A club of 8 students chooses a president, a vice president and a secretary. In how many ways can the three offices be filled?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(13)(A). Written to TExES Mathematics 4–8 (115) Domain I, competency 003
Between which two consecutive whole numbers does √150 lie?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(2)(B). Written to TExES Mathematics 4–8 (115) Domain I, competency 001
What is 0.000083 written in scientific notation?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(2)(C). Written to TExES Mathematics 4–8 (115) Domain I, competency 001
What is 7/8 ÷ 3/5?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(3)(A). Written to TExES Mathematics 4–8 (115) Domain I, competency 002
What is the greatest common factor of 90 and 126?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(7)(A). Written to TExES Mathematics 4–8 (115) Domain I, competency 003
Show all 60 questions (55 more)
Number concepts, continued
What is the product (2 + 5i)(3 − i)?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 4–8 (115) Domain I, competency 002
What is the value of −6 − (−9) + (−4) × 2?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(3)(D). Written to TExES Mathematics 4–8 (115) Domain I, competency 002
Which equation has no solution in the integers but has a solution in the rational numbers?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(2)(A). Written to TExES Mathematics 4–8 (115) Domain I, competency 001
Which list orders −0.4, −3/8, 1/3 and 0.3 from least to greatest?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(2)(D). Written to TExES Mathematics 4–8 (115) Domain I, competency 001
Which number equals (2^3 × 2^5) ÷ 2^6?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 4–8 (115) Domain I, competency 002
Patterns and algebra 12
A culture of 700 bacteria doubles every 5 hours. How many bacteria are there after 20 hours?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(9)(C). Written to TExES Mathematics 4–8 (115) Domain II, competency 006
A plumber charges $45 for a visit plus $60 for each hour of work. What is the cost of a visit with 3.5 hours of work?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(5)(I). Written to TExES Mathematics 4–8 (115) Domain II, competency 005
For f(x) = x^2, what is the slope of the secant line through the points where x = 1 and x = 4?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(3)(A). Written to TExES Mathematics 4–8 (115) Domain II, competency 007
In which set of ordered pairs is y a function of x?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(5)(G). Written to TExES Mathematics 4–8 (115) Domain II, competency 004
The sequence 9, 15, 21, 27, … continues by the same rule. Which expression gives its 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 4–8 (115) Domain II, competency 004
What are the solutions of x^2 + 4x − 45 = 0?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(8)(A). Written to TExES Mathematics 4–8 (115) Domain II, competency 006
What is the 7th term of the geometric sequence 4, 12, 36, 108, …?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 4–8 (115) Domain II, competency 004
What is the slope of the line through (−3, 4) and (5, −12)?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(4)(A). Written to TExES Mathematics 4–8 (115) Domain II, competency 005
What is the vertex of the graph of f(x) = (x + 5)^2 − 2?19 Texas Administrative Code §111.39, Texas Essential Knowledge and Skills for Mathematics, Algebra I (Legal Information Institute copy), (c)(6)(B). Written to TExES Mathematics 4–8 (115) Domain II, competency 006
Which ordered pair satisfies both y = 2x + 1 and y = −x + 7?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(9). Written to TExES Mathematics 4–8 (115) Domain II, competency 005
y varies directly with x, and y = 18 when x = 4. What is y when x = 10?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(5)(E). Written to TExES Mathematics 4–8 (115) Domain II, competency 005
y varies inversely with x, and y = 12 when x = 5. What is y when x = 15?19 Texas Administrative Code §111.40, Texas Essential Knowledge and Skills for Mathematics, Algebra II (Legal Information Institute copy), (c)(6)(L). Written to TExES Mathematics 4–8 (115) Domain II, competency 006
Geometry and measurement 12
