This IB Maths AI HL 3.12 resource introduces applications of vectors in kinematics and motion, and is fully aligned with the IB Applications and Interpretation HL syllabus.

Students learn how vectors can be used to model objects moving with constant velocity in two and three dimensions. The notes explain how position vectors change over time and how the constant velocity model connects directly to the vector equation of a line.

The resource develops students’ ability to interpret motion using vector equations, including finding initial positions, calculating positions after a given time, and determining the distance between two moving objects in 3D. Students are guided through the standard IB exam approach of first finding the relevant position vectors and then applying the distance formula.

The notes also introduce motion in a straight line using parametric vector equations. Students learn how to identify the velocity vector, calculate speed as the magnitude of velocity, and convert a vector equation into a Cartesian equation of the path.

Projectile-style vector motion is then explored through parametric equations. Students practise writing separate equations for horizontal and vertical motion, eliminating the parameter, and using a quadratic model to find the maximum height of a projectile.

The resource finishes by connecting variable velocity to calculus, preparing students for later work on differentiation, integration, position, velocity, and displacement.

Ideal for IB Maths AI HL teachers teaching vector applications, kinematics, parametric motion, projectile-style motion, and the connection between vectors and calculus.

This pairs great with our slidedeck!