Unofficial practice for TExES Mathematics 7–12 (235): number, algebra through calculus, geometry, statistics, reasoning and teaching, every answer worked out.
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Unofficial practice questions, not affiliated with the Texas Education Agency or Pearson. Bank checked October 12, 2026.
The equation x^2 − 6x + 13 = 0 has no real solution. What are its solutions in the complex numbers?19 Texas Administrative Code §111.40, Texas Essential Knowledge and Skills for Mathematics, Algebra II (Legal Information Institute copy), (c)(4)(F). Written to TExES Mathematics 7–12 (235) Domain I, competency 002
The Euclidean algorithm is applied to 1001 and 364. The remainders are 273, then 91, then 0. What is the greatest common divisor?Wikipedia, Euclidean algorithm. Written to TExES Mathematics 7–12 (235) Domain I, competency 003
Evaluate 125^(2/3) ÷ 81^(3/4).19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(11)(B). Written to TExES Mathematics 7–12 (235) Domain I, competency 001
Multiply the complex numbers 6 − 5i and 3 + 4i.19 Texas Administrative Code §111.40, Texas Essential Knowledge and Skills for Mathematics, Algebra II (Legal Information Institute copy), (c)(7)(A). Written to TExES Mathematics 7–12 (235) Domain I, competency 002
What is the modulus (absolute value) of the complex number 5 − 12i?Wikipedia, Complex number. Written to TExES Mathematics 7–12 (235) Domain I, competency 002
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Number concepts, continued
What is the remainder when 7^4 is divided by 5?Wikipedia, Modular arithmetic. Written to TExES Mathematics 7–12 (235) Domain I, competency 003
Which expression equals √72 + √50 − √8?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(11)(A). Written to TExES Mathematics 7–12 (235) Domain I, competency 001
Which positive number x satisfies x^(3/4) = 27?19 Texas Administrative Code §111.40, Texas Essential Knowledge and Skills for Mathematics, Algebra II (Legal Information Institute copy), (c)(7)(H). Written to TExES Mathematics 7–12 (235) Domain I, competency 001
Patterns and algebra 20
$2,000 is invested at 5% a year, compounded continuously. Which expression gives its value after 8 years?Wikipedia, Compound interest. Written to TExES Mathematics 7–12 (235) Domain II, competency 008
A ball is thrown upward. Its height in feet after t seconds is h(t) = −16t^2 + 48t + 28. What is the maximum height?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(7)(A). Written to TExES Mathematics 7–12 (235) Domain II, competency 006
A curve is given by f(x) = 2x^3 − 9x + 4. How steep is its tangent line at x = −2?Wikipedia, Derivative. Written to TExES Mathematics 7–12 (235) Domain II, competency 010
A function is defined by f(x) = (7 − 4x)/5. Which rule defines its inverse?19 Texas Administrative Code §111.40, Texas Essential Knowledge and Skills for Mathematics, Algebra II (Legal Information Institute copy), (c)(2)(B). Written to TExES Mathematics 7–12 (235) Domain II, competency 005
A line crosses the point (6, −5) at a right angle to the line 2x + 7y = 3. What is its equation?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(2)(F). Written to TExES Mathematics 7–12 (235) Domain II, competency 006
A proof by mathematical induction first shows a statement holds for n = 1. What must the induction step then show?Wikipedia, Mathematical induction. Written to TExES Mathematics 7–12 (235) Domain II, competency 004
A student solves √(3x + 10) = x + 2 by squaring both sides and finds x = 2 and x = −3. Which conclusion is right?19 Texas Administrative Code §111.40, Texas Essential Knowledge and Skills for Mathematics, Algebra II (Legal Information Institute copy), (c)(4)(G). Written to TExES Mathematics 7–12 (235) Domain II, competency 007
A tide gauge is modeled by y = 5sin(πx/4) − 2. What are the amplitude and the period of the model?19 Texas Administrative Code §111.42, Texas Essential Knowledge and Skills for Mathematics, Precalculus (Texas Education Agency file of Chapter 111, Subchapter C), (c)(2)(G). Written to TExES Mathematics 7–12 (235) Domain II, competency 009
An infinite geometric series begins 45 − 15 + 5 − 5/3 + … . To what value does it converge?19 Texas Administrative Code §111.42, Texas Essential Knowledge and Skills for Mathematics, Precalculus (Texas Education Agency file of Chapter 111, Subchapter C), (c)(5)(E). Written to TExES Mathematics 7–12 (235) Domain II, competency 004
Evaluate log_3(54) − log_3(2).19 Texas Administrative Code §111.42, Texas Essential Knowledge and Skills for Mathematics, Precalculus (Texas Education Agency file of Chapter 111, Subchapter C), (c)(5)(G). Written to TExES Mathematics 7–12 (235) Domain II, competency 008
Evaluate the integral of 4x^3 − 6x over the interval from x = −1 to x = 2.Wikipedia, Fundamental theorem of calculus. Written to TExES Mathematics 7–12 (235) Domain II, competency 010
