Analyze straight lines, general and standard forms of circles, and solve geometric problems involving tangents, normals, and intersections.

Master advanced integration methods including u-substitution, integration by parts, and partial fractions for definite and indefinite integrals.

Construct, analyze, and evaluate formal mathematical arguments using deduction, exhaustion, contradiction, contrapositive, and induction across number theory and algebra.

Analyze quadratic functions in depth, evaluate discriminants across real and complex roots, and solve quadratic and linear inequalities in one and two variables.

Manipulate algebraic expressions with rational exponents and surds, apply polynomial division and theorems, and simplify complex algebraic fractions.

Model complex random phenomena using set operations, advanced combinatorial counting, and geometric area representations.

Represent, summarize, and interpret univariate datasets using graphical representations, measures of central tendency, position, and dispersion.

Construct formal algebraic proofs for fundamental, compound angle, and double angle identities, and convert linear combinations to harmonic forms.

Determine tangent and normal equations, find extrema, analyze curve behavior, and solve real-world optimization problems.

Evaluate definite integrals to calculate the total geometric area under a curve and enclosed between intersecting curves.

Summarize bivariate categorical data, calculate joint, marginal, and conditional relative frequencies, and test for independence.

Fit linear, quadratic, and exponential models to bivariate data, evaluate fit via residuals and correlation, and distinguish correlation from causation.

Master radian measure, circular sector geometry, unit circle evaluations, and angular-to-linear velocity kinematics.