This is a free EQAO Grade 9 math practice test: 25 questions drawn from Winny Math's MTH1W practice bank, five from each of the course's five strands, ordered from easy to hard within each strand. Every question has a worked solution you can open after you try it. There is no sign-up, no email wall and no timer. Print it, work through it with a calculator, then use the strand checklist below to see where your prep time should go.
What the real assessment looks like
The EQAO Grade 9 Assessment of Mathematics is written online, near the end of the MTH1W course, in two sessions that EQAO calls stages. Together the two stages hold about 54 questions, most of them multiple choice or short numeric answers, plus a short student questionnaire. The questions draw on all five strands of the Ontario MTH1W curriculum, and the assessment counts toward the course mark. Since the 2025 to 2026 school year it is worth at least 10% and up to 30% of the final grade, with each school setting the share. Our EQAO Grade 9 math guide covers the scoring levels and the timing in detail.
This page does not copy the digital format. It gives you the math. Do EQAO's official sample test on a computer as well, so the on-screen tools are not a surprise on the day.
Show the worked solution and mark yourself. Each question is labelled with its strand and a level from 1 (easy) to 5 (hard) so you can see whether your mistakes are careless slips on easy questions or real gaps on the hard ones.
Strand checklist
After marking, tick the strands where you got at least four of five right. Anything left unticked is where the next two weeks of practice should go.
- Number (questions 1 to 5): powers, fractions, rates, order of operations and percent problems.
- Algebra (questions 6 to 10): intercepts, solving equations with variables on both sides, rate of change, slope and modelling with equations.
- Data (questions 11 to 15): mean, median, the effect of an outlier and using a linear model to answer a question.
- Geometry and Measurement (questions 16 to 20): unit conversion, similar triangles, composite areas and composite volumes.
- Financial Literacy (questions 21 to 25): compound interest, currency exchange, simple versus compound growth and a pay-off-or-invest decision.
Number (questions 1 to 5)
Powers, fractions, proportional reasoning and percent.
Evaluate (−2)⁴.
Show the worked solution
The bracket means the whole of −2 is raised to the fourth power, so multiply four factors of −2: (−2) × (−2) × (−2) × (−2). Two negatives make a positive, so the first pair gives 4 and the second pair gives 4, and 4 × 4 = 16. An even exponent on a negative base always gives a positive answer. Answer: 16.
Add 1/3 + 1/4.
Show the worked solution
Fractions need a common denominator before they can be added. The lowest common multiple of 3 and 4 is 12, so rewrite each fraction: 1/3 = 4/12 and 1/4 = 3/12. Add the numerators and keep the denominator: 4/12 + 3/12 = 7/12. It cannot be simplified further. Answer: 7/12.
A factory produces 360 units in 4 hours. At this rate, how many hours will it take to produce 900 units?
Show the worked solution
Find the unit rate first: 360 ÷ 4 = 90 units per hour. Then divide the target by the rate: 900 ÷ 90 = 10. You can check with a proportion, 360/4 = 900/t, which gives 360t = 3600 and t = 10. Answer: 10 hours.
Evaluate (1/2 + 1/3) × 2/5.
Show the worked solution
Brackets first. 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Now multiply by 2/5: multiply numerators and denominators, (5 × 2)/(6 × 5) = 10/30, and simplify by dividing top and bottom by 10 to get 1/3. A shortcut is to cancel the 5s before multiplying. Answer: 1/3.
Find the original price of an item that costs $84 after a 30% discount.
Show the worked solution
A 30% discount leaves 70% of the original price, so the sale price is 0.70 × original. Set up the equation 0.70 × original = 84 and divide both sides by 0.70: original = 84 ÷ 0.70 = 120. Check: 30% of $120 is $36, and $120 − $36 = $84. The common mistake is to add 30% of $84 back on, which gives $109.20 and is wrong. Answer: $120.
Algebra (questions 6 to 10)
Intercepts, equations, rate of change, slope and modelling.
