Study Notes
In algebra, variation refers to the relationship between two quantities where one quantity changes as the other does.
- Direct Variation — a relationship where one quantity increases or decreases at the same rate as another. Example: If z is directly proportional to m, then z = km, where k is a constant.
- Inverse Variation — a relationship where one quantity increases as the other decreases. Example: If x is inversely proportional to y, then xy = k, where k is a constant.
Exam Tips
Key Definitions to Remember
- Direct Variation: A relationship where two quantities increase or decrease together at the same rate.
- Inverse Variation: A relationship where one quantity increases as the other decreases.
Common Confusions
- Confusing direct variation with inverse variation.
- Forgetting to solve for the constant k before finding unknown values.
Typical Exam Questions
- What is the value of z when m = 7, if z is directly proportional to m and z = 20 when m = 4? z = 35
- How do you express x varies inversely as y? xy = k
- If x is inversely proportional to y and x = 2 when y = 3, find x when y = 6. x = 1
What Examiners Usually Test
- Ability to set up and solve equations for direct and inverse variation.
- Understanding the concept of proportionality and how to apply it to solve problems.