Math proficiency test PDF: 50 printable practice questions with answers

Q: Are these the real Ontario MPT test questions?

No. The Education Quality and Accountability Office (EQAO), for the Ontario College of Teachers keeps its question bank private. Every question here is original and written from the The Ontario Curriculum: Mathematics (Grades 1–8, 2020; Grade 9, 2021), the material the real test is based on. Understanding the rules, not memorising answers, is what helps on test day.

Q: How do I save the Ontario MPT questions and answers as a PDF?

Press the print button and choose Save as PDF instead of a printer. Menus, buttons and ads are hidden when you print, and the answer key starts on a new page after question 50.

Q: How many questions are on the printable sheet?

50, chosen from all 9 topics in our bank of 125 questions. For more, use the online practice tests, which show the correct answer and an explanation after every question.

50 original Ontario MPT practice questions on one printable sheet, with a separate answer key, an explanation and the handbook chapter for every answer. Print it or save it as a PDF. Free; not the official test.

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This page puts 50 original practice questions for the Ontario Mathematics Proficiency Test for Teachers (MPT) on one sheet you can print or save as a PDF. They are drawn evenly from our 9 topics (mpt requirement, format and scoring, number: fractions, decimals, percents and ratios, algebra, patterns and coding, data and probability, spatial sense: geometry and measurement, financial literacy, pedagogy: the mathematics curriculum and pedagogy: assessment and evaluation, among others), so one sitting covers the whole test, not just the easy chapters.

The answer key starts on a new page after the last question. Each answer has a short explanation and the chapter of the The Ontario Curriculum: Mathematics (Grades 1–8, 2020; Grade 9, 2021) it comes from, so you can check the rule in the official source instead of memorising our wording. These are not the official test questions: the Education Quality and Accountability Office (EQAO), for the Ontario College of Teachers does not publish its question bank. When the sheet feels easy, sit a timed mock exam of 60 questions (you need 43 correct to pass our mock).

