Compound Units, Alloy Density Mixing & Area/Volume Prefix Scaling

Surd Rationalisation, Difference-of-Squares & Laws of Indices

Truncation vs. Rounding Error Intervals, Standard Form & Bounds

Non-Linear Proportionality (y ∝ x^n) & Reverse Percentage Compounding

Two-Component Mixing, Dilution Alligation & Combined Work Rates

2D/3D Geometric Similarity Scaling (k, k^2, k^3) & Frustums

Algebraic Subject Rearrangement, Rational Fractions & Completing the Square

Simultaneous Linear Combinations, Straight-Line Gradients & Inequalities

Circle Theorems, Tangent-Radius Right Angles & Shaded Sector Mensuration (Degrees)

3D Mensuration (Cylinder/Sphere/Cone) & Right-Triangle Trigonometry in Degrees

Mean Deviation Balancing, Grouped Median Interpolation & Unequal-Width Histograms

Multi-Stage Conditional Probability Trees (Without Replacement) & Algebraic Venn Overlaps

Regular Polygon Exterior Angles (360°/n), 3-Figure Bearings, Clock Angles & 2D Vectors/Transformations

Polynomial Division by a Quadratic & Linear Remainder Theorem (R(x) = mx + n)

Disguised Radical Equations & Principal Square Root Domain Filtering (√x ≥ 0)

Coupled Arithmetic & Geometric Progressions and Sum to Infinity (S_∞)

Sigma Notation (Fence-Post n-m+1 Terms) & Periodic Recurrence Relations (u_{n+1} = f(u_n))

Circle Coordinate Geometry, Tangent Discriminants & Extremal Distances

Radian Sector Mensuration & Counting Trigonometric Roots in Transformed Intervals

Laws of Logarithms, Disguised Exponential Quadratics (a^{2x} + b a^x + c = 0) & Log Inequalities

Power-Rule Differentiation of Expanded Rational Powers (x^n) & Tangent/Normal Geometry

Stationary Point Classification, Monotonic Cubics & Constrained 2D/3D Optimisation

Definite Integration of Rational Powers (x^n, n ≠ -1) & Area Enclosed Between Curves

Odd/Even Function Integral Symmetry over [-a, a] & Linear Integral Transformations

Multi-Step Graph Transformations (af(bx+c)+d), Modulus Reflections & Root Counting

Binomial Expansion (a + bx)^n Term Isolation, Constant Terms & Multi-Bracket Coefficients

Sine Rule, Cosine Rule, Triangle Area (½ab sin C), The Ambiguous Case & 3D Pyramid Angles

Quadratic Discriminant (b^2 - 4ac), Root-Difference Identities & Parameter Range Inequalities

Series-Parallel Resistor Networks, Potential Dividers & Variable Sensor Meter Tables

Electrical Power Dissipation (P = IV = I^2R = V^2/R), Grid Efficiency & Energy (E = VIt)

Magnetic Flux Patterns & Motor Effect Force on Current-Carrying Conductors (F = BIL)

1D Multi-Stage Kinematics (v–t Graph Areas/Gradients) & Constant-Acceleration SUVAT

1D Coupled Multi-Body Resultant Force (F_net = ma), Lifts & Internal Tension

Equilibrium of Coplanar Forces, Drag/Terminal Velocity Balancing & Tension-Spring/Pulley Systems

Hooke's Law, Springs in Series (½k) vs. Parallel (2k) & Elastic Potential Energy (½kx^2)

1D Momentum Conservation, Vector Rebound Impulse (FΔt = Δp) & Collisions

Work-Energy-Power Conservation (ΔE_p = mgΔh, E_k = ½mv^2) & Resistive Drag Work

Specific Heat Capacity (Q = mcΔT), Latent Heat (Q = mL) & Electrical Heating Curves (Pt = mcΔT)

Wave Equation (v = fλ), Refraction Invariance, Pulse-Echo Sonar (d = ½vt), Relative Waves & Redshift

Nuclear Decay Chains (α, β⁻, γ), Isotope Algebra & Background-Corrected Half-Life Calculus

Electromagnetic Induction (Faraday/Lenz Coil Graphs), AC Generators & Transformer Scaling (V_p/V_s = N_p/N_s)

Hydrostatic Fluid Pressure (P = ρgh), Archimedes Upthrust, Composite Density & Ideal Gas Pistons (P_1V_1 = P_2V_2)

Thermal Conduction Rod Scaling (Q̇ ∝ AΔT/L), Convection Density Currents & Radiative Power (P ∝ R^2 T^4)