1. Differentiation, Graphs, and Stationary Points | Derivative simplification, intervals of function decrease, curve sketching, tangent equations, area between curve and lines. 2. Algebraic Techniques and Proof | Solving higher-degree equations via substitution, proving identities, binomial expansion coefficient, polynomial root and symmetry properties. 3. Coordinate Geometry and Circle Properties | Finding line gradients, tangent equations, intersection with axes, calculating distances between points, circle centers and non-intersection conditions. 4. Vectors and Triangle Area Ratios | Vector operations, proof of collinearity, finding ratios from vector geometry, area comparisons using position vectors. 5. Trigonometry and Equations | Solving trigonometric equations, converting trig identities, finding number of solutions, use of compound angle relationships. 6. Modeling and Exponentials | Fuel tank volume-distance linear model, growth models of plant height, limiting values, rate of change interpretation, model evaluation from real data.