# Test Information Guide

## Overview and Test ObjectivesField 77: Middle School Mathematics/Science

### Test Overview

Format Computer-based test (CBT); 100 multiple-choice questions, 2 open-response items 4 hours (does not include 15-minute CBT tutorial) 240

The Massachusetts Tests for Educator Licensure (MTEL) are designed to measure a candidate's knowledge of the subject matter contained in the test objectives for each field. The MTEL are aligned with the Massachusetts educator licensure regulations and, as applicable, with the standards in the Massachusetts curriculum frameworks.

The test objectives specify the content to be covered on the test and are organized by major content subareas. The chart below shows the approximate percentage of the total test score derived from each of the subareas.

The test assesses a candidate's proficiency and depth of understanding of the subject at the level required for a baccalaureate major according to Massachusetts standards. Candidates are typically nearing completion of or have completed their undergraduate work when they take the test.

Pie chart of approximate test weighting outlined in the table below.

### Test Objectives

Table outlining test content and subject weighting by sub area and objective.
Subareas Range of Objectives Approximate Test Weighting
Multiple-Choice
I Number System and Quantity 01–02 10%
II Algebra, Functions, and Modeling 03–07 12%
III Geometry and Measurement 08–11 10%
IV Statistics and Probability 12–13 8%
V Technology / Engineering 14–16 10%
VI Earth and Space Science 17–20 10%
VII Life Science 21–24 10%
VIII Physical Science 25–29 10%
80%
Open-Response
IX Integration of Knowledge and Understanding
Statistics, Probability, and Algebra 30 10%
Key Concepts in Earth and Space Science, Life Science, or Physical Science 31 10%
20%

#### Subarea I–Number System and Quantity

##### Objective 0001: Apply the structure and properties of number systems.
For example:
• Apply and extend understanding of the place value system to represent, estimate, and perform operations on the full system of real numbers in a variety of ways (e.g., graphic, numerical, physical, symbolic).
• Reason about the order and absolute value of rational numbers.
• Apply and extend understanding of number systems (e.g., complex numbers, irrational numbers).
• Analyze the relationships between operations (e.g., multiplication as repeated addition).
• Apply and extend understanding of prime and composite numbers, divisibility, least common multiples, and greatest common factors to model and solve real-world and mathematical problems.
• Analyze standard algorithms for operations on real numbers (e.g., decimals, fractions, integers).
• Justify and apply order of operations and the use of inverse and identity elements to solve problems.
• Model and solve problems using the properties of integer exponents (e.g., scientific notation).
• Apply and extend understanding of number properties (e.g., associative, commutative, distributive) to model and solve problems.
##### Objective 0002: Use rational numbers, ratios, and proportional relationships.
For example:
• Represent fractions, arithmetic operations on fractions, and problems involving fractions using a variety of visual models (e.g., area models, diagrams, tiles) and equations.
• Solve real-world and mathematical problems with integers and other rational numbers (e.g., decimals, fractions).
• Apply ratios, rates, unit rates, and proportionality to solve a variety of problems, including percent problems (e.g., discounts, interest, percent increase and decrease, taxes, tips).
• Solve problems involving conversions between decimals (e.g., finite, repeating), percents, and fractions using visual models and strategies based on place value and properties of operations.
• Compare and interpret rational numbers (e.g., equivalent fractions, multiplication as scaling with fractions).
• Use benchmark numbers, rounding, and number sense to estimate mentally and assess the reasonableness of solutions to problems.

