• 50 questions

OAE Middle Grades Mathematics Practice Test

Unofficial practice questions and a study guide to the four domains of Ohio's OAE Middle Grades Mathematics assessment, code 030.

Which of these is a rational number that is not an integer?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: 1 to 4 pick, Enter checks.

Print covers the next 50 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 50 questions, 102 minutes.

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Unofficial practice questions, not affiliated with the Ohio State Board of Education or Evaluation Systems, Pearson. Bank checked October 14, 2026.

Next step OAE Mathematics practice testNES Middle Grades Mathematics

All 50 questions

Domain I: Number sense and operations 9

  • A gear with 36 teeth drives a gear with 24 teeth. While the larger gear makes 10 full turns, how many turns does the smaller gear make? OAE Middle Grades Mathematics (030) assessment framework, Domain I Number Sense and Operations, competency 0002 (operations)
  • A school year has 180 days of 6.5 hours each. Which is the best estimate of the number of seconds a student spends in school that year? OAE Middle Grades Mathematics (030) assessment framework, Domain I Number Sense and Operations, competency 0001 (numbers)
  • A shelf board 8 1/4 feet long is sawn into brackets 3/4 foot long, with no waste. How many brackets are there, and which product finds the number? OAE Middle Grades Mathematics (030) assessment framework, Domain I Number Sense and Operations, competency 0002 (operations)
  • A student evaluates 42 − 18 ÷ 6 × 5 + 3² and gets 29. What is the correct value, and what went wrong? OAE Middle Grades Mathematics (030) assessment framework, Domain I Number Sense and Operations, competency 0002 (operations)
  • A student finds 47 × 36 by adding 1,200 + 240 + 210 + 42. Which property makes this partial-products method work? OAE Middle Grades Mathematics (030) assessment framework, Domain I Number Sense and Operations, competency 0002 (operations)
Show all 50 questions (45 more)

Domain I: Number sense and operations, continued

  • A student rewrites the base-ten number 266 as a base-five numeral. Which numeral is correct? OAE Middle Grades Mathematics (030) assessment framework, Domain I Number Sense and Operations, competency 0001 (numbers)
  • A teacher cuts a 252 cm strip and a 360 cm strip of border into pieces of one equal length, as long as possible, with nothing left over. How long is each piece? OAE Middle Grades Mathematics (030) assessment framework, Domain I Number Sense and Operations, competency 0001 (numbers)
  • After a 25% raise, a wage is $18.50 an hour. What was the wage before the raise? OAE Middle Grades Mathematics (030) assessment framework, Domain I Number Sense and Operations, competency 0002 (operations)
  • Which of these is a rational number that is not an integer? OAE Middle Grades Mathematics (030) assessment framework, Domain I Number Sense and Operations, competency 0001 (numbers)

Domain II: Algebra and functions 18

  • A club has $150 for T-shirts. The printer charges a $30 setup fee plus $8 a shirt. What is the greatest number of shirts the club can buy? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0005 (linear relations and applications)
  • A diver's position in meters, measured upward from the surface, is d = −40 + 2.5t after t minutes of rising. What do −40 and 2.5 tell you? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0005 (linear relations and applications)
  • A function g is defined by g(x) = 3f(x). The graph of f passes through (4, −2) and crosses the x-axis at 7. Which statement is true of the graph of g? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0003 (patterns, relations, and functions)
  • A line passes through (−4, −1) and (8, 8). Which is its equation? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0005 (linear relations and applications)
  • A mapping sends each of the 30 students in a class to his or her birth month. Why is this mapping a function while its reverse, from month to student, is not? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0003 (patterns, relations, and functions)
  • A parabola crosses the x-axis at −1 and 5 and passes through (0, −10). Which equation fits? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0006 (nonlinear relations)
  • A rectangular pen is built against a barn wall, using 60 m of fence for the other three sides. What is the greatest area the pen can enclose? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0006 (nonlinear relations)
  • A student must write this in symbols: take a number n, add 5, square the result, then take away half of n. Which expression is correct? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0004 (algebraic techniques and applications)
  • A teacher needs 10 liters of a 34% acid solution and has a 20% solution and a 55% solution to mix. How many liters of the 20% solution does she use? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0005 (linear relations and applications)
  • Job A pays $100 the first week and $50 more each week after. Job B pays $1 the first week and doubles each week. In which week does Job B's weekly pay first pass Job A's? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0006 (nonlinear relations)
  • The pattern 7, 11, 15, 19, … continues by adding 4. What is its 50th term? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0003 (patterns, relations, and functions)
  • The terms of a sequence are 2, 5, 10, 17, 26. Its first differences are 3, 5, 7, 9, and its second differences are all 2. What kind of rule fits, and what is the next term? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0003 (patterns, relations, and functions)
  • To clear y from 3x + 4y = 10 and 5x − 6y = 4, a student multiplies the first equation by 3 and the second by 2 and then adds them. What results? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0005 (linear relations and applications)
  • Which expression equals (2x³y)² ÷ (4x²y⁵), for x and y not zero? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0004 (algebraic techniques and applications)
  • Which is the factored form of 10x² − 11x − 6? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0004 (algebraic techniques and applications)
  • Which three points show y directly proportional to x? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0003 (patterns, relations, and functions)
  • Which values of x make |3x + 6| = 15 true? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0004 (algebraic techniques and applications)
  • Which values of x satisfy 9 − 4x > 25? OAE Middle Grades Mathematics (030) assessment framework, Domain II Algebra and Functions, competency 0004 (algebraic techniques and applications)

