100+ Free OSAT Middle Level/Intermediate Mathematics (225) Practice Questions

Number Properties and Number Sense (Subarea I)

Structure and properties of the real number system, classifying rational and irrational numbers, place value, scientific notation, radicals and exponents, matrices and their operations, evaluating conjectures with counterexamples, operations on real and complex numbers, ratios, proportional reasoning, percentages, primes, factors, divisibility, greatest common factors, and least common multiples.

Relations, Functions, and Algebra (Subarea II)

Distinguishing relations from functions, analyzing domain, range, symmetry, intercepts, and extrema, function transformations, composition and inverse functions, translating words to algebra, manipulating expressions and equations, linear functions and systems of equations and inequalities, quadratic and higher-order polynomial functions, and advanced radical, rational, absolute value, exponential, and logarithmic functions including calculus foundations.

Measurement and Geometry (Subarea III)

Comparing and converting measurements, formulas for angles, length, perimeter, area, and volume, proportional and spatial reasoning with scale factors, the Pythagorean theorem, Euclidean geometry of lines, angles, similarity, congruence, circles and polygons, special right triangles and trigonometric ratios, and coordinate and transformational geometry using distance, midpoint, and slope.

Probability and Statistics (Subarea IV)

Theoretical and experimental probability, the fundamental counting principle, permutations and combinations, probability rules and graphic representations, the normal probability distribution, random sampling techniques, interpreting data in various graphic formats, measures of central tendency and variation, and evaluating statistical claims to make predictions.

Pedagogical Content Knowledge (Subarea V)

One constructed-response assignment analyzing lesson plans, student work, and assessments, applying standards-based learning goals, identifying mathematical strengths and needs, describing instructional strategies tied to the Standards for Mathematical Practice, and using data to inform differentiation and future instruction. This bank includes pedagogy-style multiple-choice items to build those skills.