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
17%

Covers the real number system, number theory, rational and irrational numbers, complex numbers, and proof-based reasoning. Competencies C001–C005.

  • 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
  • Evaluating student reasoning and proof-writing
Domain II — Patterns, Algebra & Functions High priority
18%

The largest content domain. Covers algebraic reasoning, functions, equations and inequalities, and an introduction to abstract algebra. Competencies C006–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
Domain III — Geometry & Measurement Medium priority
18%

Euclidean and non-Euclidean geometry, transformations, coordinate geometry, and measurement. Competencies C011–C015.

  • 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
17%

Data analysis, probability models, statistical inference, and research design. Competencies C016–C020.

  • Measures of centre and spread
  • Counting principles, permutations, combinations
  • Discrete and continuous probability distributions
  • Normal distribution and Z-scores
  • Correlation, regression, and causation
Domain V — Mathematical Processes & Pedagogy High priority
13%

The most-missed domain. Tests how you think about teaching mathematics — problem-solving strategies, student misconceptions, instructional methods. Competency C021.

  • Polya's problem-solving framework
  • Common student misconceptions in algebra and geometry
  • Bloom's Taxonomy applied to mathematics
  • Concrete-Representational-Abstract (CRA) progression
  • Formative assessment and using student work to guide instruction
Domain VI — Mathematical Learning, Instruction & Assessment High priority
17%

Calculus and advanced topics: limits, derivatives, integrals, sequences and series. Competencies vary by form.

  • Limits and continuity
  • Differentiation rules (chain, product, quotient)
  • Applications of derivatives (optimisation, related rates)
  • Definite and indefinite integrals
  • Sequences and series — convergence tests, geometric series
Practice by domain → Full study guide →