MTEL Test Study Guides | MTEL Test Flashcards

MTEL Middle School Mathematics and Science Test Breakdown

Number Sense and Operations has four subareas with a total of nine to 11 questions and counts 8 percent 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 14 to 16 questions and counts 12 percent 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 notations; 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 10 to 12 questions and counts 9 percent 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 seven to nine questions and counts 6 percent 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 five to seven questions and counts 5 percent 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 of 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.

History, Philosophy and Methodology of Science has four subareas with a total of nine to 11 questions and counts 8 percent of the final score.

Scientific Thought and Inquiry: history and importance of significant people, ideas, theories and discoveries; empirical data and verifiable reasoning; evidence and logic; science and technology in ancient China and Greece; development of science in the 17th, 18th, 19th and 20th centuries; and the impact of social, religious and economic factors on science and technology through the years.
Research and Experimental Design: principles, procedures and considerations, formulating hypotheses, planning research projects, setting up and conducting investigations, sampling techniques, and using control and experimental groups.
Gathering, Organizing, Interpreting, Evaluating and Communicating: strategies, tools and technologies, measurement methods, devices and formats, making predictions and drawing conclusions, and models and methods for communicating data.
Use of Tools, Equipment and Materials: practice, procedures and requirements for safe use, storage and disposal, procedures for preventing and dealing with accidents and injuries, and the use and care of chemicals and living organisms.

Chemistry has four subareas with a total of nine to 11 questions and counts 8 percent of the final score.

Matter: atomic and molecular structure, the atom, how atomic structures explain chemical behavior, the periodic table, mixtures and pure substances and symbols, formulas, and equations.
Physical Changes in Matter: characteristics of the various states of matter, properties of common materials, energy, mass, conservation and mixtures, and solutions.
Chemical Changes in Matter: descriptions of properties and composition of reactants and products, using conservation to analyze reactions, characteristics and effects of chemical bonds, and factors that impact rates of reaction.
Kinetic Molecular Model of Matter: uses of kinetic molecular theory; and relationship between pressure, temperature and volume of gases and between temperature and kinetic energy.

Physics has four subareas with a total of nin to 11 questions and counts 8 percent of the final score.

Force, Motion, Work and Power: Newton’s’ laws, mass and inertia, mass and weight, force, displacement, velocity, acceleration and momentum, distance versus time, graphs, and the basics of simple machines.
Energy: concepts, conservations, forms, classifications, relationships, transfer and conversion, collisions, entropy, and thermodynamics.
Sound and Light Waves: transverse and longitudinal waves, waves and oscillations, speed and energy, properties of sound and light, properties, interactions and behaviors in various media, behavior of light in different situations, and the electromagnetic spectrum.
Electricity, Magnetism and Electromagnetism: static electricity, electron flow and electric current, components and diagrams of simple electric circuits, magnets and magnetic fields, and the principle of electromagnetism.

Biology has four subareas with a total of nine to 11 questions and counts 8 percent of the final score.

Life Processes of Living Organisms: differences between living and nonliving organisms, basic plant and animal cell structure and functions, growth and reproduction, photosynthesis and cellular respiration, homeostasis and metabolism, and the organization, structure and functions of major biological systems and how they interact.
Inheritance of Characteristics: how characteristics are passed from one generation to the next, environmental factors, mutations, DNA, genes, and chromosomes.
Biological Evolution: principles, theories, processes and scientific evidence concerning the origin and evolution of life; investigative methods; genetic and phenotypic variations; environmental influences; natural selection and the correlation between evolutionary relationships; and taxonomy.
Populations, Communities, Ecosystems and Biomes: biotic and abiotic factors; strategies used to obtain food, water, shelter and oxygen; relationship between all organisms in an ecosystem and their reaction to change; food webs and food chains; ecological succession; and factors that control and influence population size.

Earth and Space Science has four subareas with a total of nine to 11 questions and counts 8 percent of the final score.

Geologic History: theories of the origin and history of the earth; methods used to determine the relative and actual age of inorganic and organic material; structure, composition and layers of the earth; formation, types and characteristics of mineral, rocks and soils; plate tectonics; change in the earth’s crust; how glaciers, water and wind change the earth’s structure; topographic features; maps used in science; and the effects of catastrophic phenomena.
Hydrosphere: properties of oceans and surface and ground water and how the water cycle affects ground water, oceans, rivers, lakes and watersheds.
Atmosphere, Weather and Climate: characteristics of the atmosphere, how the uneven heating of the earth’s surface influences weather, energy transfer, air pressure, cloud formation and precipitation, equipment and techniques to monitor and predict the weather and climate change, and interpreting meteorological data.
Solar System and Universe: characteristics, movements and interactions of the planets, sun, moon, stars and other celestial objects, and theories of the origin and evolution of the universe.

MTEL Middle School Mathematics and Science Test Practice Questions