• 48 questions

NES Middle Grades Math Test Practice

Unofficial practice for NES Middle Grades Mathematics, test 203, spread like its four domains, with the working after every answer.

Which fraction in lowest terms equals 3.6 × 10⁻⁴?

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

Print covers the next 48 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 48 questions, 96 minutes.

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Unofficial practice questions, not affiliated with Pearson, which owns the National Evaluation Series. Bank checked October 12, 2026.

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All 48 questions

Number sense and operations 8

  • A band director wants to set out 675 chairs in equal rows. Counting one long row of 675 and 675 rows of one chair, how many different numbers of rows are possible? NES Middle Grades Mathematics (203) framework, competency 0001 (numbers)
  • A carpenter cuts shelves 1 3/8 feet long from a board 10 feet long. How many full shelves does she get, and how much of the board is left over? NES Middle Grades Mathematics (203) framework, competency 0002 (operations)
  • A shopper has a coupon for 25% off, and sales tax is 8%. Does it matter whether the register takes the coupon off before or after adding the tax? NES Middle Grades Mathematics (203) framework, competency 0002 (operations)
  • A student finds 25 × 48 by writing 25 × (4 × 12) = (25 × 4) × 12 = 100 × 12. Which property lets her move the parentheses? NES Middle Grades Mathematics (203) framework, competency 0002 (operations)
  • In base eight the places are worth 1, 8, 64 and 512. What is the value of the digit 5 in the base-eight numeral 3524? NES Middle Grades Mathematics (203) framework, competency 0001 (numbers)
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Number sense and operations, continued

  • To multiply 37 × 24 by partial products, a student has written 600, 120 and 28. Which partial product is still missing? NES Middle Grades Mathematics (203) framework, competency 0002 (operations)
  • Which fraction in lowest terms equals 3.6 × 10⁻⁴? NES Middle Grades Mathematics (203) framework, competency 0001 (numbers)
  • Which of these numbers is irrational? NES Middle Grades Mathematics (203) framework, competency 0001 (numbers)

Algebra and functions 16

  • A cart rolls down a ramp, and the distance it has covered after t seconds is d = 3t² meters. What is its average speed between t = 2 and t = 5? NES Middle Grades Mathematics (203) framework, competency 0006 (nonlinear relations and concepts of calculus)
  • A function is defined by f(x) = 2x + 1 for x < 3 and f(x) = x² − c for x ≥ 3. For which value of c is f continuous at x = 3? NES Middle Grades Mathematics (203) framework, competency 0006 (nonlinear relations and concepts of calculus)
  • A line crosses the x-axis at 6 and the y-axis at −4. Which is an equation of the line? NES Middle Grades Mathematics (203) framework, competency 0005 (linear relations and applications)
  • A tank holds 900 liters of water and drains at a steady rate. After 12 minutes it holds 660 liters. In the equation V = mt + b for the volume after t minutes, what are m and b? NES Middle Grades Mathematics (203) framework, competency 0005 (linear relations and applications)
  • A theater sells 200 tickets a night at $10 each. For every $1 added to the price, 10 fewer tickets are sold. Which price brings in the most money? NES Middle Grades Mathematics (203) framework, competency 0006 (nonlinear relations and concepts of calculus)
  • A tile pattern has 5 tiles in figure 1, 8 in figure 2 and 11 in figure 3, and it keeps growing the same way. How many tiles are in figure 40? NES Middle Grades Mathematics (203) framework, competency 0003 (patterns, relations, and functions)
  • After treatment, the weeds in a lake cover 12% less area each month than the month before. They cover 3,400 m² now. Which expression gives the area covered 5 months from now? NES Middle Grades Mathematics (203) framework, competency 0006 (nonlinear relations and concepts of calculus)
  • Find every real solution of √(2x + 7) = x − 4. NES Middle Grades Mathematics (203) framework, competency 0004 (algebraic techniques and applications)
  • For which value of k does the system 2x + 3y = 7 and 4x + ky = 10 have no solution? NES Middle Grades Mathematics (203) framework, competency 0005 (linear relations and applications)
  • For which values of x is 7 − 2(3x + 1) > 4x − 15 true? NES Middle Grades Mathematics (203) framework, competency 0004 (algebraic techniques and applications)
  • In a class of 28 students, one table lists the pairs (student, birth month). A second table lists the same pairs turned around: (birth month, student). Which statement is true? NES Middle Grades Mathematics (203) framework, competency 0003 (patterns, relations, and functions)
  • Start with the graph of y = 2ˣ. Flip it over the x-axis, then slide it up 4 units. Which rule gives the result? NES Middle Grades Mathematics (203) framework, competency 0003 (patterns, relations, and functions)
  • Two gears mesh. The small gear has 12 teeth and turns at 40 revolutions per minute. How fast does the large gear, which has 30 teeth, turn? NES Middle Grades Mathematics (203) framework, competency 0003 (patterns, relations, and functions)
  • Which expression is equivalent to (x⁻²y³)² ÷ (xy⁻¹), where x and y are not zero? NES Middle Grades Mathematics (203) framework, competency 0004 (algebraic techniques and applications)
  • Which inequality says "the sum of a number n and 9, divided by 4, is no more than 6"? NES Middle Grades Mathematics (203) framework, competency 0004 (algebraic techniques and applications)
  • Which line is perpendicular to 5x + 2y = 8 and passes through (10, 1)? NES Middle Grades Mathematics (203) framework, competency 0005 (linear relations and applications)