#### Subarea II–Algebra, Functions, and Modeling

##### Objective 0003: Use patterns to model and solve problems.
For example:
• Make conjectures about patterns presented in numerical, geometric, and tabular forms.
• Represent patterns and relations using symbolic notation.
• Identify patterns of change created by linear, quadratic, and exponential functions.
• Model and solve problems using patterns, relations, sequences, and series (e.g., arithmetic, Fibonacci, geometric).
• Identify, express, and apply patterns of change in proportional, linear, and inversely proportional situations.
##### Objective 0004: Apply algebraic techniques to expressions and equations.
For example:
• Translate between verbal descriptions and algebraic sentences that represent mathematical situations in various forms (e.g., graphic, numerical, symbolic, tabular).
• Model situations with algebraic expressions, equations, and inequalities, including those with fractional and decimal coefficients and those with infinitely many or no solutions.
• Evaluate algebraic expressions for a given value of a variable and express one variable in terms of another variable.
• Apply properties of real numbers in algebraic contexts to manipulate and simplify algebraic expressions (e.g., polynomials, rational expressions) and solve equations and inequalities, including those with fractional and decimal coefficients and integer exponents.
##### Objective 0005: Demonstrate knowledge of relations and functions.
For example:
• Distinguish between relations and functions using a variety of representations (e.g., graphic, symbolic, tabular, verbal) and use relations and functions to describe relationships between quantities.
• Analyze various representations (e.g., graphic, symbolic, tabular, verbal) of functions and relations with respect to their characteristics (e.g., continuity, domain, intercepts, inverses).
• Generate, interpret, and translate between various representations (e.g., algebraic, graphic, tabular) of real-world situations.
• Identify and analyze piecewise-defined functions and addition, subtraction, and composition of functions from real-world and mathematical situations.
• Identify the effects of transformations such as the function f of quantity x plus k comma k plus the function f of x� comma and k times the function f of x. on the graph of a function.
##### Objective 0006: Apply the properties of linear relations and functions.
For example:
• Analyze connections between proportional relationships, direct variation, rates of change, and linear models and use these connections to build linear functions.
• Analyze the relationship between the equation of a line and its graph and interpret slope and intercepts in real-world and mathematical contexts.
• Determine the equation of a line from different types of information (e.g., graph, one point and slope, two points).
• Apply a variety of methods for solving systems of linear equations and inequalities (e.g., elimination, graphing, substitution).
• Apply knowledge of linear equations and inequalities, systems of equations, linear functions, and slope of a line to analyze situations and solve problems.
##### Objective 0007: Apply the principles and properties of nonlinear relations and functions.
For example:
• Identify and express patterns of change in quadratic and exponential functions and the types of real-world relationships that these functions can model.
• Translate between different representations (e.g., algebraic, graphic, tabular, verbal) of quadratic and exponential functions.
• Analyze properties and features of quadratic relations, functions, and systems (e.g., graphs, maxima/minima, real roots).
• Model and solve problems involving quadratic relations, functions, and systems using a variety of techniques (e.g., completing the square, factoring, graphing, quadratic formula).
• Model and solve problems involving exponential growth (e.g., compound interest, population growth) and decay (e.g., half-life).
• Analyze properties and graphs of linear, quadratic, exponential, and absolute value functions.

