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# Middle School Mathematics Test Objectives

Subarea

 Multiple-Choice Range of Objectives Approximate Test Weighting I. Number Sense and Operations 01–04 15% II. Patterns, Relations, and Algebra 05–10 25% III. Geometry and Measurement 11–15 18% IV. Data Analysis, Statistics, and Probability 16–17 12% V. Trigonometry, Calculus, and Discrete Mathematics 18–20 10% 80% Open-Response VI. Integ ration of Knowledge and Understanding 21 20%

SUBAREAS:

NUMBER SENSE AND OPERATIONS
PATTERNS, RELATIONS, AND ALGEBRA
GEOMETRY AND MEASUREMENT
DATA ANALYSIS, STATISTICS, AND PROBABILITY
TRIGONOMETRY, CALCULUS, AND DISCRETE MATHEMATICS
INTEGRATION OF KNOWLEDGE AND UNDERSTANDING

NUMBER SENSE AND OPERATIONS [15%]

0001 Understand the structure of numeration systems and multiple representations
of numbers.

For example: place value; number bases (e.g., base 2, base 10); order
relations; relationships between operations (e.g., multiplication as repeated
additions); number factors and divisibility; prime and composite numbers;
prime factorization; multiple representations of numbers (e.g., physical
models, diagrams, numerals); and properties of early numeration systems
(e.g., Mayan, Mesopotamian, Egyptian).

0002 Understand principles and operations related to integers, fractions , decimals,
percents, ratios, and proportions .

For example: order of operations ; identity and inverse elements;
associative, commutative, and distributive properties; absolute value;
operations with signed numbers ; multiple representations (e.g., area
models for multiplication) of number operations; analyzing standard
algorithms for addition, subtraction , multiplication, and division of integers
and rational numbers; number operations and their inverses; and the origins
and development of standard computational algorithms.

0003 Understand and solve problems involving integers, fractions, decimals,
percents, ratios, and proportions.

For example: solving a variety of problems involving integers, fractions,
decimals, percents (including percent increase and decrease), ratios,
proportions, and average rate of change; and using estimation to judge
the reasonableness of solutions to problems.

0004 Understand the properties of real numbers and the real number system.

For example: rational and irrational numbers; properties (e.g., closure,
distributive, associative) of the real number system and its subsets;
operations and their inverses; the real number line; roots and powers ; the
laws of exponents; scientific notation; using number properties to prove
theorems (e.g., the product of two even numbers is even); and problems
involving real numbers and their operations.

PATTERNS, RELATIONS, AND ALGEBRA [25%]

0005 Understand and use patterns to model and solve problems.

For example: making conjectures about patterns presented in numeric,
geometric, or tabular form; representing patterns and relations using symbolic
notation; identifying patterns of change created by functions
(e.g., linear, quadratic, exponential); and using finite and infinite series
and sequences (e.g., Fibonacci, arithmetic, geometric) to model and solve
problems.

0006 Understand how to manipulate and simplify algebraic expressions and
translate problems into algebraic notation.

For example: the nature of a variable; evaluating algebraic expressions for
a given value of a variable; the relationship between standard computational
algorithms and algebraic processes; expressing direct and inverse relationships
algebraically; expressing one variable in terms of another; manipulating and
simplifying algebraic expressions; solving equations; and using algebraic
expressions to model situations.

0007 Understand properties of functions and relations.

For example: the difference between functions and relations; the
generation and interpretation of graphs that model real-world situations;
multiple ways of representing functions (e.g., tabular, graphic, verbal,
symbolic); properties of functions and relations (e.g., domain, range,
continuity); piecewise-defined functions; addition, subtraction, and
composition of functions; and graphs of functions and their transformations
[e.g., the relationships among f(x), f(x + k), and f(x) + k].

0008 Understand properties and applications of linear relations and functions.

For example: the relationship between linear models and rate of change;
direct variation; graphs of linear equations; slope and intercepts of lines;
finding an equation for a line; methods of solving systems of linear equations
and inequalities (e.g., graphing, substitution); and modeling and solving
problems using linear functions and systems.

0009 Understand properties and applications of quadratic relations and functions.

For example: methods of solving quadratic equations and inequalities
(e.g., factoring, completing the square, quadratic formula, graphing); real
and complex roots of quadratic equations; graphs of quadratic functions;
quadratic maximum and minimum problems; and modeling and solving
problems using quadratic relations, functions, and systems.

0010 Understand properties and applications of exponential, polynomial, rational,
and absolute value functions and relations.

For example: problems involving exponential growth (e.g., population
growth, compound interest) and decay (e.g., half-life); inverse variation;
modeling problems using rational functions; properties and graphs of
polynomial
, rational, and absolute value functions; and the use of graphing
calculators and computers to find numerical solutions to problems involving
exponential, polynomial, rational, and absolute value functions.

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