Study Notes
In mathematics, proportion refers to the relationship between two quantities where one quantity is a constant multiple of the other. This can be expressed as either direct or inverse variation using algebraic expressions.
- Direct Proportion — A relationship where two quantities increase or decrease at the same rate. Example: If z is proportional to m, then z = km, where k is a constant. If z = 20 when m = 4, then z = 5m.
- Inverse Proportion — A relationship where one quantity increases as the other decreases. Example: If b varies inversely as e, then b = k/e, where k is a constant. If b = 6 when e = 2, then k = 12.
Exam Tips
Key Definitions to Remember
- Direct Proportion: x ∝ y or x = ky
- Inverse Proportion: x ∝ 1/y or x = k/y
Common Confusions
- Confusing direct and inverse relationships
- 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
- Calculate the value of b when e = 12 if b varies inversely as e and b = 6 when e = 2. b = 1
- What is the water temperature at a depth of 12 km if it varies inversely with depth and is 6°C at 4 km? Temperature = 2°C
What Examiners Usually Test
- Ability to set up and solve equations for direct and inverse proportion
- Understanding of how to manipulate algebraic expressions to find unknown values