What is (2 − 3i)² written in the form a + bi?Lamar University, Paul's Online Math Notes, Algebra, Complex Numbers. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain I, competency 002
What is the greatest common divisor of 96 and 180?Wikipedia, Greatest common divisor, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain I, competency 003
Which of these sets of numbers is closed under subtraction?Wikipedia, Integer, Algebraic properties. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain I, competency 001
Show all 60 questions (57 more)
Patterns and algebra 7
A pattern of tiles uses 12 tiles in its first figure, 19 in the second and 26 in the third, growing by the same amount each time. How many tiles are in the 30th figure?Wikipedia, Arithmetic progression, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain II, competency 004
A surveyor measures two sides of a triangular lot as 7 m and 15 m, with a 60° angle between them. How long is the third side?Texas Educator Certification Examination Program, Definitions and Formulas (the page the exam supplies), Trigonometry. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain II, competency 009
A workshop's weekly profit in dollars from making x chairs is P(x) = −2x² + 120x − 1,000. What is the greatest weekly profit?Lamar University, Paul's Online Math Notes, Algebra, Parabolas. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain II, competency 006
For which value of k is x − 2 a factor of f(x) = x³ − 3x² + kx − 2?Wikipedia, Polynomial remainder theorem, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain II, competency 007
The function f(x) = x³ − 6x² has two critical points. At which one does the second-derivative test show a local minimum?Lamar University, Paul's Online Math Notes, Calculus I, The Shape of a Graph, Part II, Second Derivative Test. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain II, competency 010
What is the natural domain of f(x) = √(x − 3) ÷ (x − 5) over the real numbers?Wikipedia, Domain of a function, Natural domain. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain II, competency 005
Which values of x satisfy log₃ x + log₃ (x − 6) = 3?Lamar University, Paul's Online Math Notes, Algebra, Logarithm Functions, More Properties of Logarithms. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain II, competency 008
Geometry and measurement 4
An engineering model is built at one tenth of full size in every dimension. What fraction of the real object's volume does the model have?Wikipedia, Square–cube law, Description. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain III, competency 011
In Hilbert's axiom system for Euclidean geometry, which of these is a primitive notion, used without a definition?Wikipedia, Primitive notion, Examples. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain III, competency 012
Points A, B and C lie on a circle with center O. Angle AOB measures 100°, and C lies on the major arc AB. What is the measure of angle ACB?Wikipedia, Inscribed angle, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain III, competency 013
Which vector is perpendicular to (2, 3)?Wikipedia, Dot product, Geometric definition. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain III, competency 014
Probability and statistics 3
A poll of 400 people has a margin of error of about 5 points. The same poll is repeated with 1,600 people. About what margin of error results?Wikipedia, Margin of error, Effect of finite sample size. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IV, competency 017
For the data set 2, 3, 3, 4, 28 the mean is 8 and the median is 3. Why does the median describe a typical value better here?Wikipedia, Median, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IV, competency 015
For two events, P(A) = 0.50, P(B) = 0.40 and P(A and B) = 0.20. What is P(A or B)?Texas Educator Certification Examination Program, Definitions and Formulas (the page the exam supplies), Probability. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IV, competency 016
Mathematical processes and perspectives 2
A bacterial culture doubles in number every 3 hours while nutrients last. Which kind of function models the population over time?Wikipedia, Exponential growth, Examples. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain V, competency 019
A student claims that n² + n + 41 is prime for every whole number n, and shows it for n = 0 to 10. What settles whether the claim is true?Wikipedia, Counterexample, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain V, competency 018
Mathematical learning, instruction and assessment 2
A federal practice guide on teaching algebra recommends putting solved problems in front of students. What are students meant to do with them?Institute of Education Sciences, What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students, Recommendation 1. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VI, competency 020
A unit's objective is that students model situations with quadratic functions. The unit test asks only for trinomials to be factored. What is the flaw?Carnegie Mellon University, Eberly Center, Align Assessments, Objectives, Instructional Strategies. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VI, competency 021
Scientific inquiry and processes 3
A teacher swaps the mercury thermometers in a lab for alcohol ones so that a less hazardous material does the same job. Which level of the hierarchy of hazard controls is this?Wikipedia, Hierarchy of hazard controls, Components of the hierarchy. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VII, competency 022
"All swans are white" is a standard example of a falsifiable claim. What single observation would contradict it?Wikipedia, Falsifiability, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VII, competency 023
The Michelson–Morley experiment of 1887 found no difference in the speed of light along different directions of Earth's motion. Which idea did that result count against?Wikipedia, Michelson–Morley experiment, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VII, competency 024
Physics 8
