1. Functions and Graphs | Solving inequalities using graphical methods, rewriting quadratic functions in completed square form, and finding function inverses with domain and range. 2. Trigonometry and Identities | Proving trigonometric identities, solving trigonometric equations, and applying them to specific angle ranges. 3. Calculus and Differentiation | Finding stationary points, determining the nature of extrema, differentiating algebraic and exponential functions, and solving related rates problems. 4. Coordinate Geometry and Tangents | Finding the equation of tangents to curves, determining intersection points with straight lines, and analyzing geometric properties. 5. Series and Expansions | Using binomial expansion, solving equations involving series, and determining conditions for specific terms to be constants. 6. Integration and Area Calculation | Evaluating definite and indefinite integrals, applying integration to find enclosed areas between curves and lines. 7. Vectors and Mechanics | Calculating displacements, velocities, and acceleration, solving motion problems using vector methods, and expressing acceleration in terms of displacement. 8. Probability and Combinatorics | Solving permutation and combination problems, determining event probabilities, and analyzing grouping constraints in probability distributions.