Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Solve integrated problems in personal finance.
• Interpret and analyze statistical data.
• Apply measurement skills to practical problems.
• Work with maps, plans, and scale drawings.
• Critically evaluate information from various sources.

Lesson summary

This week, we're focusing on integrated exam preparation using mixed real-life tasks. This means we'll be tackling problems that combine several different mathematical literacy skills within a single, realistic scenario. This is crucial because real life doesn't present neatly compartmentalized math problems. Instead, you need to identify the relevant information, choose the appropriate tools (formulas, graphs, etc.), and apply them correctly to solve the problem. Being able to integrate these skills is vital not just for exams, but for making informed decisions about your finances, health, and everyday life in South Africa.

Lesson notes

2.1 Personal Finance: Loans and Investments Understanding loan repayments is essential for making informed financial decisions. Let's consider different loan types and repayment options. The most common type of loan uses compound interest.

The formula for compound interest is: A = P(1 + i)^n Where: A = Final amount (including principal and interest) P = Principal amount (the initial loan amount) i = Interest rate per compounding period (annual interest rate divided by the number of compounding periods per year) n = Number of compounding periods (number of years multiplied by the number of compounding periods per year) Let's say you want to take out a personal loan of R50,000 to start a small business. The bank offers you a loan with an annual interest rate of 12% compounded monthly, and you plan to repay it over 5 years.

Calculate the monthly interest rate (i): i = 12% / 12 = 0.01 Calculate the total number of compounding periods (n): n = 5 years * 12 months/year = 60 months Calculate the total amount to be repaid (A): A = 50000(1 + 0.01)^60 = R90,568.02 This tells you that over 5 years, you'll repay a total of R90,568.

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2. To find the monthly repayment, you need to use a loan repayment formula (which is more complex than the compound interest formula shown above and is often provided in exams): M = P [i(1+i)^n] / [(1+i)^n - 1] Where M is the monthly repayment.

Using the same example: M = 50000 [0.01(1+0.01)^60] / [(1+0.01)^60 - 1] = R1,509.47 This means you'll pay R1,509.47 per month. For investments, similar concepts apply, but you're aiming to grow your money. Investments can include fixed deposits, unit trusts, and shares. Understanding the risk and potential returns of each is crucial. 2.2 Data Handling: Interpreting Graphs and Statistics Data is all around us. The ability to read and interpret data presented in graphs, charts, and tables is critical.

Bar graphs: Compare different categories.

Pie charts: Show proportions of a whole.

Line graphs: Show trends over time.

Histograms: Show the distribution of data. Consider a bar graph showing the number of reported crimes in different provinces in South Africa. Analyzing this graph helps identify which provinces have higher crime rates and where resources need to be allocated. Pay attention to the axes, units, and legends when interpreting graphs. Always critically evaluate the source of the data and potential biases. For example, a graph showing unemployment rates might be misleading if it only includes people actively seeking employment and excludes discouraged job seekers. 2.3 Measurement: Area, Volume, and Conversions Measurement is a fundamental skill. We use it every day, from cooking to DIY projects.

Common formulas include: Area of a rectangle: Area = length × width Area of a triangle: Area = 1/2 × base × height Area of a circle: Area = π × radius² Volume of a rectangular prism (box): Volume = length × width × height Volume of a cylinder: Volume = π × radius² × height Let's say you want to paint a rectangular room that is 4 meters long, 3 meters wide, and 2.5 meters high. You need to paint the four walls. Calculate the area of each of the two longer walls: Area = 4m * 2.5m = 10m² Calculate the area of each of the two shorter walls: Area = 3m * 2.5m = 7.5m² Calculate the total area to be painted: Total area = (2 10m²) + (2 7.5m²) = 35m² Now, if one liter of paint covers 10m², you would need 35m² / 10m²/liter = 3.5 liters of paint. You'd probably buy 4 liters to be safe. 2.4 Maps, Plans and other Representations of the Physical World Understanding scale is vital when working with maps and plans.

A scale of 1:100 means that 1 cm on the map represents 100 cm (or 1 meter) in real life.

If a map has a scale of 1:50,000, and the distance between two towns on the map is 5 cm, the actual distance is 5 cm * 50,000 = 250,000 cm = 2,500 meters = 2.5 kilometers. 2.5 Critical Evaluation of Information Not all information is accurate or unbiased. Critical thinking skills are essential for evaluating information presented in news articles, advertisements, and other sources.

Look for: Source reliability: Who created the information? Are they trustworthy?

Bias: Does the source have a particular agenda?

Evidence: Is the information supported by credible evidence?

Logic: Does the argument make sense?

Misleading statistics: Are statistics being used to manipulate the audience? For example, an advertisement claiming a product is "99% effective" might be misleading if the sample size was very small or the study was not conducted properly. Always question assumptions and look for alternative perspectives. Guided Practice (With Solutions)

Question 1: You are planning a weekend trip from Johannesburg to Durban. The distance is approximately 560 km. Your car's fuel consumption is 8 liters per 100 km. Petrol costs R22.50 per liter. You also estimate toll fees will cost R250 each way. Calculate the total cost of fuel and toll fees for the round trip.