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Ontario Grade 9 Math MTH1W review and practice
Review Ontario Grade 9 Mathematics (MTH1W) with a topic checklist, original diagnostic questions, worked answers, and a seven-day study plan.
MTH1W study guide
What to review for Ontario Grade 9 Mathematics
Use this checklist to find your weakest area before repeating questions you already know.
Number sets, exponents, scientific notation, fractions, ratios, rates, percentages, and proportional reasoning.
Expressions, like terms, the distributive property, equations, variables, loops, and tracing code.
Tables, graphs, rates of change, initial values, and comparing linear with non-linear relationships.
Collecting and displaying data, evaluating graphs, modelling questions, assumptions, and interpreting results.
Measurement conversions, Pythagorean relationships, area, surface area, volume, and effects of changing dimensions.
Budgets, appreciation, depreciation, borrowing costs, and comparing financial choices.
Eight-question MTH1W diagnostic
Try each question without opening the answer. Write down the topic for every question you miss; that topic becomes part of your study plan.
Classify −7, 0.25, and √5 as integer, rational, irrational, or real. Include every set that applies.
Show answer
−7 is an integer, rational number, and real number. 0.25 = 1/4, so it is rational and real. √5 is irrational and real.
Simplify (3x²)(2x³).
Show answer
Multiply the coefficients and add exponents with the same base: 3 × 2 = 6 and x² × x³ = x⁵. The result is 6x⁵.
A jacket costs CAD 80 and is discounted by 25%. What is the sale price before tax?
Show answer
The discount is 0.25 × 80 = CAD 20. Subtract it from the original price: 80 − 20 = CAD 60.
Simplify 3(2x − 4) + 5x.
Show answer
Distribute first: 6x − 12 + 5x. Combine like terms to get 11x − 12.
A table contains the points (1, 5), (2, 8), and (3, 11). Find the constant rate of change and the equation.
Show answer
The output increases by 3 when the input increases by 1, so the rate is 3. Using y = 3x + b and the point (1, 5), b = 2. The equation is y = 3x + 2.
A graph comparing two test scores starts its vertical axis at 78 instead of 0. What misleading impression might this create?
Show answer
The visual difference between the scores can look much larger than the actual numerical difference. Always inspect the scale before interpreting a graph.
A right triangle has legs of 6 cm and 8 cm. Find the hypotenuse.
Show answer
Use the Pythagorean relationship: c² = 6² + 8² = 36 + 64 = 100, so c = 10 cm.
A CAD 1,200 laptop loses 15% of its value in one year. What is its value after that year?
Show answer
The loss is 0.15 × 1,200 = CAD 180. Its new value is 1,200 − 180 = CAD 1,020.
Turn your diagnostic into a study plan
Review the questions you missed, then practise mixed problems under a time limit.
Choose two weak topics. Read one lesson and complete several questions for each before trying the diagnostic again.
Start with prerequisite skills and work one topic at a time. Focus on explaining each step rather than memorizing answers.
A seven-day MTH1W review schedule
- Day 1: number sets, fractions, rates, and percentages.
- Day 2: exponents and scientific notation.
- Day 3: expressions, equations, and coding.
- Day 4: tables, graphs, and linear relations.
- Day 5: data literacy and mathematical modelling.
- Day 6: geometry, measurement, and financial literacy.
- Day 7: mixed practice, corrections, and a second diagnostic attempt.
Continue with free curriculum-aligned lessons
Browse the complete MTH1W learning path
Open the exact expectation you need, read its lesson, then use targeted practice or AI Blackboard when you need another explanation.
MTH1W review questions students ask
What is MTH1W?
MTH1W is Ontario’s de-streamed Grade 9 Mathematics course. It includes number, algebra, coding, linear relations, data, geometry, measurement, mathematical modelling, and financial literacy.
How should I study for an MTH1W test or exam?
Begin with a mixed diagnostic, identify the topics behind your mistakes, review those lessons, and then solve new questions without looking at examples. Finish by correcting every error in writing.
Is this MTH1W review free?
Yes. This review page and published curriculum lessons are free to read. Optional AI tools and live tutoring are available when you want additional support.
Is DoAssignment an official Ontario curriculum website?
No. DoAssignment is an independent study resource aligned to Ontario curriculum expectations. Students should follow instructions and assessment requirements from their school and teacher.