EDEXCEL GCSE HIGHER MATHS - What is Changing the Subject and Rearranging Formulas

Edexcel GCSE Higher Maths: Changing the Subject and Rearranging Formulas

This tutorial will cover the essential skills of changing the subject of a formula and rearranging equations. These skills are crucial for solving problems in a variety of mathematical contexts.

What is Changing the Subject of a Formula?

Changing the subject of a formula means rearranging the equation to solve for a different variable. For example, the formula for the area of a rectangle is:

A = l * w

where:

• A = Area
• l = Length
• w = Width

If we want to find the length (l) of a rectangle, we need to change the subject of the formula to be "l".

How to Change the Subject of a Formula

1. Identify the subject: Determine the variable you want to isolate.
2. Isolate the subject: Use inverse operations to move all other terms to the opposite side of the equation.
3. Simplify: Combine like terms and ensure the subject is by itself.

Example 1: Finding the Length of a Rectangle

Formula: A = l * w

To find "l":

1. Divide both sides by "w": A / w = (l * w) / w
2. Simplify: A / w = l

Therefore, the formula for finding the length of a rectangle is l = A / w.

Example 2: Rearranging a More Complex Formula

Formula: v = u + at

To find "a":

1. Subtract "u" from both sides: v - u = (u + at) - u
2. Simplify: v - u = at
3. Divide both sides by "t": (v - u) / t = (at) / t
4. Simplify: (v - u) / t = a

Therefore, the formula for finding "a" is a = (v - u) / t.

Rearranging Formulas with Fractions

When dealing with fractions in a formula, the following steps are helpful:

1. Get rid of the fraction: Multiply both sides by the denominator.
2. Simplify: Combine like terms and isolate the subject.

Example: Rearranging a Formula with a Fraction

Formula: y = (x + 2) / 3

To find "x":

1. Multiply both sides by 3: 3y = (x + 2) / 3 * 3
2. Simplify: 3y = x + 2
3. Subtract 2 from both sides: 3y - 2 = (x + 2) - 2
4. Simplify: 3y - 2 = x

Therefore, the formula for finding "x" is x = 3y - 2.

Key Points to Remember

• Always use inverse operations to isolate the desired variable.
• Keep the equation balanced by performing the same operation on both sides.
• Simplify the equation after each step.
• Practice with different formulas to become comfortable with rearranging equations.

By mastering the skills of changing the subject and rearranging formulas, you will gain confidence in solving mathematical problems and a better understanding of the relationships between variables.