Find the x-intercept of y = 3x − 12.
Show the worked solution
The x-intercept is where the line crosses the x-axis, which is where y = 0. Substitute y = 0: 0 = 3x − 12. Add 12 to both sides to get 12 = 3x, then divide by 3: x = 4. The line crosses the x-axis at the point (4, 0). Answer: x = 4.
Solve: 7x + 2 = 4x + 20.
Show the worked solution
Collect the x terms on one side and the numbers on the other. Subtract 4x from both sides: 3x + 2 = 20. Subtract 2 from both sides: 3x = 18. Divide by 3: x = 6. Check by substituting back: 7(6) + 2 = 44 and 4(6) + 20 = 44, so both sides agree. Answer: x = 6.
A graph shows a line with y-intercept 3, passing through the point (4, 15). Find the rate of change.
Show the worked solution
The y-intercept 3 means the line passes through (0, 3). Rate of change is the change in y divided by the change in x between two points on the line: (15 − 3) ÷ (4 − 0) = 12 ÷ 4 = 3. So y rises by 3 for every 1 unit increase in x, and the equation of the line is y = 3x + 3. Answer: 3.
Find the slope of the line through (−3, 4) and (2, −6).
Show the worked solution
Slope is rise over run: (y₂ − y₁) ÷ (x₂ − x₁). Take (−3, 4) as the first point and (2, −6) as the second. Rise: −6 − 4 = −10. Run: 2 − (−3) = 2 + 3 = 5. Slope = −10 ÷ 5 = −2. The line falls 2 units for every 1 unit to the right. The common slip is the double negative in the run; subtracting −3 means adding 3. Answer: −2.
A gym offers Plan A: $15 per month plus a $40 sign-up fee, and Plan B: $25 per month with no fee. After how many months will both plans cost the same total?
Show the worked solution
Let m be the number of months. Plan A costs 40 + 15m and Plan B costs 25m. Set them equal: 40 + 15m = 25m. Subtract 15m from both sides: 40 = 10m, so m = 4. Check: after 4 months Plan A is 40 + 60 = $100 and Plan B is 4 × 25 = $100. Before 4 months Plan B is cheaper; after 4 months Plan A is cheaper. Answer: 4 months.
Data (questions 11 to 15)
Measures of central tendency and using a model to answer a question.
Find the mean of this data set: 4, 6, 8, 10, 12.
Show the worked solution
The mean is the sum of the values divided by how many values there are. Sum: 4 + 6 + 8 + 10 + 12 = 40. There are 5 values, so 40 ÷ 5 = 8. For a set that increases by the same step each time, the mean is also the middle value, which is a quick check. Answer: 8.
Find the median of this data set: 2, 5, 5, 8, 10, 14.
Show the worked solution
The data is already in order. With 6 values there is no single middle value, so the median is the average of the two middle ones, the 3rd and 4th: 5 and 8. (5 + 8) ÷ 2 = 13 ÷ 2 = 6.5. The median does not have to be one of the data values. Answer: 6.5.
Calculate the mean of this data set: 8, 9, 10, 11, 65. Then explain in one sentence why the mean is a poor summary here.
Show the worked solution
Sum: 8 + 9 + 10 + 11 + 65 = 103. Divide by 5: 103 ÷ 5 = 20.6. The mean is 20.6, yet four of the five values are between 8 and 11. The single outlier, 65, pulls the mean far above the typical value, so the median (10) describes this set better. EQAO likes this reasoning: say which measure fits and why. Answer: 20.6, and the outlier 65 distorts it.
A membership is modelled by C = 30m + 60, where C is the total cost in dollars after m months. Find how many months until the total cost reaches $270.
Show the worked solution
Substitute C = 270 and solve for m: 270 = 30m + 60. Subtract 60 from both sides: 210 = 30m. Divide by 30: m = 7. In context, the 60 is the one-time starting cost (the initial value) and the 30 is the monthly charge (the rate of change), so after 7 months the total is 60 + 7 × 30 = 270. Answer: 7 months.