Measurement and geometry 12

  • A blueprint uses a scale of 1 cm to 2.5 m. On the blueprint a room measures 3.2 cm by 4.4 cm. What is the floor area of the real room? NES Middle Grades Mathematics (203) framework, competency 0007 (measurement principles, procedures, and applications)
  • A cylindrical water tank has a radius of 2 m and a height of 5 m. Using 3.14 for π and 1 m³ = 1,000 L, how many liters does it hold? NES Middle Grades Mathematics (203) framework, competency 0007 (measurement principles, procedures, and applications)
  • A length is recorded as 8.4 cm, measured to the nearest tenth of a centimeter. Between which values does the actual length L lie? NES Middle Grades Mathematics (203) framework, competency 0007 (measurement principles, procedures, and applications)
  • A net is made of two congruent triangles and three rectangles. Which solid does it fold into? NES Middle Grades Mathematics (203) framework, competency 0008 (Euclidean geometry in two and three dimensions)
  • A pizza 14 inches across is cut into equal slices, each with a 40° angle at the center. What is the area of the top of one slice? NES Middle Grades Mathematics (203) framework, competency 0008 (Euclidean geometry in two and three dimensions)
  • A snail crawls at a steady 1.3 centimeters per second. How many meters does it cover in one hour? NES Middle Grades Mathematics (203) framework, competency 0007 (measurement principles, procedures, and applications)
  • A triangle has sides of 7 cm, 10 cm and 12 cm. What kind of triangle is it? NES Middle Grades Mathematics (203) framework, competency 0008 (Euclidean geometry in two and three dimensions)
  • Four angles of a pentagon measure 97°, 113°, 121° and 134°. What is the measure of the fifth angle? NES Middle Grades Mathematics (203) framework, competency 0008 (Euclidean geometry in two and three dimensions)
  • Point K(−2, 6) is translated 5 units right and 3 units down, and the result is then reflected across the x-axis. Where does K end up? NES Middle Grades Mathematics (203) framework, competency 0009 (coordinate and transformational geometry)
  • Triangle ABC has vertices A(2, 1), B(6, 1) and C(2, 4). It is dilated by a scale factor of 3 about the origin. How long is the image of side BC? NES Middle Grades Mathematics (203) framework, competency 0009 (coordinate and transformational geometry)
  • What is the length of the segment with endpoints A(−3, 4) and B(5, −2)? NES Middle Grades Mathematics (203) framework, competency 0009 (coordinate and transformational geometry)
  • Which regular polygon cannot tile the plane by itself, with no gaps and no overlaps? NES Middle Grades Mathematics (203) framework, competency 0009 (coordinate and transformational geometry)