Domain III: Measurement and geometry 14

  • A chord 16 cm long lies 6 cm from the center of a circle. What is the circle's radius? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0008 (Euclidean geometry in two and three dimensions)
  • A circle's diameter has endpoints (−3, 2) and (5, −4). What are the circle's center and radius? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0009 (coordinate and transformational geometry)
  • A field is a rectangle 80 m long and 40 m wide with a semicircle on each 40 m end. To the nearest square meter, what is its area? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0007 (measurement principles, procedures, and applications)
  • A garden bed 12 feet by 9 feet is covered with mulch 3 inches deep. How many cubic yards of mulch is that? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0007 (measurement principles, procedures, and applications)
  • A length is reported as 12.4 cm, measured to the nearest tenth of a centimeter. Which interval holds the true length L? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0007 (measurement principles, procedures, and applications)
  • A photo editor enlarges a shape to 3 times its size while holding the point (1, 1) fixed. The shape has a corner at (2, 4). Where does that corner go? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0009 (coordinate and transformational geometry)
  • A plane slices through a cube. Which shape can the cross section NOT be? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0008 (Euclidean geometry in two and three dimensions)
  • A scale model is built at 1 : 20. The model's floor covers 300 cm². What area does the real floor cover? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0007 (measurement principles, procedures, and applications)
  • A soccer field is 105 m long and 68 m wide. What is its area in hectares? (1 hectare = 10,000 m².) OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0007 (measurement principles, procedures, and applications)
  • A square, a regular hexagon and one more regular polygon meet at a point with no gap and no overlap. How many sides does the third polygon have? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0008 (Euclidean geometry in two and three dimensions)
  • The diagonals of a quadrilateral bisect each other. What is the most that can be concluded about the quadrilateral? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0008 (Euclidean geometry in two and three dimensions)
  • The edges of a three-sided garden bed measure 7 m, 9 m and 12 m. What kind of angle lies opposite the longest edge, and what shows it? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0008 (Euclidean geometry in two and three dimensions)
  • Triangle PQR has vertices P(1, 1), Q(7, 3) and R(3, 5). Which description fits it? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0009 (coordinate and transformational geometry)
  • Which capital letter, drawn in plain block form, has half-turn rotational symmetry but no line of symmetry? OAE Middle Grades Mathematics (030) assessment framework, Domain III Measurement and Geometry, competency 0009 (coordinate and transformational geometry)