For which function does f(−x) = −f(x) hold for every real number x?19 Texas Administrative Code §111.42, Texas Essential Knowledge and Skills for Mathematics, Precalculus (Texas Education Agency file of Chapter 111, Subchapter C), (c)(2)(D). Written to TExES Mathematics 7–12 (235) Domain II, competency 005
The function f(x) = (3x^2 − 3x − 18)/(x^2 − 9) is graphed. Which features does the graph have?19 Texas Administrative Code §111.42, Texas Essential Knowledge and Skills for Mathematics, Precalculus (Texas Education Agency file of Chapter 111, Subchapter C), (c)(2)(K) and (L). Written to TExES Mathematics 7–12 (235) Domain II, competency 007
In an arithmetic sequence the 7th term is 31 and the 12th term is 56. Which formula gives the nth term?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(12)(D). Written to TExES Mathematics 7–12 (235) Domain II, competency 004
On the decibel scale a change of 10 dB is a power ratio of 10. One sound is 30 dB louder than another. How many times greater is its power?Wikipedia, Decibel. Written to TExES Mathematics 7–12 (235) Domain II, competency 008
On the unit circle, what is tan(5π/3)?19 Texas Administrative Code §111.42, Texas Essential Knowledge and Skills for Mathematics, Precalculus (Texas Education Agency file of Chapter 111, Subchapter C), (c)(2)(P). Written to TExES Mathematics 7–12 (235) Domain II, competency 009
Where cos x is not zero, (sec^2 x − 1)cos^2 x simplifies to which expression?19 Texas Administrative Code §111.42, Texas Essential Knowledge and Skills for Mathematics, Precalculus (Texas Education Agency file of Chapter 111, Subchapter C), (c)(5)(M). Written to TExES Mathematics 7–12 (235) Domain II, competency 009
Which interval holds every x with |4 − 3x| < 11?19 Texas Administrative Code §111.40, Texas Essential Knowledge and Skills for Mathematics, Algebra II (Legal Information Institute copy), (c)(6)(F). Written to TExES Mathematics 7–12 (235) Domain II, competency 007
With f(x) = 2x − 7 and g(x) = x^2 + 3x, what are the values of f(g(−1)) and g(f(−1)), in that order?19 Texas Administrative Code §111.42, Texas Essential Knowledge and Skills for Mathematics, Precalculus (Texas Education Agency file of Chapter 111, Subchapter C), (c)(2)(B). Written to TExES Mathematics 7–12 (235) Domain II, competency 005
Written in the form a(x − h)^2 + k, f(x) = 2x^2 − 12x + 11 has its vertex at which point?19 Texas Administrative Code §111.40, Texas Essential Knowledge and Skills for Mathematics, Algebra II (Legal Information Institute copy), (c)(4)(D). Written to TExES Mathematics 7–12 (235) Domain II, competency 006
Geometry and measurement 12
A drone hovers 120 meters above flat ground. Its camera sights a marker at an angle of depression of 30°. About how far is the marker from the point on the ground under the drone?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(9)(A). Written to TExES Mathematics 7–12 (235) Domain III, competency 011
A lawn sprinkler waters a sector with a radius of 18 feet through a central angle of 80°. How much lawn does it water?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(12)(C). Written to TExES Mathematics 7–12 (235) Domain III, competency 013
The area under f(x) = x^2 + 1 from x = 1 to x = 7 is estimated with 3 rectangles of width 2, each as tall as the curve at its left edge. What is the estimate?Wikipedia, Riemann sum. Written to TExES Mathematics 7–12 (235) Domain III, competency 011
Each exterior angle of a regular polygon measures 22.5°. What is the sum of the polygon's interior angles?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(5)(A). Written to TExES Mathematics 7–12 (235) Domain III, competency 013
The equation x^2 + y^2 + 10x − 8y + 5 = 0 is a circle. Where is its center, and how long is its radius?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(12)(E). Written to TExES Mathematics 7–12 (235) Domain III, competency 014
Given the vectors u = ⟨−2, 5⟩ and v = ⟨4, −3⟩, find 3u − 2v.19 Texas Administrative Code §111.42, Texas Essential Knowledge and Skills for Mathematics, Precalculus (Texas Education Agency file of Chapter 111, Subchapter C), (c)(4)(J). Written to TExES Mathematics 7–12 (235) Domain III, competency 014
In hyperbolic geometry, what is true of a triangle's angle sum?Wikipedia, Hyperbolic geometry. Written to TExES Mathematics 7–12 (235) Domain III, competency 012
In triangles ABC and DEF, AB = DE, BC = EF and angle A is congruent to angle D. Why is this not enough to prove the triangles congruent?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(6)(B). Written to TExES Mathematics 7–12 (235) Domain III, competency 012
Lines m and n are parallel. A transversal forms alternate interior angles of (7x − 19)° and (4x + 32)°. What is the measure of each of these angles?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(6)(A). Written to TExES Mathematics 7–12 (235) Domain III, competency 012