A cyclist rides at 15 miles per hour. What is that speed in feet per second? (1 mile = 5,280 feet)19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(4)(H). Written to TExES Mathematics 4–8 (115) Domain III, competency 008
A cylinder has a radius of 6 inches and a height of 11 inches. What is its volume?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(7)(A). Written to TExES Mathematics 4–8 (115) Domain III, competency 010
A ship sails 10 miles due east and then due north until it is 26 miles in a straight line from its start. How far north did it sail?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(7)(C). Written to TExES Mathematics 4–8 (115) Domain III, competency 008
A trapezoid has bases of 9 cm and 16 cm and a height of 6 cm. What is its area?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(8)(D). Written to TExES Mathematics 4–8 (115) Domain III, competency 010
The angles of a triangle measure x, 2x and 3x degrees. What is the measure of the largest angle?19 Texas Administrative Code §111.27, Texas Essential Knowledge and Skills for Mathematics, Grade 7 (Legal Information Institute copy), (b)(11)(C). Written to TExES Mathematics 4–8 (115) Domain III, competency 009
Every side of a rectangle is tripled in length. How does its area change?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(10)(D). Written to TExES Mathematics 4–8 (115) Domain III, competency 010
In a right triangle, the side opposite angle A is 9 and the hypotenuse is 15. What is cos A?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 4–8 (115) Domain III, competency 008
The point (4, −6) is dilated by a scale factor of 3/2 with the origin as the center. What is its image?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(3)(C). Written to TExES Mathematics 4–8 (115) Domain III, competency 011
The point (−2, 7) is rotated 90° counterclockwise about the origin. What is its image?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(10)(C). Written to TExES Mathematics 4–8 (115) Domain III, competency 011
Two parallel lines are cut by a transversal. Alternate interior angles measure (4x + 6)° and (6x − 28)°. What is the measure of each angle?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(8)(D). Written to TExES Mathematics 4–8 (115) Domain III, competency 009
What is the distance between the points (−3, 2) and (12, 10)?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(7)(D). Written to TExES Mathematics 4–8 (115) Domain III, competency 011
Which set of three lengths can form a triangle?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(8)(A). Written to TExES Mathematics 4–8 (115) Domain III, competency 009
Probability and statistics 10
A bag holds 4 red and 6 blue marbles. Two are drawn without replacement. What is the probability that both are red?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 4–8 (115) Domain IV, competency 013
A bag holds 6 red, 4 blue and 5 green tiles. One tile is drawn at random. What is the probability that it is not green?19 Texas Administrative Code §111.27, Texas Essential Knowledge and Skills for Mathematics, Grade 7 (Legal Information Institute copy), (b)(6)(E). Written to TExES Mathematics 4–8 (115) Domain IV, competency 013
A fair coin is tossed and a spinner with eight equal sections numbered 1 to 8 is spun. What is the probability of heads and a number greater than 5?19 Texas Administrative Code §111.27, Texas Essential Knowledge and Skills for Mathematics, Grade 7 (Legal Information Institute copy), (b)(6)(I). Written to TExES Mathematics 4–8 (115) Domain IV, competency 013
A trend line for a scatterplot is y = 2.5x + 10, where x is hours of study and y is a quiz score. Which score does it predict for 12 hours?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(5)(D). Written to TExES Mathematics 4–8 (115) Domain IV, competency 014
Five quiz scores are 70, 72, 75, 78 and 80. A sixth score of 15 is added. Which measure changes least?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(12)(B). Written to TExES Mathematics 4–8 (115) Domain IV, competency 012
In a random sample of 50 students, 16 ride a bicycle to school. The school has 750 students. About how many would be expected to ride a bicycle?19 Texas Administrative Code §111.27, Texas Essential Knowledge and Skills for Mathematics, Grade 7 (Legal Information Institute copy), (b)(6)(F). Written to TExES Mathematics 4–8 (115) Domain IV, competency 014