Statistics, probability and discrete mathematics 12

  • A ball is dropped from a height of 9 m. Each bounce takes it back up to 2/3 of the height it just fell from. What total distance, up and down, does the ball approach as it keeps bouncing? NES Middle Grades Mathematics (203) framework, competency 0012 (discrete mathematics)
  • A drawer holds 4 black socks and 6 white socks. Two socks are pulled out at random. What is the probability that they match? NES Middle Grades Mathematics (203) framework, competency 0011 (probability)
  • A forecast gives a 30% chance of rain on each day. Which use of a table of random digits 0 to 9 simulates one day fairly? NES Middle Grades Mathematics (203) framework, competency 0011 (probability)
  • A principal wants to estimate what share of the school's 600 students favor a later start time. Which sample is least likely to be biased? NES Middle Grades Mathematics (203) framework, competency 0010 (principles and techniques of statistics)
  • A spinner with five equal sections numbered 1 to 5 is spun, and a fair number cube numbered 1 to 6 is rolled. What is the probability that the two numbers add to 7? NES Middle Grades Mathematics (203) framework, competency 0011 (probability)
  • Biologists tag 60 fish in a pond and release them. A week later they net 150 fish and find that 12 carry tags. About how many fish live in the pond? NES Middle Grades Mathematics (203) framework, competency 0010 (principles and techniques of statistics)
  • Five students, among them Ana and Ben, line up in a random order. What is the probability that Ana and Ben stand next to each other? NES Middle Grades Mathematics (203) framework, competency 0011 (probability)
  • Set A holds the multiples of 3 from 1 to 30, and set B holds the multiples of 5 from 1 to 30. How many numbers are in A ∪ B? NES Middle Grades Mathematics (203) framework, competency 0012 (discrete mathematics)
  • Six quiz scores are 4, 6, 7, 7, 9 and 27. The 27 turns out to be a typing error for 9. What happens to the mean and the median when it is corrected? NES Middle Grades Mathematics (203) framework, competency 0010 (principles and techniques of statistics)
  • Three boys and two girls stand in a row for a photo, and the two girls must take the two end places. In how many ways can the five children be arranged? NES Middle Grades Mathematics (203) framework, competency 0012 (discrete mathematics)
  • What is the mean absolute deviation of the data set 3, 6, 6, 7, 8, 12? NES Middle Grades Mathematics (203) framework, competency 0010 (principles and techniques of statistics)
  • Which statement is the negation of "Every student in the class passed the test"? NES Middle Grades Mathematics (203) framework, competency 0012 (discrete mathematics)

How this list was compiled: Our own questions, written to the test framework for NES Middle Grades Mathematics, test 203, read 2026-10-12 on the National Evaluation Series site (https://www.nestest.com/static/docs/NES_Framework_203.pdf; test page https://www.nestest.com/test/203): Number Sense and Operations (competencies 0001 to 0002, 17%), Algebra and Functions (0003 to 0006, 33%), Measurement and Geometry (0007 to 0009, 25%) and Statistics, Probability, and Discrete Mathematics (0010 to 0012, 25%). The bank holds 4 questions for each of the 12 competencies. Every answer is worked in its explanation and was computed a second time from the numbers in the question. Licence: Questions, choices and explanations are original work of this site.

How it works

This NES Middle Grades Math test practice has 48 questions of our own, four for each competency of test 203. It is unofficial and not affiliated with Pearson, which owns the National Evaluation Series.

Read the full guide

NES Middle Grades Mathematics practice test: the four domains

On the framework read October 12, 2026, test 203 weights Number Sense and Operations 17%, Algebra and Functions 33%, Measurement and Geometry 25%, and Statistics, Probability, and Discrete Mathematics 25%. The bank holds 8, 16, 12 and 12 questions.

Timing

Exam mode keeps the real test's pace of two minutes a question: 48 questions in 96 minutes.

What a missed question tells you

Each explanation works the numbers and ends with its competency, 0001 to 0012, so a wrong answer points to one line of the framework.

  • The real test supplies an on-screen calculator and a formulas sheet, so practice with a formula page open.
  • A third of the score is algebra and functions, competencies 0003 to 0006. Start there if time is short.

Questions and answers

Is this an NES middle school math practice test?

Yes. The National Evaluation Series calls the test Middle Grades Mathematics, code 203. These 48 questions are our own, written to its twelve competencies; none is taken or reworded from a real test or the study guide's samples.

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

150 multiple-choice questions. The test page gives 5 hours of testing time plus 15 minutes for a tutorial and nondisclosure agreement, so the appointment is 5 hours and 15 minutes.

What is the passing score for NES Middle Grades Math?

The test page shows a national benchmark of 220 on the scaled score and links passing scores for Arizona, New Hampshire, Oklahoma, Oregon, Tennessee and Washington. A number right here does not convert to that scale.

Is calculus on the NES Middle Grades Mathematics test?

Only its concepts. Competency 0006 asks for limits, continuity and rates of change and their use in real-world problems. Four questions here cover a revenue maximum, exponential decay, continuity and an average rate of change.

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