IB Math AI 5.4 - Tangents & Normals Notes

This IB Maths AI SL 5.4 – Tangents & Normals (Student Notes) resource provides clear, focused notes to help students understand how derivatives are used to form equations of tangent and normal lines. The material builds from the geometric idea of a tangent as a line that “just touches” a curve to the calculus concept that the tangent’s gradient is given by the derivative at a point. Students also learn how normals relate to tangents through perpendicular gradients.

Step-by-step explanations show how to identify the point on the curve, calculate the derivative to find the gradient, and apply point–slope form to write equations of tangent lines. The notes highlight common mistakes, such as confusing negative signs and reciprocals when finding normal gradients, and include worked examples that model the full reasoning process. Technology checks encourage students to verify their results graphically using a GDC or graphing software.

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