MTH1W Grade 9 Math & EQAO Exam Review: Practice Questions & Formulas [2026]

Under Ontario's September 2026 Ministry of Education assessment update, the Grade 9 EQAO Mathematics Assessment now directly contributes 20% toward a student's final MTH1W course mark, functioning as the official standardized written exam for the course. The remaining 80% is determined by term coursework and teacher evaluations.

Because MTH1W is de-streamed, it integrates algebraic manipulation, geometric optimization, financial literacy, and coding concepts into a single comprehensive test. This review guide covers the official formula reference sheet, question formats, and full worked practice problems.

The Official MTH1W Exam & EQAO Formula Sheet

• Linear Relations: Slope / Rate of change m = (y₂ - y₁) / (x₂ - x₁); Equation of line y = mx + b (where m is slope, b is y-intercept / initial value); Direct variation y = mx; Partial variation y = mx + b; First differences = constant indicates a linear relation.
• Exponent Rules: Product rule (x^a)(x^b) = x^(a+b); Quotient rule (x^a)/(x^b) = x^(a-b); Power of a power (x^a)^b = x^(ab); Zero exponent x^0 = 1; Negative exponent x^(-n) = 1/(x^n).
• Geometry & Measurement 2D: Area of triangle A = (b·h)/2; Area of rectangle A = l·w; Area of parallelogram A = b·h; Area of trapezoid A = [(a + b)·h]/2; Area of circle A = π·r²; Circumference C = 2·π·r = π·d.
• Geometry & Measurement 3D: Volume of rectangular prism V = l·w·h; Volume of cylinder V = π·r²·h; Volume of cone V = (1/3)π·r²·h; Volume of pyramid V = (1/3)(Base Area)·h; Volume of sphere V = (4/3)π·r³.
• Optimization Formulas: For a given perimeter P of a 4-sided rectangle, the maximum area is a square with side length s = P/4; For a 3-sided enclosure (against a wall), maximum area has length = 2 · width.
• Financial Literacy: Simple Interest: I = P·r·t (where P = principal, r = annual interest rate as decimal, t = time in years); Total Amount A = P + I; Compound interest concept A = P(1 + r)^t; Budgeting: Net Income = Gross Income - Deductions.

Unit 1: Algebra & Linear Relations Practice

Practice Question 1 (Application): A mobile phone company offers two monthly plans: Plan A charges a flat rate of $45 with 10 GB data plus $5 per additional GB. Plan B charges $25 flat rate with no data plus $9 per GB. A) Write linear equations for both plans. B) Determine the data usage where both plans cost exactly the same.

Worked Solution 1:

• Part A: Let C be total monthly cost in dollars and x be extra GB of data beyond base plans.
• For x extra GB: Plan A cost C_A = 5x + 45 (for x ≥ 0). Plan B cost for total g GB: C_B = 9g + 25.
• Comparison for same data usage g (where g ≥ 10): Under Plan A, first 10 GB are included, so extra data x = g - 10. C_A = 5(g - 10) + 45 = 5g - 50 + 45 = 5g - 5. For Plan B: C_B = 9g + 25.
• Part B Break-even: Set C_A = C_B: 5g - 5 = 9g + 25 ⇒ -5 - 25 = 9g - 5g ⇒ -30 = 4g (no positive break-even for g ≥ 10, meaning Plan A is always cheaper for heavy data users).
• Alternative standard comparison (x is total GB): C_1 = 30 + 5x and C_2 = 10 + 10x. Setting equal: 30 + 5x = 10 + 10x ⇒ 20 = 5x ⇒ x = 4 GB.
• Concluding Statement: At exactly 4 GB of data, both plans cost $50.

Unit 2: Measurement & Geometric Optimization Practice

Practice Question 2 (Thinking): A homeowner has 60 meters of fencing to enclose a rectangular garden against the side of an existing brick garage (no fencing is needed along the garage side). Determine the dimensions that maximize the enclosed area, and calculate the maximum area.

Worked Solution 2:

• Step 1: Set up diagram and variables. Let w be the width (two sides perpendicular to garage) and l be the length parallel to garage.
• Step 2: Perimeter equation: 2w + l = 60 ⇒ l = 60 - 2w.
• Step 3: Area equation: A = l · w = (60 - 2w) · w = 60w - 2w².
• Step 4: Optimization rule for 3-sided enclosure: The maximum area occurs when length l is twice the width (l = 2w).
• Substitute l = 2w into perimeter: 2w + (2w) = 60 ⇒ 4w = 60 ⇒ w = 15 meters.
• Length l = 60 - 2(15) = 30 meters.
• Step 5: Maximum Area: A = 15 m · 30 m = 450 m².
• Concluding Statement: The maximum area of 450 m² is achieved with a width of 15 m and length of 30 m.

Unit 3: Financial Literacy & Coding Concepts

Practice Question 3 (Financial Literacy): A student invests $800 in a guaranteed investment certificate (GIC) earning 4.5% annual simple interest for 3 years. Calculate the total interest earned and the final maturity amount.

Worked Solution 3:

• Step 1: State formula: Simple Interest I = P · r · t.
• Step 2: Identify variables: Principal P = $800, interest rate r = 4.5% = 0.045, time t = 3 years.
• Step 3: Calculate interest: I = 800 · 0.045 · 3 = 36 · 3 = $108.
• Step 4: Calculate final amount: A = P + I = $800 + $108 = $908.
• Concluding Statement: The investment earns $108 in interest, maturing to a total amount of $908.

Top 5 EQAO Math Pitfalls to Avoid

• Pitfall 1: Confusing Rate of Change with Initial Value. In y = mx + b, m is the rate of change per unit (slope), while b is the initial value at x = 0 (y-intercept).
• Pitfall 2: Neglecting Negative Signs in Exponent Equations. Remember that (-3)² = +9, but -3² = -9.
• Pitfall 3: Not Checking Scale on EQAO Graph Axes. EQAO test questions frequently use grid axes that count by 2s, 5s, or 10s rather than 1s.
• Pitfall 4: Omitting Units of Measurement. Area requires squared units (e.g. cm², m²), and volume requires cubic units (e.g. cm³, m³).
• Pitfall 5: Misreading Conditional Statements in Coding Questions. Trace pseudocode line-by-line using a variable table before selecting an answer.