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MTEL Mathematics Test Breakdown

Number Sense and Operations has three subareas with a total of 14 to 16 questions and counts 12percent of the final score.

Structure of Numeration Systems: solve problems using integers, fractions, decimals, percents, ratios and proportions, place value, order relationships and relationships between operations; representation of numbers and operations, absolute value, signed numbers, origin and development of computational algorithms, estimating and characteristics of early numeration systems.
Real and Complex Numbers and Number Systems: properties, representations and operations of rational and irrational numbers, number systems and their subsets, roots and powers, scientific notation, using numbers to prove theorems and solving problems using these types of numbers.
Principles of Number Theory: number factors and divisibility, prime and composite numbers, Euclid’s algorithm, Mersenne primes and perfect numbers, Fermat’s Last Theorem, and basic arithmetic.

Patterns, Relations and Algebra has seven subareas with a total of 27 to 29 questions and counts 235 of the final score.

Use of Patterns to Model and Solve Problems: numeric, geometric and tabular forms, symbolic notations, change created by functions, iterative and recursive functions, Pascal’s triangle and the binomial theorem, and using finite and infinite series and sequences.
Properties of Functions and Relations: functions and differences; representation of functions; addition, subtraction and composition; inverse functions; and functional graphs and their changes.
Linear Relations and Functions: properties and applications; linear models and rate of change; direct variation; graphs, slopes and intercepts; line equation; absolute value; and using various methods to model and solve problems.
Linear and Abstract Algebra: properties and applications; matrices and determinant;, properties of vectors and vector spaces; and the definition, and characteristics of groups, rings and fields.
Quadratic Relations and Functions: properties, applications, manipulations and simplifications; real and complex roots; graphs and the relationship between them and symbolic representations; maximum and minimum and modeling; and solving problems.
Polynomial, Radical, Rational and Absolute Value Functions and Relations: properties and applications, inverse and joint variation, manipulating and simplifying expressions, horizontal and vertical asymptotes, properties and graphs of modeling, and solving problems.
Exponential and Algorithmic Functions and Relations: properties, applications and simplifications; graphs, exponential growth, decay and compound interest; and using the inverse relationship to solve problems.

Geometry and Measurement has 5 subareas with a total of 23 to 25 questions and counts 19percent of the final score.

Measurement: principles, concepts and procedures, unit conversions, dimensional analysis, degree and radian measure, indirect measurement, effects of changing linear dimension and measurement errors, rounding on computed quantities, and solving various problems.
Axiomatic Structure of Euclidian Geometry: terms, postulates, theorems and relationships; axioms of algebra; distances and angles; parallel and perpendicular lines and graphs; triangles and circles; Pythagorean theorem; and the development of geometry in different cultures.
Theorems within Euclidian Geometry: direct and indirect methods of proof; properties of lines, circles, polygons, triangles, special triangles, parallelograms and other quadrilaterals; and geometric constructions.
Applying Euclidian geometry to Two and Three Dimensional Objects: solving problems related to special right triangles, arcs, angles and segments, prisms, cylinders, cones and pyramids; drawings, projections and cross-sections; creating three-dimensional figures from two-dimensional shapes; and solving problems using two and three dimensional models.
Coordinate and Transformational Geometry: principles, properties, axioms and characteristics of non-Euclidian geometry; rectangular and polar coordinates; geometric figures in the coordinate plane; three-dimensional coordinate systems; classification of figures, dilations, translations, rotations, reflections and glide-reflections; types of symmetry; and changes in the coordinate plane.

Data Analysis, Statistics and Probability has three subareas with a total of 12 to 14 questions and counts 10percent of the final score.

Descriptive Statistics: principles, concepts and applications; tables, charts and graphs; central tendency and dispersion; frequency distributions; and percentile scores and their effects on data changes.
Collecting and Analyzing Data: sampling techniques; methods for gathering data and designing experiments; inferring population data from statistics; sample size, correlation and regression models; and curve fitting.
Probability: principles, concepts and solving problems; simple and compound events; simulations; ratio; and random variables and distributions.

Trigonometry, Calculus and Discrete Mathematics has five subareas with 19 to 21 total questions and counts 16percent of the final score.

Trigonometry: properties, functions and identities; degree and radian measure; right triangle trig, sines and cosines; graphs and properties; equations; and using trigonometric functions to model occasional events.
Limit, Continuity and Rate of Change: concepts and solving problems; limits of algebraic functions, sequences and series; continuous and discontinuous functions; secant line; and average rate of change.
Differential Calculus: line tangent, derivatives, differentiation, analyzing the graphic representation of a function, verifying the function is the solution to an equation, and the development of differential calculus.
Integral Calculus: area under a curve, the limit if a Riemann sum, fundamental theorem, techniques and applications of integration, and solving differential equations with separation of variables.
Discrete/Finite Mathematics: principles, sets, counting techniques, finance, recursive patterns and relations, iteration, algorithms, linear programming, matrices and features, and applications of graphs and trees.

MTEL Mathematics Test Practice Questions