Exam-style question
Try this first
Which answer avoids the common misconception in the binomial expansion of (a + bx)^n for positive integer n?.
- A.D1: avoid assuming that checking examples is not the same as proving the general statement
- B.Use any familiar GCSE calculation even if it ignores the binomial expansion of (a + bx)^n for positive integer n
- 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 D1: avoid assuming that checking examples is not the same as proving the general statement.
- This option is best because state the assumption, justify each logical step, and identify the conclusion, then checks that the notation, restrictions and conclusion match the AQA A-level Mathematics objective.
This answer is tied to the objective: D1 Understand and use the binomial expansion of (a + bx)^n for positive integer n; use the notations n!, nCr and binomial coefficients; link to binomial probabilities; extend to any rational n including use for approximation; be aware that the expansion is valid for |bx/a| < 1, with proof not required..
Explanation
Why this works
Use the explanation to connect the worked answer back to D1 Understand and use the binomial expansion of (a + bx)^n for positive integer n; use the notations n!, nCr and binomial coefficients; link to binomial probabilities; extend to any rational n including use for approximation; be aware that the expansion is valid for |bx/a| < 1, with proof not required..
D1: avoid assuming that checking examples is not the same as proving the general statement is the correct option. It directly supports the binomial expansion of (a + bx)^n for positive integer n by requiring the student to state the assumption, justify each logical step, and identify the conclusion.
The other options are weaker because they hide the reasoning, ignore restrictions, or use a generic calculation that may not fit the objective.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: recall.
- 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.