Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Apply financial maths to real-life scenarios like loans and investments.
• Analyse data from tables and graphs to draw conclusions.
• Solve problems involving measurement for practical tasks.
• Use maps and scale drawings to find distances and locations.
• Critically evaluate information to spot bias and inaccuracies.

Lesson summary

This week focuses on consolidating your Mathematical Literacy skills through integrated exam preparation. We will be tackling mixed real-life tasks that draw on various topics you've covered throughout the year. This is crucial because the final exam requires you to apply your knowledge across different areas to solve practical problems. These skills are vital for managing your personal finances, interpreting data in news articles, making informed decisions as a consumer, and participating effectively in your community and the broader South African society. Mathematical Literacy is not just about calculations; it's about using numbers to understand and navigate the world around you.

Lesson notes

This week's focus requires integrating knowledge from several key areas.

Let's recap some crucial concepts: 2.

1. Financial Mathematics: Simple Interest: Calculated only on the principal amount.

Formula: Simple Interest = (Principal × Rate × Time) / 100 or I = PRT, where R is annual rate and T is in years.

Compound Interest: Interest earned on both the principal and accumulated interest.

Formula: A = P(1 + R/n)^(nT)*, where: A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) R = the annual interest rate (as a decimal) n = the number of times that interest is compounded per year T = the number of years the money is invested or borrowed for Inflation: The rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling.

Exchange Rates: The value of one currency in relation to another. Understanding exchange rates is crucial for international transactions, investments, and tourism.

Budgeting: A plan for managing income and expenses.

Loans: Agreements to borrow money, typically with interest charged.

Investments: Putting money into assets (e.g., stocks, bonds, property) with the expectation of future profit.

Example 1: Compound Interest and Inflation Sipho invests R10,000 in a fixed deposit account that pays 8% interest per year, compounded quarterly. He plans to leave the money for 5 years. If the average annual inflation rate is 5% during this period, calculate: a) The amount Sipho will have after 5 years. b) The real value of his investment after 5 years (taking inflation into account).

Solution: a)

Using the compound interest formula: A = P(1 + R/n)^(nT) P = R10,000 R = 0.08 n = 4 (quarterly compounding) T = 5 A = 10000(1 + 0.08/4)^(4*5) A = 10000(1 + 0.02)^20 A = 10000(1.02)^20 A ≈ R14,859.47 b) To calculate the real value, we need to adjust for inflation.

We can use the following formula: Real Value = Future Value / (1 + Inflation Rate)^Number of Years Real Value = 14859.47 / (1 + 0.05)^5 Real Value = 14859.47 / (1.05)^5 Real Value = 14859.47 / 1.27628 Real Value ≈ R11,642.86 Explanation: This example illustrates how compound interest grows an investment, but also how inflation erodes the purchasing power of that investment. It's important to consider both when making financial decisions. 2.

2. Data Handling: Mean: The average of a set of numbers.

Median: The middle value in a sorted set of numbers.

Mode: The value that appears most frequently in a set of numbers.

Range: The difference between the highest and lowest values in a set of numbers.

Interpreting Graphs: Being able to read and understand different types of graphs (bar graphs, pie charts, line graphs, histograms) is essential for drawing conclusions from data.

Correlation: A statistical measure that expresses the extent to which two variables are linearly related (positive, negative, or no correlation).

Sampling: The process of selecting a subset of a population to represent the whole.

Example 2: Analysing Crime Statistics A table shows the number of reported burglaries in Gauteng over the past 5 years: | Year | Number of Burglaries | |---|---| | 2019 | 55,000 | | 2020 | 60,000 | | 2021 | 58,000 | | 2022 | 65,000 | | 2023 | 70,000 | a) Calculate the percentage increase in burglaries from 2019 to 2023. b) Calculate the average number of burglaries per year over the 5-year period. c) What conclusion can you draw from this data about the trend in burglaries in Gauteng?

Solution: a) Percentage Increase = [(New Value - Old Value) / Old Value] * 100 Percentage Increase = [(70,000 - 55,000) / 55,000] * 100 Percentage Increase = (15,000 / 55,000) * 100 Percentage Increase ≈ 27.27% b) Average = (55,000 + 60,000 + 58,000 + 65,000 + 70,000) / 5 Average = 308,000 / 5 Average = 61,600 c)

Conclusion: The data indicates a general upward trend in the number of reported burglaries in Gauteng over the past 5 years. There was a significant increase of approximately 27.27% from 2019 to 2023, with an average of 61,600 burglaries reported annually.

Explanation: This example demonstrates how to analyze data presented in a table to calculate percentage changes and averages, and then draw conclusions based on the calculated values. 2.

3. Measurement: Perimeter: The total distance around the outside of a two-dimensional shape.

Area: The amount of surface a two-dimensional shape covers.

Volume: The amount of space a three-dimensional object occupies.

Conversions: Converting between different units of measurement (e.g., meters to centimeters, liters to milliliters).

Scale Drawings: Representations of objects or spaces at a reduced or enlarged size, maintaining proportions.

Example 3: Home Renovation You are planning to tile your kitchen floor, which measures 4 meters long and 3 meters wide. The tiles you want to use are square and measure 30cm x 30cm. a) Calculate the area of the kitchen floor in square meters.