EQAO Grade 9 Mathematics Assessment 3 — Questions and Answers
Question 1: The hypotenuse of a right triangle is 13 cm and one leg is 5 cm. What is the length of the other leg?
- 8 cm
- 12 cm (Correct answer)
- 10 cm
- 11 cm
Correct answer: 12 cm
Using the Pythagorean theorem: 5² + b² = 13², so 25 + b² = 169, giving b = 12 cm.
Question 2: Which of the following is a correct first step to solve 2x + 5 = 13?
- Divide both sides by 2
- Subtract 5 from both sides (Correct answer)
- Add 5 to both sides
- Multiply both sides by 2
Correct answer: Subtract 5 from both sides
Subtracting 5 from both sides isolates the term with the variable: 2x = 8.
Question 3: A taxi charges a flat fee of $3.00 plus $1.50 per kilometre. Which equation models the total fare F for k kilometres?
- F = 3.00k + 1.50
- F = 1.50k − 3.00
- F = 3.00 + 1.50k (Correct answer)
- F = 4.50k
Correct answer: F = 3.00 + 1.50k
The flat fee is the initial value and the per-kilometre rate is the slope: F = 3.00 + 1.50k.
Question 4: What is the area of a triangle with base 10 cm and height 6 cm?
- 60 cm²
- 30 cm² (Correct answer)
- 16 cm²
- 120 cm²
Correct answer: 30 cm²
Area of a triangle = ½ × base × height = ½ × 10 × 6 = 30 cm².
Question 5: Which scatter plot trend indicates a positive correlation?
- Points go from upper left to lower right
- Points are clustered in the centre
- Points go from lower left to upper right (Correct answer)
- Points are randomly scattered
Correct answer: Points go from lower left to upper right
A positive correlation means as x increases, y also increases, so points trend from lower left to upper right.
Question 6: Simplify: (x³)(x²)
- x⁶
- x⁵ (Correct answer)
- 2x⁵
- x
Correct answer: x⁵
When multiplying powers with the same base, add exponents: x³ × x² = x^(3+2) = x⁵.
Question 7: A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
- 94.2 cm³
- 282.6 cm³ (Correct answer)
- 188.4 cm³
- 565.2 cm³
Correct answer: 282.6 cm³
Volume = πr²h = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cm³.
EQAO Grade 9 Mathematics Assessment 3
The hypotenuse of a right triangle is 13 cm and one leg is 5 cm.
What is the length of the other leg?