Graph absolute value functions, determine domain and range, and solve single and double-case absolute value equations and inequalities.

Derive polygon and circle formulas through informal dissection and limit arguments, compute measures of complex composite figures, and analyze proportional and non-proportional dimensional scaling.

Solve multi-step linear equations, literal equations, and systems of linear equations in two variables using algebraic methods and geometric interpretations.

Analyze ordinary annuities, calculate regular payments and future values of sinking funds, model loan repayments, and compute progressive income taxes.

Apply linearity properties and basic integration rules to evaluate indefinite integrals for polynomials, 1/x, e^x, sin(x), and cos(x), and solve initial value problems.

Apply first and second derivatives to analyze monotonicity, concavity, points of inflection, graph behavior, and solve real-world optimization problems.

Derive explicit and recursive formulas for arithmetic sequences, calculate partial sums using sigma notation, and model linear progression phenomena.

Transform general lines and planes into special positions using successive auxiliary reference planes to solve metric and spatial problems.

Construct pictorial and curved-surface spatial representations using isometric, dimetric, trimetric, cylindrical, and spherical projections.

Analyze bivariate relationships, fit least-squares regression lines, interpret correlation coefficients, and examine residuals.

Prove and apply theorems concerning central, inscribed, and circumscribed angles, tangent lines, and intersecting chords.

Calculate bounds of rounded numbers and determine error propagation across multi-step arithmetic, geometric, and physical calculations.