A 12 V battery is connected across a 4 Ω resistor and a 6 Ω resistor wired in parallel. What current does the battery supply?Wikipedia, Series and parallel circuits, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VIII, competency 028
A 50 kg student stands on a scale in an elevator that is accelerating downward at 1.8 m/s². With g = 9.8 m/s², what force does the scale read?HyperPhysics, Georgia State University, Newton's Laws, Newton's Second Law. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VIII, competency 026
A marble rolls off a level platform 4.9 m above the floor at 6.0 m/s. Taking g as 9.8 m/s² and ignoring air resistance, how far from the base of the platform does it land?HyperPhysics, Georgia State University, Trajectories, Horizontal Launch. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VIII, competency 025
A roller-coaster car starts from rest at the top of a hill and drops 20 m. Ignoring friction and taking g as 9.8 m/s², about how fast is it moving at the bottom?HyperPhysics, Georgia State University, Conservation Laws, Conservation of Energy. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VIII, competency 029
An FM station broadcasts at 100 MHz. Radio waves travel at 3.0 × 10⁸ m/s. What is the wavelength of the signal?HyperPhysics, Georgia State University, Traveling Wave Relationship. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VIII, competency 031
An ideal heat engine runs between a hot reservoir at 500 K and a cold reservoir at 300 K. What is the greatest efficiency it can have?Wikipedia, Carnot heat engine, Carnot's theorem. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VIII, competency 030
The momentum of an electron is doubled. What happens to its de Broglie wavelength?Wikipedia, Matter wave, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VIII, competency 032
Two masses attract each other with gravitational force F. Each mass is doubled and the distance between their centers is doubled. What is the new force?HyperPhysics, Georgia State University, Gravity, Gravity. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain VIII, competency 027
Chemistry 8
A particle has 26 protons, 30 neutrons and 24 electrons. Which symbol describes it?Wikipedia, Atomic number, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IX, competency 033
A stockroom has 12 M hydrochloric acid. What volume of it must be diluted with water to make 250 mL of 3.0 M acid?Purdue University, General Chemistry Topic Review, Solutions, Dilution. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IX, competency 037
Chlorine gas is bubbled through a bromide solution: Cl₂ + 2 Br⁻ → 2 Cl⁻ + Br₂. Which species is the oxidizing agent?Wikipedia, Oxidizing agent, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IX, competency 040
How many valence electrons must appear in the Lewis structure of the sulfate ion, SO₄²⁻?Purdue University, General Chemistry Topic Review, Lewis Structures, step 1. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IX, competency 035
In 2 Al + 3 Cl₂ → 2 AlCl₃, how many moles of AlCl₃ form when 0.60 mol of Cl₂ reacts with excess aluminum?Purdue University, General Chemistry Topic Review, Chemical Reactions, Mole Ratios. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IX, competency 036
Samples of H₂, N₂, O₂ and CO₂ are held at the same temperature. In which gas do the molecules have the highest average speed?Purdue University, General Chemistry Topic Review, The Kinetic Molecular Theory, Graham's Laws of Diffusion and Effusion. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IX, competency 034
Solutions of hydrochloric acid and acetic acid have the same molar concentration. Why does the hydrochloric acid have the lower pH?Wikipedia, Acid strength, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IX, competency 041
Which nuclear process releases the energy that powers the Sun?Wikipedia, Nuclear fusion, In astrophysics. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain IX, competency 039
Science learning, instruction and assessment 2
A physics teacher writes four tasks on specific heat. Which one calls for thinking at Create, the top level of the revised Bloom's taxonomy?Wikipedia, Bloom's taxonomy, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain X, competency 042
A science department wants lab reports marked the same way in every classroom. Pairs of teachers score the same sample reports and compare their marks. What are they checking?Wikipedia, Inter-rater reliability, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain X, competency 043
The engineering method 10
A 15-tooth pinion drives a 60-tooth gear. How many turns must the pinion make for the gear to turn once?Wikipedia, Gear train, Gear ratio. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 044
A crowbar lifts a 600 N load that sits 0.20 m from the fulcrum. The worker pushes down 1.2 m from the fulcrum on the other side. What effort balances the load?Wikipedia, Lever, Law of the lever. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 044
A firm invests $1,000 at 10% annual interest, compounded twice a year. Using A = P(1 + r/n)^(nt), what is the investment worth after one year?Texas Educator Certification Examination Program, Definitions and Formulas (the page the exam supplies), Algebra. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 045
A steel rod with a cross-sectional area of 2.0 × 10⁻⁴ m² carries a tensile load of 5,000 N. What is the stress in the rod?Wikipedia, Stress (mechanics), lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 044
A student wants to measure the current through a resistor in a prototype circuit. How should the ammeter be connected?Wikipedia, Ammeter, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 048
A team must design a model bridge that holds 5 kg and costs no more than $20 in materials. In the engineering design process, what is the $20 limit?TeachEngineering, University of Colorado Boulder, Engineering Design Process, Ask: Identify the Need & Constraints. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 047
For which inputs does a two-input NAND gate give an output of 0?Wikipedia, NAND gate, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 044