Jump to the answer key

1.A survey about school lunches asks only students in the chess club. What is the main problem?
1. Chess club members cannot answer surveys
2. The sample is not representative of all students
3. The survey has too many questions
4. Lunch is not a suitable survey topic
2.In the Ontario curriculum, how do overall expectations differ from specific expectations?
1. Overall ones are optional, while specific ones are required
2. Overall ones apply only to the Grade 9 math course
3. Specific ones are never assessed or evaluated by teachers
4. Overall ones describe general knowledge; specific ones give the detail
3.Which quadrilateral always has four equal sides but not necessarily four right angles?
1. Rhombus
2. Rectangle
3. Trapezoid
4. Kite
4.What score must applicants reach to pass the MPT?
1. 70% overall, averaged across components
2. 60% on each component over two attempts
3. 50% on the mathematics part only
4. 70% on each component in the same attempt
5.$1,000 is invested at 5% per year, compounded annually. What is it worth after 2 years?
1. $1,100.00
2. $1,105.00
3. $1,050.00
4. $1,102.50
6.A growing pattern has 5, 9, 13, 17 tiles in figures 1 to 4. Which expression gives the tiles in figure n?
1. n + 4
2. 4n + 5
3. 4n + 1
4. 5n
7.Between which two consecutive whole numbers does √50 lie?
1. 5 and 6
2. 24 and 26
3. 7 and 8
4. 6 and 7
8.According to Learning for All, why must learners be appropriately challenged?
1. Only the most advanced students need any challenge
2. Students learn best when every task feels easy
3. New learning should be neither too difficult nor too easy
4. Challenge should be avoided to reduce student stress
9.According to Growing Success, what is the primary purpose of assessment?
1. To decide report card comments only
2. To rank students against each other
3. To improve student learning
4. To fill the gradebook with marks
10.A spinner lands on blue 18 times in 60 spins. What is the experimental probability of blue?
1. 0.3
2. 0.18
3. 0.42
4. 0.6
11.How many strands are in the Ontario Grades 1–8 mathematics curriculum (2020)?
1. Five
2. Six
3. Seven
4. Four
12.A rectangular prism is 5 cm by 4 cm by 3 cm. What is its volume?
1. 60 cm³
2. 94 cm³
3. 47 cm³
4. 12 cm³
13.Since what date has the MPT been a certification requirement for most Ontario College of Teachers applicants?
1. January 1, 2023
2. September 1, 2019
3. February 1, 2025
4. July 1, 2026
14.A $60 sweater is 25% off, and 13% HST is charged on the sale price. What is the total?
1. $45.00
2. $50.85
3. $58.80
4. $52.80
15.Solve 2(x + 4) = 5x − 7.
1. x = 5
2. x = 3.7
3. x = −5
4. x = 1
16.A class of 35 students has 40% who walk to school. How many students walk?
1. 14
2. 21
3. 4
4. 40
17.A teacher notices three students struggling with fractions after whole-class lessons and gives them small-group sessions twice a week. Which tier is this?
1. Tier 3 (clinical)
2. No tier applies
3. Tier 1 (universal)
4. Tier 2 (targeted)
18.How many categories of knowledge and skills are in the achievement chart?
1. Three
2. Four
3. Five
4. Six
19.Which is an example of qualitative data?
1. Favourite season of each student
2. Number of siblings each student has
3. Time to run 100 m in seconds
4. Height of each student in cm
20.Which is an example of a social-emotional learning skill named in the Ontario math curriculum?
1. Memorizing all multiplication tables up to 12
2. Completing worksheets as quickly as possible
3. Working alone without ever asking any questions
4. Recognizing sources of stress and coping with challenges
21.Two angles are supplementary. One measures 128°. What is the other?
1. 232°
2. 128°
3. 52°
4. 62°
22.How soon after the test is the MPT Applicant Report posted?
1. At the end of the school year
2. Within 10 days
3. Within 24 hours
4. Within 3 months
23.In a Grade 3 financial literacy lesson, which item is best classified as a need?
1. Winter boots
2. A second bicycle
3. Concert tickets
4. A video game
24.In the Ontario Grades 1–8 math curriculum (2020), in which strand do coding expectations appear?
1. Financial Literacy
2. Data
3. Algebra
4. Spatial Sense
25.A student says 0.3 × 0.2 = 0.6. What is the correct product, and what error did the student make?
1. 6; the decimal point should be dropped
2. 0.5; the numbers should be added
3. 0.06; the decimal places were not counted
4. 0.6; the answer is already correct
26.In the tiered approach, what does Tier 1 provide?
1. A referral to an outside specialist
2. High-quality instruction for all students
