MTEL Mathematics (63) study plan

Diagnose baseline by completing a full-length timed practice test under exam conditions and recording raw scores per subarea (number sense, algebra, geometry, functions, trigonometry, probability/statistics, calculus)

Rank the seven subareas by percentage correct and convert the ranking into a weighted weekly study allocation that gives the three weakest subareas the most time

Build a formula and definition reference sheet covering number properties, exponent and radical rules, and algebraic manipulation techniques

Solve 30 mixed number-sense and algebraic-manipulation problems without a calculator, then rework every missed item and write the underlying rule it tested

Solve and graph linear equations, inequalities, and systems in two variables, including absolute-value inequalities, and verify solutions by substitution

Factor and expand polynomial expressions up to degree three and apply the remainder and factor theorems to locate roots

Simplify rational expressions, solve rational equations, and identify extraneous solutions

Apply exponent and logarithm laws to solve exponential and logarithmic equations, stating domain restrictions explicitly

Classify functions and analyze domain, range, symmetry, increasing/decreasing intervals, and end behavior from equations and tables

Compose functions and find inverse functions algebraically, confirming each inverse by checking f(f-inverse(x)) equals x

Transform parent functions (shifts, stretches, reflections) and sketch the resulting graphs accurately

Model word problems with linear, quadratic, and exponential functions and interpret the parameters in context

Prove and apply triangle congruence and similarity criteria, including the Pythagorean theorem and special right triangles

Compute perimeter, area, surface area, and volume for polygons, circles, prisms, cylinders, pyramids, cones, and spheres

Apply coordinate geometry to find distances, midpoints, slopes, and equations of parallel and perpendicular lines

Derive and use the equation of a circle and convert between standard and general form by completing the square

Convert between degrees and radians and evaluate all six trigonometric functions at standard and quadrantal angles using reference angles

Prove and apply Pythagorean, sum, difference, and double-angle identities to simplify expressions and solve equations

Graph sine, cosine, and tangent functions and identify amplitude, period, phase shift, and vertical shift

Solve right and oblique triangles using the law of sines and law of cosines, including the ambiguous case

Compute probabilities using the addition and multiplication rules, conditional probability, and independence, and distinguish permutations from combinations

Calculate and interpret measures of center, spread, and position, including standard deviation, z-scores, and percentile rank

Interpret normal distributions and apply the empirical rule to estimate probabilities and percentages

Design and interpret data displays (histograms, box plots, scatterplots) and describe correlation versus causation

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

Compute derivatives using power, product, quotient, and chain rules and interpret the derivative as an instantaneous rate of change

Apply derivatives to find tangent lines, critical points, and intervals of increase and decrease

Compute basic antiderivatives and definite integrals and interpret the definite integral as net area

Complete two full-length timed practice tests under exam conditions and record subarea scores for each

Review every missed item from both tests and reclassify errors as content gaps, procedural slips, or time-management issues

Re-drill the three weakest subareas with targeted problem sets until accuracy exceeds 85% on each

Finalize a condensed one-page reference sheet of formulas and definitions to review in the final days