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Unofficial practice questions, not affiliated with the Massachusetts Department of Elementary and Secondary Education or Pearson. Bank checked October 9, 2026.
A bottling line fills 150 bottles in 4 minutes. At that rate, how many bottles does it fill in 14 minutes?Answer: 525. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0002
A ferry cut its one-way fare from $25.00 to $21.25. What was the percent decrease?Answer: 15%. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0002
A kayak listed at $640 is discounted 15%, and a 6.25% sales tax is charged on the discounted price. What does the buyer pay?Answer: $578.00. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0002
A number line activity uses four cards: −|−3|, −2.5, |−2| and 9/4. Which row shows the cards from least to greatest?Answer: −|−3|, −2.5, |−2|, 9/4. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0001
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Subarea I: Number system and quantity, continued
A student sorts four numbers into a rational group and an irrational group. Which number belongs in the irrational group?Answer: √50. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0001
One batch of bread takes 2 1/4 cups of flour. How many batches can be made from 15 3/4 cups?Answer: 7. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0002
Two harbor beacons flash together at 9:00 p.m. One flashes every 12 seconds and the other every 20 seconds. After how many seconds do they next flash at the same moment?Answer: 60. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0001
What is (3.2 × 10⁵) × (5 × 10⁻²) in scientific notation?Answer: 1.6 × 10⁴. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0001
What is the value of 18 − 6 ÷ 3 × 2 + 4²?Answer: 30. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0001
Which fraction is equal to the repeating decimal 0.1666…, in which the 6 repeats?Answer: 1/6. Source: MTEL Middle School Mathematics (65) test objectives, subarea I Number System and Quantity. Written to MTEL Middle School Mathematics (65), objective 0002
Subarea II: Algebra, functions and modeling 15
A candle is 20 cm tall when it is lit, and its height in centimeters after t hours is H = 20 − 2.5t. What does the −2.5 represent?Answer: The candle gets 2.5 cm shorter each hour. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0006
A pattern begins 3, 12, 48, … and each term is the same multiple of the one before. What is the sixth term?Answer: 3,072. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0003
A savings account opens with $4,000 and earns 3% interest, compounded once a year. With no other deposits, what is the balance after 2 years?Answer: $4,243.60. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0007
A table pairs x = 0, 1, 2, 3 with y = 5, 10, 20, 40. Which kind of function models the pattern of change?Answer: Exponential. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0003
A teacher needs an example of a linear equation in one variable that has no solution. Which equation works?Answer: 3(x + 2) = 3x + 8. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0004
A youth league ordered 75 shirts for $690. Adult sizes cost $11 each and youth sizes $8 each. How many adult shirts were ordered?Answer: 30. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0006
The area of a trapezoid is A = ½h(b₁ + b₂). Which expression gives b₁?Answer: 2A/h − b₂. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0004
The height in meters of a model rocket, t seconds after launch, is h(t) = −5t² + 40t + 2. What is its greatest height?Answer: 82 m. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0007
How does the graph of g(x) = f(x − 3) + 2 compare with the graph of f?Answer: Shifted 3 units right and 2 units up. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0005
Let f(x) = 3x − 2 and g(x) = x² + 1. What is g(f(2))?Answer: 17. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0005
The rows of a lecture hall hold 14, 17, 20, … seats, the same number more in each row. How many seats are in row 25?Answer: 86. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0003
What are the solutions of x² − 3x − 40 = 0?Answer: 8 and −5. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0007
What value of x solves (2/3)x − 5 = (1/6)x + 4?Answer: 18. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0004
Which equation describes the line through (−2, 7) and (4, −5)?Answer: y = −2x + 3. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0006
Which set of ordered pairs is a relation but not a function?Answer: {(1, 2), (1, 3), (2, 4)}. Source: MTEL Middle School Mathematics (65) test objectives, subarea II Algebra, Functions, and Modeling. Written to MTEL Middle School Mathematics (65), objective 0005
Subarea III: Geometry and measurement 10
A 20-foot ladder leans against a wall and makes a 60° angle with the ground. To the nearest tenth of a foot, how high up the wall does it reach?Answer: 17.3 ft. Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0008
A paper cone cup has the same rim radius and the same depth as a cylindrical glass that holds 54π cm³. How much does the cone cup hold?Answer: 18π cm³. Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0010
A rectangular planter is rebuilt with its length, width and depth each doubled. How does the volume of soil it holds change?Answer: It is 8 times as great. Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0008
A signpost 1.5 m tall casts a shadow 2 m long. At the same moment a tree casts a shadow 14 m long. How tall is the tree?Answer: 10.5 m. Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0009
A snail moves 15 centimeters per minute. What is its speed in meters per hour?Answer: 9. Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0008