3. Intensive support for a few students only
4. A separate special education class
27.Which level of the achievement chart represents the provincial standard?
1. Level 3
2. Level 2
3. Level 1
4. Level 4
28.On a scatter plot, as hours of practice increase, the number of errors decreases. What relationship is shown?
1. A causal proof
2. A negative correlation
3. A positive correlation
4. No correlation
29.A teacher links a fractions lesson to sharing pizza at home and to music rhythms. Which mathematical process is the focus?
1. Connecting
2. Problem solving
3. Reasoning and proving
4. Reflecting
30.Using the π key, what is the volume of a cylinder with a 4 cm radius and 10 cm height, to the nearest cm³?
1. 503 cm³
2. 1 005 cm³
3. 251 cm³
4. 126 cm³
31.What are the two scored components of the MPT?
1. Mathematics and pedagogy
2. Pedagogy and classroom management
3. Science and mathematics
4. Reading and writing
32.A credit card balance of $2,000 has an annual interest rate of 19.95%. About how much interest is charged for one month if the balance is unpaid?
1. $33.25
2. $19.95
3. $166.67
4. $399.00
33.Simplify the expression 4(x − 3) + 2x.
1. 4x − 12
2. 6x − 3
3. 6x − 12
4. 6x − 7
34.A student claims 1/3 + 1/4 = 2/7. Which model best shows why this is wrong?
1. A hundreds chart that shows only the even numbers
2. A bar graph of the class's favourite fruits
3. A number line showing 1/3 alone is already more than 2/7
4. A tally chart of the class's votes for team names
35.What does "readiness" mean in differentiated instruction?
1. What the student currently knows and can do in this unit
2. Whether the student completed last night's homework
3. The student's general level of intelligence
4. The student's exact age measured in months
36.How many fundamental principles of assessment does Growing Success set out?
1. Three
2. Five
3. Ten
4. Seven
37.Which graph is best for showing how a class's heights are distributed across intervals such as 140–149 cm and 150–159 cm?
1. A circle graph
2. A pictograph of pets
3. A line graph
4. A histogram
38.What does Strand A of the 2020 Ontario math curriculum combine?
1. Number sense and operations with fractions and decimals
2. Data collection and simple probability experiments
3. Social-emotional learning skills and the mathematical processes
4. Geometry and the measurement of three-dimensional objects
39.A right triangle has legs of 9 m and 12 m. How long is the hypotenuse?
1. 21 m
2. 108 m
3. 15 m
4. 10.5 m
40.An internationally educated teacher was certified by the College in 2026. When must the MPT be passed?
1. Before applying to the College
2. Within two years of initial certification
3. Within six months of arriving in Canada
4. Never; the requirement does not apply
41.A student earns $400 a month and plans to save 15%. How much does she save in 6 months?
1. $90
2. $60
3. $2,040
4. $360
42.A pattern repeats red, blue, blue, green. What colour is the 23rd item?
1. Blue
2. Red
3. Green
4. Yellow
43.The temperature is −7 °C at dawn and rises 12 degrees by noon. What is the noon temperature?
1. 5 °C
2. −19 °C
3. 19 °C
4. −5 °C
44.How does differentiated instruction differ from UDL, according to Learning for All?
1. DI replaces the curriculum, while UDL simply follows it
2. DI targets specific needs; UDL gives broad planning principles
3. There is no real difference between the two approaches
4. DI is only for gifted students, and UDL is for all the others
45.Students use success criteria to check their own work and set next steps. Which kind of assessment is this?
1. Assessment of learning
2. Norm-referenced assessment
3. Assessment as learning
4. Diagnostic testing
46.Find the median of the even-sized set 3, 9, 4, 12, 7, 10.
1. 8
2. 7.5
3. 9
4. 7
47.A student chooses between a number line, a calculator and mental math to solve a problem. Which mathematical process is this?
1. Reflecting
2. Connecting
3. Communicating
4. Selecting tools and strategies
48.A 2.4 m board is cut into pieces 30 cm long. How many pieces are there?
1. 0.08
2. 12
3. 8
4. 80
49.Where can the MPT be written?
1. Only at the offices of the Ontario College of Teachers
2. Only at home, with no supervision of any kind
3. Only at a faculty of education, during a class
4. At an approved test centre or online with remote proctoring
50.Which is the better buy: 6 granola bars for $4.20 or 8 bars for $5.20?
1. They cost the same per bar
2. 6 bars, at $0.70 per bar
3. 8 bars, at $0.65 per bar
4. 8 bars, at $0.60 per bar

