EQAO - Education Quality and Accountability Office Grade 9 Mathematics Assessment Questions and Answers 1 — Questions and Answers
Question 1: A cell phone plan costs a flat fee of $20 per month, plus an additional $0.15 for each gigabyte (GB) of data used. Which equation correctly models the total monthly cost, C, for using 'g' gigabytes of data?
- C = 20g + 0.15
- C = 0.15g + 20 (Correct answer)
- C = 20.15g
- g = 0.15C + 20
Correct answer: C = 0.15g + 20
The total cost (C) is the sum of the fixed flat fee and the variable cost based on data usage. The flat fee is $20, which is the initial value or y-intercept. The variable cost is $0.15 multiplied by the number of gigabytes (g), which represents the rate of change or slope. Therefore, the correct equation is C = 0.15g + 20.
Question 2: A cone-shaped paper cup has a height of 10 cm and a radius of 4 cm. Which of the following is the closest to the maximum volume of water the cup can hold? (Use V = (1/3)πr²h)
- 125.7 cm³
- 418.9 cm³
- 167.6 cm³ (Correct answer)
- 502.7 cm³
Correct answer: 167.6 cm³
To find the volume, substitute the given values into the formula V = (1/3)πr²h. With r=4 and h=10, the calculation is V = (1/3) * π * (4)² * 10 = (1/3) * π * 16 * 10 ≈ 167.55. The closest answer is 167.6 cm³.
Question 3: The expression (3x² - 5x + 2) - (x² - 5x - 4) is simplified. Which of the following is the correct result?
- 2x² - 10x - 2
- 4x² - 10x - 2
- 2x² + 6 (Correct answer)
- 2x² - 2
Correct answer: 2x² + 6
To simplify, distribute the negative sign to the second polynomial: 3x² - 5x + 2 - x² + 5x + 4. Then, combine like terms: (3x² - x²) + (-5x + 5x) + (2 + 4) = 2x² + 0x + 6, which simplifies to 2x² + 6.
Question 4: A scatter plot shows the relationship between the number of hours a student studies for a test and their final test score. The points on the plot generally trend from the bottom left to the top right. Which of the following best describes the relationship?
- Negative correlation
- No correlation
- Positive correlation (Correct answer)
- Constant correlation
Correct answer: Positive correlation
A trend from the bottom left to the top right indicates that as one variable (hours studied) increases, the other variable (test score) also tends to increase. This is the definition of a positive correlation.
Question 5: A school trip requires 1 chaperone for every 8 students. If 112 students are going on the trip, how many chaperones are needed?
- 12
- 14 (Correct answer)
- 15
- 16
Correct answer: 14
This is a proportional reasoning problem. Set up a proportion: (1 chaperone / 8 students) = (x chaperones / 112 students). To solve for x, you can cross-multiply (1 * 112 = 8 * x) or simply divide the total number of students by the number of students per chaperone: 112 / 8 = 14.
Question 6: Which of the following scenarios can be best modeled by a linear relation?
- The height of a ball that is thrown into the air over time.
- The total amount paid for a gym membership that has a monthly fee. (Correct answer)
- The area of a square as the length of its side increases.
- The population of bacteria that doubles every hour.
Correct answer: The total amount paid for a gym membership that has a monthly fee.
A linear relation has a constant rate of change. A gym membership with a monthly fee increases by the same amount each month, which is a constant rate. The height of a ball follows a quadratic (non-linear) path. The area of a square increases quadratically (A=s²). The population of bacteria grows exponentially, not linearly.
EQAO - Education Quality and Accountability Office Grade 9 Mathematics Assessment Questions and Answers 1
A cell phone plan costs a flat fee of $20 per month, plus an additional $0.15 for each gigabyte (GB) of data used.
Which equation correctly models the total monthly cost, C, for using 'g' gigabytes of data?