CSET Mathematics (211/212/213) study plan

Compute fluently with rational and irrational numbers in exact form, including simplifying radicals and rationalizing denominators without a calculator.

Classify numbers within the real and complex systems and justify closure properties of each subset with counterexamples where closure fails.

Solve problems involving ratios, proportions, percents, and unit conversions drawn from measurement and scaling contexts.

Apply divisibility rules, prime factorization, GCD, and LCM to solve number-theory problems and verify results by alternate methods.

Extend number work to complex numbers: perform arithmetic in rectangular form, compute moduli and conjugates, and interpret results geometrically in the complex plane.

Translate between verbal descriptions, tables, graphs, and symbolic rules for linear, quadratic, and exponential relationships.

Solve linear equations and inequalities, including absolute-value and compound inequalities, and express solution sets in interval and set-builder notation.

Set up and solve systems of two and three linear equations, interpreting consistency and dependence geometrically.

Factor polynomials completely over the integers and rationals, and connect factors to zeros, intercepts, and multiplicity behavior on graphs.

Analyze polynomial and rational functions: end behavior, asymptotes, domain restrictions, and sign charts.

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and interpret the discriminant in context.

Apply the Remainder and Factor Theorems and the Rational Root Theorem to locate and verify roots.

Manipulate exponential and logarithmic expressions, solve exponential and logarithmic equations, and identify extraneous solutions.

Model growth and decay situations and justify the choice of model from data patterns.

Generate and analyze arithmetic and geometric sequences and series, deriving and applying the relevant sum formulas.

Connect function transformations (shifts, stretches, reflections) across function families and produce equations from given graphs.

Prove and apply triangle congruence and similarity criteria, and use proportional reasoning in similar figures to find unknown lengths and areas.

Apply the Pythagorean Theorem and its converse, special right triangles, and trigonometric ratios to solve right-triangle problems.

Derive and apply coordinate-geometry formulas for distance, midpoint, slope, and equations of circles and lines.

Compute perimeter, area, surface area, and volume for standard and composite figures, and justify formulas through dissection or decomposition arguments.

Analyze circles: inscribed angles, chords, tangents, arc measures, and the relationships among them, applying each theorem to numerical problems.

Perform transformations (translations, rotations, reflections, dilations) in the coordinate plane and describe resulting invariants.

Compute probabilities using the addition and multiplication rules, conditional probability, and independence, distinguishing these from mutually exclusive events.

Organize data with appropriate displays and compute and interpret measures of center, spread, and position (mean, median, standard deviation, z-scores, percentiles).

Model bivariate data with scatterplots and least-squares regression lines, interpret correlation and residuals, and recognize the limits of correlation versus causation.

Design and critique sampling methods and experiments, identifying bias, confounding variables, and appropriate scope of inference.

Compute limits algebraically and graphically, including one-sided limits and limits at infinity, and identify points of discontinuity.

Apply the definition of derivative and differentiation rules (power, product, quotient, chain) to compute derivatives and interpret them as instantaneous rates of change.

Use derivatives to analyze function behavior (increasing/decreasing intervals, extrema, concavity, inflection points) and solve applied optimization and related-rates problems.

Compute definite and indefinite integrals using standard techniques and the Fundamental Theorem of Calculus, and interpret definite integrals as net accumulation and area.

Summarize key historical developments in mathematics (for example, the emergence of non-Euclidean geometry, the rigorization of calculus, or the development of probability) and explain their conceptual significance.

Explain and apply problem-solving and proof methodology: direct proof, proof by contradiction, counterexample, and the role of multiple representations in teaching a concept.