OSAT Advanced Mathematics (211) study plan

Solve linear, quadratic, polynomial, and rational equations and inequalities, justifying each step and checking for extraneous solutions.

Determine domain, range, symmetry, and end behavior of polynomial, rational, radical, and piecewise functions from symbolic and tabular representations.

Build and interpret composition and inverse functions, including restricting domains so inverses exist.

Translate word problems into linear and quadratic models, then critique assumptions, units, and reasonableness of results.

Solve exponential and logarithmic equations and apply growth and decay models to contextual problems.

Solve systems of linear equations by substitution, elimination, and matrix methods, and interpret solutions geometrically.

Classify numbers within the real and complex systems and apply field properties, absolute value, and order of operations in multi-step expressions.

Use proportional reasoning, unit analysis, and number-theory ideas such as divisibility, primes, and modular reasoning to simplify computations.

Prove key triangle, quadrilateral, and circle theorems using congruence, similarity, and angle relationships.

Solve coordinate-geometry problems involving distance, midpoint, slope, parallel and perpendicular lines, and equations of circles.

Compute perimeter, area, surface area, and volume of composite figures, including sectors, segments, prisms, cylinders, cones, and spheres.

Analyze transformations, congruence, and similarity, and use scale factors to relate lengths, areas, and volumes.

Evaluate measurement precision, significant figures, and percent error in applied contexts.

Evaluate limits algebraically and graphically, including one-sided limits, infinite limits, and limits at infinity.

Differentiate polynomial, rational, radical, exponential, logarithmic, and trigonometric functions using product, quotient, and chain rules.

Apply derivatives to tangent lines, rates of change, optimization, and curve analysis including increasing/decreasing intervals, concavity, and extrema.

Compute definite and indefinite integrals using basic antiderivatives and the Fundamental Theorem of Calculus.

Solve trigonometric equations and verify identities using Pythagorean, sum and difference, double-angle, and half-angle identities.

Graph sine, cosine, tangent, and inverse trigonometric functions, identifying amplitude, period, phase shift, and asymptotes.

Apply the Law of Sines and Law of Cosines to oblique triangles, including ambiguous cases.

Connect radian measure, the unit circle, and arc length or sector area to calculus contexts such as trigonometric limits and derivatives.

Compute probabilities using conditional probability, independence, permutations, combinations, and the binomial distribution.

Calculate and interpret descriptive statistics, including mean, median, standard deviation, z-scores, and percentiles.

Analyze scatterplots and regression models, interpret correlation and residuals, and distinguish correlation from causation.

Solve triangle and vector application problems that require trigonometry in real-world measurement contexts.

Construct mathematical models from verbal descriptions, selecting appropriate functions, graphs, tables, or statistical tools.

State assumptions, define variables and units, and evaluate model limitations and reasonableness of results.

Compare competing models using residuals, rates of change, and contextual fit, and communicate recommendations.

Apply problem-solving processes of representation, strategic reasoning, justification, and reflection to multi-step unfamiliar problems.

Diagnose remaining weaknesses across all eight domains using timed practice and a domain-level error tally.

Re-solve missed items from weeks 1 through 7 without notes and explain each corrected method in writing.

Complete two timed mixed-domain sections under exam conditions, pacing at 75 seconds per item or faster.

Consolidate formulas, theorems, and calculator procedures into a final one-page exam-day sheet.