Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Solve complex problems involving finance (budgets, loans, interest).
• Analyse and interpret data from graphs, tables, and maps.
• Apply measurement and scaling principles to practical problems.
• Interpret and apply probability concepts to real-world scenarios.
• Work confidently with rates, ratios, and proportions (e.g., VAT, consumption rates).

Lesson summary

This week's focus is on integrated exam preparation. This means we will be tackling real-life tasks that draw on various Mathematical Literacy skills and knowledge learned throughout the year. Exam questions are rarely isolated to one specific skill; they often require you to combine multiple concepts to solve a problem. This integrated approach mirrors real-life situations where we don't use maths in neatly compartmentalised sections. For example, planning a trip involves budgeting (finance), calculating distances and travel times (measurement and data handling), and possibly converting currencies (number and calculations).

Lesson notes

This week, we will weave together the concepts covered throughout the year. Here's a recap of some crucial areas, with specific emphasis on their integration: Finance: Simple and compound interest, calculating loan repayments (understanding amortization schedules), budgeting, income and expenditure, tax (PAYE, VAT), understanding bank statements and transaction fees, comparing financial products (e.g., different bank accounts, loan options). It's crucial to understand the impact of interest rates and how different loan terms affect total repayment amounts.

Measurement: Units of measurement (metric system), conversions between units (e.g., cm to m, ml to L), calculating area, perimeter, volume, reading scales on measuring instruments, map scales and distance calculations. Be mindful of the appropriate units for different contexts and avoid errors in conversions.

Data Handling: Collecting, organizing, and representing data (tables, bar graphs, pie charts, line graphs), interpreting data (identifying trends, making predictions), calculating measures of central tendency (mean, median, mode), range, probability. Understanding the limitations of data and potential biases is critical.

Probability: Basic probability calculations (e.g., probability of drawing a specific card from a deck), understanding independent and dependent events, using probability to make predictions. Rates, Ratios and Proportions: Understanding the difference between rates (e.g., km/h) and ratios (e.g., 2:3), solving proportion problems (e.g., scaling a recipe), applying these concepts to real-world scenarios (e.g., calculating fuel consumption, understanding unemployment rates).

Worked example

Example 1: Budgeting and Loan Repayment

Scenario: Thando earns a gross monthly salary of R15,

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0. Her deductions include PAYE (25%), UIF (1%), and medical aid (R800). She wants to buy a used car that costs R80,

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0. The bank offers her a loan at an interest rate of 13% per annum, compounded monthly, over 5 years. She also needs to budget for car insurance (R600 per month) and petrol (R1,200 per month). Can she afford the car?

Solution:

Calculate Net Salary:

PAYE: R15,000 0.25 = R3,750

UIF: R15,000 0.01 = R150

Total Deductions: R3,750 + R150 + R800 = R4,700

Net Salary: R15,000 - R4,700 = R10,300

Calculate Monthly Loan Repayment:

We use the loan repayment formula: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

Where:

M = Monthly repayment

P = Principal loan amount (R80,000)

i = Monthly interest rate (13% per annum / 12 months = 0.13/12 = 0.010833)

n = Number of months (5 years 12 months/year = 60 months)

M = 80000 [ 0.010833(1 + 0.010833)^60 ] / [ (1 + 0.010833)^60 – 1 ]

M ≈ 80000 [ 0.010833(1.932) ] / [ 1.932 - 1]

M ≈ 80000 [ 0.02093 ] / [ 0.932]

M ≈ 1674.4 / 0.932

M ≈ R1796.56 (Rounded to the nearest cent)

Calculate Total Monthly Expenses:

Loan Repayment: R1796.56

Car Insurance: R600

Petrol: R1,200

Total: R1796.56 + R600 + R1200 = R3596.56

Determine Affordability:

Remaining Income: R10,300 - R3596.56 = R6703.44

Conclusion: Thando can afford the car, as she has R6703.44 remaining after covering all car-related expenses.

However, she needs to consider other living expenses to ensure she has enough money to cover everything.