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 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, 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.