Summary
This topic covers the concepts of ratio, proportion, and rates of change, including how to convert between units, use scale factors, and solve problems involving percentages and interest.
- Ratio — The relationship in amount between two or more things. Example: 3 : 2 (three to two)
- Direct Proportion — When one value increases or decreases, another value increases or decreases respectively. Example: When the price of gas increases, the food price also increases.
- Inverse Proportion — When one value increases, another value decreases. Example: The time taken to complete a task decreases with the increase in the number of workers.
- Percentage — A number that can be expressed as a fraction of 100. Example: A television set was sold at a loss of 10%.
- Simple Interest — Method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. Example: Simple Interest = Principal × Time × Rate / 100
- Compound Interest — Interest earned on both the initial principal and the interest that has been added to it. Example: Total Amount = Principal (1 + Rate/100)^time
- Speed — The distance traveled divided by the time taken. Example: Speed = Distance / Time
Exam Tips
Key Definitions to Remember
- Ratio
- Direct Proportion
- Inverse Proportion
- Percentage
- Simple Interest
- Compound Interest
- Speed
Common Confusions
- Mixing up direct and inverse proportion
- Misinterpreting percentage increase and decrease
- Confusing simple interest with compound interest
Typical Exam Questions
- How do you convert a ratio to its simplest form? Divide both terms by their greatest common divisor.
- What is the formula for calculating simple interest? Simple Interest = Principal × Time × Rate / 100
- How do you calculate speed? Speed = Distance / Time
What Examiners Usually Test
- Ability to convert between units and use scale factors
- Solving problems involving percentage change
- Calculating interest and understanding its applications
- Applying ratio and proportion in real-world contexts