The radius of a cone is doubled and its height is cut in half. How does the volume change?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(10)(B). Written to TExES Mathematics 7–12 (235) Domain III, competency 011
Segment AB is a diameter of a circle, and C is another point on the circle. Angle CAB measures 37°. What is the measure of angle ABC?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(12)(A). Written to TExES Mathematics 7–12 (235) Domain III, competency 013
Vertex P(−7, 2) of a triangle is reflected across the line y = x, and the image is then translated 6 units up. What are the coordinates of the final image?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(3)(B). Written to TExES Mathematics 7–12 (235) Domain III, competency 014
Probability and statistics 8
A data set has first quartile 22 and third quartile 38. By the 1.5 × IQR rule, which value is an outlier?Wikipedia, Interquartile range. Written to TExES Mathematics 7–12 (235) Domain IV, competency 015
A food truck sells 40 lunches on a dry day and 15 on a rainy day, at a profit of $6 a lunch. Rain falls on 20% of days. What is its expected profit for one day?Wikipedia, Expected value. Written to TExES Mathematics 7–12 (235) Domain IV, competency 016
A month of daily high temperatures has a mean of 25 °C and a standard deviation of 4 °C. Each reading is converted with F = 1.8C + 32. What are the mean and standard deviation in °F?Wikipedia, Standard deviation. Written to TExES Mathematics 7–12 (235) Domain IV, competency 015
A spinner lands on red with probability 0.3. A class spins it 20 times, then 2,000 times. By the law of large numbers, which result should the class expect?Wikipedia, Law of large numbers. Written to TExES Mathematics 7–12 (235) Domain IV, competency 017
Across 40 towns, yearly ice cream sales and yearly sunburn cases have a correlation coefficient of r = 0.91. What does this value support?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(4)(A) and (B). Written to TExES Mathematics 7–12 (235) Domain IV, competency 017
Of 200 students, 80 are in band, 50 play a sport and 30 do both. A band student is picked at random. What is the probability that the student plays a sport?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(13)(D). Written to TExES Mathematics 7–12 (235) Domain IV, competency 016
Temperature in degrees Celsius has equal steps but no true zero, so 20 °C is not "twice as hot" as 10 °C. Which level of measurement is this?Wikipedia, Level of measurement. Written to TExES Mathematics 7–12 (235) Domain IV, competency 015
Two names are drawn at random, without replacement, from 5 seniors and 3 juniors. What is the probability that both are seniors?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(13)(C). Written to TExES Mathematics 7–12 (235) Domain IV, competency 016
Processes and perspectives 6
A conditional statement is true, and its converse is also true. What can then be written?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(4)(B). Written to TExES Mathematics 7–12 (235) Domain V, competency 018
A linear model fitted to the heights of children aged 2 to 12 predicts a height of 250 cm at age 30. What does this show about the model?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(2)(A). Written to TExES Mathematics 7–12 (235) Domain V, competency 019
A student claims that 2^n − 1 is prime whenever n is prime. Which prime n shows that the claim is false?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(4)(C). Written to TExES Mathematics 7–12 (235) Domain V, competency 018
A student measures the angles of twelve triangles, finds that each set adds to 180°, and states that this is true of every triangle. Until it is proved, what is the statement?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(4)(A). Written to TExES Mathematics 7–12 (235) Domain V, competency 018
To prove by contradiction that there is no smallest positive rational number, a proof supposes that q is the smallest. Which number then gives the contradiction?Wikipedia, Proof by contradiction. Written to TExES Mathematics 7–12 (235) Domain V, competency 018
Which formula gives the area A of a circle in terms of its circumference C?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(12)(E). Written to TExES Mathematics 7–12 (235) Domain V, competency 019
Learning, instruction and assessment 6
A class solves x^2 − 5x + 6 = 0 by factoring and again with the quadratic formula, then discusses when each method is the better choice. Which IES algebra recommendation is this?Institute of Education Sciences, What Works Clearinghouse practice guide, Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students, recommendation 3. Written to TExES Mathematics 7–12 (235) Domain VI, competency 020
