GCSE Maths Practice: order-of-operations-bidmas
This Higher question combines two powers with a division before a final subtraction, testing precise BIDMAS sequencing.
Complete each bracket and power fully before dividing, then subtract at the end.
Two Powers with Subtraction and Division
Higher-tier order of operations questions often combine multiple brackets, more than one power, and at least one division before a final addition or subtraction. The key is to apply BIDMAS precisely at every stage, not just once at the beginning. Treat each bracket as a mini-problem, finish it cleanly, then move to indices, and only then handle any divisions or multiplications. Subtraction and addition should be left until the very end.
Method That Scales
- Evaluate brackets first. Simplify each bracket independently so that powers apply to single numbers, not to multi-step expressions.
- Apply indices (powers) next. Squaring or cubing changes magnitude quickly, so complete this stage fully before mixing in other operations.
- Resolve any divisions or multiplications. If a power feeds into a division, complete that division before combining results with + or −.
- Finish with addition or subtraction. Only after all higher-priority steps are done should the totals be combined.
This disciplined sequence prevents common slips such as subtracting too early or forgetting that a denominator must be processed after its own power is evaluated.
Frequent Pitfalls
- Power misplacement: applying an index to the wrong part of a bracketed term.
- Skipping internal order: not following BIDMAS again inside a bracket.
- Division timing errors: subtracting the raw squared value instead of the divided outcome.
Marking each completed stage (B → I → D/M → A/S) on your working line helps you audit your process quickly.
Why This Matters
Handling two powers in the same expression mirrors situations where different quantities scale at different rates—areas vs. volumes, or squared vs. cubed components in physics and engineering models. Division between these powered results often represents rates or averaging, so sequencing them correctly is essential for valid conclusions.
Exam Technique
Write one operation per line. Replace each bracket with its simplified value, then write the powered result explicitly, and only then perform any division or multiplication. Keep subtraction or addition to the last line. This format not only reduces errors but also earns method marks even if an arithmetic slip occurs later.
Quick Self-Check
- Were all brackets simplified before powers?
- Were all powers evaluated before any division or multiplication?
- Was subtraction left until the end?
If any answer is ‘no’, rewrite the steps in the correct order. Consistent structure is what turns harder BIDMAS questions into reliable marks at Higher level.