Exam-style question
Try this first
When simplifying a rational expression, what must be true before a factor is cancelled?.
- A.B6: check notation, restrictions and final form
- B.Use any familiar GCSE calculation even if it ignores Manipulate polynomials algebraically
- C.Write only the final answer without showing the mathematical method
- D.Change the notation or restrictions to make the algebra look simpler
Model answer
What a good answer should say
- The correct answer is B6: check notation, restrictions and final form.
- A factor can be cancelled only after the numerator and denominator have been factorised, and excluded values from the original denominator must still be stated.
This answer is tied to the objective: B6 Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use the factor theorem; simplify rational expressions including by factorising and cancelling, and algebraic division by linear expressions only..
Explanation
Why this works
Use the explanation to connect the worked answer back to B6 Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use the factor theorem; simplify rational expressions including by factorising and cancelling, and algebraic division by linear expressions only..
The correct option, B6: check notation, restrictions and final form, is supported because rational expressions can only be simplified by cancelling common factors, not common terms. The original denominator may impose restrictions even after cancellation.
The distractors are weaker because they hide the factorisation step or remove terms in a way that changes the expression.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: application.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.