Domain I: Mathematical processes and number sense 9
A caterer estimates the cost of 38 lunches at $11.85 each by computing 40 × $12. Is the estimate high or low, and why?OAE Mathematics (027) assessment framework, Domain I Mathematical Processes and Number Sense, competency 0001 (mathematical problem solving)
A gear with 36 teeth meshes with a gear of 48 teeth. After how many turns of the smaller gear do the same two teeth meet again?OAE Mathematics (027) assessment framework, Domain I Mathematical Processes and Number Sense, competency 0003 (number theory)
A seedling is 4.2 cm tall on day 3 and 9.0 cm tall on day 15. What is its average rate of growth over that time?OAE Mathematics (027) assessment framework, Domain I Mathematical Processes and Number Sense, competency 0001 (mathematical problem solving)
A student finds that 3 + 5, 7 + 9 and 11 + 13 are all even and concludes that the sum of any two odd numbers is even. How should the argument be classified?OAE Mathematics (027) assessment framework, Domain I Mathematical Processes and Number Sense, competency 0002 (mathematical communication, connections, and reasoning)
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Domain I: Mathematical processes and number sense, continued
Enrollment at a school rose from 640 students to 736. What was the percent increase?OAE Mathematics (027) assessment framework, Domain I Mathematical Processes and Number Sense, competency 0001 (mathematical problem solving)
Our numerals 0 to 9 and place-value notation reached Europe through the work of Arabic-speaking scholars. Where did this system of numerals originate?Wikipedia, "Hindu–Arabic numeral system". Written to OAE Mathematics (027) framework, competency 0002
Two statements are true: "If it rains, the game is canceled" and "The game was not canceled." Which conclusion follows by valid deduction?OAE Mathematics (027) assessment framework, Domain I Mathematical Processes and Number Sense, competency 0002 (mathematical communication, connections, and reasoning)
What is (2 − 3i) ÷ (1 + i), written in the form a + bi?OAE Mathematics (027) assessment framework, Domain I Mathematical Processes and Number Sense, competency 0003 (number theory)
Which of these sets, with the operation named, is NOT a group?OAE Mathematics (027) assessment framework, Domain I Mathematical Processes and Number Sense, competency 0003 (number theory)
Domain II: Patterns, algebra and functions 12
A bakery's daily profit in dollars from muffins sold at p dollars each is P(p) = −40p² + 360p − 500. Which price gives the greatest profit?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0005 (linear, quadratic, and higher-order polynomial functions)
A boat travels 24 km upstream in 3 hours and makes the return trip downstream in 2 hours. What is the speed of the current?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0005 (linear, quadratic, and higher-order polynomial functions)
A machine cost $25,000 new and loses 20% of its value each year. What is it worth after 3 years?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0006 (exponential and logarithmic functions)
A relation pairs each student with every club the student has joined, and Maya has joined two clubs. Why is the relation not a function from students to clubs?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0004 (relations and functions)
The function f(x) = x² − 6x, restricted to x ≥ 3, has an inverse. What is f⁻¹(x)?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0004 (relations and functions)
If log₅ x = 3 and log₅ y = −1, what is log₅ (x²y)?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0006 (exponential and logarithmic functions)
Let f(x) = √(x + 1) and g(x) = x² − 5. What is (g ∘ f)(8)?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0004 (relations and functions)
What are all the real roots of x³ − 4x² + x + 6 = 0?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0005 (linear, quadratic, and higher-order polynomial functions)
What is the inverse of f(x) = e^(2x)?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0006 (exponential and logarithmic functions)
What is the solution of |3x + 1| > 8?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0007 (rational, radical, absolute value, and piece-wise defined functions)
What is the solution set of √(2x + 3) = x?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0007 (rational, radical, absolute value, and piece-wise defined functions)
Which lines are vertical asymptotes of f(x) = (x² − 9) ÷ (x² − 2x − 3)?OAE Mathematics (027) assessment framework, Domain II Patterns, Algebra, and Functions, competency 0007 (rational, radical, absolute value, and piece-wise defined functions)
Domain III: Measurement and geometry 9
