How to Rearrange a Formula

Getting Started with Formula Rearrangement

This is your practice paper for changing the subject of a formula - one of those essential GCSE skills that looks harder than it actually is. You've got everything from simple linear rearrangements to trickier ones involving squares and fractions.

The key thing to remember is that you're basically doing algebra in reverse. Instead of substituting numbers, you're moving terms around to isolate the letter you want.

Top Tip: Always show your working step by step - even if you make a mistake, you can still pick up marks for the right method!

Basic Linear Rearrangements

Questions 1-3 are your warm-up exercises with simple linear formulas. These follow the same pattern: get the term with your target letter on one side, then divide or multiply to isolate it.

For example, with f = 5c - 8, you'd add 8 to both sides first, then divide by 5. It's just like solving equations, but you're working with letters instead of numbers.

These questions are worth 2 marks each, so expect to show two clear steps in your working.

Multi-Variable Formulas

Questions 4-6 introduce formulas with multiple variables - don't let this throw you off! The process is exactly the same, you're just moving around more letters.

When you see something like m = 5n + 2p and need to make p the subject, treat everything else as if it were a number. Subtract 5n from both sides, then divide by 2.

The key is staying organised and taking it one step at a time - rushing leads to silly mistakes that cost you easy marks.

Stepping Up the Difficulty

Now things get more interesting with squares and physics formulas. Question 7 involves n², which means you'll need to square root both sides after rearranging.

Questions 8 and 9 use classic physics equations that you might recognise from science lessons. The v = u + at formula is particularly important - knowing how to rearrange it will help in both maths and physics exams.

Remember: When dealing with squares, don't forget the ± symbol when you take the square root (though sometimes the context tells you which sign to use).

Advanced Techniques

Question 10 brings in square roots and fractions together - this is where careful working really pays off. You'll need to square both sides first to get rid of the square root, then work with the fraction.

These questions are worth 3 marks, indicating you need to show more steps. Plan your approach before diving in, and remember that with square roots, you usually need to isolate the root first before squaring.

Fractional Coefficients

Questions 12-14 focus on formulas with fractions as coefficients. When you see something like y = ½x + 6, remember that dividing by ½ is the same as multiplying by 2.

These questions test whether you really understand how fractions work in algebra. The key is to multiply by the reciprocal (flip the fraction upside down) rather than trying to divide by fractions.

Question 14 is worth 3 marks, suggesting there might be a bit more manipulation involved than the others.

Challenge Questions

The final set brings together everything you've learned with complex rearrangements. Question 15 has everything equal to zero, Question 16 involves cubes, and Question 17 combines fractions with multiple terms.

These are the questions that separate the good students from the great ones. Take your time, work methodically, and don't panic if they look complicated at first glance.

Exam Strategy: If you're running out of time, prioritise the 2-mark questions over the 3-mark ones - they're usually quicker and give you more points per minute spent.