MTLE Math Practice Tests Free

Unofficial practice for both subtests of Minnesota's MTLE Mathematics (Grades 5–12) test, codes 207 and 208.

Subtest

Subtest 1 (207): number sense; functions, algebra and calculus. Subtest 2 (208): measurement and geometry; data, probability and discrete math; mathematical processes.

Which of these lengths is an irrational number of units?

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 24 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 24 questions, 38 minutes.

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Unofficial practice questions, not affiliated with the Minnesota Professional Educator Licensing and Standards Board or Pearson. Bank checked October 13, 2026.

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Subtest 1: all 24 questions

Number sense 10

  • A Boundary Waters outfitter in Ely charges a flat fee plus a rate per day for a canoe. A 4-day trip costs $178 and a 9-day trip costs $353. What is the flat fee? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0003
  • A lesson on place value writes 366, the number of days in a leap year, in base seven. Which numeral results? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0001
  • A maple syrup maker near Grand Marais has 12 liters of concentrate that is 20% sugar. How many liters of a 65% concentrate must be added to make a blend that is 50% sugar? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0003
Show all 24 questions (21 more)

Number sense, continued

  • A ski shop in Duluth marks a pair of skis up 60% over cost, then sells them at 25% off the marked price. By what percent does the sale price exceed cost? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0003
  • A teacher asks for the exact value of 32^(3/5) divided by 81^(3/4). What is it? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0002
  • A tile setter lays 252 square tiles as one solid rectangle, with the same number of tiles in every row. Counting a single strip of 252 either way, how many different numbers of rows are possible? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0002
  • On a quiz about complex numbers, a student multiplies 5 − 2i by 3 + 4i. Which result is correct? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0001
  • Today is a Tuesday. Which day of the week falls 1,000 days from today? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0002
  • Two meshed gears have 42 teeth and 56 teeth. One tooth on each gear is painted where the gears touch. After how many full turns of the smaller gear do the painted teeth next meet? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0002
  • Which of these lengths is an irrational number of units? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0001

Functions, algebra and calculus 14

  • A drone's height above a field is h(t) = −t³ + 12t² meters for t from 0 to 12 seconds. At what time is the drone climbing fastest? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0007
  • A farmer near Northfield has 180 meters of fence for a rectangular pen. A straight riverbank forms one side, so only three sides need fence. What is the largest area the pen can enclose? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0006
  • A guy wire runs from the top of a 24-meter radio mast to an anchor 7 meters from the base of the mast. What is the sine of the angle the wire makes with the ground? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0007
  • A lake stocked with 4,000 trout loses 12% of the fish that remain each season. Which expression gives the number left after n seasons? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0006
  • A machine fills syrup bottles to 355 milliliters. A bottle passes inspection when its volume v is within 4 milliliters of that target. Which inequality describes the passing bottles? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0005
  • A rain barrel drains through a hose at a steady rate. It holds 340 liters after 6 minutes and 250 liters after 15 minutes. How much did the barrel hold when the hose was opened? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0006
  • A savings balance follows B = 800 · 2^(t/9), with t in years. After how many years does the balance reach $6,400? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0006
  • A student simplifies the fraction (3x² − 27)/(x² − x − 12) by factoring. For x ≠ 4 and x ≠ −3, which result is right? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0005
  • A teacher asks for the domain of h(x) = ln(x − 4) / √(9 − x) over the real numbers. Which set is it? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0004
  • At a county fair food stand, 3 hot dogs and 2 lemonades cost $23.50, and 2 hot dogs and 4 lemonades cost $25. What does one lemonade cost? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0005
  • One store takes $15 off a price and then applies a 20% discount. A rival applies the 20% discount first and then takes $15 off. On a $120 item, how much less does the rival charge? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0004
  • The product of two consecutive positive odd integers is 323. What is the larger integer? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0005
  • The rule F = (9/5)C + 32 turns a Celsius reading into Fahrenheit. Which rule is its inverse, giving Celsius from Fahrenheit? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0004
  • Water flows into a tank at r(t) = 6t + 4 liters per minute, with t in minutes. How much water enters during the first 5 minutes? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 1, objective 0007

