Moderate -0.8 This is a straightforward verification question requiring only substitution of standard definitions and basic algebraic manipulation. With just 2 marks and a direct 'show that' format, it's a routine exercise testing recall of hyperbolic function definitions rather than problem-solving ability, making it easier than average despite being Further Maths content.
Question 2:
2 | Recalls correct definitions of cosh x
and sinh x | AO1.2 | B1 | ex+e−x2 ex−e−x2
cosh2x−sinh2x≡ −
2 2
e2x+2+e−2x e2x−2+e−2x
≡ −
4 4
4
≡
4
≡1
Demonstrates clearly that
cosh2x−sinh2x≡1 AG
Award only for completely correct
argument including expansion and
simplification | AO2.1 | R1
Total | 2
Q | Marking Instructions | AO | Marks | Typical Solution
Use the definitions of $\cosh x$ and $\sinh x$ in terms of $e^x$ and $e^{-x}$ to show that $\cosh^2 x - \sinh^2 x = 1$
[2 marks]
\hfill \mbox{\textit{AQA Further Paper 1 Q2 [2]}}