structural Factorisation and Equation Families
- Additional Mathematics Synthesis Guide 17: R-Form Trigonometry, Amplitude, Phase, Maxima and Modelling
- Additional Mathematics Synthesis Guide 18: Linear Law Transformations, Straight-Line Graphs, Parameter Recovery and Model Checking
- Additional Mathematics Synthesis Guide 19: Trigonometric Calculus — Differentiation, Integration, Stationary Points and Exact Areas
- Additional Mathematics Synthesis Guide 20: Coordinate Circles, Lines, Chords, Tangents and Intersection Conditions
Guides 21–30
- Additional Mathematics Synthesis Guide 21: Quadratic Functions, Completing the Square, Global Bounds and Modelling
- Additional Mathematics Synthesis Guide 22: Simultaneous Equations, Line–Curve Intersections, Discriminants and Tangency Conditions
- Additional Mathematics Synthesis Guide 23: Binomial Theorem, General Terms, Coefficient Extraction and Parameter Problems
- Additional Mathematics Synthesis Guide 24: Cubic Polynomials, Factor and Remainder Theorems, Roots, Multiplicity and Graph Structure
- Additional Mathematics Synthesis Guide 25: Calculus Rule Selection — Rational Powers, Product, Quotient and Chain Rules
- Additional Mathematics Synthesis Guide 26: Connected Rates of Change — Geometry, Variables, Units and Constraints
- Additional Mathematics Synthesis Guide 27: Partial Fractions — Repeated Linear Factors, Quadratic Factors and Reconstruction
- Additional Mathematics Synthesis Guide 28: Principal Values, Inverse Trigonometric Functions, Graphs, Symmetry and Interval Solutions
- Additional Mathematics Synthesis Guide 29: Surds, Conjugates, Rationalising Denominators, Surd Equations and Exact Verification
- Additional Mathematics Synthesis Guide 30: Integration Rule Selection — Rational Powers, Exponentials, Trigonometric Forms and Reverse Chain Rule
Guides 31–40
- Additional Mathematics Synthesis Guide 31: Increasing and Decreasing Functions, Derivative Sign Charts, Stationary Inflexions and Second-Derivative Decisions
- Additional Mathematics Synthesis Guide 32: Transformed Trigonometric Graphs — Amplitude, Period, Midline, Tangent Structure and Modelling
- Additional Mathematics Synthesis Guide 33: Exponential and Logarithmic Functions — Laws, Change of Base, Inverse Graphs, Equations and Models
- Additional Mathematics Synthesis Guide 34: Trigonometric Identity Engineering — Addition Formulae, Double Angles, Simplification, Proof and Equation Reduction
- Additional Mathematics Synthesis Guide 35: Kinematics from Calculus — Displacement, Velocity, Acceleration, Direction Changes and Total Distance
- Additional Mathematics Synthesis Guide 36: Graph-to-Equation Reconstruction — Quadratics, Exponentials, Trigonometric Functions and Parameter Recovery
- Additional Mathematics Synthesis Guide 37: Domains, Ranges, Restrictions and Admissible Solutions Across A-Math
- Additional Mathematics Synthesis Guide 38: Parameter Thresholds and Number of Solutions — Discriminants, Tangency, Range and Intersections
- Additional Mathematics Synthesis Guide 39: Proof and Justification — Algebra, Geometry, Trigonometry and Calculus
- Additional Mathematics Synthesis Guide 40: Exactness, Approximation, Calculator State, Rounding and Verification
Guides 41–50
- Additional Mathematics Synthesis Guide 41: Representation Switching — Words, Equations, Graphs, Geometry and Rates
- Additional Mathematics Synthesis Guide 42: Backward Reasoning and Target Decomposition — Let the Required Answer Choose the Route
- Additional Mathematics Synthesis Guide 43: Linked Multi-Stage Problems — Hence, Result Handoffs, Parameters and Preserving Conditions
- Additional Mathematics Synthesis Guide 44: Mathematical Modelling — Formulation, Variables, Assumptions, Parameter Meaning, Validation and Return to Context
- Additional Mathematics Synthesis Guide 45: Symmetry and Invariants — Reflections, Periodicity, Paired Roots and Graph Structure
- Additional Mathematics Synthesis Guide 46: Case Splitting and Branch Control — Equations, Inequalities, Trigonometric Intervals and Domain Conditions
- Additional Mathematics Synthesis Guide 47: Information Filtering and Sufficiency — Relevant Data, Hidden Constraints, Redundancy and Unique Determination
- Additional Mathematics Synthesis Guide 48: Comparative Solution Design — Alternative Methods, Reliability, Efficiency and Independent Verification
- Additional Mathematics Synthesis Guide 49: Counterexamples and Theorem Boundaries — Testing Claims, Conditions and Invalid Shortcuts
- Additional Mathematics Synthesis Guide 50: Generalisation from Cases to Families — Patterns, Parameters, Conjectures and Exact Rules
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