# 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.

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.

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.

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.

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.

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