Further Maths hyperbolic functions test to download as PDF

This Further Maths hyperbolic functions test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 16-18, and the full answers are on a separate page.

⏱️ Duration : 60 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Identities and a quadratic
(a) Prove, using exponentials, that \(\cosh2x=2\cosh^2x-1\). [2]
(b) Solve \(\cosh2x=3\cosh x-2\). [2]
Question 2 – An exponential equation
Solve \(2\sinh x+\cosh x=2\), giving the answer as a natural logarithm. [4]
Question 3 – Differentiation
Differentiate with respect to \(x\):
1. \(y=x\sinh2x\) [2]
2. \(y=\cosh^23x\), giving the answer in the form \(k\sinh6x\) [2]
Question 4 – Integration
(a) Find the exact value of \(\displaystyle\int_0^2\dfrac{dx}{\sqrt{x^2+4}}\). [2]
(b) Use integration by parts to show that \(\displaystyle\int_0^1x\sinh x\,dx=e^{-1}\). [3]
Question 5 – Problem: the hanging cable
A cable hangs in the shape \(y=10\cosh\dfrac x{10}\) between two posts at \(x=\pm15\) (metres).
1. Find the height of each post. [1]
2. Find the length of the cable, using the fact that its length is \(\int\cosh\dfrac x{10}\,dx\) over the span. [2]

How to use this Further Maths hyperbolic functions test

First, revise with the hyperbolic functions lesson and the worksheet. Then sit the test in one go, with a timer set to 60 minutes. After that, mark your work with the hyperbolic functions test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Further Maths hyperbolic functions test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.