Domain IV: Statistics and probability 9

  • A cereal box holds one of 6 prizes, each equally likely. Which simulation estimates how many boxes it takes to collect all six? OAE Middle Grades Mathematics (030) assessment framework, Domain IV Statistics and Probability, competency 0011 (principles of probability and techniques for determining probability)
  • A class of 20 has a mean test score of 78. Two students, with scores of 60 and 96, move away. What is the mean of the 18 who remain? OAE Middle Grades Mathematics (030) assessment framework, Domain IV Statistics and Probability, competency 0010 (principles and techniques of statistics)
  • A forecast gives a 40% chance of rain on Saturday and a 30% chance on Sunday, independent of each other. What is the chance of rain on at least one of the two days? OAE Middle Grades Mathematics (030) assessment framework, Domain IV Statistics and Probability, competency 0011 (principles of probability and techniques for determining probability)
  • A locker code is 3 different digits from 0 to 9, in order. A thief tries one such code at random. What is the probability that it opens the locker? OAE Middle Grades Mathematics (030) assessment framework, Domain IV Statistics and Probability, competency 0011 (principles of probability and techniques for determining probability)
  • A point is picked at random on the part of a number line from 0 to 12. Using the lengths on the line, what is the probability that it lies within 2 units of 5? OAE Middle Grades Mathematics (030) assessment framework, Domain IV Statistics and Probability, competency 0011 (principles of probability and techniques for determining probability)
  • A school has 300 sixth graders, 250 seventh graders and 200 eighth graders. A sample of 60 is drawn so that each grade keeps its share of the school. How many seventh graders are in the sample? OAE Middle Grades Mathematics (030) assessment framework, Domain IV Statistics and Probability, competency 0010 (principles and techniques of statistics)
  • A study of 40 students finds a correlation of r = −0.92 between days absent and final grade. What does that support? OAE Middle Grades Mathematics (030) assessment framework, Domain IV Statistics and Probability, competency 0010 (principles and techniques of statistics)
  • A teacher has the ages of 200 runners and wants a display that shows how many fall in each 10-year interval. Which display fits? OAE Middle Grades Mathematics (030) assessment framework, Domain IV Statistics and Probability, competency 0010 (principles and techniques of statistics)
  • A teacher lists eight quiz scores in order: 4, 7, 7, 10, 13, 16, 18, 22. What is the interquartile range? OAE Middle Grades Mathematics (030) assessment framework, Domain IV Statistics and Probability, competency 0010 (principles and techniques of statistics)

How this list was compiled: Our own questions, written to the assessment framework for Ohio Assessments for Educators field 030, Middle Grades Mathematics, read 2026-10-14 on the program's site (https://www.oh.nesinc.com/CONTENT/STUDYGUIDE/OH_SG_OBJ_030.htm; test page https://www.oh.nesinc.com/TestView.aspx?f=HTML_FRAG/OH030_TestPage.html): 125 multiple-choice questions in 255 minutes, passing score 220; Number Sense and Operations (competencies 0001 to 0002, 19%), Algebra and Functions (0003 to 0006, 36%), Measurement and Geometry (0007 to 0009, 27%) and Statistics and Probability (0010 to 0011, 18%). The bank holds 9, 18, 14 and 9 questions. Each question names the competency it was written to; every answer is worked in its explanation and was recomputed as a check. Licence: Questions, choices and explanations are original work of this site.

How it works

Fifty questions of our own follow the four domains of Ohio's Middle Grades Mathematics assessment, code 030, from place value to simulation. This is unofficial practice, with no tie to the Ohio State Board of Education or Evaluation Systems, Pearson.

Read the full guide

OAE Middle Grades Mathematics study guide: the four domains

The published framework, read October 14, 2026, gives algebra and functions the largest share, 36%, then measurement and geometry 27%, number sense and operations 19%, and statistics and probability 18%. The bank's 18, 14, 9 and 9 questions follow those shares.

Calculator, formulas and the 0% competency

Candidates get an on-screen scientific calculator and a formulas page. Discrete mathematics appears in the framework as a twelfth competency worth 0% of the score, so no question here is spent on it.

Pacing

The real test leaves about 2 minutes a question. The timed version on this page keeps that pace: 102 minutes for its 50 questions.

  • The explanations show the working and often name the slip behind a tempting wrong choice, so try each problem on paper first.

Questions and answers

Is this OAE Middle Grades Mathematics 030 practice test free?

It is free and needs no account. All 50 problems were written for this site to the competencies of test 030, with the working shown, and none is taken from the real assessment or its sample questions.

Is there an official OAE Middle Grades Mathematics study guide?

The testing program posts one at no charge: a study guide for 030 holding the assessment design and the framework these problems follow. It also sells a preparation course. Neither was copied here.

How many questions are on the OAE Middle Grades Mathematics test?

125, all multiple-choice, in 4 hours 15 minutes of testing after a 15-minute tutorial. Candidates who test with an online proctor take Domains I and II first, then Domains III and IV after an optional 15-minute break.

What is the passing score for OAE Middle Grades Mathematics?

The test page for 030 gives 220. Scores are reported from 100 to 300 and reflect how many multiple-choice questions were answered correctly, so a count of right answers on this page does not convert to it.

Which Ohio licenses need the Middle Grades Mathematics test?

Two rows of the program's license table name 030: the Middle Childhood (4–9) license in mathematics, beside Assessment of Professional Knowledge 002 and Foundations of Reading 190, and the Middle Childhood Generalist endorsement in mathematics (4–6), as one of two choices.

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