A vertex of a triangle is at (4, −2). The triangle is rotated 90° counterclockwise about the origin. Where is the image of the vertex?Answer: (2, 4). Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0011
A wheelchair ramp rises 5 feet over a horizontal run of 12 feet. How long is the sloping surface of the ramp?Answer: 13 ft. Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0010
On a coordinate map of a park, a fountain is at (−3, 2) and a gate is at (5, −4). One unit stands for 10 meters. How far apart are they in a straight line?Answer: 100 m. Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0011
Points A, B and C lie on a circle, and the arc from A to C that does not contain B measures 136°. What is the measure of inscribed angle ABC?Answer: 68°. Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0010
Two parallel lines are cut by a transversal. Two interior angles on the same side of the transversal measure (3x + 10)° and (2x + 20)°. What is x?Answer: 30. Source: MTEL Middle School Mathematics (65) test objectives, subarea III Geometry and Measurement. Written to MTEL Middle School Mathematics (65), objective 0009
Subarea IV: Statistics and probability 5
A jar holds 7 green tickets and 5 yellow tickets. Two students each draw one ticket at random and keep it. What is the probability that both tickets are green?Answer: 7/22. Source: MTEL Middle School Mathematics (65) test objectives, subarea IV Statistics and Probability. Written to MTEL Middle School Mathematics (65), objective 0013
A scatter plot of weekly practice hours against errors in a recital has a correlation coefficient of r = −0.92. What does this show?Answer: A strong negative linear association. Source: MTEL Middle School Mathematics (65) test objectives, subarea IV Statistics and Probability. Written to MTEL Middle School Mathematics (65), objective 0012
A square board measures 10 inches on each side and has a circle of radius 3 inches painted on it. A dart lands at a random point on the board. About what is the probability that it lands inside the circle?Answer: 0.28. Source: MTEL Middle School Mathematics (65) test objectives, subarea IV Statistics and Probability. Written to MTEL Middle School Mathematics (65), objective 0013
A teacher adds 5 points to every score on a quiz. Which measure of the data set stays the same?Answer: The standard deviation. Source: MTEL Middle School Mathematics (65) test objectives, subarea IV Statistics and Probability. Written to MTEL Middle School Mathematics (65), objective 0012
The data set 4, 7, 8, 10, 12, 15, 21 is shown in a box plot. What is the interquartile range?Answer: 8. Source: MTEL Middle School Mathematics (65) test objectives, subarea IV Statistics and Probability. Written to MTEL Middle School Mathematics (65), objective 0012
How this list was compiled: Our own questions, written to the test objectives of MTEL Middle School Mathematics, field 65, as the test information guide prints them on the Massachusetts Tests for Educator Licensure website (https://www.mtel.nesinc.com/Content/StudyGuide/MA_SG_OBJ_65.htm and https://www.mtel.nesinc.com/TestView.aspx?f=HTML_FRAG/MA065_TestPage.html, read 2026-10-09): 85 multiple-choice questions and 2 open-response items in 4 hours; multiple-choice subareas I Number System and Quantity (20 to 22 questions, 20% of the score, objectives 0001 and 0002), II Algebra, Functions, and Modeling (31 to 33, 30%, objectives 0003 to 0007), III Geometry and Measurement (20 to 22, 20%, objectives 0008 to 0011) and IV Statistics and Probability (10 to 12, 10%, objectives 0012 and 0013), and the open-response subarea, 20%. This bank holds 10, 15, 10 and 5. Every answer is arithmetic or reasoning from the numbers in the question, and each was worked out a second time before the bank was written. Licence: Questions, choices and explanations are original work of this site.
How it works
This MTEL middle school math practice test follows field 65: 40 questions of our own in its four multiple-choice subareas. It is unofficial and not affiliated with, endorsed by or sponsored by the Massachusetts Department of Elementary and Secondary Education or Pearson.
Read the full guide
The four subareas
By the test objectives: number system and quantity, 20 to 22 questions; algebra, functions and modeling, 31 to 33; geometry and measurement, 20 to 22; statistics and probability, 10 to 12. This bank holds 10, 15, 10 and 5, in that order.
Timing
The MTEL site sets one clock for the whole test and lists no separate time for the multiple-choice part, so exam mode here is untimed.
Worked answers
Each explanation shows the steps and names the slip behind a tempting wrong choice. Every answer was worked out a second time from the numbers in the question.
The MTEL site lets you read the formula sheet before test day. Know what is on it and what is not.
The two open-response items are written, so they are not practiced here.
Questions and answers
How many questions are on the MTEL middle school math test?
The test information guide lists 85 multiple-choice questions and 2 open-response items in 4 hours of testing time. The MTEL site adds that some questions may not count toward the score.
What score do you need to pass MTEL Middle School Mathematics?
The MTEL site gives a qualifying score of 240. Multiple-choice questions are 80% of the score and the open-response items 20%, so the number right on this page is not a prediction.
Is there an MTEL middle school math study guide?
The MTEL site has a test information guide for field 65, with the objectives and sample questions, and a practice test. This page is separate practice: our own questions, grouped by the same four subareas.
Can you use a calculator on the MTEL middle school math test?
Only the one the test supplies. The MTEL site says standard four-function calculators are provided on screen, and that formulas are provided on screen with the test.