Applications of A-level Maths

A Level Mathematics is where school maths turns into a powerful engine for understanding the modern world—and in this talk we’ll see how every topic unlocks exciting, meaningful applications. We’ll start with pure maths, where algebra and functions become the language of modelling: from building predictive formulas for business and epidemiology to shaping the logic behind AI systems. Graphs and transformations help us interpret real data, while sequences and series explain finance (compound interest), population growth, and algorithms. Trigonometry connects directly to navigation, engineering, and digital signal processing; exponentials and logarithms model everything from radioactive decay to earthquakes and sound intensity; and differentiation becomes the mathematics of change—optimising profit, minimising energy use, designing the fastest rollercoaster drop, or training machine learning models. Integration then turns rates into totals, powering distance-from-velocity calculations, drug concentration over time, and the physics behind work and energy. We’ll also highlight the elegance and utility of vectors, which drive 3D graphics, robotics and aircraft motion, and show how parametric equations and advanced modelling make curves and motion controllable and predictable. Then we’ll bring in statistics, where sampling, hypothesis testing, probability distributions (including the normal distribution), correlation and regression allow us to judge medical trials, detect bias, forecast outcomes, and separate real effects from coincidence. Finally, mechanics reveals the maths behind the physical universe: kinematics, forces, Newton’s laws, momentum, and projectiles—the same tools used in sport science, crash investigations, spaceflight planning, and video game physics engines. By the end, you’ll see A Level Maths not as separate chapters, but as a connected set of ideas that lets you describe, predict and optimise the world with confidence.