#### Subarea III–Geometry and Measurement

##### Objective 0008: Apply principles, concepts, and procedures related to measurement.
For example:
• Apply and extend understanding of quantities and units to convert within measurement systems and use these conversions in solving multistep, real-world problems.
• Apply formulas to find measures (e.g., area, length, volume) involving two- and three-dimensional figures (e.g., composite shapes) including those with fractional measures.
• Analyze the effect of changing linear dimensions on measures of length, area, or volume.
• Calculate and analyze the effect of measurement error and rounding on computed quantities.
• Use degrees to calculate, estimate, and analyze angle measures (e.g., coterminal angles).
• Solve real-world and mathematical problems using right triangle trigonometry (e.g., cosine, sine, tangent).
##### Objective 0009: Apply the principles of Euclidean geometry and proof.
For example:
• Identify, use, and understand the relationships between the building blocks (e.g., postulates, undefined terms) of Euclidean geometry.
• Classify geometric relationships and solve problems using the properties of lines (e.g., parallel, perpendicular) and angles (e.g., supplementary, vertical).
• Apply the principles of congruence, similarity, and proportional and spatial reasoning (e.g., indirect measurement, informal geometric constructions, scale drawings) to solve real-world and mathematical problems.
• Analyze and prove theorems within the axiomatic structure of Euclidean geometry.
##### Objective 0010: Apply properties of two- and three-dimensional figures.
For example:
• Classify plane figures in a hierarchy based on their properties (e.g., angles, diagonals, sides).
• Apply deductive reasoning to justify properties of and relationships between triangles, quadrilaterals, and other polygons.
• Apply the Pythagorean theorem and its converse to solve real-world and mathematical problems and to derive special right triangle relationships.
• Apply properties of arcs, angles, and segments associated with circles to solve real-world and mathematical problems.
• Analyze the properties and compare the measures (e.g., surface area, volume) of three-dimensional figures (e.g., cones, cylinders, prisms, pyramids, spheres).
• Translate between two- and three-dimensional representations of geometric figures (e.g., conic sections, cross sections, nets, perspective and isometric drawings).
• Derive properties of three-dimensional figures from two-dimensional figures.
##### Objective 0011: Apply the principles and properties of coordinate and transformational geometries.
For example:
• Classify, represent, and analyze geometric figures (e.g., circles, polygons) in the coordinate plane.
• Apply concepts of distance, midpoint, slope, and parallel and perpendicular lines to classify and analyze figures in the coordinate plane.
• Apply transformations (e.g., dilations, reflections, rotations, translations) to figures in the coordinate plane and analyze their effects on congruence, similarity, and symmetry.
• Use coordinate and transformational geometry to prove theorems and solve problems.

#### Subarea IV–Statistics and Probability

##### Objective 0012: Understand the principles, techniques, and applications of statistics.
For example:
• Construct and interpret frequency distributions, tables, charts, and graphs (e.g., box plots, dot plots, histograms, stem-and-leaf plots).
• Describe and summarize numerical data sets by identifying clusters, modes (e.g., peaks), gaps, and symmetry and by considering the context in which the data were collected.
• Use measures of center (e.g., mean, median) and measures of variability (e.g., interquartile range, standard deviation) for numerical data from random samples to draw informal comparative inferences about two populations, and determine the effects of transformations on these measures.
• Demonstrate knowledge of normal probability distributions and use percentile scores to solve problems.
• Evaluate real-world situations to determine appropriate sampling techniques and methods for gathering and organizing data.
• Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, interpret correlation coefficients, and solve problems involving linear regression models.
##### Objective 0013: Understand the principles of probability.
For example:
• Use and interpret a variety of representations for situations involving probability (e.g., organized lists, tables, tree diagrams, Venn diagrams).
• Compute theoretical probabilities for simple and compound events using a variety of approaches (e.g., addition and multiplication rules).
• Select simulations to generate frequencies for compound events.
• Make connections between probability and geometry.
• Use probability models to explore and understand real-world phenomena.

