1. Algebra, Surds, and Proof | Solving equations involving square roots and fractions, rationalising denominators, applying algebraic manipulation and proof techniques in integration and inequalities. 2. Coordinate Geometry and Circles | Tangent equations using derivatives, deriving equations of lines and circles, determining geometric conditions for circle placement in quadrants. 3. Calculus – Differentiation and Integration | Tangent equations, stationary points, area under curves using definite integrals, interpreting exponential decay models in real-world contexts. 4. Trigonometry and Transformations | Solving trigonometric equations, applying transformations to graphs (scaling, translation), identifying minimum values and graphical mappings. 5. Binomial Expansion and Exponentials | Expanding using binomial theorem with unknown coefficients, determining values of constants using coefficient comparisons, solving exponential growth/logarithmic models. 6. Vectors, Geometry, and Modeling | Bearing and speed problems using vectors, structural angle calculations in design scenarios, temperature and view count models using exponential and logarithmic functions.