Two phone plans are compared. Plan A costs $20 per month with no fee. Plan B costs a $50 sign-up fee plus $12 per month. After how many months do the two plans cost the same?
Show the worked solution
Write a model for each plan with m months. Plan A: C = 20m. Plan B: C = 12m + 50. Set them equal: 20m = 12m + 50. Subtract 12m: 8m = 50. Divide by 8: m = 6.25. Both plans cost $125 at that point. Since you pay by the month, interpret the answer: Plan A is cheaper for the first 6 months, and from month 7 on Plan B is cheaper. Answer: 6.25 months.
Geometry and Measurement (questions 16 to 20)
Conversions, similar triangles, composite areas and volumes. Use π ≈ 3.14.
Convert 20 miles to kilometres (1 mile ≈ 1.609 km).
Show the worked solution
Multiply the number of miles by the number of kilometres in one mile: 20 × 1.609 = 32.18. A quick sense check: a kilometre is shorter than a mile, so the number of kilometres must be bigger than the number of miles, and 32 is bigger than 20. Answer: about 32.18 km.
A tree casts a 15 m shadow. At the same time, a 2 m tall person casts a 3 m shadow. Find the height of the tree.
Show the worked solution
The sun makes the same angle for both, so the person and their shadow form a triangle similar to the tree and its shadow. Corresponding sides are in the same ratio: height ÷ shadow = 2 ÷ 3. For the tree, height ÷ 15 = 2 ÷ 3, so height = 15 × 2 ÷ 3 = 10. Answer: 10 m.
Find the area of a composite shape made of a triangle (base 6 cm, height 4 cm) sitting on top of a rectangle (6 cm by 5 cm) that shares the triangle's base.
Show the worked solution
Split the shape into its two pieces and add. Triangle: ½ × base × height = ½ × 6 × 4 = 12 cm². Rectangle: 6 × 5 = 30 cm². Total area = 12 + 30 = 42 cm². Sketching the shape and labelling each piece before calculating is what stops the base from being counted twice. Answer: 42 cm².
Find the area of a composite shape made of a 10 cm by 6 cm rectangle with a semicircle (radius 3 cm) attached to one of the 6 cm sides. Use π ≈ 3.14.
Show the worked solution
Rectangle: 10 × 6 = 60 cm². The semicircle's diameter is the 6 cm side, so its radius is 3 cm. A full circle would be π × 3² = 3.14 × 9 = 28.26 cm², and half of that is 14.13 cm². Total area = 60 + 14.13 = 74.13 cm². Answer: about 74.13 cm².
A silo is a cylinder (radius 2 m, height 8 m) with a cone on top (same radius, height 3 m). Find the total volume. Use π ≈ 3.14.
Show the worked solution
Cylinder: V = πr²h = 3.14 × 2² × 8 = 3.14 × 4 × 8 = 100.48 m³. Cone: V = ⅓πr²h = ⅓ × 3.14 × 4 × 3 = 12.56 m³. Total volume = 100.48 + 12.56 = 113.04 m³. The one-third factor on the cone is the mark most often lost here. Answer: about 113.04 m³.
Financial Literacy (questions 21 to 25)
Interest, exchange rates and a real money decision.
You invest $1000 at 4% annual compound interest. Find the amount after 1 year.
Show the worked solution
Growing by 4% means multiplying by 1.04 (100% of the original plus 4% more). $1000 × 1.04 = $1040. Equivalently, the interest is 4% of $1000, which is $40, and $1000 + $40 = $1040. After one year, simple and compound interest give the same amount; they only differ from the second year on. Answer: $1040.
If the exchange rate is 1 CAD = 0.74 USD, how many US dollars do you get for 500 CAD?
Show the worked solution
Each Canadian dollar buys 0.74 US dollars, so multiply: 500 × 0.74 = 370. Sense check: the US dollar is worth more here, so you should end up with fewer US dollars than Canadian dollars, and 370 is less than 500. To convert the other way you would divide by 0.74. Answer: $370 USD.