#### Subarea V–Technology / Engineering

##### Objective 0014: Apply knowledge of engineering design.
For example:
• Apply knowledge of engineering design practices to define a problem and to identify the criteria and constraints associated with the problem, including the following: materials; time; cost; and societal, scientific, and engineering restrictions.
• Apply knowledge of the iterative design process, including constructing a prototype, testing a prototype, comparing design solutions, and modifying design solutions to improve a prototype.
• Demonstrate knowledge of the systematic process used to evaluate an engineering design or interpret results, including the use of models (e.g., mathematical, physical, computer simulations).
• Demonstrate knowledge of the relationship between the components of a product or device to its function, including addressing the design features and limitations of the product or device.
##### Objective 0015: Demonstrate knowledge of tools, materials, and manufacturing.
For example:
• Apply knowledge of scientific concepts to the development and general functioning of tools, materials, and manufacturing processes in a real-world context.
• Demonstrate knowledge of the selection and appropriate use of tools in a variety of contexts, including manufacturing processes, engineering projects, and classroom activities.
• Demonstrate knowledge of how products are created using basic processes in manufacturing systems (e.g., forming, separating, conditioning, assembling, finishing), quality control, and safety.
• Demonstrate knowledge of the composition of different materials and the effect of manufacturing processing (e.g., magnetization, heating, cutting) on a material's composition.
• Demonstrate knowledge of the relationship between the use of a material (e.g., metal, plastic, wood) and the material's physical and chemical properties (e.g., flexibility, ductility, thermal conductivity, electrical conductivity, melting point).
• Apply knowledge of safety procedures and hazards associated with a workspace or classroom setting (e.g., practices and requirements related to the safe use and storage of tools and equipment, the use and proper disposal of materials, procedures for preventing or responding to accidents and injuries).
##### Objective 0016: Demonstrate knowledge of technological systems.
For example:
• Analyze the interdependence of science, engineering, and technology, including the use of scientific principles and engineering design to explain the development, production, general functioning, and improvement of various technologies (e.g., radio, air conditioner, internal combustion engine).
• Demonstrate knowledge of the principles and technological applications of heat, mechanics, electricity, magnetism, and electromagnetism, including information transfer by waves.
• Demonstrate knowledge of the functioning of different components of a communication system, including source, encoder, transmitter, receiver, decoder, and storage, and the benefits and drawbacks of different communication systems (e.g., radio, television, print, Internet).
• Demonstrate knowledge of structural and transportation systems, including the relationship of the components and design of a structure to its intended use; how transportation systems are designed to move people and goods; and the design of subsystems of a transportation vehicle, including structural, propulsion, guidance, suspension, and control.
• Apply knowledge of the concepts of systems engineering to model components of a communication, structural, or transportation system.

#### Subarea VI–Earth and Space Science

##### Objective 0017: Demonstrate knowledge of the components of the solar system and universe and their interactions.
For example:
• Demonstrate knowledge of the Big Bang theory of the origin and evolution of the universe and supporting evidence (i.e., expansion of the universe, cosmic microwave background radiation, hydrogen-helium ratio).
• Demonstrate knowledge of the types and characteristics of celestial objects, including galaxies and stars.
• Demonstrate knowledge of the formation and structure of the solar system, including the types and characteristics of objects in the solar system (e.g., planets, moons, comets, asteroids) and the movement of celestial objects relative to Earth.
• Demonstrate knowledge of the role of gravity in the universe, in the solar system, and on Earth and of the concepts of Kepler's laws of planetary motion.
• Apply knowledge of the movements and interactions of the Sun, the Moon, and Earth (e.g., seasons, Moon phases, tides, eclipses).
