TExES Mathematics 7-12 Online Center
This TExES Mathematics 7-12 Online Center brings together practice, lessons, worksheets, flashcards and review tools. Choose the resource that matches the skill you want to work on next.
TExES Mathematics 7-12 Practice Center
Take a full form, then read the explanation under every question you missed. Sort the misses two ways: the mathematics you could not do, and the question you could have answered if you had recognized what it was asking sooner. Those two piles call for different work.
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TExES Mathematics 7-12 at a glance
This is the Texas secondary mathematics content exam, the one behind the Mathematics: Grades 7-12 certificate. It is a college-level test. Calculus is on it, trigonometry is on it in quantity, and the statistics runs through inference. Two features shape how you prepare. Domain II, patterns and algebra, is a third of the exam by itself. And unlike Mathematics 4-8, this exam provides no calculator: you bring an approved graphing model, and staff clear its memory before and after you test.
| Test code | 235 (Mathematics 7-12) |
|---|---|
| Status | Current, offered year round by appointment. No retirement notice and no successor code have been posted for this exam. |
| Number of questions | 100 selected-response questions. There is no constructed-response assignment. |
| Time limit | 5 hours total appointment time: 15 minutes for the tutorial and compliance agreement, then 4 hours 45 minutes of testing. |
| Calculator | You must bring your own graphing calculator, and you may not bring its manual. Approved models include the TI-73, the TI-83 and TI-84 families, and the TI-Nspire Handheld with the TI-84 Plus Keypad. Staff clear the calculator memory before and after testing, so back up anything you want to keep. |
| Reference materials | A Definitions and Formulas page is supplied on-screen as part of the exam. |
| Format | Computer-administered at a Pearson Professional Center |
| Passing score | 240 on a scale of 100 to 300. |
Texas publishes approximate percentages by domain: Number Concepts 14 percent, Patterns and Algebra 33 percent, Geometry and Measurement 19 percent, Probability and Statistics 14 percent, Mathematical Processes and Perspectives 10 percent, and Mathematical Learning, Instruction and Assessment 10 percent. On a 100-question form those percentages read directly as question counts, so Domain II is worth about 33 questions and the two non-content domains are worth about 20 between them. Texas publishes no percentage for any individual competency, so none is claimed here.
The six domains, in plain language
Texas states each of the 21 competencies. Here is what each domain asks of you, with its published weight.
Domain II: Patterns and algebra (33 percent)
Seven competencies, a third of the exam, running from sequences to integral calculus.
- Patterns, recursion, arithmetic and geometric series, and mathematical induction
- Function attributes: domain and range, composition, inverses, transformations
- Linear and quadratic functions, systems, and the discriminant
- Polynomial, rational, radical, absolute value, and piecewise functions
- Exponential and logarithmic functions, growth and decay, log scales
- Trigonometric and circular functions, identities, and periodic models
- Limits, derivatives, integrals, and the Fundamental Theorem of Calculus
Domain III: Geometry and measurement (19 percent)
Measurement as a process, Euclidean geometry as an axiomatic system, and the coordinate plane.
- Dimensional analysis, perimeter, area, surface area, and volume
- The effect of a scale change on length, area, and volume
- Axiomatic structure, congruence, similarity, and proof
- Polygons, circles, cross sections, nets, and multiple views of solids
- Transformations, symmetry, and coordinate geometry
- Conic sections, vectors, and transformation matrices
Domain I: Number concepts (14 percent)
The real numbers, the complex numbers, and number theory used to model problems.
- Structure and properties of the real number system and its subsets
- Complex numbers: conjugates, magnitude, rectangular and polar form
- Prime factorization, divisibility, greatest common divisor, modular arithmetic
- Properties of vectors and matrices compared with number systems
- Ratio, proportion, percent, and counting techniques
- Estimation and judging whether an answer is reasonable
Domain IV: Probability and statistics (14 percent)
Describing data, computing probability, and drawing inferences from a sample.
- Data displays, center, spread, shape, and skewness
- Effects of linear transformations on summary statistics
- Sample spaces, conditional probability, and independence
- Binomial, geometric, uniform, and normal distributions
- Sampling, confidence intervals, and hypothesis testing
- Regression, residuals, correlation, and linearizing nonlinear data
Domain V: Mathematical processes and perspectives (10 percent)
Reasoning about mathematics itself, and communicating it.
- Proof, including indirect proof and counterexample
- Valid conclusions from given premises
- Inductive conjecture and deductive verification
- More than one route to a solution, and comparing them
- Multiple representations and translation between them
- Precise terminology and mathematics used in other disciplines
Domain VI: Mathematical learning, instruction and assessment (10 percent)
How secondary students learn mathematics, and how you would respond.
- Building on prior knowledge and planning to the TEKS
- Concrete to representational to abstract instruction
- Manipulatives, technology, and tools that fit the idea
- Questioning that produces mathematical discourse
- Formative and summative assessment and their purposes
- Reading error patterns and adjusting instruction
A study routine for a 285-minute exam
Time is not the pressure here. Four hours forty-five for a hundred questions leaves close to three minutes each. The pressure is range: this exam reaches from modular arithmetic to hypothesis testing, and no candidate is equally strong across all of it.
Complete topic map
Forty-seven lessons on the algebra, geometry, and data work underneath this exam, each opening in a new tab, followed by the advanced content and the teaching topics that 235 adds. Lessons on those are on the way.