A triangle has sides of 11, 60 and 61 units. Which statement about the triangle is true?OAE Mathematics (027) assessment framework, Domain III Measurement and Geometry, competency 0009 (Euclidean geometry in two and three dimensions)
Aluminum has a density of 2.7 grams per cubic centimeter. What is its density in kilograms per cubic meter?OAE Mathematics (027) assessment framework, Domain III Measurement and Geometry, competency 0008 (measurement principles and procedures)
How does the graph of y = f(x − 4) + 2 compare with the graph of y = f(x)?OAE Mathematics (027) assessment framework, Domain III Measurement and Geometry, competency 0010 (coordinate and transformational geometry)
How many diagonals does a convex polygon with 12 sides have?OAE Mathematics (027) assessment framework, Domain III Measurement and Geometry, competency 0009 (Euclidean geometry in two and three dimensions)
Segment AB has endpoints A(−2, 3) and B(6, −3). What are its midpoint and its length?OAE Mathematics (027) assessment framework, Domain III Measurement and Geometry, competency 0010 (coordinate and transformational geometry)
The sides of a rectangle are measured as 8 cm and 5 cm, each to the nearest centimeter. What is the least possible area of the rectangle?OAE Mathematics (027) assessment framework, Domain III Measurement and Geometry, competency 0008 (measurement principles and procedures)
Tangents drawn at the two ends of an arc of 130° meet at point P outside the circle. What is the measure of angle P?OAE Mathematics (027) assessment framework, Domain III Measurement and Geometry, competency 0009 (Euclidean geometry in two and three dimensions)
Two cylinders are similar. Their heights are 4 cm and 10 cm, and the smaller has a volume of 32 cm³. What is the volume of the larger?OAE Mathematics (027) assessment framework, Domain III Measurement and Geometry, competency 0008 (measurement principles and procedures)
What kind of conic section is the graph of 9x² − 4y² = 36?OAE Mathematics (027) assessment framework, Domain III Measurement and Geometry, competency 0010 (coordinate and transformational geometry)
Domain IV: Trigonometry and calculus 9
A Ferris wheel of radius 20 m turns once every 40 seconds, and its axle is 24 m above the ground. Which function gives a rider's height t seconds after passing the lowest point?OAE Mathematics (027) assessment framework, Domain IV Trigonometry and Calculus, competency 0011 (trigonometric functions)
A midpoint Riemann sum with 2 equal subintervals estimates the area under f(x) = x² + 1 on [0, 4]. What is its value?OAE Mathematics (027) assessment framework, Domain IV Trigonometry and Calculus, competency 0013 (integral calculus)
An open-top box with a square base must hold 32 cm³. Which side length of the base uses the least material?OAE Mathematics (027) assessment framework, Domain IV Trigonometry and Calculus, competency 0012 (differential calculus)
Two sides of a triangle measure 9 and 14, and the angle between them is 30°. What is the area of the triangle?OAE Mathematics (027) assessment framework, Domain IV Trigonometry and Calculus, competency 0011 (trigonometric functions)
What is the area of the region enclosed by the parabola y = 9 − x² and the x-axis?OAE Mathematics (027) assessment framework, Domain IV Trigonometry and Calculus, competency 0013 (integral calculus)
What is the derivative of f(x) = e^(3x) cos x?OAE Mathematics (027) assessment framework, Domain IV Trigonometry and Calculus, competency 0012 (differential calculus)
What is the limit of (x³ − 27) ÷ (x − 3) as x approaches 3?OAE Mathematics (027) assessment framework, Domain IV Trigonometry and Calculus, competency 0012 (differential calculus)
What is the value of the definite integral of sin x from x = 0 to x = π/3?OAE Mathematics (027) assessment framework, Domain IV Trigonometry and Calculus, competency 0013 (integral calculus)
Which expression is identical to (1 − sin² x) ÷ (sin x cos x)?OAE Mathematics (027) assessment framework, Domain IV Trigonometry and Calculus, competency 0011 (trigonometric functions)
Domain V: Statistics, probability and discrete mathematics 9
A basketball player makes 80% of her free throws, and the shots are independent. What is the probability that she makes exactly 2 of 3?OAE Mathematics (027) assessment framework, Domain V Statistics, Probability, and Discrete Mathematics, competency 0015 (principles and techniques of probability)
A box holds 6 good bulbs and 4 defective ones. Two bulbs are drawn without replacement. What is the probability that exactly one is defective?OAE Mathematics (027) assessment framework, Domain V Statistics, Probability, and Discrete Mathematics, competency 0015 (principles and techniques of probability)
A data set has mean 50 and standard deviation 6. Every value is doubled and then increased by 10. What are the new mean and standard deviation?OAE Mathematics (027) assessment framework, Domain V Statistics, Probability, and Discrete Mathematics, competency 0014 (principles and techniques of statistics)
