# Mathematics (Grades 5–12) Subtest 2

## Subarea I.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 figures and shapes (e.g., length, capacity, angle measure)
- 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 the dimensions of a figure or shape on its area and volume

0009
Analyze figures and shapes in two and three dimensions.

- applying the properties of polygons and circles to solve mathematical and real-world problems
- applying the properties of two- and three-dimensional shapes to solve mathematical and real-world problems
- analyzing formal and informal arguments and proofs
- evaluating arguments, reasoning, and the validity of conclusions
- analyzing systems of geometry, including Euclidean, non-Euclidean, and projective geometries

0010
Analyze figures and shapes using coordinate and transformational geometry.

- analyzing two- and three-dimensional figures and shapes in the coordinate plane
- applying geometric properties and the concepts of distance, midpoint, and slope in 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
- analyzing the use of the techniques of coordinate geometry in geometric proofs
- applying vectors and polar and parametric equations to solve problems