This IB Maths AI SL 5.4 – Tangents and Normals resource develops students’ understanding of how derivatives are used to form equations of tangent and normal lines to curves. Learners connect the gradient function to the slope of a curve at a point, apply point–slope form to write tangent equations, and use the concept of perpendicular gradients to construct normal lines. Clear definitions and structured notes build precision with key calculus language and geometric interpretation.

Guided examples lead students step-by-step through differentiating functions, finding gradients at specific x-values, identifying points on curves, and forming equations of tangent lines. Practice questions extend this to normals and require students to verify results using graphing technology, reinforcing the visual idea that a tangent “just touches” the curve while the normal is perpendicular at the same point. Tasks also include problems where derivative information and given points must be combined, strengthening algebraic and conceptual links.