• Apply knowledge of the use of science practices in exploring and understanding content related to the solar system and universe, such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0018: Apply knowledge of Earth's geosphere, geologic history, and processes.
For example:
• Demonstrate knowledge of the geologic timescale and the history of Earth, including supporting evidence (e.g., relative and absolute dating, stratigraphy, distribution of fossils).
• Demonstrate knowledge of the structure and composition of Earth, including evidence that supports the current model of Earth's structure (e.g., seismic waves, meteorites, magnetic field).
• Apply knowledge of the theory of plate tectonics and supporting evidence (e.g., continental and ocean floor features, crustal rock age, distribution of fossils), including processes that drive plate movement.
• Demonstrate knowledge of the characteristics of and the processes that form minerals, soils, and rocks (igneous, sedimentary, and metamorphic).
• Apply knowledge of constructive and destructive processes (e.g., weathering, erosion, deposition) that shape Earth's geologic features, including interpreting the processes involved in the formation of topographic features of Earth.
• Apply knowledge of the use of science practices in exploring and understanding content related to Earth's geosphere, geologic history, and processes; such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0019: Demonstrate knowledge of Earth's hydrosphere, atmosphere, weather, and climate.
For example:
• Demonstrate knowledge of the processes that transfer energy within and between Earth's systems; the effects (e.g., ocean circulation, Coriolis effect) of these processes; and the interrelationships among Earth's geosphere, biosphere, hydrosphere, and atmosphere.
• Apply knowledge of the physical and chemical properties of sea water and fresh water; the physical processes that drive the hydrologic cycle; and the characteristics of, distribution of, and interrelationships between surface and subsurface water reserves (e.g., aquifers, watersheds, lakes, rivers, glaciers, oceans).
• Apply knowledge of how the Sun's energy affects weather and climate.
• Demonstrate knowledge of the structure of the atmosphere and characteristics of its different layers, the movement of air in the atmosphere, air pressure, and factors that affect cloud formation.
• Demonstrate knowledge of atmospheric and geographic factors that produce different types of weather, including factors that control regional climate conditions.
• Demonstrate knowledge of weather maps, data, equipment, and techniques to predict and explain weather events.
• Apply knowledge of the use of science practices in exploring and understanding content related to Earth's hydrosphere, atmosphere, weather, and climate; such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0020: Demonstrate knowledge of natural resources, natural hazards, and human impacts on the environment.
For example:
• Demonstrate knowledge of the characteristics, origins, and uses of renewable and nonrenewable energy resources (e.g., geothermal, solar, fossil fuels) and the benefits and risks associated with the extraction, use, and management of these resources.
• Demonstrate knowledge of the sources, limits, and uses of natural resources; the patterns of global distribution of natural resources due to geologic processes; and how human activity (e.g., deforestation, agriculture) affects the availability and quality of natural resources.
• Demonstrate knowledge of the causes and consequences of hazardous weather, tsunamis, volcanoes, and earthquakes; factors contributing to the extent of damage caused by hazardous events (e.g., distance, air quality, epicenter, geologic substrate); methods used to forecast hazardous events; and measures taken to limit their damage.
• Apply knowledge of the anthropogenic and natural causes, scientific evidence, and potential impacts of global climate change, including the greenhouse effect and the roles of Earth systems in producing and absorbing greenhouse gases (e.g., methane sources, buffering capacity of oceans, photosynthesis).
• Analyze the impact on society and the environment that can result from the use of natural and synthetic materials (e.g., plastics, fertilizers, antibiotics, pesticides).
• Demonstrate knowledge of the ways in which science and technology can be used to solve natural and societal problems, including strategies to reduce human impacts on the environment and to maintain or increase standards of living.
• Apply knowledge of the use of science practices in exploring and understanding content related to natural resources, natural hazards, and human impacts on the environment; such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.

