Study Notes
Changing the subject of a formula involves rearranging it so that a different variable becomes the main focus or 'subject'. This process requires understanding the correct order of operations and using inverse operations to isolate the desired variable.
- Subject of a Formula — the variable that is isolated on one side of the equation.
Example: In the equation y = mx + c, y is the subject. - Cross Multiplication — a method used to eliminate fractions by multiplying across the equals sign.
Example: If a/b = c/d, then ad = bc. - Inverse Operations — operations that reverse the effect of another operation, used to isolate variables.
Example: If x + 3 = 7, subtract 3 from both sides to isolate x. - Factorisation — expressing an equation as a product of its factors to simplify and isolate a variable.
Example: y(m+n) = n² - mn can be factorised to y = (n² - mn)/(m+n).
Exam Tips
Key Definitions to Remember
- Subject of a formula: the variable isolated on one side of the equation
- Inverse operations: operations that reverse the effect of another operation
- Cross multiplication: a method to eliminate fractions by multiplying across the equals sign
Common Confusions
- Forgetting to apply inverse operations correctly
- Not considering both positive and negative solutions when removing square roots
Typical Exam Questions
- Make x the subject of the formula? Rearrange the equation so x is isolated on one side.
- Rearrange the formula to make l the subject? Use inverse operations to isolate l.
- Make y the subject of the formula? Factorise and rearrange to solve for y.
What Examiners Usually Test
- Ability to correctly rearrange formulas to change the subject
- Understanding of inverse operations and their application
- Correct application of algebraic techniques like cross multiplication and factorisation