Exam-style question
Try this first
Which statement shows sound differentiation reasoning for the derivative of f(x) as the gradient of the tangent to y =…?.
- A.G1: check notation, restrictions and final form
- B.Use any familiar GCSE calculation even if it ignores the derivative of f(x) as the gradient of the tangent to y =…
- 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 G1: 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: G1 Understand and use the derivative of f(x) as the gradient of the tangent to y = f(x) at a general point; understand the gradient of the tangent as a limit and as a rate of change; sketch the gradient function for a given curve; understand second derivatives; differentiate from first principles for small positive integer powers of x and for sin x and cos x; understand and use the second derivative as the rate of change of gradient, including links to convex and concave sections and points of inflection..
Explanation
Why this works
Use the explanation to connect the worked answer back to G1 Understand and use the derivative of f(x) as the gradient of the tangent to y = f(x) at a general point; understand the gradient of the tangent as a limit and as a rate of change; sketch the gradient function for a given curve; understand second derivatives; differentiate from first principles for small positive integer powers of x and for sin x and cos x; understand and use the second derivative as the rate of change of gradient, including links to convex and concave sections and points of inflection..
G1: check notation, restrictions and final form is the correct option. It directly supports the derivative of f(x) as the gradient of the tangent to y =… 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.