Answer key with explanations

1. B — The sample is not representative of all students
A sample drawn from one club may not reflect the whole school, which biases the results. A random sample of all students would be more representative.
Data and probability · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 3 Data strand, Data — sampling
2. D — Overall ones describe general knowledge; specific ones give the detail
Overall expectations describe the general knowledge and skills students demonstrate by the end of a grade; specific expectations describe them in greater detail. Both are mandatory, and Growing Success says evaluation focuses on the overall expectations.
Pedagogy: the mathematics curriculum · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 6 Curriculum context, Curriculum context — strands and processes
3. A — Rhombus
A rhombus has four equal sides; its angles need not be 90°. A rectangle has four right angles but not necessarily equal sides; a kite has two pairs of equal adjacent sides.
Spatial sense: geometry and measurement · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 4 Spatial Sense strand, Spatial sense — geometric properties
4. D — 70% on each component in the same attempt
EQAO requires 70% or higher on each component, mathematics and pedagogy, in the same attempt. A high math score cannot make up for a low pedagogy score.
MPT requirement, format and scoring · Based on: EQAO Mathematics Proficiency Test page and FAQ (2026), Ch. 1 Requirement and format, EQAO MPT page (2026)
5. D — $1,102.50
Year 1: 1,000 × 1.05 = $1,050. Year 2: 1,050 × 1.05 = $1,102.50. $1,100 is simple interest, which ignores interest earned on interest.
Financial literacy · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 5 Financial Literacy strand, Financial literacy — compound interest
6. C — 4n + 1
The pattern grows by 4 each time, so it is 4n plus a constant; figure 1 has 4(1) + 1 = 5. 4n + 5 would give 9 for figure 1, and 5n grows by 5.
Algebra, patterns and coding · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 2 Algebra strand, Algebra — patterns
7. C — 7 and 8
7² = 49 and 8² = 64, and 49 < 50 < 64, so √50 is between 7 and 8 (just above 7). 24 and 26 halve 50 instead of taking the square root.
Number: fractions, decimals, percents and ratios · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 1 Number strand, Number — square roots
8. C — New learning should be neither too difficult nor too easy
One of the ideas behind differentiation is that learners need tasks that stretch them without overwhelming them, so they feel safe enough to accept the challenge of new learning.
Pedagogy: learning for all students · Based on: Learning for All, K–12 (Ontario, 2013), Ch. 8 Learning for all, Learning for All
9. C — To improve student learning
Growing Success states that the primary purpose of assessment is to improve student learning. Ontario uses criterion-referenced, not norm-referenced, assessment, so ranking students is not the goal.
Pedagogy: assessment and evaluation · Based on: Growing Success: Assessment, Evaluation and Reporting in Ontario Schools (2010), Ch. 7 Assessment and evaluation, Growing Success, ch. 4
10. A — 0.3
Experimental probability = observed ÷ trials = 18 ÷ 60 = 0.3. As the number of trials grows, it tends to approach the theoretical probability.
Data and probability · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 3 Data strand, Data — experimental probability
11. B — Six
The 2020 curriculum has six strands: A Social-Emotional Learning Skills in Mathematics and the Mathematical Processes, B Number, C Algebra, D Data, E Spatial Sense and F Financial Literacy.
Pedagogy: the mathematics curriculum · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 6 Curriculum context, Curriculum context — strands and processes
12. A — 60 cm³
V = l × w × h = 5 × 4 × 3 = 60 cm³. 94 is the surface area (2(20 + 15 + 12) = 94 cm²).
Spatial sense: geometry and measurement · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 4 Spatial Sense strand, Spatial sense — volume
13. C — February 1, 2025
The Ontario College of Teachers states that, as of February 1, 2025, successfully completing the MPT is a certification requirement for most applicants.
MPT requirement, format and scoring · Based on: EQAO Mathematics Proficiency Test page and FAQ (2026), Ch. 1 Requirement and format, OCT MPT requirement (2026)
14. B — $50.85
Sale price = 0.75 × 60 = $45.00. Total = 45.00 × 1.13 = $50.85. $45.00 forgets the tax, and $52.80 adds and subtracts the percents together (12% off).
Financial literacy · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 5 Financial Literacy strand, Financial literacy — discounts and tax
15. A — x = 5
Expand: 2x + 8 = 5x − 7. Subtract 2x: 8 = 3x − 7. Add 7: 15 = 3x, so x = 5. Check: 2(9) = 18 and 5(5) − 7 = 18.
Algebra, patterns and coding · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 2 Algebra strand, Algebra — equations
16. A — 14
40% of 35 = 0.4 × 35 = 14 (10% is 3.5, so 40% is 4 × 3.5). 21 is the 60% who do not walk.
Number: fractions, decimals, percents and ratios · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 1 Number strand, Number — percent
17. D — Tier 2 (targeted)
Extra small-group support for some students, beyond good whole-class teaching, is targeted Tier 2 support. Tier 3 is more intensive and may involve specialists.
Pedagogy: learning for all students · Based on: Learning for All, K–12 (Ontario, 2013), Ch. 8 Learning for all, Learning for All
18. B — Four
The achievement chart has four categories: Knowledge and Understanding, Thinking, Communication, and Application.
Pedagogy: assessment and evaluation · Based on: Growing Success: Assessment, Evaluation and Reporting in Ontario Schools (2010), Ch. 7 Assessment and evaluation, Growing Success, ch. 3
19. A — Favourite season of each student