A student solves −3x > 12 and writes x > −4. What should the teacher address?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(5)(B). Written to TExES Mathematics 7–12 (235) Domain VI, competency 021
A teacher asks students what 2(x + 3)^2 − 5(x + 3) = 0 has in common with 2u^2 − 5u = 0 before anyone solves it. Which IES algebra recommendation is this?Institute of Education Sciences, What Works Clearinghouse practice guide, Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students, recommendation 2. Written to TExES Mathematics 7–12 (235) Domain VI, competency 020
A unit test is given after instruction ends and is used to assign each student a grade for the unit. Which kind of assessment is this?Wikipedia, Summative assessment. Written to TExES Mathematics 7–12 (235) Domain VI, competency 021
For a factoring task, students decide for themselves whether to use algebra tiles, paper and pencil or a graphing calculator. Which Texas process standard does this practice?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(1)(C). Written to TExES Mathematics 7–12 (235) Domain VI, competency 020
On a quiz, several students expand (2x − 5)^2 as 4x^2 + 25. Which misunderstanding should the teacher plan to address?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(10)(B). Written to TExES Mathematics 7–12 (235) Domain VI, competency 021
How this list was compiled: Our own questions, written to the exam framework of TExES Mathematics 7–12 (235) in Section 3 of the preparation manual on the Texas Educator Certification Examination Program website, https://www.tx.nesinc.com/Content/StudyGuide/TX_SG_obj_235.htm (copyright Texas Education Agency), read 2026-10-12: 100 selected-response questions in six domains, Number Concepts about 14%, Patterns and Algebra 33%, Geometry and Measurement 19%, Probability and Statistics 14%, Mathematical Processes and Perspectives 10%, and Mathematical Learning, Instruction and Assessment 10%. This bank holds 60: 8, 20, 12, 8, 6 and 6. Every number in a question is made up for the question, and each computed answer was worked out a second time from the numbers in the question (2026-10-12). 41 questions name the standard they practice in the Texas Essential Knowledge and Skills for Mathematics, 19 Texas Administrative Code Chapter 111, Subchapter C: Algebra I, Algebra II and Geometry in the Legal Information Institute copies and Precalculus in the Texas Education Agency's own file, each opened 2026-10-12. 17 rest on a Wikipedia article and 2 on the Institute of Education Sciences practice guide on algebra, named and linked under them (each opened 2026-10-12). Licence: Questions, choices and explanations are original work of this site.
How it works
A free TExES 235 practice test: 60 questions of our own across the six domains of Mathematics 7–12, each one worked out. Unofficial, and not affiliated with or endorsed by the Texas Education Agency or Pearson.
Read the full guide
Six domains, weighted like the exam
Number Concepts is about 14% of the exam, Patterns and Algebra 33%, Geometry and Measurement 19%, Probability and Statistics 14%, Mathematical Processes and Perspectives 10%, and Mathematical Learning, Instruction and Assessment 10%. This bank holds 8, 20, 12, 8, 6 and 6.
Length and timing
The exam asks 100 selected-response questions in 4 hours 45 minutes of testing. Exam mode gives these 60 questions 171 minutes, the same pace.
Through precalculus and calculus
Algebra here runs from sequences and inverse functions to logarithms, trigonometry, a derivative and an integral. Computed questions name the Texas standard they practice, Algebra I to Precalculus.
Wrong choices come from common slips, such as leaving i^2 as 1 or not reversing an inequality. The explanation names the slip.
Questions and answers
Is this TExES 235 practice test free?
Yes. All 60 questions are free in the browser, with no account. A question sheet with its answer key prints for work on paper.
What is on the TExES 235 exam?
Mathematics 7–12: 21 competencies in six domains, by its preparation manual. They run from real and complex numbers through functions, trigonometry and calculus, Euclidean and coordinate geometry, and probability and statistics to reasoning, instruction and assessment.
What score do you need to pass the TExES Mathematics 7-12 exam?
The exam's page gives a passing score of 240. That is a scaled score, and some questions on the real exam may not count, so a number right here cannot be turned into it.
Can you use a calculator on the TExES 235?
Yes, your own. The exam's page says you must bring a graphing calculator from its approved list, and that a Definitions and Formulas page is shown on screen.
Are these real TExES 235 questions?
No. Every question is our own, with numbers invented for it and each computed answer worked a second time. None is taken or reworded from the real exam or from the sample questions in the manual.