Mathematics 9709,31 Oct Nov 2024

1. Polynomial Factorization & Remainders | Finding Unknown Coefficients – Using the factor and remainder theorems to determine the values of unknown coefficients in a polynomial.

2. Implicit Differentiation & Gradient Calculation | Logarithmic Function Derivatives – Differentiating an implicitly defined function and calculating the gradient at a specific point.

3. Trigonometric Identities & Equation Solving | Secant & Tangent Transformations – Proving trigonometric identities and solving equations within a specified range.

4. Root Approximation & Iterative Methods | Exponential & Logarithmic Equations – Confirming the existence of a root graphically, estimating its location, and refining the root using iteration.

5. Partial Fractions & Series Expansion | Rational Function Decomposition – Expressing a rational function in partial fractions and determining coefficients in its series expansion.

6. Vectors & Line Equations | Intersection & Direction Angles – Finding vector equations of lines, determining intersection conditions, and calculating angles between directions.