Resources | Subject Notes | Mathematics
This section covers mathematical concepts frequently encountered in everyday life, focusing on practical applications of number skills. We will explore topics such as currency conversions, time calculations, distance-speed-time problems, and basic financial concepts.
Understanding currency, making change, and calculating costs are essential everyday skills.
Converting between different currencies involves using exchange rates. The formula for conversion is:
$Amount = $Amount \times \text{Exchange Rate}$
Example: Converting £50 to USD at an exchange rate of 1 £ = 1.25 USD
$50 \times 1.25 = $62.50
Calculating the change given after a purchase involves subtraction.
Change = Amount Paid - Cost of Item
Example: Paying with a £10 note for an item costing £4.75
Change = £10.00 - £4.75 = £5.25
Basic budgeting involves calculating totals, discounts, and percentages.
Example: A shirt costs £20 and is 20% off. Calculate the discounted price.
Discount Amount = 20% of £20 = 0.20 x £20 = £4
Discounted Price = £20 - £4 = £16
Calculating durations, dates, and times is a common requirement.
Adding and subtracting time involves converting to hours and minutes.
Example: Calculate the time elapsed between 9:15 am and 11:45 am.
From 9:15 am to 10:00 am is 45 minutes.
From 10:00 am to 11:45 am is 1 hour and 45 minutes.
Total time elapsed = 1 hour 45 minutes + 45 minutes = 2 hours 30 minutes.
Determining the day of the week for a given date or finding the date after a certain number of days.
Example: If today is Wednesday, what day will it be in 10 days?
10 days after Wednesday is Saturday.
Understanding the concept of time zones and calculating time differences between them.
Example: If it is 12:00 pm in London (GMT) and 5:00 pm in New York (EST), what is the time difference?
New York is 5 hours behind London.
5:00 pm - 5 hours = 12:00 pm.
Calculating distances, speeds, and times involved in travel.
The fundamental formula relating distance, speed, and time is:
Distance = Speed x Time
Time = Distance / Speed
Speed = Distance / Time
Example: A car travels at a speed of 60 km/h for 2 hours. Calculate the distance traveled.
Distance = 60 km/h x 2 h = 120 km
Calculating arrival times based on departure times, distances, and speeds.
Example: A train leaves at 10:00 am and travels for 3 hours at a speed of 80 km/h. What time will it arrive?
Distance = 80 km/h x 3 h = 240 km
Arrival time = 10:00 am + 3 hours = 1:00 pm
Basic financial concepts such as interest, profit, and loss.
Calculating the interest earned or paid on a principal amount.
Simple Interest = Principal x Rate x Time
Example: Calculate the simple interest on £100 at a rate of 5% per year for 2 years.
Simple Interest = £100 x 0.05 x 2 = £10
Determining the profit or loss made on a transaction.
Profit = Selling Price - Cost Price
Loss = Cost Price - Selling Price
Example: A shop buys an item for £20 and sells it for £25.
Profit = £25 - £20 = £5
Table: Summary of Everyday Mathematics
| Topic | Key Concepts | Formula | Example |
|---|---|---|---|
| Money | Currency conversion, making change, budgeting | $Amount = $Amount \times \text{Exchange Rate} | Converting £50 to USD at an exchange rate of 1 £ = 1.25 USD |
| Time | Duration calculations, calendar calculations, time zones | Time Elapsed = End Time - Start Time | Calculating the time between 9:15 am and 11:45 am |
| Travel | Distance-speed-time, journey planning | Distance = Speed x Time | Calculating the distance traveled by a car |
| Finance | Simple interest, profit and loss | Simple Interest = Principal x Rate x Time | Calculating simple interest on an investment |