CAEC - Canadian Adult Education Credential Mathematics with a Calculator Questions and Answers 1 — Questions and Answers
Question 1: An electronics store is offering a 20% discount on a television that originally costs $1,250. If the sales tax is 13% (HST), what is the final price of the television after the discount and tax are applied?
- $1,150.00
- $1,130.00 (Correct answer)
- $1,000.00
- $1,412.50
Correct answer: $1,130.00
First, calculate the discount amount: $1,250 * 0.20 = $250. Subtract the discount from the original price to get the sale price: $1,250 - $250 = $1,000. Next, calculate the sales tax on the sale price: $1,000 * 0.13 = $130. Finally, add the sales tax to the sale price to find the final cost: $1,000 + $130 = $1,130.00.
Question 2: A rectangular community garden has a length of 25.5 metres and a width of 15.2 metres. The organizers want to build a fence around the entire garden. What is the total length of fencing required in metres?
- 40.7 metres
- 387.6 metres
- 81.4 metres (Correct answer)
- 60.8 metres
Correct answer: 81.4 metres
The length of fencing required is the perimeter of the rectangle. The formula for the perimeter of a rectangle is P = 2(length + width). Substitute the given values: P = 2(25.5m + 15.2m). First, add the length and width: 25.5 + 15.2 = 40.7 metres. Then, multiply the sum by 2: P = 2 * 40.7 = 81.4 metres.
Question 3: A car travels at an average speed of 85 kilometres per hour. How long will it take the car to travel a distance of 446.25 kilometres?
- 5 hours 15 minutes (Correct answer)
- 5 hours 25 minutes
- 4 hours 45 minutes
- 5.5 hours
Correct answer: 5 hours 15 minutes
To find the time, use the formula: Time = Distance / Speed. Time = 446.25 km / 85 km/h = 5.25 hours. To convert the decimal part of the hour into minutes, multiply it by 60: 0.25 * 60 = 15 minutes. Therefore, the total time is 5 hours and 15 minutes.
Question 4: A recipe for a batch of 12 muffins requires 1.5 cups of flour. If you want to make 30 muffins, which of the following proportions correctly represents the amount of flour (x) needed?
- 12 / 1.5 = x / 30
- 1.5 / 12 = 30 / x
- 12 / 30 = x / 1.5
- 1.5 / 12 = x / 30 (Correct answer)
Correct answer: 1.5 / 12 = x / 30
The relationship is a direct proportion. The ratio of flour to muffins must remain constant. The correct proportion is (flour for first batch) / (muffins in first batch) = (flour for second batch) / (muffins in second batch). This gives the equation 1.5 / 12 = x / 30.
Question 5: A loan of $5,000 is taken out with a simple interest rate of 4.5% per year. What is the total amount of interest paid after 3 years?
- $225.00
- $675.00 (Correct answer)
- $5,675.00
- $750.00
Correct answer: $675.00
The formula for simple interest is I = Prt, where I is the interest, P is the principal amount ($5,000), r is the annual interest rate (0.045), and t is the time in years (3). I = $5,000 * 0.045 * 3. Calculating this gives: I = $225 * 3 = $675.00.
Question 6: The volume of a cylindrical storage tank is given by the formula V = πr²h. If the tank has a radius (r) of 3 metres and a height (h) of 8 metres, what is its approximate volume? (Use π ≈ 3.14159)
- 75.39 m³
- 150.80 m³
- 226.19 m³ (Correct answer)
- 50.27 m³
Correct answer: 226.19 m³
Substitute the given values into the volume formula: V = πr²h. V ≈ 3.14159 * (3 m)² * 8 m. First, calculate the square of the radius: 3² = 9 m². Then, multiply the values together: V ≈ 3.14159 * 9 m² * 8 m. V ≈ 28.27431 * 8 m. V ≈ 226.19448 m³. The closest answer is 226.19 m³.