In a hydraulic press, 100 N is applied to a piston of area 0.010 m². The output piston has an area of 0.50 m². What force does the output piston deliver?HyperPhysics, Georgia State University, Pascal's Principle, Hydraulic Press. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 044
What is the decimal value of the binary number 1101?Wikipedia, Binary number, Counting in binary. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 045
Which data structure removes items in last-in, first-out order?Wikipedia, Stack (abstract data type), lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XI, competency 046
The engineering profession 8
A student team patents the ornamental shape of a product they designed. How long is the term of a United States design patent?U.S. Patent and Trademark Office, Patent essentials, How long is a patent valid?. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XII, competency 050
An engineer adds up a product's environmental impacts from raw material extraction through use to final disposal. What is this method called?Wikipedia, Life-cycle assessment, lead section. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XII, competency 049
In Project Based Learning as PBLWorks defines it, how do students gain knowledge and skills?PBLWorks, Buck Institute for Education, What is PBL?. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XII, competency 052
On the most commonly accepted path to a Professional Engineer license, which two exams does a candidate typically pass?National Council of Examiners for Engineering and Surveying, Licensure. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XII, competency 050
Students use a bench grinder that can throw particles. Under OSHA's eye and face protection rule, what must their eye protection provide for that hazard?OSHA, 29 CFR 1910.133, Eye and face protection, paragraph (a)(2). Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XII, competency 051
Table G-16 of OSHA's occupational noise rule sets permissible exposures. For how many hours a day does it permit a sound level of 90 dBA?OSHA, 29 CFR 1910.95, Occupational noise exposure, Table G-16. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XII, competency 051
What does the first fundamental canon of the NSPE Code of Ethics for Engineers tell engineers to hold paramount?National Society of Professional Engineers, Code of Ethics for Engineers, Fundamental Canons. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XII, competency 050
Which device, invented in 1947, went on to take the place of the vacuum tube in most electronic equipment?Wikipedia, Transistor, Comparison with vacuum tubes. Written to TExES Mathematics/Physical Science/Engineering 6–12 (274) Domain XII, competency 049
How this list was compiled: Our own questions, written to the exam framework of TExES Mathematics/Physical Science/Engineering 6–12 (274) 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_274.htm (copyright Texas Education Agency), read 2026-10-12: 135 selected-response questions in twelve domains, Number Concepts about 5%, Patterns and Algebra 12%, Geometry and Measurement 7%, Probability and Statistics 5%, Mathematical Processes and Perspectives 3%, Mathematical Learning, Instruction and Assessment 3%, Scientific Inquiry and Processes 5%, Physics 13%, Chemistry 14%, Science Learning, Instruction and Assessment 3%, The Engineering Method 17%, The Engineering Profession 13%. This bank holds 60 in those shares: 3, 7, 4, 3, 2, 2, 3, 8, 8, 2, 10 and 8. Every fact was read on the public page named under its question (58 pages, each opened 2026-10-12): the Definitions and Formulas page the exam itself supplies, Paul's Online Math Notes at Lamar University, HyperPhysics at Georgia State University, Purdue University's general chemistry review, OSHA regulations, the U.S. Patent and Trademark Office, NCEES, the NSPE Code of Ethics, the What Works Clearinghouse, Carnegie Mellon University, TeachEngineering, PBLWorks and Wikipedia. Twenty-eight answers are arithmetic from a rule the source gives. Licence: Questions, choices and explanations are original work of this site.
How it works
A Math/Physical Science/Engineering TExES practice test for exam 274: 60 questions of our own across its twelve domains. Unofficial: not affiliated with, endorsed by or sponsored by the Texas Education Agency or Pearson.
Read the full guide
Twelve domains, three subjects
Mathematics is about 35% of the exam in six domains, physical science 35% in four, and engineering 30% in two: The Engineering Method 17% and The Engineering Profession 13%. The 60 questions here split 21, 21 and 18.
Timing
The timed exam here gives 60 questions 127 minutes, the pace of the real exam.
Where answers were checked
Among the sources: the exam's own Definitions and Formulas page, Paul's Online Math Notes at Lamar University, HyperPhysics, Purdue University's chemistry review, OSHA, the U.S. Patent and Trademark Office, NCEES and the NSPE Code of Ethics. A little over half the questions cite a Wikipedia article.
The real exam supplies a formulas page, a constants page and a periodic table. You bring your own approved graphing calculator.
Three questions here use the formulas page itself: the law of cosines, compound interest and the addition rule for probability.
Questions and answers
Is there a TExES Math/Physical Science/Engineering practice exam study guide?
The Texas Educator Certification Examination Program publishes a free preparation manual for exam 274. Its Section 3 lists the twelve domains and 52 competencies, and each practice question here names the competency it was written to.
Is this the TExES Physical Science 6-12 practice test?
No. Physical Science 6–12 is a separate exam, code 237, with 100 questions. Exam 274 adds mathematics and engineering, so only the 21 science questions here, most of them physics and chemistry, overlap with it.
How many questions are on TExES 274?
135 selected-response questions, by the exam's page on the program site, in a 5-hour appointment with 4 hours 45 minutes of testing. The page adds that some questions may be trial items that do not count.
Are these real TExES 274 questions?
No. Each was written for this page from one competency of the published framework and one public source. The manual's sample questions were not used, and no exam question is copied or reworded.