• 50 questions

Middle Level Math OSAT Practice Test

Unofficial practice for Oklahoma's OSAT Middle Level/Intermediate Mathematics test, field 225, weighted like its four selected-response subareas.

What is (2 + 3i)²?

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Unofficial practice questions, not affiliated with Oklahoma's Office of Educational Quality and Accountability or Pearson. Bank checked October 13, 2026.

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All 50 questions

Subarea I: Number properties and number sense 9

  • A band director seats 84 brass players and 126 woodwind players in rows. Every row has the same number of players, and no row mixes the two sections. What is the greatest possible row size? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea I, Number Properties and Number Sense, competency 0002 (number operations and number theory)
  • A pair of boots priced at $150 is marked 30% off, and 8% sales tax is charged on the reduced price. What is the total? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea I, Number Properties and Number Sense, competency 0002 (number operations and number theory)
  • A sheet of paper is 1.0 × 10⁻⁴ meter thick. How thick is a stack of 2.5 × 10³ sheets? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea I, Number Properties and Number Sense, competency 0001 (structure and properties of the real number system)
  • A student computes 25 × 37 × 4 as (25 × 4) × 37 = 3,700. Which properties allow the factors to be reordered and regrouped this way? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea I, Number Properties and Number Sense, competency 0001 (structure and properties of the real number system)
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Subarea I: Number properties and number sense, continued

  • A student conjectures that 2n + 1 is prime whenever n is a prime number. Which prime n disproves the conjecture? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea I, Number Properties and Number Sense, competency 0001 (structure and properties of the real number system)
  • A two-week sales table is the matrix S with rows (3, −2) and (1, 4). What is 2S − I, where I is the 2 × 2 identity matrix? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea I, Number Properties and Number Sense, competency 0001 (structure and properties of the real number system)
  • An area model shows a rectangle split into four parts measuring 20 by 30, 20 by 4, 7 by 30 and 7 by 4. Which product does the model represent? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea I, Number Properties and Number Sense, competency 0002 (number operations and number theory)
  • What is (2 + 3i)²? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea I, Number Properties and Number Sense, competency 0002 (number operations and number theory)
  • Which number is rational but not an integer? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea I, Number Properties and Number Sense, competency 0001 (structure and properties of the real number system)

Subarea II: Relations, functions and algebra 20

  • A mapping diagram sends student ID numbers to locker numbers. Which situation would keep the mapping from being a function? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0003 (algebraic relations and functions)
  • A pump lowers a 300-gallon stock trough to 180 gallons in 8 minutes, working at a steady rate. Which equation models the gallons g remaining after m minutes of pumping? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0005 (linear functions and relations)
  • A quadratic function has x-intercepts −2 and 6 and passes through (0, −24). What is its vertex? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0006 (quadratic and higher-order polynomial functions)
  • A roofline on a blueprint falls 3 units for every 4 units it runs to the right, and it passes through (8, 5). At what height does it meet the y-axis? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0005 (linear functions and relations)
  • A shop marks up a price p with m(p) = 1.2p and takes a coupon off with c(p) = p − 10. What is c(m(50)), the cost of a $50 item marked up first and discounted second? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0003 (algebraic relations and functions)
  • A student is asked to combine 3√12 − √27 + √48. What is the result in simplest radical form? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0007 (advanced functions and the conceptual foundations of calculus)
  • A student solves 3(x − 4) = 2x + 5 by writing 3x − 4 = 2x + 5 and gets x = 9. What is the error, and what is the correct solution? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0004 (algebraic techniques)
  • A student translates “twelve more than a number n is at most triple the number” into symbols. Which inequality is correct? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0004 (algebraic techniques)
  • A table of values for y = f(x) includes the pair x = −4, y = 9. Which pair must appear in a table for y = f(x + 3) − 5? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0003 (algebraic relations and functions)
  • The arc of water from a garden hose follows h(d) = −0.25d² + 3d + 4, where d is the horizontal distance in feet and h the height in feet. What is the greatest height the water reaches? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0006 (quadratic and higher-order polynomial functions)
  • The area of a rectangle is 8x² + 2x − 15 square units. Which pair of binomials could be its side lengths? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0004 (algebraic techniques)
  • At a concession stand a drink, a hot dog and a pretzel cost $10 together. The hot dog costs twice as much as the drink, and the pretzel costs $2 more than the drink. What does the pretzel cost? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0005 (linear functions and relations)
  • At how many points does the graph of p(x) = x(x − 3)²(x + 1) cross the x-axis, rather than only touch it? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0006 (quadratic and higher-order polynomial functions)
  • The cost per student of a field trip is C(n) = (450 + 12n)/n dollars when n students go. As n grows very large, which value does the cost per student approach? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0007 (advanced functions and the conceptual foundations of calculus)
  • Each list gives the cost of renting a kayak for 1, 2, 3 and 4 hours. Which list shows a constant rate of change? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0005 (linear functions and relations)
  • Farm equipment worth $46,000 drops in value by 15% every year. Which expression gives what it is worth 4 years later? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0007 (advanced functions and the conceptual foundations of calculus)
  • Figures in a tile pattern use 5, 8, 11 and 14 tiles. Which expression gives the number of tiles in figure n? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0003 (algebraic relations and functions)
  • For f(x) = x² + 1, the secant line through (1, 2) and (1 + h, f(1 + h)) has slope 2 + h. What value do these slopes approach as h approaches 0, and what does it represent? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0007 (advanced functions and the conceptual foundations of calculus)
  • The surface area of a closed cylinder is S = 2πr² + 2πrh. Which equation solves the formula for the height h? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0004 (algebraic techniques)
  • The trinomial in 5x² − 6x − 1 = 0 does not factor over the integers. Which exact roots does the quadratic formula give? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea II, Relations, Functions, and Algebra, competency 0006 (quadratic and higher-order polynomial functions)