How this list was compiled: Our own questions, written to Subtest 1 (test code 207) of the Minnesota Teacher Licensure Examinations field Mathematics (Grades 5–12) in the test framework on the MTLE website (https://www.mtle.nesinc.com/Content/Worksheets/MN207_208_FrameworkWorksheet.html; test page https://www.mtle.nesinc.com/TestView.aspx?f=HTML_FRAG/MN207_TestPage.html, read 2026-10-13): the test page gives 48 multiple-choice questions in 1 hour 15 minutes, passing score 228, with an on-screen scientific calculator and a formulas page; Number Sense (objectives 0001 to 0003, 43%) and Functions, Algebra, and Calculus (0004 to 0007, 57%). This set holds 24: 10 and 14. Every answer was worked out twice. Licence: Questions, choices and explanations are original work of this site.

Subtest 2: all 24 questions

Measurement and geometry 9

  • A cell tower stands at the point (−2, 5) on a coordinate map and reaches every point within 8 units. Which equation describes the edge of its coverage? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0010
  • A design tool turns the point (6, −2) by 180° about the origin and then reflects the result across the x-axis. Where does the point end up? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0010
  • A floodlight on a barn lights a sector of a circle with a radius of 12 meters and a central angle of 150°. What area does it light? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0008
Show all 24 questions (21 more)

Measurement and geometry, continued

  • A model of a grain silo is built at a scale of 1 to 20 and has a volume of 0.9 cubic meter. What is the volume of the real silo? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0008
  • A quadrilateral is inscribed in a circle, and one of its angles measures 74°. What is the measure of the angle opposite it? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0009
  • A stained-glass window has the shape of a convex polygon with 12 sides, and a lead strip runs along every diagonal. How many diagonals are there? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0009
  • A storage chest in an ice-fishing house measures 2 feet by 3 feet by 6 feet inside. What is the longest fishing rod that fits, laid from one corner to the opposite corner? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0009
  • The tip of a wind turbine blade on Buffalo Ridge moves at 176 feet per second. What is that in miles per hour? (1 mile = 5,280 feet) Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0008
  • What is an equation of the perpendicular bisector of the segment that joins (1, 2) and (7, 10)? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0010

Data, probability and discrete math 9

  • A course grade weights homework 20%, quizzes 30% and the final exam 50%. A student earns 90 on homework, 80 on quizzes and 70 on the final. What is the course grade? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0011
  • A jar holds 20 tokens numbered 1 through 20. One token is drawn and put back, and then a token is drawn again. What is the probability that both draws show a perfect square? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0012
  • A locker code is 3 different digits chosen from 0 through 9, and the order of the digits matters. How many codes are possible? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0013
  • A pile of logs has 24 logs in its bottom layer. Each layer above has 2 fewer logs, and the top layer has 6. How many logs are in the pile? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0013
  • A raffle sells 200 tickets at $5 each. One ticket wins $400 and four tickets win $50 each. What is the expected net result of buying one ticket? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0012
  • At a curling bonspiel, each of 9 teams plays every other team exactly once. How many games are played? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0013
  • Of the 40 cabins at a lake resort, 22 have a fireplace, 15 have a dock and 9 have both. A guest is assigned at random to one of the cabins with a dock. What is the probability that it also has a fireplace? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0012
  • Over five January days the high temperatures in International Falls were −22°, −15°, −9°, −4° and 20° Fahrenheit. What are the mean and the median? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0011
  • Walleye weights in a lake survey are roughly normal, with a mean of 2.4 pounds and a standard deviation of 0.5 pound. About what percent of the fish weigh more than 3.4 pounds? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0011

