NES General Curriculum Subtest 2: Mathematics, Science, and Technology/Engineering (828) Practice Tests

Competencies 0011–0015 make up about 48% of the test. They ask you to apply number theory, structures of numeration systems and operations, and arithmetic properties to the real number system using the Standards for Mathematical Practice; apply properties and applications of fractions, ratios, rates, and proportions using the Standards for Mathematical Practice; apply knowledge of patterns, algebraic relationships, and functions using the Standards for Mathematical Practice, and more.

• Competency 0011: Apply number theory, structures of numeration systems and operations, and arithmetic properties to the real number system using the Standards for Mathematical Practice. Skills tested: Identify developmental foundations and progressions related to the concept of number (e.g., counting, recognition of numerals, one-to-one correspondence, cardinality, comparing quantitative values, subitizing, conservation of number, number structures); Analyze the structures and properties of the base-ten numeration system, including interpretation and representation of place value; Distinguish between prime and composite numbers, and generate factors and multiples using prime factorization; Compare, sort, and order numbers, including fractions and decimals (e.g., on a number line); Apply rounding and estimating to whole numbers, decimals, and percentages, and judge the effect of those estimations on the results; Apply the properties of operations, and recognize relationships between operations (e.g., multiplication as repeated additions); Analyze strategies based on place value, properties of operations, and relationships between operations; Analyze and convert among various representations (e.g., graphic, pictorial, verbal) of numbers and of number operations; Evaluate and justify standard and nonstandard computational algorithms and computational strategies; Interpret multiple representations/models of addition, subtraction, multiplication, and division of whole numbers and decimals, and use these operations to evaluate expressions; Apply knowledge of areas of mathematical content (e.g., counting and cardinality, operations and algebraic thinking, number and operations in base ten), and identify strategies for integrating mathematics content across other content areas and into students' play and everyday lives; Model diverse real-world and scientific situations and solve corresponding mathematical problems involving whole numbers, decimals, fractions, and percentages.
• Competency 0012: Apply properties and applications of fractions, ratios, rates, and proportions using the Standards for Mathematical Practice. Skills tested: Demonstrate knowledge of fractions as numbers (e.g., unit fraction, relative size, relation to the whole, relation to division); Interpret multiple representations of fractions (including mixed numbers), test for equivalency between and compare two or more fractions, and represent equivalent fractions; Apply and extend knowledge of procedures for adding, subtracting, multiplying, and dividing fractions, and justify why procedures for operations with fractions make sense; Apply rounding and estimating methods to expressions with fractions, and judge the effect of those estimations on the results; Analyze multiple representations for modeling operations involving fractions; Demonstrate knowledge of the connections between fractions, ratios, and rates; Apply ratio and rate concepts, and use ratio and rate language to describe relationships and situations; Analyze multiple representations of proportional relationships (e.g., equations, tape diagrams, double number lines, tables), and solve proportional relationships for a missing value; Apply proportional reasoning to calculate a percent, and use percents to find unknown values; Model diverse real-world and scientific situations and solve corresponding mathematical problems involving fractions, ratios, rates, and proportions (e.g., mixtures, speeds, scale factors, scale drawings).
• Competency 0013: Apply knowledge of patterns, algebraic relationships, and functions using the Standards for Mathematical Practice. Skills tested: Apply properties of numbers and operations to interpret and explain relationships (e.g., the product of two even numbers is even); Interpret graphs that model diverse real-world situations, including those representing linear and nonlinear relationships; Apply the concepts of equality, equation, variable, and function to express relationships algebraically; Recognize, extend, and analyze patterns using a variety of representations (e.g., verbal, numeric, graphic, symbolic); Manipulate, simplify, and critique algebraic expressions using the properties of operations and relations; Solve equations and inequalities either to determine an unknown value or to express one variable in terms of another; Identify, calculate, and interpret features of linear relationships (e.g., slope, solutions to an equation, intercept values); Use algebra to solve word problems involving fractions, ratios, proportions, and percentages; Calculate and interpret the meaning of a rate of change, and analyze situations characterized by a constant rate of change; Model diverse real-world and scientific situations and solve corresponding mathematical problems involving algebraic expressions, equations, inequalities, and linear relations.
• Competency 0014: Apply concepts of geometry using the Standards for Mathematical Practice. Skills tested: Identify and classify two- and three-dimensional figures according to their characteristics (e.g., sides, angles, faces, vertices, edges); Determine area and volume of composite figures by composition and decomposition using standard and nonstandard units; Justify area and volume formulas obtained through compositions and decompositions of unit squares or unit cubes, including formulas for the area of rectangles and volume of rectangular prisms; Calculate surface area and volume of common three-dimensional figures; Determine the measures of radius, diameter, circumference, and area of a circle, and recognize the relationships among these characteristics; Interpret and use nets representing three-dimensional figures; Classify and analyze figures in the coordinate plane using distance, slope, and parallel and perpendicular lines; Analyze the effects of translations, rotations, and reflections on figures in the coordinate plane; Classify angles and analyze relationships between related angles in polygons and intersecting lines; Model diverse real-world and scientific situations and solve corresponding mathematical problems involving two- and three-dimensional figures and coordinate geometry.
• Competency 0015: Apply principles, concepts, and procedures related to measurement and data using the Standards for Mathematical Practice. Skills tested: Select appropriate units and methods of measurement for a given application (e.g., direct versus indirect measurement, relationship of a measurement to the size of the unit); Perform unit conversions within a measurement system; Model diverse real-world and scientific situations and solve corresponding mathematical problems involving money, length, perimeter, area, volume, mass, capacity, density, elapsed time, temperature, angles, and rates of change; Analyze the relationships between linear dimensions on measures of perimeter, area, and/or volume (e.g., the effect of changing the dimensions of a shape on its area, maximizing area by changing a dimension); Interpret and compare data represented in tables, charts, and graphs (e.g., picture graphs, bar graphs, dot plots, histograms, box plots, circle graphs); Calculate and analyze measures of central tendency (i.e., mean, median, and mode) and dispersion (i.e., range and interquartile range); Select appropriate graphs or numerical summaries to represent the distribution of categorical or numerical data, and compare data distributions in terms of differences in center, variability, and shape; Analyze sampling techniques used to collect data for diverse real-world and scientific situations; Develop and justify appropriate inferences, interpolations, and extrapolations from a set of data; Apply fundamental principles of probability, including analyzing simulations and probability models of diverse real-world and scientific situations.

