MTTC Mathematics (Secondary) (022) study plan

Classify numbers into rational, irrational, real, complex, integer, and natural sets, justifying each classification with a written criterion.

Compute fluently with fractions, decimals, percents, exponents, radicals, and scientific notation without a calculator, then verify with one.

Solve and graph linear inequalities, absolute-value equations, and compound inequalities, stating the solution set in both interval and set-builder notation.

Explain in writing how the real number system is closed (or not closed) under each of the four basic operations, giving one counterexample where closure fails.

Apply proportional reasoning to solve rate, mixture, and scaling problems, showing the setup before the arithmetic.

Convert among number bases and interpret place-value structure in base-ten and non-base-ten systems.

Translate verbal relationships into algebraic expressions and equations, then check the translation against the original wording.

Identify and extend arithmetic, geometric, and figurate patterns, and write an explicit rule for each sequence you generate.

Solve linear systems in two and three variables by substitution, elimination, and matrix methods, and interpret the geometric meaning of each solution type.

Factor polynomials completely and solve polynomial equations of degree three or higher using factoring, the rational root theorem, and the remainder theorem.

Graph quadratic, polynomial, rational, exponential, and logarithmic functions, stating domain, range, intercepts, asymptotes, and end behavior for each.

Compose and invert functions and determine whether an inverse is a function, justifying with the horizontal line test.

Model real-world situations with linear, quadratic, exponential, and logarithmic functions, and defend the choice of model in two or three sentences.

Derive and apply formulas for perimeter, area, surface area, and volume of two- and three-dimensional figures, including composite figures.

Apply the Pythagorean theorem, distance formula, and midpoint formula to coordinate-geometry problems.

Convert units within and across the metric and customary systems using dimensional analysis, tracking significant units at each step.

Prove and apply triangle congruence and similarity criteria, and use similarity ratios to find unknown lengths and areas.

Apply circle theorems involving chords, tangents, secants, inscribed angles, and arc measure to solve multi-step problems.

Perform and describe transformations (translation, rotation, reflection, dilation) on the coordinate plane, including composition of transformations.

Construct formal two-column or paragraph proofs for angle, triangle, and quadrilateral relationships, citing each theorem used.

Compute and interpret measures of center, spread, and position (mean, median, mode, range, standard deviation, quartiles, z-scores) for a given data set.

Select and construct appropriate displays (histogram, box plot, scatter plot, two-way table) and describe the shape and unusual features of each distribution.

Compute probabilities using addition and multiplication rules, conditional probability, and the binomial distribution, distinguishing independent from dependent events.

Analyze counting problems with permutations, combinations, and the fundamental counting principle, and recognize when order matters.

Evaluate the six trigonometric functions at standard and quadrantal angles, and solve right and oblique triangles using the law of sines and law of cosines.

Verify trigonometric identities and solve trigonometric equations over a stated interval.

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

Differentiate and integrate polynomial, exponential, logarithmic, and trigonometric functions, and apply the derivative to rate-of-change and optimization problems.

Complete two full-length timed practice exams under test conditions, then analyze results by domain to rank your weakest areas.

Re-teach your three weakest sub-topics by writing an explanation and two original problems for each, then solving them from scratch.

Build a one-page formula and theorem sheet from memory, then check it against your notes and correct gaps.

Set a pacing plan that allocates time across the five domains in proportion to their weightings.