Counting, place value, and operations
Fractions and decimals
Ratios, proportion, and percent
Algebraic thinking and patterns
The coordinate plane
Measurement and geometry
Data, statistics, and probability
Advanced algebra, sequences, and series (lessons on the way)
- 48Polynomial division, the Remainder Theorem, and the Factor Theorem
- 49Complex numbers, conjugates, modulus, and polar form
- 50Quadratics over the complex numbers and what the discriminant tells you
- 51Rational expressions, restrictions, and extraneous roots
- 52Systems in three variables, matrices, and determinants
- 53Vectors and matrix representations of transformations
- 54Arithmetic and geometric sequences, series, and the infinite geometric sum
- 55Mathematical induction
- 56Finance problems built on sequences: interest, annuities, and amortization
Functions in depth (lessons on the way)
- 57Domain, range, and reasonable domains for a modeling situation
- 58Composition, one-to-one functions, and inverses
- 59Even and odd functions and tests for symmetry
- 60Transformations of a parent function and their effect on the formula
- 61Asymptotes, end behavior, and points of discontinuity
- 62Piecewise and step functions
- 63Exponential and logarithmic functions and the log laws
- 64Logarithmic scales: Richter, decibel, and pH
Trigonometry (lessons on the way)
- 65Radian measure and the unit circle
- 66The six trigonometric functions and their graphs
- 67Amplitude, period, frequency, and phase shift
- 68The Pythagorean identities
- 69Sum, difference, and double angle formulas
- 70Inverse trigonometric functions and their restricted ranges
- 71The Law of Sines, the Law of Cosines, and the ambiguous case
- 72Modeling periodic phenomena
Calculus (lessons on the way)
- 73Limits, one-sided limits, and limits at infinity
- 74Continuity and the Intermediate Value Theorem
- 75The derivative as a limit and as a rate of change
- 76Power, product, quotient, and chain rules
- 77Implicit differentiation
- 78Critical points, concavity, and the first and second derivative tests
- 79Related rates and optimization
- 80Antiderivatives and u-substitution
- 81The definite integral and both parts of the Fundamental Theorem
- 82Riemann sums, area between curves, and volumes of revolution
Advanced geometry (lessons on the way)
- 83Axiomatic systems: undefined terms, postulates, theorems, and counterexamples
- 84Triangle congruence and similarity criteria
- 85The four triangle centers
- 86Circle theorems and the power of a point
- 87Arc length and sector area
- 88Conic sections and their standard equations
- 89Transformations, compositions, and their coordinate rules
- 90Cross sections, nets, and volumes of solids
- 91Structuring a two-column proof and an indirect proof
- 92Euclidean compared with hyperbolic and elliptic geometry
Statistics and inference (lessons on the way)
- 93Measurement scales: nominal, ordinal, interval, and ratio
- 94Shape, center, spread, and skewness in a distribution
- 95The effect of a linear transformation on center and spread
- 96The normal distribution, z-scores, and the empirical rule
- 97Binomial and geometric distributions, expected value, and variance
- 98Conditional probability, independence, and the addition and multiplication rules
- 99Geometric probability from ratios of areas
- 100Sampling methods, bias, and the sampling distribution
- 101The law of large numbers and the Central Limit Theorem
- 102Confidence intervals and what they do and do not claim
- 103Hypothesis testing in outline
- 104Least squares regression, residuals, correlation, and linearizing data
Domain V: reasoning, proof, and communication
- 105Direct proof, indirect proof, and counterexample
- 106Deriving valid conclusions from a set of premises
- 107Inductive conjecture compared with deductive verification
- 108Comparing two correct solution paths to the same problem
- 109Judging whether an answer is reasonable in context
- 110Judging how well a model represents the situation it came from
- 111Translating one representation of an idea into another
- 112Using precise mathematical terminology and standard notation
Domain VI: how students learn mathematics, and assessment
- 113Building new work on what students already know
- 114Moving instruction from concrete to representational to abstract
- 115Choosing a manipulative, tool, or technology that fits the idea
- 116Questioning that opens up mathematical discourse
- 117Supporting English learners in a mathematics classroom
- 118Reading student work and naming the specific error
- 119Formative compared with summative assessment, and what each is for
- 120Writing a task that exposes a misconception rather than hiding it
- 121Using assessment results to decide what to teach next
- 122Aligning a lesson to the TEKS
Before test day
Two habits protect more points here than any last-minute review. Set the calculator to radians before you touch a trigonometry question, because an answer computed in degrees comes out plausible rather than obviously wrong. And check every solution to a radical or rational equation against the original, because an extraneous root will be sitting there among the choices. Then remember that a fifth of this exam asks about reasoning and about students. On any item that shows you student work, name the specific error in your own words before you read the options.
A USEFUL NEXT STEP
TExES Mathematics 7-12: study questions
What can I study in this TExES Mathematics 7-12 Online Center?
This TExES Mathematics 7-12 Online Center includes practice, lessons, worksheets, flashcards and review tools. Topics on the page include Domain II: Patterns and algebra (33 percent), Domain III: Geometry and measurement (19 percent), Domain I: Number concepts (14 percent).
How should I use the TExES Mathematics 7-12 resources?
Choose a topic or practice activity from this Online Center. Review the linked explanation, try the practice, and use the result to decide what to study next. Check each resource’s directions for its format and access requirements.
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