Exam-style question
Try this first
Which justification is needed when rationalising a denominator containing a binomial surd?.
- A.B2: justify each step using the relevant algebra and functions rule
- B.Use any familiar GCSE calculation even if it ignores Use and manipulate surds
- 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 B2: justify each step using the relevant algebra and functions rule.
- The conjugate is used because multiplying by a matching conjugate creates a difference of two squares, removing the surd from the denominator while preserving equivalence.
This answer is tied to the objective: B2 Use and manipulate surds, including rationalising the denominator..
Explanation
Why this works
Use the explanation to connect the worked answer back to B2 Use and manipulate surds, including rationalising the denominator..
The correct option, B2: justify each step using the relevant algebra and functions rule, is supported because rationalising a binomial denominator depends on the conjugate and the identity (a+b)(a-b)=a^2-b^2. The explanation should show why the surd disappears from the denominator, not just state a final fraction.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: understanding.
- 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.