Exam-style question
Try this first
Which statement shows sound trigonometry reasoning for the standard small angle approximations of sine?.
- A.E2: check notation, restrictions and final form
- B.Use any familiar GCSE calculation even if it ignores the standard small angle approximations of sine
- 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 E2: check notation, restrictions and final form.
- This option is best because use radians, exact values, identities or interval restrictions as the question requires, then checks that the notation, restrictions and conclusion match the AQA A-level Mathematics objective.
This answer is tied to the objective: E2 Understand and use the standard small angle approximations of sine, cosine and tangent, including sin theta approximately theta, cos theta approximately 1 - theta^2/2, and tan theta approximately theta where theta is in radians..
Explanation
Why this works
Use the explanation to connect the worked answer back to E2 Understand and use the standard small angle approximations of sine, cosine and tangent, including sin theta approximately theta, cos theta approximately 1 - theta^2/2, and tan theta approximately theta where theta is in radians..
E2: check notation, restrictions and final form is the correct option. It directly supports the standard small angle approximations of sine by requiring the student to use radians, exact values, identities or interval restrictions as the question requires.
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: 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.