Mathematical processes 6

  • A student writes: “Squaring a number always gives a result larger than the number.” Which number is a counterexample? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0014
  • A teacher writes: “If a number is divisible by 6, then it is divisible by 3.” Which choice states the converse and judges it correctly? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0014
  • Algebra tiles are laid out as a rectangle with side lengths x + 3 and x + 2. Which product does the rectangle show? Our own question, answer worked out twice. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0014
  • Before students read a textbook section on rational functions, a teacher directly teaches the words “asymptote” and “domain”. According to Put Reading First, what does teaching specific words before reading help? Put Reading First, third edition (National Institute for Literacy), Vocabulary Instruction. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0015
  • In a mathematics textbook the words “product”, “root” and “volume” carry meanings unlike their everyday ones. What is the capacity of one word to have several related meanings called? Wikipedia, Polysemy. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0015
  • Students write “quadrilateral”, “parallelogram”, “rhombus” and “square” in boxes and join them with arrows labeled “is a kind of”. What is this kind of diagram called? Wikipedia, Concept map. Outline: MTLE Mathematics (Grades 5–12) framework, Subtest 2, objective 0015

How this list was compiled: Our own questions, written to Subtest 2 (test code 208) of the Minnesota Teacher Licensure Examinations field Mathematics (Grades 5–12) in the test framework on the MTLE website (https://www.mtle.nesinc.com/Content/Worksheets/MN207_208_FrameworkWorksheet.html; test page https://www.mtle.nesinc.com/TestView.aspx?f=HTML_FRAG/MN207_TestPage.html, read 2026-10-13): the test page gives 48 multiple-choice questions in 1 hour 15 minutes, passing score 227, with an on-screen scientific calculator and a formulas page; Measurement and Geometry (objectives 0008 to 0010, 38%), Data, Probability, and Discrete Math (0011 to 0013, 37%) and Mathematical Processes (0014 and 0015, 25%). This set holds 24: 9, 9 and 6. Every computed answer was worked out twice; the three questions on reading in mathematics (objective 0015) rest on Put Reading First and the Wikipedia articles Polysemy and Concept map. Licence: Questions, choices and explanations are original work of this site.

How it works

These free MTLE math practice tests follow Mathematics (Grades 5–12), Minnesota's secondary math licensure test, with 24 questions for each subtest. They are unofficial, and neither the Minnesota Professional Educator Licensing and Standards Board nor Pearson is connected with them.

Read the full guide

MTLE math study guide: what each subtest weighs

The MTLE framework, read October 13, 2026, weights Subtest 1 as Number Sense 43% and Functions, Algebra, and Calculus 57%. Subtest 2 is Measurement and Geometry 38%, Data, Probability, and Discrete Math 37% and Mathematical Processes 25%. Our two sets follow nearly those shares: 10 and 14 questions, then 9, 9 and 6.

Secondary math MTLE practice test: calculator, formulas and time

The test page says an on-screen scientific calculator and a formulas page come with the real test. The timed exam here keeps the real pace, 24 questions in 38 minutes, and no question calls for graphing. Three questions cover objective 0015, reading in mathematics.

  • Every question's source line names its subtest and objective, so a missed question points to one line of the framework.

Questions and answers

Are these MTLE math practice tests free?

Yes, and nothing asks for a sign-up. All 48 questions were written for this page from the objectives of the published framework, and every computed answer was worked out twice. No question comes from the real test or the official practice tests.

How many questions are on the MTLE math test?

The test page, read October 13, 2026, lists 48 multiple-choice questions for each of the two subtests, with 1 hour 15 minutes of testing time per subtest after a 15-minute tutorial.

What is a passing score on MTLE Mathematics?

The test page sets 228 for Subtest 1 and 227 for Subtest 2, and a license needs both. Those are scaled scores, so a count of right answers on this page is given without a pass or fail.

Is this the MTLE test for middle school math?

No. Minnesota lists a separate Middle Level Mathematics (Grades 5–8) test. This page follows the framework of Mathematics (Grades 5–12), whose objective 0007 is trigonometry and calculus.

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