Qualitative (categorical) data describe qualities, such as a favourite season. Heights, counts and times are quantitative data.
Data and probability · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 3 Data strand, Data — data types
20. D — Recognizing sources of stress and coping with challenges
The curriculum's SEL skills include identifying and managing emotions, recognizing sources of stress and coping with challenges, maintaining positive motivation and perseverance, building relationships, developing self-awareness, and thinking critically and creatively.
Pedagogy: the mathematics curriculum · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 6 Curriculum context, Curriculum context — strands and processes
21. C — 52°
Supplementary angles add to 180°: 180 − 128 = 52°. 62° is a subtraction slip, 128° repeats the given angle, and 232° adds instead of subtracting.
Spatial sense: geometry and measurement · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 4 Spatial Sense strand, Spatial sense — angles
22. B — Within 10 days
EQAO posts an Applicant Report, marked Successful or Not Yet Successful, to the applicant's MPT account within 10 days, and sends an email notice.
MPT requirement, format and scoring · Based on: EQAO Mathematics Proficiency Test page and FAQ (2026), Ch. 1 Requirement and format, EQAO MPT page (2026)
23. A — Winter boots
Needs are things required for health and safety, such as winter boots in a Canadian winter. The other items are wants that are nice to have.
Financial literacy · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 5 Financial Literacy strand, Financial literacy — needs and wants
24. C — Algebra
The Ministry describes coding as part of the Algebra strand, where students explore and work with code starting in Grade 1. Data, Spatial Sense and Financial Literacy are separate strands.
Algebra, patterns and coding · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 2 Algebra strand, Algebra — coding
25. C — 0.06; the decimal places were not counted
3 × 2 = 6, and the factors have two decimal places in total, so the product is 0.06. The student kept only one decimal place. Area models (0.3 of 0.2 of a square) show why the product is smaller than both factors.
Number: fractions, decimals, percents and ratios · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 1 Number strand, Number — decimals
26. B — High-quality instruction for all students
Tier 1 is universal: good instruction and assessment for the whole class. Tier 2 adds targeted support for some students, and Tier 3 provides more intensive, individualized support.
Pedagogy: learning for all students · Based on: Learning for All, K–12 (Ontario, 2013), Ch. 8 Learning for all, Learning for All
27. A — Level 3
Level 3 is the provincial standard: the student shows the knowledge and skills with considerable effectiveness. Level 4 surpasses it, level 2 approaches it and level 1 is much below.
Pedagogy: assessment and evaluation · Based on: Growing Success: Assessment, Evaluation and Reporting in Ontario Schools (2010), Ch. 7 Assessment and evaluation, Growing Success, ch. 3
28. B — A negative correlation
When one variable increases as the other decreases, the points trend downward: a negative correlation. A correlation alone does not prove cause.
Data and probability · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 3 Data strand, Data — scatter plots
29. A — Connecting
Connecting means relating mathematical ideas to each other, to other subjects and to students' lives. The other processes focus on justifying, looking back or solving.
Pedagogy: the mathematics curriculum · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 6 Curriculum context, Curriculum context — strands and processes
30. A — 503 cm³
V = πr²h = π × 16 × 10 ≈ 502.65, so about 503 cm³. 126 uses r instead of r², 251 is half the volume, and 1 005 doubles it.
Spatial sense: geometry and measurement · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 4 Spatial Sense strand, Spatial sense — volume
31. A — Mathematics and pedagogy
The MPT has a mathematics component (Grades 3 to 9 content) and a pedagogy component (curriculum, assessment and evaluation, and learning for all). An optional questionnaire is not scored.
MPT requirement, format and scoring · Based on: EQAO Mathematics Proficiency Test page and FAQ (2026), Ch. 1 Requirement and format, EQAO MPT page (2026)
32. A — $33.25
Monthly rate ≈ 19.95% ÷ 12 ≈ 1.6625%. Interest ≈ 2,000 × 0.199 5 ÷ 12 = $33.25. $399 is a full year, and $166.67 is 2,000 ÷ 12.
Financial literacy · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 5 Financial Literacy strand, Financial literacy — credit
33. C — 6x − 12
Distribute: 4x − 12, then collect like terms: 4x + 2x = 6x, giving 6x − 12. 6x − 3 forgets to multiply 3 by 4.
Algebra, patterns and coding · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 2 Algebra strand, Algebra — simplifying
34. C — A number line showing 1/3 alone is already more than 2/7
On a number line 1/3 ≈ 0.33 is already greater than 2/7 ≈ 0.29, so adding 1/4 cannot give 2/7. The other models do not represent fraction size.
Number: fractions, decimals, percents and ratios · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 1 Number strand, Number — fractions
35. A — What the student currently knows and can do in this unit
Learning for All explains that readiness is not general ability but the student's current knowledge, understanding and skill in relation to a particular sequence of learning.
Pedagogy: learning for all students · Based on: Learning for All, K–12 (Ontario, 2013), Ch. 8 Learning for all, Learning for All
36. D — Seven
Growing Success is built on seven fundamental principles, such as being fair, transparent and equitable, being ongoing and varied, and developing students' self-assessment skills.
