1. Functions and Graphing | Finding stationary points of a function, sketching graphs, determining intercepts, and solving inequalities related to quadratic equations. 2. Trigonometric Equations and Graphs | Sketching trigonometric functions, determining intercepts, solving equations involving sine and tangent functions. 3. Quadratic Equations and Logarithms | Determining values of parameters for no real roots, simplifying logarithmic expressions, and solving logarithmic equations. 4. Polynomial Algebra and Factor Theorem | Using polynomial division and factor theorem to determine coefficients, verifying remainder conditions, and solving for unknowns. 5. Exponential and Logarithmic Relationships | Drawing straight-line graphs from logarithmic transformations, estimating parameters, and interpolating values from graphs. 6. Differentiation and Integration | Derivatives of logarithmic functions, second derivatives, definite integrals, and expressing integrals in specific forms. 7. Coordinate Geometry and Intersection Points | Finding intersection points of curves and lines, using perpendicular bisectors, and solving for unknown coordinates. 8. Vectors and Geometric Proofs | Expressing vector quantities in terms of parameters, solving for unknowns, and using vector geometry for collinear points. 9. Sequences and Series | Finding sums of arithmetic and geometric progressions, determining limits of infinite series, and solving recurrence relations. 10. Probability and Combinatorics | Counting arrangements with restrictions, calculating probabilities of independent and dependent events, and applying binomial probability models.