Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Convert and calculate with units of time.
• Interpret and use Celsius and Fahrenheit scales.
• Calculate and interpret rates like speed and unit price.
• Calculate simple and compound interest.
• Interpret tariffs for water and electricity.

Lesson summary

This week, we delve into the critical area of measurement, focusing specifically on time, temperature, and rates. Understanding these concepts is essential for navigating everyday life in South Africa, from managing your time effectively to understanding utility bills and making informed decisions about travel and finance. Imagine planning a trip from Johannesburg to Cape Town, or calculating the cost of electricity based on your consumption – these require a solid grasp of time, rates, and often, temperature. This knowledge empowers you to make better decisions, manage your resources wisely, and participate more fully in your community and the economy.

Lesson notes

2.1 Time Units of Time: The basic unit of time is the second (s).

We then build upon this: 60 seconds = 1 minute (min) 60 minutes = 1 hour (h) 24 hours = 1 day 7 days = 1 week Approximately 4 weeks = 1 month Approximately 30/31 days = 1 month (February has 28 or 29 days) 12 months = 1 year 365 days = 1 year (366 in a leap year) 10 years = 1 decade 100 years = 1 century Time Calculations: Adding Time: When adding time, remember that when you exceed 60 minutes, you need to carry over to the hours. Similarly, if you exceed 24 hours, you carry over to the days.

Subtracting Time: When subtracting time, you might need to borrow from the next higher unit. For example, if you need to subtract 45 minutes from 1 hour 20 minutes, you borrow 1 hour (60 minutes) from the 1 hour, leaving you with 0 hours and 80 minutes.

Elapsed Time: Elapsed time is the duration between two points in time. To calculate elapsed time, subtract the start time from the end time. Be careful to handle AM and PM correctly. Remember that military time (24-hour clock) eliminates this AM/PM ambiguity.

Example 1: Sipho starts his shift at work at 7:45 AM and finishes at 4:30 P

M. How long is his shift?

Solution: Convert to 24-hour time: 7:45 AM remains 07:45, 4:30 PM becomes 16:

3

0. Subtract: 16:30 - 07:

4

5. We need to borrow an hour: 15:90 - 07:45 = 08:45 Therefore, Sipho's shift is 8 hours and 45 minutes long.

Example 2: A bus departs Johannesburg at 10:15 PM and arrives in Durban at 6:30 AM the next day. How long is the bus journey?

Solution: Convert to 24-hour time: 10:15 PM becomes 22:15, 6:30 AM remains 06:

3

0. We need to calculate the time passed from 22:15 to 06:30 the next day. The easiest way is to calculate to midnight, and then from midnight to 6:

3

0. From 22:15 to 00:00 is 1 hour and 45 minutes.

From 00:00 to 06:30 is 6 hours and 30 minutes.

Add these together: 1 hour 45 minutes + 6 hours 30 minutes = 8 hours and 15 minutes. The bus journey is 8 hours and 15 minutes long. 2.2 Temperature Scales: The two main temperature scales are Celsius (°C) and Fahrenheit (°F). In South Africa, we primarily use Celsius.

Conversion Formulas: Celsius to Fahrenheit: °F = (°C × 9/5) + 32 Fahrenheit to Celsius: °C = (°F - 32) × 5/9 Understanding Temperature: 0 °C is the freezing point of water. 100 °C is the boiling point of water. Normal human body temperature is approximately 37 °

C. Example 3: Convert 25 °C to Fahrenheit.

Solution: °F = (25 × 9/5) + 32 °F = (45) + 32 °F = 77 Therefore, 25 °C is equal to 77 °

F. Example 4: Convert 95 °F to Celsius.

Solution: °C = (95 - 32) × 5/9 °C = (63) × 5/9 °C = 35 Therefore, 95 °F is equal to 35 °C. 2.3 Rates Definition: A rate is a ratio that compares two quantities with different units. Common examples include speed, unit price, and fuel consumption.

Formula: Rate = Quantity 1 / Quantity 2 Speed: Speed is the rate at which an object moves.

It is calculated as: Speed = Distance / Time Unit Price: Unit price is the cost of one item or one unit of a product.

It is calculated as: Unit Price = Total Cost / Number of Units Fuel Consumption: Fuel consumption is the amount of fuel a vehicle uses to travel a certain distance. It is often expressed in litres per 100 kilometres (L/100 km). Fuel Consumption = Litres Used / (Distance Travelled / 100)

Example 5: A car travels 360 km in 4 hours. What is its average speed?

Solution: Speed = Distance / Time Speed = 360 km / 4 hours Speed = 90 km/h The car's average speed is 90 km/h.

Example 6: A packet of 2 kg of sugar costs R

3

2. What is the unit price per kg?

Solution: Unit Price = Total Cost / Number of Units Unit Price = R32 / 2 kg Unit Price = R16/kg The unit price of sugar is R16 per kg.

Example 7: A car uses 45 litres of petrol to travel 500 km. What is the car's fuel consumption in L/100 km?

Solution: Fuel Consumption = Litres Used / (Distance Travelled / 100) Fuel Consumption = 45 litres / (500 km / 100) Fuel Consumption = 45 litres / 5 Fuel Consumption = 9 L/100 km The car's fuel consumption is 9 L/100 km. 2.4 Interest Simple Interest: Simple interest is calculated only on the principal amount. Simple Interest = Principal Rate * Time (I = PRT)

Compound Interest: Compound interest is calculated on the principal amount and the accumulated interest. Amount = Principal (1 + Rate)^Time (A = P(1+R)^T)

Example 8: Calculate the simple interest on R5000 invested at 8% per annum for 3 years. I = 5000 0.08 * 3 = R1200 Example 9: Calculate the compound interest on R5000 invested at 8% per annum for 3 years. A = 5000 (1 + 0.08)^3 = 5000 * (1.08)^3 = R6298.56 The compound interest = R6298.56 - R5000 = R1259.71 2.5 Tariffs Tariff: A tariff is a fee or rate charged for a service, like water or electricity. They often have different tiers, meaning the price per unit increases as you use more.

Example 10: A municipality charges the following for electricity: R1.50 per kWh for the first 100 kWh, and R2.20 per kWh for every kWh thereafter.