Pedagogy: assessment and evaluation · Based on: Growing Success: Assessment, Evaluation and Reporting in Ontario Schools (2010), Ch. 7 Assessment and evaluation, Growing Success, ch. 1
37. D — A histogram
A histogram shows the frequency of continuous data grouped into intervals. Circle graphs show parts of a whole, and line graphs show change over time.
Data and probability · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 3 Data strand, Data — graphs
38. C — Social-emotional learning skills and the mathematical processes
Strand A pairs social-emotional learning (SEL) skills with the mathematical processes. It is taught and assessed in the context of the other five strands, not in isolation.
Pedagogy: the mathematics curriculum · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 6 Curriculum context, Curriculum context — strands and processes
39. C — 15 m
c² = 9² + 12² = 81 + 144 = 225, so c = 15 m. 21 adds the legs, a common error when students skip squaring.
Spatial sense: geometry and measurement · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 4 Spatial Sense strand, Spatial sense — Pythagorean relationship
40. B — Within two years of initial certification
The College says internationally educated teachers certified after the requirement began must pass the MPT within two years of their initial certification, or the certificate expires.
MPT requirement, format and scoring · Based on: EQAO Mathematics Proficiency Test page and FAQ (2026), Ch. 1 Requirement and format, OCT MPT requirement (2026)
41. D — $360
Monthly savings = 0.15 × 400 = $60; over 6 months: 60 × 6 = $360. $60 is one month only, and $2,040 is what she spends.
Financial literacy · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 5 Financial Literacy strand, Financial literacy — budgeting
42. A — Blue
The core has 4 items. 23 ÷ 4 = 5 remainder 3, so item 23 matches the 3rd item of the core: blue.
Algebra, patterns and coding · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 2 Algebra strand, Algebra — patterns
43. A — 5 °C
Start at −7 and move 12 up the number line: −7 + 12 = 5 °C. −19 moves the wrong way, and −5 reverses the sign of the result.
Number: fractions, decimals, percents and ratios · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 1 Number strand, Number — integers
44. B — DI targets specific needs; UDL gives broad planning principles
Learning for All says UDL provides broad principles for planning for a diverse group, while differentiated instruction lets teachers address specific skills and difficulties. The approaches overlap and work together.
Pedagogy: learning for all students · Based on: Learning for All, K–12 (Ontario, 2013), Ch. 8 Learning for all, Learning for All
45. C — Assessment as learning
Assessment as learning develops students' capacity to monitor their own progress, set goals and reflect, often through self- and peer assessment. Assessment of learning is evaluation for reporting.
Pedagogy: assessment and evaluation · Based on: Growing Success: Assessment, Evaluation and Reporting in Ontario Schools (2010), Ch. 7 Assessment and evaluation, Growing Success, ch. 4
46. A — 8
Order the data: 3, 4, 7, 9, 10, 12. With 6 values the median is the mean of the two middle values: (7 + 9) ÷ 2 = 8.
Data and probability · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 3 Data strand, Data — median
47. D — Selecting tools and strategies
Deciding which tool or strategy fits a problem is the process of selecting tools and strategies. Reflecting is thinking back on one's work, connecting links ideas, and communicating shares thinking.
Pedagogy: the mathematics curriculum · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 6 Curriculum context, Curriculum context — strands and processes
48. C — 8
Convert to the same unit: 2.4 m = 240 cm. 240 ÷ 30 = 8 pieces. 80 converts with an extra zero.
Spatial sense: geometry and measurement · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 4 Spatial Sense strand, Spatial sense — measurement
49. D — At an approved test centre or online with remote proctoring
EQAO offers sessions in person at approved test centres and online with remote proctoring, booked through the official MPT website.
MPT requirement, format and scoring · Based on: EQAO Mathematics Proficiency Test page and FAQ (2026), Ch. 1 Requirement and format, EQAO MPT page (2026)
50. C — 8 bars, at $0.65 per bar
Unit prices: 4.20 ÷ 6 = $0.70 and 5.20 ÷ 8 = $0.65. The lower unit price, $0.65, makes the 8-bar box the better buy.
Financial literacy · Based on: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 5 Financial Literacy strand, Financial literacy — unit price

Original practice questions by Canada Exam Prep, written from the official handbook. Not official test questions. Free to print for personal study.

FAQ

Ontario MPT questions and answers (printable): common questions

Are these the real Ontario MPT test questions?

No. The Education Quality and Accountability Office (EQAO), for the Ontario College of Teachers keeps its question bank private. Every question here is original and written from the The Ontario Curriculum: Mathematics (Grades 1–8, 2020; Grade 9, 2021), the material the real test is based on. Understanding the rules, not memorising answers, is what helps on test day.

How do I save the Ontario MPT questions and answers as a PDF?

Press the print button and choose Save as PDF instead of a printer. Menus, buttons and ads are hidden when you print, and the answer key starts on a new page after question 50.

How many questions are on the printable sheet?

50, chosen from all 9 topics in our bank of 125 questions. For more, use the online practice tests, which show the correct answer and an explanation after every question.

Math proficiency test PDF: 50 printable practice questions with answers