Competencies 0016–0019 make up about 42% of the test. They ask you to apply knowledge of Earth and space science principles and the Science and Engineering Practices to interpret and analyze phenomena; apply knowledge of life science principles and the Science and Engineering Practices to interpret and analyze phenomena; apply knowledge of physical sciences principles and the Science and Engineering Practices to interpret and analyze phenomena, and more.

• Competency 0016: Apply knowledge of Earth and space science principles and the Science and Engineering Practices to interpret and analyze phenomena. Skills tested: Demonstrate knowledge of the solar system, including its structure and the relationships among objects in the solar system (e.g., the Moon's effect on Earth, the change of seasons, lunar phases); Demonstrate knowledge of the forces that shape Earth's surface (e.g., erosion, weathering, deposition, volcanism) and evidence of these forces; Recognize the structure and patterns of Earth's features (e.g., earthquake epicenters, deep-ocean trenches, mountain ranges, volcanoes, bodies of water), including analyzing Earth's features through maps and other models; Analyze the components and processes of the water cycle and where water is found on Earth (e.g., watersheds); Apply knowledge of the difference between weather and climate, of factors that affect weather and climate (e.g., proximity to large bodies of water, mountains, energy input from the Sun), of the patterns that predict typical weather in an area, and of tools (e.g., thermometer, rain gauge) and systematic methods for making quantitative observations of local weather conditions that describe patterns over time; Demonstrate knowledge of the effects of natural events (e.g., floods, hurricanes, blizzards, earthquakes, extreme heat, fires) and ways to predict, minimize, and mitigate these effects; Analyze the ways humans use their local and global renewable and nonrenewable resources, the impact of humans on the environment (e.g., pollution, climate change, deforestation), and ways to minimize that impact (e.g., reusing, recycling, or composting resources; reducing energy consumption; improving drinking water); Apply knowledge of the use of science and engineering practices in exploring and understanding content related to the Earth and space sciences, such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, constructing explanations, and communicating and evaluating data and conclusions.
• Competency 0017: Apply knowledge of life science principles and the Science and Engineering Practices to interpret and analyze phenomena. Skills tested: Identify the basic characteristics of life that distinguish organisms from nonliving things (e.g., cellular structure, growth, reproduction); Demonstrate knowledge of the basic structures of plants and animals (e.g., leaves, flowers, wings, eyes) and how body structures and systems (e.g., root, circulatory, digestive) interact to carry out essential functions of life (e.g., obtaining energy and nutrients, maintaining internal conditions, responding to stimuli); Identify the basic principles of heredity, and distinguish between inherited characteristics and characteristics influenced by interaction with the environment; Demonstrate knowledge of how species adapt and evolve over time as a result of differences in characteristics between individuals that can provide advantages in survival and reproduction, and demonstrate knowledge of the use of evidence (e.g., fossil record, anatomical similarities) to support arguments about changes in life-forms throughout the history of Earth and about evolutionary relationships between organisms; Analyze how organisms interact with one another and their environments, including ways in which the structures and behaviors of animals and plants help them survive and reproduce; Demonstrate knowledge of the cycling of matter and flow of energy between living and nonliving parts of an ecosystem, and analyze the interactions of organisms with their environment and interactions between organisms; Apply knowledge of the use of science and engineering practices in exploring and understanding content related to life science, such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, constructing explanations, and communicating and evaluating data and conclusions.
