TExES Math 7-12 Competency Domains

Every question on the TExES Mathematics 7-12 (235) maps to one of six competency domains. Here is the complete blueprint — weights, key topics, and where most candidates lose points.

The Six Domains

Domain I — Number Concepts Medium priority
14%

Covers the real number system, complex numbers, and number theory. Competencies C001–C003.

  • Properties of real numbers (closure, commutativity, associativity, distributivity)
  • Prime factorisation, GCF, LCM
  • Density of rational and irrational numbers on the number line
  • Complex number arithmetic and the complex plane
  • Divisibility, modular arithmetic, and prime factorisation reasoning
Domain II — Patterns, Algebra & Functions High priority
33%

The largest content domain. Covers patterns, algebra, functions, equations and inequalities — and differential and integral calculus (Competency 010). Competencies C004–C010.

  • Polynomial, rational, exponential, and logarithmic functions
  • Systems of equations and inequalities
  • Matrices and their applications
  • Groups, rings, and fields (abstract algebra basics)
  • Number patterns, sequences, and mathematical induction
  • Differential and integral calculus — limits, derivatives, integrals (C010)
Domain III — Geometry & Measurement Medium priority
19%

Euclidean geometry, transformations, coordinate geometry, and measurement. Competencies C011–C014.

  • Triangle congruence and similarity theorems
  • Circle theorems and arc-angle relationships
  • Geometric transformations (translation, reflection, rotation, dilation)
  • Coordinate geometry proofs
  • Surface area and volume — prisms, pyramids, cylinders, cones, spheres
Domain IV — Probability & Statistics Medium priority
14%

Data analysis, probability models, and statistics. Competencies C015–C017.

  • Measures of center and spread
  • Counting principles, permutations, combinations
  • Discrete and continuous probability distributions
  • Normal distribution and z-scores
  • Correlation, regression, and causation
Domain V — Mathematical Processes & Perspectives High priority
10%

Tests how you reason about and communicate mathematics — problem-solving processes, mathematical connections, and the nature of mathematical thinking. Competencies C018–C019.

  • Polya's problem-solving framework
  • Inductive and deductive reasoning, conjecture and proof
  • Multiple representations and connections between mathematical ideas
  • Real-world modeling and quantitative fluency
  • Implications of current research in mathematics education for teachers
Domain VI — Mathematical Learning, Instruction & Assessment High priority
10%

Tests how you plan, deliver and assess mathematics instruction — teaching methods, responding to misconceptions, and assessment design. Competencies C020–C021.

  • Research-informed instructional strategies and CRA progression
  • Common student misconceptions and targeted interventions
  • Bloom's Taxonomy applied to mathematics objectives
  • Formative and summative assessment design
  • Using student work and questioning to guide instruction
Practice by domain → Full study guide →