Algebra, Functions, Geometry and Trigonometry 0.2.1

Learning outcomes

1. Transform expressions and solve equations, inequalities, systems, and parameterized families while preserving domains and solution logic.
2. Analyse functions as mappings and move among symbolic, graphical, tabular, inverse, composition, and transformed representations.
3. Solve coordinate geometry problems involving lines, distance, conics, loci, intersections, and parametric descriptions.
4. Use radians, unit-circle definitions, identities, sinusoidal models, and the laws of sines and cosines in exact and numerical problems.
5. Use vector components, magnitudes, dot products, angles, decomposition, and projection to solve geometric problems.
6. Choose and validate elementary functional forms, reason about scaling, and solve mixed algebraic/trigonometric models with sensitivity checks.
7. Integrate algebra, functions, geometry, trigonometry, vectors, logarithms, and model validation in an independent survey-and-signal capstone.