Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Analyse and interpret data from tables and graphs.
• Apply financial math concepts like interest and tax.
• Use measurement and scaling for practical problems.
• Interpret and apply probability in situations of risk.
• Solve problems involving time, distance, and speed.

Lesson summary

This week's focus is on integrating various Mathematical Literacy concepts through real-life scenarios, preparing you for the final examinations. Mathematical Literacy is crucial because it equips you with the skills to make informed decisions in everyday life, manage personal finances, understand societal issues, and participate effectively in the South African economy. By tackling mixed real-life tasks, you'll learn to identify relevant information, apply appropriate mathematical tools, and interpret results within their context. This integrated approach moves beyond isolated skills and simulates the complexities of real-world problem-solving.

Lesson notes

This section revisits key concepts and demonstrates how they interconnect in real-life scenarios. 2.1 Data Handling and Interpretation: Tables: Organizing information in rows and columns for easy comparison. Consider a table showing unemployment rates by province in South Africa. Understanding how to read and compare these rates is vital.

Graphs: Visual representations of data (bar graphs, pie charts, line graphs, scatter plots). Each graph type suits different data types. For example, a pie chart is great for showing proportions (e.g., household expenditure), while a line graph shows trends over time (e.g., fuel price changes).

Charts: Similar to graphs, but can incorporate more complex data relationships (e.g., flow charts for project management).

Example: A table shows the average monthly household income and expenditure for a family in Gauteng: | Category | Income (ZAR) | Expenditure (ZAR) | |----------------|--------------|-------------------| | Salary | 12000 | | | Grants | 1500 | | | Rent/Mortgage | | 4000 | | Food | | 3000 | | Transport | | 1500 | | Utilities | | 1000 | | Education | | 800 | | Entertainment | | 500 | | Other Expenses | | 700 | Calculations: To analyze this, calculate the total income (12000 + 1500 = ZAR 13500) and total expenditure (4000+3000+1500+1000+800+500+700 = ZAR 11500). Then calculate the surplus (13500 - 11500 = ZAR 2000). This shows the family has a surplus of ZAR

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0. Understanding these calculations empowers the family to make informed budgeting decisions. 2.2 Financial Mathematics: Simple Interest: Interest calculated only on the principal amount.

Formula: A = P(1 + rt)*, where A is the final amount, P is the principal, r is the interest rate, and t is the time period.

Compound Interest: Interest calculated on the principal and accumulated interest.

Formula: A = P(1 + r/n)^(nt)*, where n is the number of times interest is compounded per year.

Inflation: The rate at which the general level of prices for goods and services is rising, diminishing the purchasing power of money.

Exchange Rates: The value of one currency expressed in terms of another. Crucial for understanding the cost of imported goods and international travel.

Taxation: Money levied by the government on income, property, or goods to fund public services. Understanding PAYE (Pay As You Earn), VAT (Value Added Tax), and other taxes is vital.

Example: You take out a loan of R50,000 at a simple interest rate of 10% per annum for 3 years. Calculate the total amount you will repay.

Calculation: Using the simple interest formula: A = 50000(1 + 0.10 * 3) = 50000(1 + 0.3) = 50000(1.3) = R65,

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0. You will repay a total of R65,

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0. Example: You invest R10,000 in an account that pays 8% interest compounded annually for 5 years. Calculate the final amount.

Calculation: Using the compound interest formula: A = 10000(1 + 0.08/1)^(1*5) = 10000(1.08)^5 = 10000(1.4693) = R14,693.

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8. You will have approximately R14,693.28 after 5 years. 2.3 Measurement and Scaling: Units of Measurement: Understanding and converting between different units (e.g., meters to centimeters, liters to milliliters).

Scale: The ratio between the size of an object in a representation (e.g., a map or blueprint) and its actual size.

Area and Volume: Calculating the area of two-dimensional shapes (e.g., a rectangular field) and the volume of three-dimensional objects (e.g., a water tank).

Example: A blueprint of a house is drawn to a scale of 1:

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0. If the length of the living room on the blueprint is 8 cm, what is the actual length of the living room in meters?

Calculation: Actual length = Blueprint length * Scale factor. Scale factor =

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0. Actual length = 8 cm * 50 = 400 cm.

Convert to meters: 400 cm / 100 cm/m = 4 meters. 2.4 Probability: Probability: The chance of an event occurring, expressed as a fraction, decimal, or percentage.

Independent Events: Events where the outcome of one does not affect the outcome of the other.

Dependent Events: Events where the outcome of one affects the outcome of the other.

Example: What is the probability of drawing a King from a standard deck of 52 playing cards?

Calculation: There are 4 Kings in a deck of 52 cards. Probability = (Favorable outcomes) / (Total possible outcomes) = 4/52 = 1/13. 2.5 Time, Distance, and Speed: Relationship: Speed = Distance / Time, Distance = Speed Time, Time = Distance / Speed.

Units: Ensuring consistent units (e.g., kilometers per hour, meters per second).

Example: A car travels from Johannesburg to Durban (approximately 560 km) at an average speed of 80 km/h. How long will the journey take?

Calculation: Time = Distance / Speed = 560 km / 80 km/h = 7 hours. Guided Practice (With Solutions)

Question 1: A local spaza shop buys a case of 24 soft drinks for R

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0. They sell each soft drink for R8. (a) Calculate the profit made on each soft drink. (b) Calculate the total profit made on the case of soft drinks. (c) What percentage profit does the spaza shop make on the case of soft drinks?