Course review
Review each learning objective in this topic, then open its concept explanation or question set.
Learning objective
• Define radians and convert between degrees and radians. • Use radians for arc length and sector area.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• 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.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• 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.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Use vectors/scalars, directed line segments, unit vectors and base vectors i, j, k. • Use components, column representation, vector algebra, magnitude, normalization and resultants.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Use vector equation r=a+lambda b in 2D and 3D. • Convert vector line equations to parametric form.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• 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.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• 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.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• 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.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• 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.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• 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.
Start with the concept explanation, then practise to create mastery evidence.