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MTEL Middle School Mathematics Test Breakdown

Number Sense and Operations has four subareas with a total of 18 to 20 questions and counts 15percent of the final score.

Numeration Systems: various representations, place value, number basis, order, relationship between operations, factors and divisibility, prime and composite numbers, prime factorization, and properties of early numeration systems.
Integers, Fractions, Decimals, Percents, Ratios and Proportions: principles, operations and representations; order, identity and inverse elements; associative, communicative and distributive properties; absolute value; signed numbers; standard algorithms for addition, subtraction, multiplication and division; operations and their inverses; and the beginnings and development of computational algorithms.
Solving Problems using integers, fractions, decimals, percents, ratios, proportions and average rate of change; and using estimation to gauge the accuracy of the solutions.
Real Numbers and the Real Number System: properties, rational and irrational numbers; operations and their inverses; the real number line, powers and roots; exponents; scientific notation; proving theorems with number properties; and solving problems using these concepts.

Patterns, Relations and Algebra has six subareas with a total of 30 to 32 questions and counts 255 of the final score.

Patterns: using them to model and solve problems; numeric, geometric and tabular forms and their functions; representations using symbolic notation; change created by function; and using finite and infinite sequences and patterns to solve problems.
Algebraic Expressions: manipulating and simplifying; transferring problems into algebraic notationsl variables; the relationship between standard computational algorithms and algebraic processes; direct and inverse relationships; solving equations; and using algebra to model situations.
Functions and Relations: properties of each and their differences; creating and interpreting graphs; various representations of functions, piece-wise functions, addition, subtraction and composition of functions; and graphs of functions and their transformation.
Linear Relations and Functions: properties, applications and relationships; linear models and rate of change; direct variation, graphs, slope and intercepts of lines; finding and solving linear equations and inequalities; and modeling and solving problems using these concepts.
Quadratic Relations and Functions: properties, applications and methods of solving equations and inequalities, real and complex roots, graphs, maximum and minimum problems, and solving problems using these concepts.
Exponential, Polynomial, Rational and Absolute Value Functions and Relations: properties and applications, exponential growth and decay, inverse variation, graphs and the use of calculators, and computers to find solutions.

Geometry and Measurement has five subareas with a total of 21 to 23 questions and counts 18percent of the final score.

Measurement: principles, concepts and procedures; units and unit conversions; changing linear dimensions; effects of measurement errors and rounding; and problems involving length, area, volume, density, mass, capacity, time, temperature, angles, rates of change, similar plane figures, and indirect measurement.
Euclidian Geometry: principles, axiomatic systems, terms and postulates; points, lines, angles and planes; congruent triangles; properties of similar triangles; justifying constructions; proving theorems; and the origin and development of geometry in different cultures.
Two Dimensional Figures: analyzing and justifying properties and relationships between triangles; quadrilaterals and other polygons, identifying plane objects; the Pythagorean theorem; special right triangles; arcs, angles and circles; composite shapes; and using these concepts to solve problems.
Three Dimensional Figures: area, volume and relationships; perspective drawings; cross sections and nets; deriving properties from two dimensional shapes; and modeling and solving problems using these concepts.
Coordinate and Transformational Geometry: principles, properties and representations; distance, midpoint, slope and parallel and perpendicular lines; dilations, translations, rotations, reflections and glide reflections; symmetry; tessellations; and using these concepts to prove theorems and solve problems.

Data Analysis, Statistics and Probability has two subareas with a total of 14 to 16 questions and counts 12percent of the final score.

Descriptive Statistics: methods of collecting, organizing, analyzing and reporting data; creating and interpreting tables, charts and graphs; measures of central tendency and dispersion; frequency distributions and percentile scores; data transformations, variables, sampling methods, inferences, interpolations and extrapolations; correlation; and solving problems involving linear regression models.
Probability: fundamental principles; representations of possible outcomes; counting strategies; simple and compound events; simulations; connections between geometry and probability; and using probability to understand real world issues.

Trigonometry, Calculus and Discrete Mathematics has three subareas with a total of 12 to 14 questions and counts 10percent of the final score.

Trigonometry: functions and identities; degree and radian measure; right triangles, sines and cosines; graphs, functions and their inverses; amplitude, period and phase shift; and using trigonometry to model real world situations.
Calculus: concepts, limits, slope and rates of change; derivative as it relates to maxima, minima, points of inflections and concavity of curves; integration; the area under a curve; differentiation and integration; and modeling and solving problems using these concepts.
Discrete/Infinite Mathematics: principles, sets, patterns and relations, iteration, algorithms, finite differences, linear programming, matrices, and graphs and trees.

MTEL Middle School Mathematics Test Practice Questions