NES Essential Academic Skills Subtest III: Mathematics study plan

Diagnose current skill level by completing a timed 25-question algebra warm-up and recording accuracy by subtopic (linear equations, inequalities, exponents, polynomials, factoring, rational expressions, radicals, quadratics, functions).

Solve and check one-variable linear equations and inequalities, including those with fractions, decimals, and variables on both sides, and graph the solution set on a number line.

Apply the laws of exponents and simplify polynomial expressions by adding, subtracting, and multiplying, including special products such as (a+b)^2 and (a+b)(a-b).

Set up word problems as linear equations (rate, mixture, consecutive-integer, and age problems) and verify answers against the original context.

Factor polynomials by greatest common factor, difference of squares, trinomials, and grouping, and use factoring to solve quadratic equations.

Simplify rational expressions and solve rational equations, identifying excluded values that make a denominator zero.

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and interpret the discriminant to predict the number of real solutions.

Translate and solve systems of two linear equations by substitution and elimination, including no-solution and infinite-solution cases.

Interpret function notation, evaluate functions from tables and graphs, and identify domain and range in context.

Perform operations with integers, fractions, decimals, and mixed numbers without a calculator, including order of operations and signed arithmetic.

Apply divisibility rules, prime factorization, greatest common factor, and least common multiple to simplify and combine fractions.

Convert among fractions, decimals, and percents, and solve percent problems including percent increase/decrease, discount, tax, and simple interest.

Solve ratio, rate, and proportion problems, including unit-rate and scale problems, using cross-multiplication and dimensional reasoning.

Estimate and check reasonableness of answers using rounding and mental math.

Convert within and between customary and metric units of length, weight/mass, and capacity using unit fractions and dimensional analysis.

Compute perimeter, area, and volume of triangles, quadrilaterals, circles, prisms, cylinders, and composite figures, selecting the correct formula and units.

Apply the Pythagorean theorem and its converse to find missing side lengths and classify triangles.

Calculate angle relationships in triangles and with parallel lines cut by a transversal, and find the sum of interior angles of polygons.

Classify two- and three-dimensional figures by properties and apply similarity and congruence criteria to find missing measures.

Compute surface area of prisms, cylinders, pyramids, and cones, and distinguish surface area from volume in applied contexts.

Solve multi-step geometry word problems by drawing a labeled diagram, stating a plan, executing it, and checking units and reasonableness.

Identify and correct common errors such as mixing radius and diameter or confusing square and cubic units.

Read and interpret data displays including bar graphs, line graphs, histograms, box plots, scatterplots, and circle graphs, and identify misleading representations.

Compute mean, median, mode, range, and interquartile range for a data set, and explain how outliers affect each measure.

Calculate and interpret basic probability for simple and compound events, including complementary events and independent events.

Distinguish sampling methods and identify biased samples or questions in survey contexts.

Solve multi-step word problems using a consistent four-step process (understand, plan, solve, check) across number sense and algebra contexts.

Identify the underlying structure in a novel problem and select an appropriate strategy such as working backward, finding a pattern, or setting up an equation.

Justify solutions in writing, explaining why a method works and why an alternative answer is incorrect.

Complete a mixed 30-question set spanning all five domains under timed conditions and analyze results by domain.

Re-drill the two heaviest domains (algebraic relationships and data analysis/probability) using your error logs until every previously missed item type is solved correctly twice.

Take two full-length timed practice tests under exam conditions and record pacing data (time per question, questions left blank).

Review all self-made formula and rule sheets and consolidate them into a single final reference page.

Practice calculator and grid-in mechanics so that answer entry does not cost time.