Unofficial practice for MTEL Middle School Mathematics/Science (77): math, technology/engineering and three sciences, each answer sourced.
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Unofficial practice questions, not affiliated with the Massachusetts Department of Elementary and Secondary Education or Pearson. Bank checked October 12, 2026.
A box of counters can be shared out equally, with none left over, among 8 students, among 12 students and among 15 students. What is the smallest number of counters the box can hold?MTEL Middle School Mathematics/Science (77) test objectives, subarea I, Number System and Quantity (read 2026-10-12). Written to objective 0001
A factory turns out 4 × 10⁵ screws a day. How many screws does it turn out in 2.5 × 10² working days? Give the answer in scientific notation.MTEL Middle School Mathematics/Science (77) test objectives, subarea I, Number System and Quantity (read 2026-10-12). Written to objective 0001
A recipe uses 2/3 cup of oil for every 1 1/2 cups of flour. How much oil goes with 6 cups of flour?MTEL Middle School Mathematics/Science (77) test objectives, subarea I, Number System and Quantity (read 2026-10-12). Written to objective 0002
The price of a jacket goes up from $80 to $92. What is the percent increase?MTEL Middle School Mathematics/Science (77) test objectives, subarea I, Number System and Quantity (read 2026-10-12). Written to objective 0002
Which statement about √50 is true?MTEL Middle School Mathematics/Science (77) test objectives, subarea I, Number System and Quantity (read 2026-10-12). Written to objective 0001
Show all 40 questions (35 more)
Subarea II: Algebra, functions and modeling 6
A bike shop charges a flat fee plus an hourly rate for repairs. A 2-hour repair costs $95 and a 5-hour repair costs $185. Which function gives the cost C, in dollars, of a repair that takes h hours?MTEL Middle School Mathematics/Science (77) formulas, the sheet shown on screen during the test (read 2026-10-12). Written to objective 0006
A gardener has 40 m of fencing for a rectangular plot. If one side is x meters long, the area is A = x(20 − x) square meters. What is the largest area the plot can have?MTEL Middle School Mathematics/Science (77) test objectives, subarea II, Algebra, Functions, and Modeling (read 2026-10-12). Written to objective 0007
A phone plan costs $18 a month plus $0.25 for each text message. For which numbers of messages t does the monthly bill stay under $30?MTEL Middle School Mathematics/Science (77) test objectives, subarea II, Algebra, Functions, and Modeling (read 2026-10-12). Written to objective 0004
Adult tickets cost $9 and child tickets cost $5. A group buys 14 tickets and pays $98. How many adult tickets did the group buy?MTEL Middle School Mathematics/Science (77) test objectives, subarea II, Algebra, Functions, and Modeling (read 2026-10-12). Written to objective 0006
An arithmetic sequence starts at 7 and has a common difference of 4. What is its 25th term?MTEL Middle School Mathematics/Science (77) test objectives, subarea II, Algebra, Functions, and Modeling (read 2026-10-12). Written to objective 0003
The graph of y = f(x) is replaced by the graph of y = f(x − 3) + 2. How has the graph moved?MTEL Middle School Mathematics/Science (77) test objectives, subarea II, Algebra, Functions, and Modeling (read 2026-10-12). Written to objective 0005
Subarea III: Geometry and measurement 5
A faucet drips 15 milliliters of water every minute. How many liters of water does it waste in one full day?MTEL Middle School Mathematics/Science (77) test objectives, subarea III, Geometry and Measurement (read 2026-10-12). Written to objective 0008
A rectangular garden gate is 0.9 m wide and 1.2 m tall. How long is a brace that runs along its diagonal, from corner to corner?MTEL Middle School Mathematics/Science (77) test objectives, subarea III, Geometry and Measurement (read 2026-10-12). Written to objective 0010
Every edge of a rectangular box is made three times as long. By what factor does the volume of the box grow?MTEL Middle School Mathematics/Science (77) test objectives, subarea III, Geometry and Measurement (read 2026-10-12). Written to objective 0008
On a scale drawing, 1 inch stands for 8 feet. A classroom is drawn as a rectangle 3.5 inches by 4.25 inches. What is the area of the real classroom?MTEL Middle School Mathematics/Science (77) test objectives, subarea III, Geometry and Measurement (read 2026-10-12). Written to objective 0009
Triangle ABC has a vertex at A(−2, 6). The triangle is dilated about the origin by a scale factor of 1/2, and the image is then reflected across the x-axis. Where is the final image of A?MTEL Middle School Mathematics/Science (77) test objectives, subarea III, Geometry and Measurement (read 2026-10-12). Written to objective 0011
Subarea IV: Statistics and probability 4
A club has 4 seventh graders and 6 eighth graders. Two members are picked at random, one after the other, to speak at an assembly. What is the probability that both are eighth graders?MTEL Middle School Mathematics/Science (77) test objectives, subarea IV, Statistics and Probability (read 2026-10-12). Written to objective 0013