Subarea III: Measurement and geometry 13

  • A kite string 80 feet long makes a 40° angle with level ground. Using sin 40° ≈ 0.64, about how far is the kite above the hand that holds the string? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0009 (Euclidean geometry in two and three dimensions)
  • A round stained-glass window has lead strips running from one point on its rim to the two ends of a 96° arc elsewhere on the rim. What angle do the two strips form where they meet? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0009 (Euclidean geometry in two and three dimensions)
  • A round stock tank is 8 feet across and filled 2 feet deep. A cubic foot holds about 7.48 gallons. About how many gallons of water are in the tank? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0008 (measurement)
  • A sprinkler delivers 2.5 gallons of water per minute. How many quarts does it deliver in one hour? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0008 (measurement)
  • A surveyor walks 1.6 kilometers due north and then 6.3 kilometers due east. How far is she, in a straight line, from her starting point? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0008 (measurement)
  • Corner T of a trapezoid drawn on a grid sits at (−8, 6). Students flip the figure over the y-axis and then enlarge it from the origin by a factor of 3/2. Where does T land? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0010 (coordinate and transformational geometries)
  • Lines p and q are parallel. A transversal forms an angle of (5x − 8)° at p, and the corresponding angle at q measures (3x + 28)°. What is x? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0009 (Euclidean geometry in two and three dimensions)
  • On a map, 2 centimeters stand for 5 kilometers. A rectangular wildlife refuge measures 6 centimeters by 4 centimeters on the map. What is its actual area? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0008 (measurement)
  • On a sunny afternoon a 5-foot fence post throws a 3-foot shadow while the windmill beside it throws a 27-foot shadow. By similar triangles, how tall is the windmill? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0009 (Euclidean geometry in two and three dimensions)
  • Quadrilateral PQRS has vertices P(1, 1), Q(6, 3), R(4, 8) and S(−1, 6). Which name do its slopes and side lengths justify? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0010 (coordinate and transformational geometries)
  • Street A on a city grid passes through (1, 2) and (5, 14). Street B must meet it at a right angle. What slope must Street B have? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0010 (coordinate and transformational geometries)
  • Two ranger stations sit at (−2, −1) and (10, 4) on a map grid marked in miles, and a relay tower is built at the midpoint between them. How far is the tower from each station? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0010 (coordinate and transformational geometries)
  • Which statement is true of every parallelogram and so can be used as a reason in a proof? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea III, Measurement and Geometry, competency 0009 (Euclidean geometry in two and three dimensions)

