Mathematics (Grades 5–12) Subtest 2

Subarea 1. Measurement and Geometry

0008

Apply principles of measurement and geometry to solve problems.

solving problems involving conversions within and between different systems of measurement, including dimensional analysis
solving mathematical and real-world problems involving measurable attributes of simple or composite shapes, regions, and solids (e.g., length, area, capacity, degree and radian angle measures)
solving mathematical and real-world problems involving indirect measurement (e.g., proportional reasoning, Pythagorean theorem, trigonometric ratios, unit circle trigonometry)
solving problems involving the effects of changing linear dimensions of a two-dimensional or three-dimensional object on its perimeter, area, and volume

0009

Analyze figures and shapes in two and three dimensions.

analyzing the relationships between points, lines (e.g., parallel, perpendicular, skew), rays, angles (e.g., supplementary, vertical), and planes
applying the properties of triangles (e.g., congruence conditions, triangle inequality, special triangles) and other polygons (e.g., properties of quadrilaterals, sum of interior angles) to solve mathematical and real-world problems
applying the properties of circles (e.g., tangents, arc length, chords, inscribed angles) to solve mathematical and real-world problems
applying the properties of three-dimensional shapes (e.g., pyramids, cones, spheres) to solve mathematical and real-world problems
analyzing and evaluating formal and informal arguments, reasoning processes, proofs, and the validity of conclusions
demonstrating knowledge of the axioms and key features (e.g., parallelism, angle sums, great circles, congruence) of Euclidean and non-Euclidean (e.g., spherical, hyperbolic, fractal) geometries

0010

Analyze figures and shapes using coordinate and transformational geometry.

classifying, representing, and analyzing two-dimensional shapes in the coordinate plane, including translating between geometric descriptions and equations of conic sections
applying geometric properties and the concepts of distance, midpoint, parallelism, and slope in two-dimensional and three-dimensional coordinate systems to solve mathematical and real-world problems
applying transformations (e.g., rotations, reflections, translations) to figures in the coordinate plane and analyzing topological properties and transformations
translating between two-dimensional and three-dimensional representations of geometric figures (e.g., cross sections, nets) and generating three-dimensional figures from two-dimensional shapes
analyzing the use of the techniques of coordinate geometry in geometric proofs