C.2 Vectors and Graph TheoryHL
HL extensions of Geometry & Trig. Radians, the unit circle, and the ambiguous case. Geometric transformations expressed as matrices. The full vector toolkit — components, position vectors, vector lines in 2D/3D, vector kinematics, scalar/vector products. Graph theory — vertices, edges, weighted graphs, adjacency and transition matrices, MST, Eulerian/Hamiltonian paths, the Chinese postman and travelling-salesman problems.
Radian measureHLSign up
Radian definition · Arc length and sector area in radians
Unit circle, Pythagorean identity, ambiguous caseHLSign up
Unit-circle definitions · sin²θ + cos²θ = 1 · Ambiguous SSA case
Geometric transformations using matricesHLSign up
Rotation, reflection, scaling matrices · Determinant as area-scale factor
Vectors — components, unit vectors, position vectorsHLSign up
Vector addition and scalar multiplication · Magnitude and unit vectors · Position vectors
Vector line equations in 2D and 3DHLSign up
r = a + λb · Parametric form
Vector kinematicsHLSign up
Position, velocity, acceleration as vectors · Constant vs variable velocity
Scalar and vector productsHLSign up
Dot product and angle between vectors · Cross product and area of parallelogram
Graph theory — vertices, edges, weighted graphsHLSign up
Vertices, edges, degrees · Weighted vs unweighted graphs
Adjacency matrices, walks, transition matricesHLSign up
Adjacency matrices and walks of length n · Transition matrices
Trees, MST, Eulerian and Hamiltonian paths, TSPHLSign up
Minimum spanning tree (Prim, Kruskal) · Eulerian and Hamiltonian paths · Chinese postman and travelling salesman