Subarea IV: Probability and statistics 8

  • A bag holds equal numbers of tiles in 8 colors. A student draws a tile, records its color and puts it back, 120 times in all, and records green 21 times. What is the experimental probability of green, and how does it compare with the theoretical probability? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea IV, Probability and Statistics, competency 0011 (probability)
  • A box plot of the weights of the show lambs at a county fair has minimum 92, lower quartile 104, median 113, upper quartile 121 and maximum 140 pounds. Which claim does the plot support? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea IV, Probability and Statistics, competency 0012 (statistics)
  • A cafeteria manager wants to learn which new entrée the school’s 600 students prefer. Which sample is most likely to represent them? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea IV, Probability and Statistics, competency 0012 (statistics)
  • A school ID code is one of 26 letters followed by two digits from 0 to 9, and the digits may repeat. How many different codes are there? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea IV, Probability and Statistics, competency 0011 (probability)
  • For 12 players who practiced between 1 and 6 hours, a scatterplot of hours practiced (x) and free throws made out of 20 (y) shows a strong linear trend with line y = 1.5x + 6. Which use of the line is best supported? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea IV, Probability and Statistics, competency 0012 (statistics)
  • The mean of a student’s first four quiz scores is 76. Which score on the fifth quiz raises the mean to exactly 80? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea IV, Probability and Statistics, competency 0012 (statistics)
  • Of 40 students, 22 take art, 18 take music and 6 take neither. What is the probability that a student picked at random takes both? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea IV, Probability and Statistics, competency 0011 (probability)
  • The ride times of a school district's bus routes are roughly normal in shape, with mean 30 minutes and standard deviation 5 minutes. Using the 68-95-99.7 rule, roughly what share of the routes take longer than 40 minutes? OSAT Middle Level/Intermediate Mathematics (225) framework, Subarea IV, Probability and Statistics, competency 0011 (probability)

How this list was compiled: Our own questions, written to the test design and framework of Oklahoma Subject Area Tests field 225, Middle Level/Intermediate Mathematics, in the study guide on the Certification Examinations for Oklahoma Educators website (https://www.ceoe.nesinc.com/Content/StudyGuide/OK_SG_OBJ_225.htm, copyright 2023 Office of Educational Quality and Accountability and Pearson Education, Inc.; test page https://www.ceoe.nesinc.com/TestView.aspx?f=HTML_FRAG/OK225_TestPage.html, read 2026-10-13): 80 selected-response questions and 1 constructed-response assignment in 4 hours, passing score 240; selected response weighs Number Properties and Number Sense (competencies 0001 to 0002) 16%, Relations, Functions, and Algebra (0003 to 0007) 34%, Measurement and Geometry (0008 to 0010) 21% and Probability and Statistics (0011 to 0012) 14%, and the constructed response (0013) 15%. The bank holds 50: 9, 20, 13 and 8, with four or five for each of the 12 selected-response competencies. Every answer is mathematics worked from the numbers in the question, and each one was worked a second time. Licence: Questions, choices and explanations are original work of this site.

How it works

This middle level math OSAT practice test gives 50 worked questions of our own for Middle Level/Intermediate Mathematics, field 225. It is unofficial, free, and not affiliated with Oklahoma's Office of Educational Quality and Accountability or with Pearson.

Read the full guide

OSAT Middle Level/Intermediate Mathematics (225): four selected-response subareas

By the framework on the CEOE site, read October 13, 2026: Number Properties and Number Sense is 16% of the test, Relations, Functions, and Algebra 34%, Measurement and Geometry 21%, and Probability and Statistics 14%. This bank holds 9, 20, 13 and 8. A written analysis of a lesson plan and student work makes up the last 15%, and this page has no practice for it.

Past middle school math

Relations, Functions, and Algebra is a third of the test and reaches into calculus. Competency 0007 asks for logarithmic and piecewise functions, limits, and the derivative and integral of polynomial functions; competency 0001 includes basic matrix operations.

  • The test page says an on-screen scientific calculator and a page of definitions and formulas are provided with the test.
  • Competency 0005 takes systems of linear equations and inequalities up to three variables.

Questions and answers

How many questions are on the OSAT Middle Level/Intermediate Mathematics test?

The test page for field 225 lists 80 selected-response questions and one constructed-response assignment, to be finished in 4 hours of testing time. Appointments are at test centers, year-round.

What is the passing score for the middle level math OSAT?

Field 225 is passed at 240, the test page says. The written assignment is part of that figure, which is why this page reports a count of right answers and never a pass or a fail.

Can I take the NES Middle Grades Mathematics test instead of OSAT 225?

The test page says candidates may take either the CEOE version or the National Evaluation Series version of this test. It advises asking your educator preparation program or the Oklahoma State Department of Education before choosing.

What math is on the OSAT Middle Level/Intermediate Mathematics test?

Real and complex numbers, number theory and matrices; functions, linear and quadratic algebra and the ideas of calculus; measurement, Euclidean and coordinate geometry and right-triangle trigonometry; probability, normal distributions and statistics.

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