1. Binomial Expansion & Approximation | Expanding \\\\((9 - 3x)^2\\\\) up to the term in \\\\(x^2\\\\), simplifying coefficients.

2. Complex Numbers & Cartesian Form | Finding square roots of \\\\(6 - 8i\\\\) by forming and solving a quartic equation.

3. Trigonometric Equations & Iteration | Showing a given trigonometric equation has one root and proving an iterative sequence converges to this root.

4. Vectors & Trapezium Properties | Finding a missing position vector, computing the intersection of diagonals, and calculating angle \\\\(ABC\\\\) using the scalar product.

5. Differential Equations & Volume Flow | Formulating and solving a differential equation governing the growth of a spherical balloon.

6. Stationary Points & Integration | Finding the stationary point of \\\\(f(x) = 3e^x - 2e^{-2x}\\\\) and evaluating a logarithmic integral using partial fractions.