Summary
This topic covers the concepts of ratio, proportion, and rates of change, including how to express and manipulate these relationships in various contexts.
- Ratio — The relationship in amount between two or more things. Example: 3 : 2 (three to two)
- Equivalent Ratios — Ratios that are the same when compared. Example: 3 : 2 = 6 : 4 (Multiplied by 2)
- Direct Proportion — When one value increases or decreases, the other does so respectively. Example: When the price of gas increases, the food price also increases.
- Inverse Proportion — When one value increases, the other decreases. Example: The time taken to complete a task decreases with the increase in the number of workers.
- Percentage — A number expressed as a fraction of 100. Example: A television set was sold at a loss of 10%.
- Simple Interest — Interest calculated on a sum at a given rate and time. Example: Simple Interest = Principal × Time × Rate / 100
- Compound Interest — Interest earned on both the initial amount and the interest earned. 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
- Confusing simple interest with compound interest
- Misinterpreting percentage increase and decrease
Typical Exam Questions
- How do you express one quantity as a fraction of another? Use the formula: part/whole
- What is the selling price if a product is sold at a loss of 10%? Subtract 10% of the cost price from the total cost.
- How do you calculate speed if a car travels 400m in 20 seconds? Speed = 400m / 20s = 20m/s
What Examiners Usually Test
- Ability to convert between units and solve problems using ratios
- Understanding of direct and inverse proportion
- Calculation of percentage changes and interest
- Application of speed, distance, and time formulas