What you’ll learn10 learning objectivesChoose one objective for a focused lesson, or study the complete topic.—AHL 3.7 (HL)—Radian measure• Define radians and convert between degrees and radians.• Use radians for arc length and sector area.Syllabus objective—AHL 3.8 (HL)—Unit circle and trigonometric equations• Define sin theta and cos theta using the unit circle; tan theta=sin theta/cos theta.• Use cos^2 theta + sin^2 theta = 1 and ambiguous sine-rule case.• Construct sin x and cos x graphs from the unit circle; solve trig equations graphically on finite intervals.Syllabus objective—AHL 3.9 (HL)—Matrix transformations and fractals• Use matrices for 2D transformations: reflections, stretches, enlargements, translations and rotations.• Compose transformations and interpret determinant as area scale factor.• Use iterative techniques to generate fractals.Syllabus objective—AHL 3.10 (HL)—Vectors• Use vectors/scalars, directed line segments, unit vectors and base vectors i, j, k.• Use components, column representation, vector algebra, magnitude, normalization and resultants.Syllabus objective—AHL 3.11 (HL)—Vector equations of lines• Use vector equation r=a+lambda b in 2D and 3D.• Convert vector line equations to parametric form.Syllabus objective—AHL 3.12 (HL)—Vector kinematics• Model constant-velocity linear motion in 2D/3D with r=r0+vt.• Find positions, intersections, paths, closest approach times and distances.• Include variable velocity in 2D; projectile and circular motion are special cases.Syllabus objective—AHL 3.13 (HL)—Scalar and vector products• Use scalar product to find angles and test perpendicular vectors.• Use vector product, right-hand rule and |v x w| for parallelogram/triangle area.• Resolve components parallel and perpendicular to another vector.Syllabus objective—AHL 3.14 (HL)—Graph theory basics• Use graph terminology: vertices, edges, adjacent items, degree, simple/complete/weighted graphs.• Represent real-world structures as weighted or unweighted graphs.• Know connected, strongly connected, directed graphs, in/out degree, subgraphs and trees.Syllabus objective—AHL 3.15 (HL)—Adjacency matrices and transition matrices• Use adjacency matrices to count k-length walks using powers of a matrix.• Use weighted adjacency tables.• Construct transition matrices for strongly connected directed/undirected graphs.Syllabus objective—AHL 3.16 (HL)—Graph algorithms• Use walks, trails, paths, circuits, cycles, Eulerian trails/circuits and Hamiltonian paths/cycles.• Use Kruskal's and Prim's algorithms for minimum spanning trees.• Solve Chinese postman problems for weighted graphs with up to four odd vertices.• Use nearest-neighbour and deleted-vertex algorithms for travelling salesman bounds.Syllabus objective
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