1. Polynomial Factorization & Roots | Finding Expressions from Graphs – Determining cubic polynomial factors from given intercepts. 2. Simultaneous Equations & Quadratics | Solving Non-Linear Systems – Substituting and solving simultaneous quadratic equations. 3. Trigonometric Graphs & Transformations | Identifying Constants – Finding amplitude, period, and phase shifts in transformed cosine functions. 4. Logarithms & Integration | Evaluating Definite Integrals – Determining constants in definite integral equations involving logarithmic functions. 5. Binomial Expansions & Series Terms | Finding Coefficients and Independent Terms – Extracting coefficients in expansions and identifying terms independent of variables. 6. Polynomial Division & Remainders | Finding Unknown Coefficients – Using factor and remainder theorems to determine missing polynomial terms. 7. Exponential & Logarithmic Relationships | Finding Functions from Graphs – Deriving exponential equations from plotted data points. 8. Differentiation & Stationary Points | Analyzing Curve Behavior – Finding first derivatives, identifying turning points, and proving uniqueness of extrema. 9. Geometric Progressions & Infinite Sums | Finding Ratios and Limits – Calculating common ratios and conditions for summability in geometric sequences. 10. Definite Integrals & Area Calculations | Finding Enclosed Regions – Computing exact enclosed areas using definite integrals of trigonometric functions. 11. Trigonometric Equations & Identities | Solving for Angles in Radians & Degrees – Finding solutions for trigonometric expressions within specified domains.