• Competency 0018: Apply knowledge of physical sciences principles and the Science and Engineering Practices to interpret and analyze phenomena. Skills tested: Demonstrate knowledge of the properties of materials and matter (e.g., color, hardness, reflectivity, electrical conductivity, thermal conductivity, response to magnetic forces, solubility), states of matter (i.e., liquid, solid, and gas) and changes in phase, and representations of matter and its interactions (e.g., the particle model); Demonstrate knowledge of pure substances, compounds, and mixtures and of physical changes and chemical reactions; Recognize forms of energy (e.g., heat, electrical, magnetic, sound, light, kinetic, potential) and that energy can change from one form to another and can transfer from place to place; Apply the basic concept of forces (e.g., gravitational, frictional, magnetic, applied) to the motion of objects; Demonstrate knowledge of gravitational forces and that gravitational forces between objects with mass are attractive and are only noticeable if one or both objects have a very large mass; Recognize changes in energy when objects collide, and relate the speed of an object to its energy; Apply the principles of the conservation of matter and energy (e.g., conservation of atoms during a reaction, conservation of energy when force is applied to an object); Apply knowledge of waves, including sound and light; methods of transferring energy and information by various types of waves (e.g., electromagnetic, mechanical) through various media; and wave phenomena (e.g., reflection, absorption, transmittal) in everyday life; Apply knowledge of the use of science and engineering practices in exploring and understanding content related to the physical sciences, such as developing and using models, planning and safely conducting investigations, applying mathematical concepts, constructing explanations, and communicating and evaluating data and conclusions.
• Competency 0019: Apply knowledge of engineering principles and practices to interpret and analyze design problems. Skills tested: Demonstrate knowledge of the processes of engineering design (i.e., defining problems; developing and using models; planning and carrying out investigations; analyzing and interpreting data; using mathematics and computational thinking; constructing explanations and designing solutions; engaging in argument from evidence; and obtaining, evaluating, and communicating information); Recognize 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 how to identify a design problem and communicate design solutions, including making improvements to existing designs; Demonstrate knowledge of how to apply engineering design practices to define a problem and to identify the criteria and constraints (e.g., materials, time, cost) associated with the problem; Recognize the selection and appropriate and safe use of tools for a design solution, including measuring tools, hand tools, fasteners, and common handheld power tools in a variety of contexts, including manufacturing processes, engineering projects, and daily activities; Apply knowledge of the iterative design process, including testing, comparing design solutions, analyzing the impact of design solutions on society, and modifying design solutions to improve a prototype in a real-world context.

Competencies 0020–0020 make up about 10% of the test. They ask you to prepare an organized, developed analysis of a scenario that integrates science/engineering and mathematics content and practices.

• Competency 0020: Prepare an organized, developed analysis of a scenario that integrates science/engineering and mathematics content and practices. Skills tested: Analyze a description or model of a situation involving a scientific phenomenon, an investigation, or an engineering design problem; Apply appropriate mathematical knowledge and skills to the given situation (e.g., to select appropriate units of measurement; to apply geometry concepts; to summarize, interpret, and/or analyze data; to model relationships with tables, graphs, and equations; to verify quantifiable data).