NYSTCE Multi-Subject: Secondary (Grades 7-12), Part Two: Mathematics (244) Practice Tests

Competency 0001 makes up about 10% of the 244 score. It covers: the real number system; ratios and proportional relationships.

• The real number system: Properties of rational numbers, ordering and absolute value; The four operations with rational numbers in problems; Arithmetic and order of operations in expressions, equations and inequalities; Rational approximations of irrational numbers; repeating decimals; Operations with scientific notation; Radicals and rational exponents using exponent properties; Units in multistep problems and formulas; Analyzing assessment data to plan instruction
• Ratios and proportional relationships: Ratio and rate reasoning; unit rates, including unit pricing and constant speed; Percents as rates per 100; finding the whole given a part; Unit conversion within and between measurement systems; Constant of proportionality in tables, graphs, equations, diagrams and descriptions; Multistep ratio and percent problems: interest, commissions, percent change, percent error; Proportional relationships, lines and linear equations; similar triangles and constant slope

Competency 0002 makes up about 40% of the 244 score. It covers: algebra; linear, quadratic and simple exponential functions.

• Algebra: Generating equivalent expressions with properties of operations; Vocabulary and structure of expressions; factoring quadratics, completing the square, exponent properties; Adding, subtracting and multiplying polynomials; zeros and factors; polynomial identities; Rewriting rational expressions; Creating and solving one-variable equations and inequalities (linear, quadratic, simple rational, exponential); Equations in two or more variables and their graphs on labeled, scaled axes; Solving equations as reasoning; two-variable systems, including graphically; Modeling real-life constraints with systems and judging solutions as viable or nonviable; Analyzing assessment data to plan algebra instruction
• Linear, quadratic and simple exponential functions: Function concept, domain and range, function notation; Interpreting features in context: intercepts, increasing intervals, maxima and minima, zeros; Analyzing linear, quadratic, square root, piecewise, polynomial and exponential functions through graphs, descriptions, algebraic forms and tables; Building functions that model relationships between two quantities; Effects of f(x + k), composition and inverse functions; Comparing linear and exponential models; interpreting parameters in context

Competency 0003 makes up about 30% of the 244 score. It covers: geometry; data, statistics and probability.

• Geometry: Transformations and congruence through rigid motions; Theorems about lines, angles, triangles and parallelograms; Formal constructions; Similarity through transformations and scale factors; Trigonometric ratios and right-triangle problems; Circle theorems; lengths, areas and circumferences; Expressing geometric properties with equations; coordinate proofs using the distance formula, midpoint formula and Pythagorean theorem; Angle measure, perimeter, area, surface area and volume, including cones, cylinders and spheres; Two-dimensional cross sections of three-dimensional objects
• Data, statistics and probability: Summarizing single-variable data: dot plots, histograms, box plots, mean, median, interquartile range, standard deviation, outliers; Two-variable data: two-way tables, scatter plots, trends, fitted functions, residuals; Linear models, the correlation coefficient, and correlation versus causation; Random processes, inference from a single sample, and simulations; Inferences from surveys, experiments and observational studies; Independence, conditional probability and compound events; Decision-making with probability and expected values

Competency 0004 makes up about 20% of the 244 score and is the constructed-response item. It covers: constructed response.

• Constructed response: Analyze and interpret student work and assessment data to monitor progress and identify strengths and needs; Identify and analyze errors or misconceptions in work samples; Describe appropriate, content-specific strategies or interventions; Generate real-world scenarios that illustrate mathematical concepts; Justify the effectiveness of the selected strategies