A principal wants to know how many hours students study each week. She surveys the first 40 students to arrive at the library before school. What is the main flaw?OAE Mathematics (027) assessment framework, Domain V Statistics, Probability, and Discrete Mathematics, competency 0014 (principles and techniques of statistics)
For the vectors u = (3, −4) and v = (2, 1), what are the dot product u · v and the magnitude of u?OAE Mathematics (027) assessment framework, Domain V Statistics, Probability, and Discrete Mathematics, competency 0016 (principles of discrete mathematics)
How many distinct arrangements can be made from the letters of the word TOMATO?OAE Mathematics (027) assessment framework, Domain V Statistics, Probability, and Discrete Mathematics, competency 0016 (principles of discrete mathematics)
The masses of apples from an orchard are normally distributed with mean 150 g and standard deviation 12 g. About what percent of the apples weigh more than 174 g?OAE Mathematics (027) assessment framework, Domain V Statistics, Probability, and Discrete Mathematics, competency 0015 (principles and techniques of probability)
Seven houses on a street sold for 4, 6, 7, 7, 9, 11 and 40 (in units of $50,000). Which measure best describes a typical price, and what is its value?OAE Mathematics (027) assessment framework, Domain V Statistics, Probability, and Discrete Mathematics, competency 0014 (principles and techniques of statistics)
What is the limit of the sequence aₙ = (3n + 1) ÷ (n + 2) as n grows without bound?OAE Mathematics (027) assessment framework, Domain V Statistics, Probability, and Discrete Mathematics, competency 0016 (principles of discrete mathematics)
How this list was compiled: Our own questions, written to the assessment framework for Ohio Assessments for Educators field 027, Mathematics, read 2026-10-12 on the program's site (https://www.oh.nesinc.com/CONTENT/STUDYGUIDE/OH_SG_OBJ_027.htm; test page https://www.oh.nesinc.com/TestView.aspx?f=HTML_FRAG/OH027_TestPage.html): 150 multiple-choice questions in 255 minutes, passing score 220; Mathematical Processes and Number Sense (competencies 0001 to 0003, 19%), Patterns, Algebra, and Functions (0004 to 0007, 24%), Measurement and Geometry (0008 to 0010, 19%), Trigonometry and Calculus (0011 to 0013, 19%) and Statistics, Probability, and Discrete Mathematics (0014 to 0016, 19%). The bank holds 3 questions for each of the 16 competencies. Every numeric answer, and the wrong answers that the explanations account for, were worked out a second time from the numbers in the question. One question on the history of numerals names the Wikipedia article it was read in on 2026-10-12. Licence: Questions, choices and explanations are original work of this site.
How it works
This free OAE math practice test follows Mathematics (027), the content assessment for Ohio's 7–12 Integrated Mathematics license: 48 questions of our own. It is unofficial and not affiliated with the Ohio State Board of Education or Evaluation Systems, Pearson.
Read the full guide
What OAE Mathematics (027) covers
The framework at oh.nesinc.com, read October 12, 2026, weighs Patterns, Algebra and Functions 24% and four domains 19% each: Mathematical Processes and Number Sense; Measurement and Geometry; Trigonometry and Calculus; and Statistics, Probability and Discrete Mathematics. This bank holds 12 algebra questions and 9 in each of the others.
Timing
The real test gives 4 hours 15 minutes, 1.7 minutes a question, and exam mode gives 82 minutes for the 48 here. With an online proctor the real test is split: 2 hours for Domains I and II, an optional 15-minute break, then 2 hours 15 minutes for Domains III to V.
After the online break you can no longer return to the questions of Domains I and II, so finish checking them before you take it.
Questions and answers
Is this OAE Mathematics 027 practice test free?
Yes, with no account and no fee. All 48 questions are ours, written to the 16 competencies of the published framework, and every numeric answer was worked out a second time. None comes from the real assessment or its sample questions.
How many questions are on the OAE math test?
150 multiple-choice questions. The test page says about 63 fall in Domains I and II and about 87 in Domains III to V, and that some questions may be under evaluation and not scored.
What is the passing score for OAE Mathematics?
220, where scores run from 100 to 300. The State Board of Education sets the minimum, and the total depends on how many multiple-choice questions are answered correctly.
Is a calculator allowed on the OAE math test?
The test page says the assessment comes with a scientific calculator on screen, along with a formulas page. It lists no other reference materials.