In how many ways can a student choose 3 books from 7 different books, if order does not matter?19 Texas Administrative Code §111.41, Texas Essential Knowledge and Skills for Mathematics, Geometry (Legal Information Institute copy), (c)(13)(A). Written to TExES Mathematics 4–8 (115) Domain IV, competency 013
What is the interquartile range of 2, 4, 5, 7, 8, 10, 12 and 15?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(12)(C). Written to TExES Mathematics 4–8 (115) Domain IV, competency 012
What is the mean absolute deviation of 1, 6, 8, 12 and 18?19 Texas Administrative Code §111.28, Texas Essential Knowledge and Skills for Mathematics, Grade 8 (Legal Information Institute copy), (b)(11)(B). Written to TExES Mathematics 4–8 (115) Domain IV, competency 012
What is the median of 4, 7, 7, 9, 13 and 20?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(12)(C). Written to TExES Mathematics 4–8 (115) Domain IV, competency 012
Processes and perspectives 6
$1,000 is invested at 5% a year for 2 years. How much more does interest compounded once a year earn than simple interest?19 Texas Administrative Code §111.27, Texas Essential Knowledge and Skills for Mathematics, Grade 7 (Legal Information Institute copy), (b)(13)(E). Written to TExES Mathematics 4–8 (115) Domain V, competency 016
A student claims that the sum of two prime numbers is always even. Which pair of primes is a counterexample?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 4–8 (115) Domain V, competency 015
A student multiplies 48.7 × 0.52 and writes 253.24. With each factor rounded to one significant digit, which estimate shows the size the product should have?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(1)(B). Written to TExES Mathematics 4–8 (115) Domain V, competency 015
A student sells 40 bracelets at $3 each. The supplies cost $52. What is the profit?19 Texas Administrative Code §111.6, Texas Essential Knowledge and Skills for Mathematics, Grade 4 (Legal Information Institute copy), (b)(10)(B). Written to TExES Mathematics 4–8 (115) Domain V, competency 016
A worker's gross pay for a month is $3,200. Taxes and other deductions come to $640. What is the net income?19 Texas Administrative Code §111.7, Texas Essential Knowledge and Skills for Mathematics, Grade 5 (Legal Information Institute copy), (b)(10)(B). Written to TExES Mathematics 4–8 (115) Domain V, competency 016
Which statement is the contrapositive of "If a quadrilateral is a rhombus, then its diagonals are perpendicular"?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 4–8 (115) Domain V, competency 015
Learning, instruction and assessment 10
A student in a mathematics intervention cannot make sense of a fraction problem written in symbols alone. Which support does the IES guide on students struggling with mathematics recommend?Institute of Education Sciences, What Works Clearinghouse practice guide, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades, Recommendation 3. Written to TExES Mathematics 4–8 (115) Domain VI, competency 017
A student writes 0.3 × 0.2 = 0.6. What is the product, and what did the student overlook?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(3)(E). Written to TExES Mathematics 4–8 (115) Domain VI, competency 019
A student writes 1/2 + 1/3 = 2/5. Which error pattern does this show?Institute of Education Sciences, What Works Clearinghouse practice guide, Developing Effective Fractions Instruction for Kindergarten Through 8th Grade, Recommendation 3. Written to TExES Mathematics 4–8 (115) Domain VI, competency 019
A teacher gives a three-question exit ticket and uses the results to regroup students for the next day's lesson. Which kind of assessment is this?Wikipedia, Formative assessment. Written to TExES Mathematics 4–8 (115) Domain VI, competency 019
A teacher hands out a fully worked solution of 3(x − 2) = 12 and asks pairs to explain why each step is allowed. 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 1. Written to TExES Mathematics 4–8 (115) Domain VI, competency 018
A teacher plans to open a unit on proportions by showing cross-multiplication on the first day. What does the IES practice guide on fractions recommend?Institute of Education Sciences, What Works Clearinghouse practice guide, Developing Effective Fractions Instruction for Kindergarten Through 8th Grade, Recommendation 4. Written to TExES Mathematics 4–8 (115) Domain VI, competency 017