Compare $2500 at 3% simple interest with $2500 at 3% compound interest, both for 3 years. Which earns more, and by how much?
Show the worked solution
Simple interest: I = Prt = 2500 × 0.03 × 3 = $225, so the total is $2725. Compound interest: A = P(1 + r)ᵗ = 2500 × 1.03³ = 2500 × 1.092727 ≈ $2731.82. Compound earns 2731.82 − 2725 = $6.82 more, because from year two the interest itself earns interest. The gap is small over 3 years and grows quickly over longer periods. Answer: compound, by about $6.82.
Find the future value of $2500 invested at 4% annual compound interest for 5 years.
Show the worked solution
Use A = P(1 + r)ᵗ with P = 2500, r = 0.04 and t = 5: A = 2500 × 1.04⁵. Work out 1.04⁵ ≈ 1.21665, then 2500 × 1.21665 ≈ 3041.63. The investment earns about $541.63 in interest over the 5 years. Keep the full decimal in your calculator until the last step so the rounding does not drift. Answer: about $3041.63.
You have $8000. You can either pay off a loan that charges 7% annual compound interest, or invest the money at an expected 5% annual compound return. Over 2 years, which option leaves you better off, and by how much?
Show the worked solution
Compare the two-year growth of each. Loan interest avoided: 8000 × (1.07² − 1) = 8000 × 0.1449 = $1159.20. Investment return: 8000 × (1.05² − 1) = 8000 × 0.1025 = $820. The loan would cost more than the investment would earn, so paying off the loan is the better choice, by 1159.20 − 820 = $339.20. The general rule: pay off debt first whenever its rate is higher than the return you can expect. Answer: pay off the loan, about $339 better.
What to do with your result
Count the strands where you missed two or more questions. Those are the strands to practise, and the free sets on Winny Math Learn are built for exactly that: every MTH1W skill has its own page with worked, step-by-step solutions and no account needed. Start with solving multi-step equations with brackets, slope from two points, adding and subtracting fractions and composite areas, or browse the full list on the Grade 9 math practice page. Our Grade 9 exam prep guide lays out a week-by-week plan for the January sitting, and the MTH1W tutoring page explains how a weekly lesson runs.
Missed a strand? Fix it before the test.
Book a free 30-minute trial. Bring your marked practice test and a tutor who took MTH1W recently will build the first lesson around the questions you missed. Solo lessons are $40 per hour, small groups $25 per student per hour. No commitment.
Book a free trial classFrequently asked questions
How many questions are on the EQAO Grade 9 math assessment?
The assessment is written online in two sessions, called stages, and has about 54 questions in total, most of them multiple choice or short answer. The exact count and the session timing can change from year to year, so check the current details on eqao.com and ask your teacher how the two sessions are scheduled at your school.
Does the EQAO Grade 9 math assessment count toward the MTH1W mark?
Yes. Since the 2025 to 2026 school year the EQAO result counts for at least 10% and up to 30% of the final MTH1W course mark, with each school setting the exact share. Ask your teacher what it is worth at your school, because that number decides how much prep time the assessment deserves.
How should I use this practice test?
Work through the 25 questions on paper with a calculator, in one sitting if you can, before opening any solution. Then open each solution and sort your mistakes by strand. The two strands with the most errors are where your prep time should go. Pair this page with EQAO's official sample test so the online tools feel familiar on the day.
Is this the real EQAO test?
No. These are tutor-written questions from Winny Math's MTH1W practice bank, chosen to match the five strands and the mix of difficulty the assessment draws from. EQAO publishes its own sample test and released questions on eqao.com, and those are the only official practice materials.
Can I get this practice test as a PDF?
Yes. Send a request through the Winny Math contact page and we will email you a printable PDF of the 25 questions with the solutions on separate pages, free, with no obligation to book a lesson.