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# Middle School Mathematics Test Objectives

GEOMETRY AND MEASUREMENT [18%]

0011 Understand principles, concepts, and procedures related to measurement.

For example: using appropriate units of measurement; unit conversions
within and among measurement systems; problems involving length, area,
volume, mass, capacity, density, time, temperature, angles, and rates of
change; problems involving similar plane figures and indirect measurement;
the effect of changing equations --slope.html">linear dimensions on measures of length, area, or
volume; and the effects of measurement error and rounding on computed
quantities (e.g., area, density, speed).

0012 Understand the principles of Euclidean geometry and use them to prove
theorems.

For example: the nature of axiomatic systems; undefined terms and
postulates of Euclidean geometry; relationships among points, lines, angles,
and planes; methods for proving triangles congruent; properties of similar
triangles; justifying geometric constructions; proving theorems within the
axiomatic structure of Euclidean geometry; and the origins and development
of geometry in different cultures (e.g., Greek, Hindu, Chinese).

0013 Apply Euclidean geometry to analyze the properties of two-dimensional figures
and to solve problems.

For example: using deduction to justify properties of and relationships
among triangles, quadrilaterals, and other polygons (e.g., length of sides,
angle measures); identifying plane figures given characteristics of sides,
angles, and diagonals; the Pythagorean theorem; special right triangle
relationships; arcs, angles, and segments associated with circles; deriving
and applying formulas for the area of composite shapes; and modeling and
solving problems involving two-dimensional figures.

0014 Solve problems involving three-dimensional shapes.

For example: area and volume of and relationships among three-dimensional
figures (e.g., prisms, pyramids, cylinders, cones); perspective
drawings; cross sections (including conic sections ) and nets; deriving
properties of three-dimensional figures from two-dimensional shapes; and
modeling and solving problems involving three-dimensional geometry.

0015 Understand the principles and properties of coordinate and transformational
geometry.

For example: representing geometric figures (e.g., triangles, circles) in the
coordinate plane; using concepts of distance, midpoint, slope, and parallel
and perpendicular lines to classify and analyze figures (e.g., parallelograms);
characteristics of dilations, translations, rotations, reflections, and glidereflections;
types of symmetry; properties of tessellations; transformations in
the coordinate plane; and using coordinate and transformational geometry to
prove theorems and solve problems.

DATA ANALYSIS, STATISTICS, AND PROBABILITY [12%]

0016 Understand descriptive statistics and the methods used in collecting,
organizing, reporting, and analyzing data.

For example: constructing and interpreting tables, algebra -help/algebra-equations-chart.html">charts , and graphs
(e.g., line plots , stem-and-leaf plots, box plots, scatter plots); measures of
central tendency (e.g., mean, median, mode) and dispersion (e.g., range,
standard deviation); frequency distributions; percentile scores; the effects
of data transformations on measures of central tendency and variability;
evaluating real-world situations to determine appropriate sampling techniques
and methods for gathering and organizing data; making appropriate
inferences, interpolations, and extrapolations from a set of data; interpreting
correlation; and problems involving linear regression models.

0017 Understand the fundamental principles of probability.

For example: representing possible outcomes for a probabilistic situation;
counting strategies (e.g., permutations and combinations); computing
theoretical probabilities for simple and compound events; using simulations
to explore real-world situations; connections between geometry and
probability (e.g., probability as a ratio of two areas ); and using probability
models to understand real-world phenomena.

TRIGONOMETRY, CALCULUS, AND DISCRETE MATHEMATICS [10%]

0018 Understand the properties of trigonometric functions and identities.

For example: degree and radian measure; right triangle trigonometry; the law
of sines and the law of cosines ; graphs and properties of trigonometric
functions and their inverses; amplitude, period, and phase shift; trigonometric
identities; and using trigonometric functions to model real-world periodic
phenomena.

0019 Understand the conceptual basis of calculus.

For example: the concept of limit; the relationship between slope and rates
of change; how the derivative relates to maxima, minima, points of inflection,
and concavity of curves ; the relationship between integration and the area
under a curve; modeling and solving basic problems using differentiation and
integration; and the development of calculus.

0020 Understand the principles of discrete/finite mathematics.

For example: properties of sets; recursive patterns and relations; problems
involving iteration; properties of algorithms; finite differences; linear
programming; properties of matrices; and characteristics and applications of
graphs and trees.

INTEGRATION OF KNOWLEDGE AND UNDERSTANDING [20%]

In addition to answering multiple -choice items, candidates will prepare written responses to
questions addressing content from the preceding objectives, which are summarized in the
objective
and descriptive statement below.

0021 Prepare an organized, developed analysis on a topic related to one or more
of the following: number sense and operations; patterns, relations, and
algebra; geometry and measurement; data analysis, statistics, and probability;
and trigonometry, calculus, and discrete mathematics.

For example: presenting a detailed solution to a problem involving one or
more of the following: place value, number base, and the structure and
operations of number systems; application of ratios and proportions in a
variety
of situations; properties, attributes, and representations of linear
functions; modeling problems using exponential functions ; the derivative
as a rate of change and the integral as area under the curve; applications of
plane and three-dimensional geometry; and design, analysis, presentation,
and interpretation of a statistical survey.

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