According to the IES practice guide on fractions, which representation should be a central tool for teaching that fractions are numbers?Institute of Education Sciences, What Works Clearinghouse practice guide, Developing Effective Fractions Instruction for Kindergarten Through 8th Grade, Recommendation 2. Written to TExES Mathematics 4–8 (115) Domain VI, competency 017
Students solve one ratio problem with a table, a double number line and an equation, then compare the methods. Which recommendation of the IES problem-solving guide for grades 4 through 8 does this follow?Institute of Education Sciences, What Works Clearinghouse practice guide, Improving Mathematical Problem Solving in Grades 4 Through 8, Recommendation 4. Written to TExES Mathematics 4–8 (115) Domain VI, competency 018
The Texas mathematics standards describe a problem-solving model. Which step does the model end with?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(1)(B). Written to TExES Mathematics 4–8 (115) Domain VI, competency 018
Which of these is a mathematical process standard in the Texas Grade 6 mathematics standards?19 Texas Administrative Code §111.26, Texas Essential Knowledge and Skills for Mathematics, Grade 6 (Legal Information Institute copy), (b)(1)(C). Written to TExES Mathematics 4–8 (115) Domain VI, competency 018
How this list was compiled: Our own questions, written to the exam framework of TExES Mathematics 4–8 (115) 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_115.htm (copyright Texas Education Agency), read 2026-10-10: 100 selected-response questions in six domains, Number Concepts about 16%, Patterns and Algebra 21%, Geometry and Measurement 21%, Probability and Statistics 16%, Mathematical Processes and Perspectives 10%, and Mathematical Learning, Instruction and Assessment 16%. This bank holds 60: 10, 12, 12, 10, 6 and 10. 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 (2026-10-10). Fifty-three questions name the standard they practice in the Texas Essential Knowledge and Skills for Mathematics, 19 Texas Administrative Code Chapter 111 (Legal Information Institute copies, opened 2026-10-10). The other seven, on instruction and assessment, rest on four practice guides of the Institute of Education Sciences and one Wikipedia article, named and linked under them (each opened 2026-10-10). Licence: Questions, choices and explanations are original work of this site.
How it works
A free TExES math 4-8 practice test: 60 questions of our own across the six domains of Mathematics 4–8 (115), 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 16% of the exam, Patterns and Algebra 21%, Geometry and Measurement 21%, Probability and Statistics 16%, Mathematical Processes and Perspectives 10%, and Mathematical Learning, Instruction and Assessment 16%. This bank holds 10, 12, 12, 10, 6 and 10.
Length, timing and tools
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. The real exam puts a definitions and formulas page and a scientific calculator on screen.
Past grade 8 content
The framework reaches beyond the middle grades: complex numbers, quadratic and exponential functions, right triangle trigonometry and the ideas behind calculus. Every computed question names the Texas standard it practices, from Grade 4 to Algebra II.
About 16% of the exam is on how students learn mathematics, instruction and assessment. Ten questions here practice it.
Many wrong choices come from one common slip, such as multiplying where the rule divides. The explanation names it.
Questions and answers
Is this TExES math 4-8 practice test online and free?
Yes. All 60 questions are free in the browser, with no account and no sign-up. Print a question sheet with its answer key to work on paper, or save it as a PDF.
Is there a TExES 4-8 math practice test for the 115 exam?
Yes, this one. Mathematics 4–8 is exam 115, and the questions follow the 19 competencies listed in its free preparation manual.
What score passes the 4-8 math TExES?
240, according to the exam's page. It is a scaled score, not a count, and the real exam can include unscored questions, so this page reports right answers without a pass or fail.
Can you use a calculator on the TExES Math 4-8 exam?
The exam's page says an on-screen scientific calculator and a Definitions and Formulas page are provided as part of the exam.
Are these real TExES Math 4-8 questions?
No. Each was written for this site with numbers made up for it, and every computed answer was worked out again. Nothing comes from the real exam or the manual's sample questions.