Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Interpret complex real-life scenarios.
• Select and apply the correct mathematical skills.
• Critically evaluate results and justify decisions.
• Communicate solutions clearly.
• Build confidence in problem-solving.

Lesson summary

This week focuses on integrated exam preparation using mixed real-life tasks. Mathematical Literacy equips you with the skills to confidently navigate everyday scenarios involving numbers, data, and finances. Mastering this subject is crucial for becoming informed citizens who can make sound decisions about their personal finances, understand news reports, and participate effectively in community matters. By tackling mixed real-life tasks, we prepare you not just for the exam, but for life beyond school. The goal is to move beyond isolated concepts and apply your knowledge holistically to solve practical problems.

Lesson notes

This section revisits key concepts crucial for tackling mixed real-life tasks. This week’s focus is integrating previously learned content in context. a)

Financial Literacy: Budgeting: Creating a financial plan to manage income and expenses. This involves understanding different types of income (e.g., salary, wages, commission) and expenses (e.g., fixed, variable, discretionary).

Compound Interest: Interest earned not only on the principal amount but also on the accumulated interest.

The formula is: A = P(1 + i)^n, where A = final amount, P = principal amount, i = interest rate per period, and n = number of periods.

Simple Interest: Interest earned only on the principal amount.

The formula is: A = P(1 + in), where A = final amount, P = principal amount, i = interest rate per year, and n = number of years.

Loan Comparisons: Evaluating different loan options based on interest rates, repayment periods, and total cost of the loan.

Taxation: Understanding different types of taxes (e.g., income tax, VAT) and their impact on personal finances.

Inflation: The rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. b)

Measurement: Area and Volume: Calculating the area of 2D shapes (e.g., squares, rectangles, circles) and the volume of 3D objects (e.g., cubes, cuboids, cylinders).

Conversions: Converting between different units of measurement (e.g., meters to centimeters, liters to milliliters). Understanding the correct units for different measurements is vital.

Scale Drawings: Interpreting and creating scale drawings to represent real-world objects or areas. c)

Data Handling: Data Collection Methods: Surveys, questionnaires, and other methods for gathering data.

Data Representation: Using tables, graphs (e.g., bar graphs, pie charts, line graphs), and charts to visually represent data.

Data Analysis: Calculating measures of central tendency (e.g., mean, median, mode) and dispersion (e.g., range) to analyze and interpret data.

Probability: Calculating the likelihood of events occurring. d)

Rates and Proportions: Rates: Comparing two quantities with different units (e.g., kilometers per hour, price per kilogram).

Proportions: Expressing the relationship between two quantities as a ratio.

Worked example

Example 1: Budgeting and Loan Comparison

Thando earns a monthly salary of R8,500 after tax. Her fixed expenses are R4,000 (rent), R1,500 (transport), and R500 (insurance). She wants to buy a new fridge that costs R6,

0

0

0. She has two loan options:

Option A: 12% simple interest over 2 years.

Option B: 10% compound interest over 1.5 years.

Calculate Thando's disposable income: R8,500 - R4,000 - R1,500 - R500 = R2,500

Calculate the total cost of Option A (Simple Interest): A = P(1 + in) = 6000(1 + 0.12 * 2) = 6000(1 + 0.24) = 6000(1.24) = R7,440

Calculate the total cost of Option B (Compound Interest): A = P(1 + i)^n = 6000(1 + 0.10)^1.

5. We need to be careful here! Because compound interest is yearly, n = 1.5 needs to be interpreted carefully.

A precise calculation yields: A = 6000 1.1^1.5 = 6000 1.1536 = R6921.60

Determine which loan is cheaper: Option B (R6921.60) is cheaper than Option A (R7,440).

Can Thando afford the monthly repayments (assuming Option B)? Monthly repayment = R6921.60 / 18 = R384.

5

3. Since R384.53 < R2,500, Thando can afford the repayments.

Example 2: Measurement and Scale Drawings

A rectangular garden measures 10 meters in length and 6 meters in width. You want to create a scale drawing of the garden using a scale of 1:

5

0. Convert meters to centimeters: 10 meters = 1000 cm; 6 meters = 600 cm.

Apply the scale to find the dimensions of the drawing:

Length: 1000 cm / 50 = 20 cm

Width: 600 cm / 50 = 12 cm

The scale drawing will be a rectangle measuring 20 cm in length and 12 cm in width.

Example 3: Data Handling and Probability

A survey of 100 students found that 60 students own a smartphone, 30 students own a laptop, and 10 students own both.

Represent this data in a Venn diagram (optional but helpful).

Calculate the probability that a randomly selected student owns a smartphone: P(Smartphone) = 60/100 = 0.6 or 60%.

Calculate the probability that a randomly selected student owns a laptop: P(Laptop) = 30/100 = 0.3 or 30%.

Calculate the probability that a randomly selected student owns both a smartphone and a laptop: P(Both) = 10/100 = 0.1 or 10%.

Calculate the probability that a randomly selected student owns EITHER a smartphone OR a laptop. P(A or B) = P(A) + P(B) - P(A and B) = 0.6 + 0.3 - 0.1 = 0.8 or 80%

Guided Practice (With Solutions)

Question 1:

A small business sells vetkoek at a local market. They sell each vetkoek for R7.

5

0. The ingredients for 10 vetkoek cost R

2

5. On a particular Saturday, they sold 120 vetkoek.