Mathematics 9709,32 Oct Nov 2024 | Cambridge AS - A Level Past Papers With Mark Scheme

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.