A square board is 10 cm on a side, and a circle of radius 5 cm is drawn inside it. A dart lands at a random point of the board. What is the probability that it lands inside the circle?MTEL Middle School Mathematics/Science (77) formulas, the sheet shown on screen during the test (read 2026-10-12). Written to objective 0013
Seven quiz scores are 6, 7, 7, 8, 8, 9 and 39. Which statement about these scores is true?MTEL Middle School Mathematics/Science (77) test objectives, subarea IV, Statistics and Probability (read 2026-10-12). Written to objective 0012
What is the interquartile range of the data 2, 4, 5, 7, 9, 12, 13, 15?MTEL Middle School Mathematics/Science (77) test objectives, subarea IV, Statistics and Probability (read 2026-10-12). Written to objective 0012
Subarea V: Technology/engineering 5
A bridge carries the weight of its own deck all the time, and the weight of trucks only while they cross. Which kind of load is each?Wikipedia, "Structural load", Types; Massachusetts framework, standard 7.MS-ETS3-4(MA) (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0016
A designer wants a handle for a cooking pot that stays cool while the pot is hot. Which of the material properties named in the Massachusetts grade 6 standard matters most for the choice?Massachusetts Science and Technology/Engineering Curriculum Framework (2016), standard 6.MS-ETS2-1(MA) and 6.MS-ETS2-2(MA) (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0015
A team tests a paper bridge, notes where it fails, changes the design and tests it again, several times over. In the Massachusetts grade 7 standard, what is this cycle for?Massachusetts Science and Technology/Engineering Curriculum Framework (2016), standard 7.MS-ETS1-4 (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0014
The Massachusetts grade 8 standard says that materials keep their composition under physical processing such as cutting, forming and sanding. When, by the same standard, may some properties of a material change?Massachusetts Science and Technology/Engineering Curriculum Framework (2016), standard 8.MS-ETS2-4(MA) (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0015
Students score three bridge designs against each criterion and each constraint in a table, then total the scores to choose one. What does the Massachusetts framework call this tool?Massachusetts Science and Technology/Engineering Curriculum Framework (2016), standard 7.MS-ETS1-2 (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0014
Subarea VI: Earth and space science 5
A student says summer comes when Earth is closest to the Sun. What does NASA give as the cause of the seasons?NASA Space Place, What Causes the Seasons? (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0017
Air warmed at the ground rises as a bubble, cools, and is replaced by cooler, denser air from around it. Which kind of heat transfer is this movement?NOAA JetStream, The Transfer of Heat Energy (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0019
Along one kind of plate boundary the plates slide horizontally past each other, and crust is neither produced nor destroyed. Which kind is it, in the U.S. Geological Survey's list?U.S. Geological Survey, This Dynamic Earth: Understanding plate motions (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0018
Rock deep in the crust is put under high heat and high pressure. It does not melt, but it is transformed into a denser, more compact rock with new minerals. What kind of rock is the result?U.S. Geological Survey, What are metamorphic rocks? (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0018
Why does the U.S. Energy Information Administration class the energy of sunshine, wind and flowing rivers as renewable?U.S. Energy Information Administration, Energy Explained: Sources of energy (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0020
Subarea VII: Life science 5
A muscle cell uses far more energy than a skin cell does. Which organelle would be expected in greater number in the muscle cell, and why?National Human Genome Research Institute, Talking Glossary: Mitochondria (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0021
A pea plant with purple flowers that carries one allele for white (Pp) is crossed with a white-flowered plant (pp). Purple is dominant. What fraction of the offspring is expected to have white flowers?Wikipedia, "Punnett square", Monohybrid cross (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0023
Grass in a meadow stores 10,000 kJ of energy as new biomass. Mice eat the grass, snakes eat the mice and hawks eat the snakes. If about 10% of the energy passes from each trophic level to the next, about how much reaches the hawks?Wikipedia, "Ecological pyramid", Pyramid of energy (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0022
In a food web diagram an arrow is drawn from a herring to a seal. What does the arrow show?NOAA Education, Aquatic food webs (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0022
Understanding Evolution, the University of California, Berkeley site, sets out natural selection with beetles: their traits vary, and there is differential reproduction. What is the third thing there must be?University of California Museum of Paleontology, Understanding Evolution: Natural selection (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0024
