Advanced A-Level Math: From Motion to Differential Equations

This module covers the application of calculus to kinematics in one and two dimensions, including projectile motion. Students will learn to use calculus for motion analysis, work with vector calculus, and model projectile trajectories.

This module focuses on friction models, moments in static contexts, and the equilibrium of rigid bodies. Students will learn about coefficients of friction, moment calculations, and solving equilibrium problems with coplanar forces.

This module covers the Normal distribution, its applications in probability and statistics. Students will learn to use the Normal distribution for probability calculations, conduct hypothesis tests, and interpret results in context.

This module introduces vector operations in two and three dimensions. Topics include vector addition, scalar multiplication, position vectors, and applying vectors to solve problems in pure mathematics.

This module covers advanced differentiation techniques including the product rule, quotient rule, and chain rule. Students will learn to differentiate implicitly and parametrically defined functions and apply differentiation to various problem types.

This module focuses on various integration techniques including integration by substitution, partial fractions, and integration by parts. Students will learn to integrate a range of functions and apply these methods to solve problems.

This module introduces first-order differential equations with separable variables. Students will learn to find analytical and particular solutions, sketch solution curves, and interpret solutions in context. The module also covers identifying limitations of differential equation solutions.