TExES Math 7-12 Study Guide

A complete, domain-by-domain study guide for the TExES Mathematics 7-12 (235) written by a mathematics professor who has helped over 1,300 educators prepare for this exam.

Before You Open a Textbook: Know the Exam

The TExES Mathematics 7-12 (235) is administered by ETS on behalf of the Texas Education Agency. It has 100 selected-response questions, a 5-hour time limit, and a passing scaled score of 240 (on a scale of 100–300).

Most candidates underestimate this exam. It is not a standard calculus final. It tests your ability to think like a mathematics teacher — which means content knowledge AND pedagogical knowledge, often in the same question.

Common mistake: Buying a generic math review book and working through it cover to cover. That approach ignores the actual exam blueprint and wastes weeks on low-weight topics.

The 12-Week Study Plan

This plan assumes you are starting from a moderate baseline (e.g., a mathematics degree or strong undergraduate coursework). Adjust timelines based on your placement diagnostic results.

Week 1
Baseline diagnostic
Take a full placement diagnostic to identify your strongest and weakest domains before touching any content.
Weeks 2–3
Domain I — Number Concepts
Real and complex numbers, number theory, rational vs irrational. Focus on proof-based reasoning, not just computation.
Weeks 4–5
Domain II — Patterns & Algebra
Polynomial, rational, exponential, logarithmic functions. Abstract algebra fundamentals. This is often the heaviest content week.
Week 6
Domain III — Geometry & Measurement
Euclidean geometry, transformations, coordinate geometry, trigonometry. Proof-writing matters here.
Week 7
Domain IV — Probability & Statistics
Descriptive stats, probability models, basic inference. Know the difference between correlation and causation cold.
Week 8
Domain V — Mathematical Processes & Pedagogy
This is the most neglected domain. Study learning progressions, instructional strategies, common student misconceptions.
Week 9
Domain VI — Functions & Calculus
Limits, continuity, derivatives, integrals, sequences and series. Do not skim this — it is 17% of the exam.
Weeks 10–11
Targeted weak-spot drilling
Return to your two weakest domains. Use adaptive practice to push your competency scores up, not more reading.
Week 12
Full mock exam + review
Take a timed, full-length practice exam under realistic conditions. Review every missed question before test day.

Domain-by-Domain Tips from a Math Professor

Domain I — Number Concepts (17%)

Most candidates do fine here but lose points on proof-based questions. Practice writing informal proofs: why is the sum of two rational numbers always rational? Why is √2 irrational? The exam will ask you to evaluate student reasoning, which means you need to know what correct reasoning looks like.

Domain II — Patterns and Algebra (18%)

The abstract algebra questions (groups, rings, modular arithmetic) catch a lot of candidates off guard. If it has been a few years since your abstract algebra course, spend a week revisiting the basics — the exam does not go deep, but it expects you to know what a group is.

Domain III — Geometry and Measurement (18%)

Know your transformation rules (translations, reflections, rotations, dilations) and how to compose them. Coordinate geometry questions are computationally heavier — practice them until they are automatic.

Domain IV — Probability and Statistics (17%)

Many candidates lose points here by confusing probability models. Make sure you can distinguish between permutations and combinations, explain the Central Limit Theorem in plain language, and interpret a p-value correctly.

Domain V — Mathematical Processes and Pedagogy (13%)

This is the domain that separates first-time passers from retakers. Study Bloom's Taxonomy as it applies to mathematics. Know the difference between procedural fluency and conceptual understanding. Be able to identify a student misconception from a worked example and suggest the correct instructional intervention.

Professor's tip: For pedagogy questions, always ask yourself — does this answer choice build understanding, or just give the student the answer? The TEA framework consistently rewards understanding over procedure.

Domain VI — Functions (17%)

Limits, derivatives, and integrals appear here but not at the depth of a university calculus exam. The exam also includes sequences, series, and convergence tests. Know the geometric series formula cold — it appears often and is a quick point if you have it memorised.

Resources Worth Using

Start adaptive practice → See practice questions