Subarea VIII: Physical science 5
A 12 V battery is connected to a 4 Ω resistor and a 2 Ω resistor wired in series. What current flows through the circuit?MTEL Middle School Mathematics/Science (77) test objectives, subarea VIII, Physical Science (read 2026-10-12). Written to objective 0029
A 1,200 kg car speeds up steadily from rest to 20 m/s in 8 s on a level road. What net force acts on the car?MTEL Middle School Mathematics/Science (77) test objectives, subarea VIII, Physical Science (read 2026-10-12). Written to objective 0028
A child on a sled starts from rest at the top of a snowy hill and gains speed all the way down. In the terms of the U.S. Energy Information Administration, which change of energy is taking place?U.S. Energy Information Administration, Energy Explained: Forms of energy (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0027
A graduated cylinder holds water up to the 50 mL mark. A stone of mass 39 g is lowered in, and the water rises to the 65 mL mark. What is the density of the stone?MTEL Middle School Mathematics/Science (77) formulas, the sheet shown on screen during the test (read 2026-10-12). Written to objective 0025
A student holds one end of an iron nail and puts the other end in a candle flame. Soon the end in the hand feels hot. Which kind of heat transfer carried the energy along the nail?NOAA JetStream, The Transfer of Heat Energy (read 2026-10-12). Written to MTEL Middle School Mathematics/Science (77), objective 0026
How this list was compiled: Our own questions, written to the test objectives of MTEL Middle School Mathematics/Science, field 77, 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_77.htm and https://www.mtel.nesinc.com/TestView.aspx?f=HTML_FRAG/MA077_TestPage.html, read 2026-10-12): 100 multiple-choice questions and 2 open-response items in 4 hours; eight multiple-choice subareas (Number System and Quantity, objectives 0001 and 0002, 10% of the score; Algebra, Functions, and Modeling, 0003 to 0007, 12%; Geometry and Measurement, 0008 to 0011, 10%; Statistics and Probability, 0012 and 0013, 8%; Technology/Engineering, 0014 to 0016, 10%; Earth and Space Science, 0017 to 0020, 10%; Life Science, 0021 to 0024, 10%; Physical Science, 0025 to 0029, 10%) and the open-response subarea, 20%. This bank holds 5, 6, 5, 4, 5, 5, 5 and 5 questions for the eight multiple-choice subareas. Every calculated answer was worked out a second time from the numbers in the question; three questions use a formula of the sheet the test shows on screen (https://www.mtel.nesinc.com/Content/Docs/MTEL_65_Formulas.pdf, read 2026-10-12). Every other fact was read on 2026-10-12 in the public page named under its question: the Massachusetts Science and Technology/Engineering Curriculum Framework (2016), NASA Space Place, the U.S. Geological Survey, NOAA, the U.S. Energy Information Administration, the National Human Genome Research Institute, UC Berkeley's Understanding Evolution, and three Wikipedia articles. Licence: Questions, choices and explanations are original work of this site.
How it works
This middle school math and science MTEL practice test asks 40 questions of our own on field 77, Middle School Mathematics/Science. 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
Eight subareas, half of them math
Number system, algebra, geometry and statistics carry 10%, 12%, 10% and 8% of the score. Technology/engineering, Earth and space science, life science and physical science carry 10% each. The 40 questions follow those weights.
No calculator
The MTEL site says calculators are prohibited, and that formulas and a periodic table are shown on screen. Every calculation here can be worked by hand, and three use a formula from that sheet.
Where the facts come from
Science facts were read on the page named under each question: NASA, the U.S. Geological Survey, NOAA, the Energy Information Administration and the Massachusetts curriculum framework. Each calculated answer was worked out twice.
The two open-response items, one on mathematics and one on science, are written analyses and are not practiced here.
Questions and answers
Is there a free practice test for MTEL 51 Middle School Math and Science?
Field 51 is gone. The MTEL site says the Middle School Mathematics/Science (51) test is retired and that the redeveloped test opened for testing on October 17, 2022. Its test list shows field 77 today, and these free questions are written to it.
How many questions are on the MTEL Middle School Math/Science test?
100 multiple-choice questions and 2 open-response assignments in 4 hours of testing time. The MTEL site adds that some questions may not count toward the score.
What is the passing score for the Middle School Math/Science MTEL?
The MTEL site gives a qualifying score of 240. Multiple-choice questions are 80% of the score and the two open-response items 20%, so a number right here carries no verdict.
What is on the MTEL practice test for middle school math and science?
The eight multiple-choice subareas of the test objectives, 29 objectives in all: four of mathematics, then technology/engineering, Earth and space science, life science and physical science. The topic filter runs one subarea at a time.