#### Subarea VII–Life Science

##### Objective 0021: Demonstrate knowledge of the characteristics and processes of living organisms.
For example:
• Demonstrate knowledge of the characteristics of life, cell theory, and the structure and function of basic chemical components of life, including nucleic acids, lipids, carbohydrates, and proteins.
• Demonstrate knowledge of basic cell structures and their functions, including comparisons among cell types (e.g., plant and animal, prokaryotic and eukaryotic).
• Demonstrate knowledge of the processes of cellular division, including binary fission, mitosis, and meiosis, and of the role of each of these processes in the differentiation of cells and the growth and reproduction of organisms.
• Analyze the processes of photosynthesis and cellular respiration (anaerobic and aerobic), including how organisms obtain, use, and store matter and energy.
• Demonstrate knowledge of the levels of biological organization (molecules, cells, tissues, organs, organ systems, and organisms), including the influence of environmental and genetic factors on the growth and development of organisms.
• Apply knowledge of the structures and functions of major systems in plants and animals and of interactions among the systems, including how the systems are involved in the processes of homeostasis and metabolism.
• Apply knowledge of the use of science practices in exploring and understanding content related to the characteristics and processes of living organisms, such as developing and using models, planning and safely conducting investigations, ethically using caring for living organisms, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0022: Apply knowledge of the characteristics of populations, communities, ecosystems, and biomes.
For example:
• Demonstrate knowledge of the biotic and abiotic factors, as well as of the interactions between them, that affect populations, communities, ecosystems, and biomes (e.g., resource availability, habitat requirements, predation, competition, disease).
• Demonstrate knowledge of the interrelationships among organisms�including humans�in ecosystems (e.g., symbiotic, competitive, predatory) and the strategies used by organisms to obtain basic requirements for life (e.g., food, shelter, water).
• Apply knowledge of matter and energy transfers in ecosystems, including the processes involved in biogeochemical cycles and the relationships among producers, consumers, and decomposers in food webs.
• Apply knowledge of the responses of ecosystems to change, including the process of ecological succession and the short- and long-term impacts of natural and anthropogenic phenomena (e.g., flooding, continental drift, construction) on ecosystems and species diversity.
• Apply knowledge of the use of science practices in exploring and understanding content related to populations, communities, ecosystems, and biomes; such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0023: Apply principles related to the inheritance of characteristics.
For example:
• Apply knowledge of animal behavioral characteristics and specialized plant structures that increase the probability of successful reproduction.
• Apply knowledge of the advantages and disadvantages of asexual and sexual reproductive strategies, including their impacts on genetic and phenotypic variation and population growth.
• Apply knowledge of genetic and phenotypic variation and the inheritance of traits that are determined by one or more genes (e.g., dominant, recessive, incomplete dominance, sex-linked).
• Demonstrate knowledge of the structure and function of DNA, genes, and chromosomes, including the basic processes of DNA replication and protein synthesis.
• Demonstrate knowledge of the influence of environmental factors on genetic material and of types of mutations and their effects, including effects on protein function.
• Apply knowledge of the use of science practices in exploring and understanding content related to the inheritance of characteristics, such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0024: Demonstrate knowledge of principles related to the theory of biological evolution.
For example:
• Demonstrate knowledge of the theories and processes associated with the origin (e.g., RNA world, primordial soup) of macromolecules and cells.
• Demonstrate knowledge of the evidence for evolution (e.g., the fossil record, homologies) and the principles and methods used to investigate evolution and evolutionary processes (e.g., population studies, artificial selection, genetic engineering).
• Apply knowledge of the principles of biological evolution (e.g., natural selection, gene flow, genetic drift), including the roles of genetic and phenotypic variation and environmental factors in speciation.
• Demonstrate knowledge of the diversity of life and the principles of biological classification, including its connection to anatomical, embryological, and genetic evidence.
• Apply knowledge of the use of science practices in exploring and understanding content related to biological evolution, such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.

