AQA A Level Further Maths
Topic questions Pure mathematics Hyperbolic functions
13 questions · 59 marks · about 1 hour
It is given that
Starting from the exponential definition of the sinh function, show that sinh p = r
Solve the equation cosh2 x = 2sinh x + 16
Give your answers in logarithmic form.
By making a suitable substitution, show that
Find the number of solutions of the equation tanh x 
cosh x
Circle your answer.
0 1 2 3
Starting from the identities for sinh 2 x and cosh 2 x, prove the identity
The function f is defined by
State the range of f
Use part (a) and part (b)(i) to prove that tanh 2x 
tanh x if x 
0
It is given that f (x) 
cosh
1 (x 
3)
Which of the sets listed below is the greatest possible domain of the function f ?
Circle your answer.
Given that 
x
1, prove that
Solve the equation
Give your answer in logarithmic form.
Show that the solutions to the equation
can be expressed in the form
where a and b are integers to be found.
Use the definition of the cosh function to prove that
Ronald says that this contradicts the result given in part (a).
Explain why Ronald is wrong.
Which one of these functions has the set 
x 
x
1
as its greatest possible domain?
Circle your answer.
Show that
where m and n are integers.
Hence find cosh6 x 
sinh6 x in the form
where a, b and k are integers.
A curve has equation y cosh x
Show that the arc length of the curve from x a to x b, where 0 
a b, is equal to
Memes
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