Question 3 - A-Level Maths

AQA Further Paper 1 2022 June — Question 3 1 marks

Exam Board	AQA
Module	Further Paper 1 (Further Paper 1)
Year	2022
Session	June
Marks	1
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Hyperbolic functions
Type	Differentiate inverse hyperbolic functions
Difficulty	Easy -1.2 This is a 1-mark multiple choice question testing direct recall of a standard hyperbolic function derivative. Students either know that d/dx(sech x) = -sech x tanh x or can quickly derive it from sech x = 1/cosh x, but no problem-solving or multi-step reasoning is required—it's purely procedural recall from the Further Maths syllabus.
Spec	4.07d Differentiate/integrate: hyperbolic functions

Given that \(y = \operatorname{sech}x\), find \(\frac{dy}{dx}\) Tick (\(\checkmark\)) one box. [1 mark] \(\operatorname{sech}x\tanh x\) \(\square\) \(-\operatorname{sech}x\tanh x\) \(\square\) \(\operatorname{cosech}x\coth x\) \(\square\) \(-\operatorname{cosech}x\coth x\) \(\square\)

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Question 3:

Answer	Marks	Guidance
3	Ticks correct answer	2.2a
Total	1
Q	Marking instructions	AO

Question 3:
3 | Ticks correct answer | 2.2a | B1 | – sech x tanh x
Total | 1
Q | Marking instructions | AO | Marks | Typical solution

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Given that $y = \operatorname{sech}x$, find $\frac{dy}{dx}$

Tick ($\checkmark$) one box.
[1 mark]

$\operatorname{sech}x\tanh x$ $\square$

$-\operatorname{sech}x\tanh x$ $\square$

$\operatorname{cosech}x\coth x$ $\square$

$-\operatorname{cosech}x\coth x$ $\square$

\hfill \mbox{\textit{AQA Further Paper 1 2022 Q3 [1]}}

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Q1 1 Q2 1 Q3 1 Q4 1 Q5 6 Q6 8 Q7 9 Q8 11 Q9 14 Q10 12 Q11 19 Q12 17