Who this worksheet is for
This Year 9 Maths handout introduces changing the subject of a formula through inverse operations, fractions and brackets. It is designed for KS3 classroom teaching, supported independent practice and revision, without tying the material to a GCSE exam board.
Each of the four teaching sections contains a core concept, one worked example and four class exercises, with space to show working. The final two pages provide worked solutions for all 16 exercises, marking points and a note that equivalent rearrangements are accepted.
6 pages · 16 exercises · Worked solutions
What the worksheet covers
- Identifying the subject and applying inverse operations to both sides
- Removing fractions and checking non-zero divisors
- Rearranging brackets using efficient choices
- Checking rearrangements by substitution
- Applications involving perimeter, temperature and taxi fares
Part 01 of a two-part Year 9 sequence. Work through Foundations before Next Steps if fractions, brackets or inverse operations are not yet secure. The included marking points are classroom guidance, not an official examination mark scheme.
Key ideas at a glance
Apply the same operation to both sides
The subject is the letter on its own. For v = u + at, subtract u and divide by t to obtain a = (v - u)/t, with t ≠ 0.
Keep the whole numerator together
For y = (x - 5)/3, multiplying by 3 gives 3y = x - 5, then x = 3y + 5. A fraction bar groups its entire numerator.
Choose an efficient route and check it
For P = 2(l + w), divide by 2 before subtracting l: w = P/2 - l. Check by substituting allowed values into the original formula.
About the author
Dr Zhiying Xin is the founder of Study with Dr and a private Maths and Science tutor with nearly seven years of experience, teaching students from 11+ and GCSE through to A-Level and university. She completed her PhD at the University of Manchester.