#### Subarea VIII–Physical Science

##### Objective 0025: Apply knowledge of the structure and properties of matter.
For example:
• Demonstrate knowledge of how the model of the structure of the atom has progressed over time.
• Apply knowledge of the development and organization of the periodic table and trends in the physical and chemical properties of elements, including atomic structure.
• Apply knowledge of the properties of atoms, elements, molecules, compounds, and mixtures, including how to classify matter.
• Demonstrate knowledge of types and characteristics of chemical bonds (e.g., covalent, ionic, hydrogen), including the effects of these bonds on the characteristics of matter.
• Demonstrate knowledge of physical and chemical properties of matter, physical and chemical changes, and factors that affect rates of reaction and chemical equilibrium (e.g., concentration, temperature, state of matter, catalysts).
• Apply knowledge of types and properties of mixtures and solutions and the characteristics and properties of acids and bases (e.g., pH, buffers, ion movement).
• Apply the concept of mass, the principle of conservation of matter, and knowledge of chemical formulas to balance chemical equations.
• Apply knowledge of the use of science practices in exploring and understanding content related to the structure and properties of matter, such as developing and using models, planning and safely conducting investigations, safely storing and disposing of hazardous materials, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0026: Apply knowledge of the states of matter, particle motion, and heat.
For example:
• Demonstrate knowledge of the different states of matter and their characteristics, changes of state and related changes in energy, and the use of models to represent states of matter.
• Apply knowledge of the relationships between pressure, temperature, and volume in gaseous systems, including the concept of the kinetic molecular theory.
• Demonstrate knowledge of energy transfer resulting from physical processes (heating and cooling, calorimetry) and chemical processes (endothermic and exothermic reactions).
• Apply knowledge of heat transfer through conduction, convection, and radiation, including using models of each mode of heat transfer and system designs that maximize or minimize thermal energy transfer.
• Apply knowledge of the use of science practices in exploring and understanding content related to the states of matter, particle motion, and heat; such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0027: Apply knowledge of different forms of energy and the conservation of energy.
For example:
• Apply knowledge of the classification and the calculation of potential and kinetic energy.
• Apply knowledge of the conservation of mechanical energy, including the processes of energy transfer (e.g., collisions, free fall, projectiles).
• Apply knowledge of forms of energy (e.g., mechanical, light, thermal, electrical, nuclear) and the transformation of energy from one form to another.
• Demonstrate knowledge of the laws of thermodynamics and the concept of entropy.
• Apply knowledge of the use of science practices in exploring and understanding content related to different forms of energy and the conservation of energy, such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0028: Apply knowledge of the concepts of force, motion, work, and power.
For example:
• Apply knowledge of Newton's laws of motion and universal gravitation, including how objects interact through gravitational fields.
• Apply knowledge of scalar and vector quantities and the vector nature of force, displacement, velocity, and acceleration.
• Analyze separate forces that act on a system (e.g., gravity, friction), the effect of separate forces on the stability of a system, and the net force acting on an object or system.
• Analyze the motion of an object in terms of distance and speed, displacement and velocity, acceleration, inertia, and momentum, including through graphs.
• Apply knowledge of the relationships among force, work, and power.
• Apply knowledge of the use of science practices in exploring and understanding content related to force, motion, work, and power; such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.
##### Objective 0029: Apply knowledge of the characteristics and properties of waves, electricity, magnetism, and electromagnetism.
For example:
• Demonstrate knowledge of the characteristics of transverse and longitudinal waves (e.g., amplitude, wavelength, frequency), changes in these properties during wave interactions, and the relationship between wave characteristics and properties of sound (e.g., loudness, pitch) and light (e.g., color, intensity).
• Apply knowledge of the effects of mirrors, lenses, and prisms on the behavior of light (e.g., reflection, refraction, diffraction, dispersion), including the behavior of sound and light waves in various media (e.g., air, water, vacuum, steel).
• Demonstrate knowledge of the characteristics and properties of the electromagnetic spectrum, including the relationships among the characteristics of electromagnetic waves (e.g., energy, wavelength, speed, frequency).
• Apply knowledge of how objects interact through electric and magnetic fields, including application of Coulomb's law.
• Demonstrate knowledge of the characteristics of electric charge and electron flow, including the properties and formation of static electricity and electric current.
• Analyze characteristics and components of simple electric circuits (e.g., power, current, batteries, resistors), including interpretation of series and parallel circuit diagrams.
• Apply knowledge of the characteristics of magnetic materials and magnetic fields, including the properties of permanent magnets.
• Apply knowledge of the use of science practices in exploring and understanding content related to waves, electricity, magnetism, and electromagnetism; such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, and communicating and evaluating data and conclusions.

#### Subarea IX–Integration of Knowledge and Understanding

In addition to answering multiple-choice items, candidates will prepare written responses to assignments addressing content summarized in the objectives below.

##### Objective 0030: Prepare an organized, developed analysis on a topic related to one or more of the following: statistics, probability, and algebra.
For example:
• Create appropriate graphs and/or diagrams, including all proper labels, to model and describe a given real-world situation.
• Apply appropriate mathematical techniques to make a prediction or comparison regarding the situation.
• Make a recommendation or argument based on the prediction or comparison.
• Discuss factors that could influence the accuracy of the prediction/comparison and recommendation/argument.
##### Objective 0031: Prepare an organized, developed analysis of a topic related to key concepts in Earth and Space Science, Life Science, or Physical Science.
For example:
• Describe the key scientific concepts that relate to a given topic.
• Use a representative graph, formula, and/or diagram with all proper labels to model the presented topic.
• Discuss how the topic relates to the concept of structure and function or cause and effect.