(a) On the axes below, sketch the graph of\[y = \cosh x\]
Indicate the value of any intercept of the curve with the axes. [2 marks]
(b) Solve the equation\[\cosh x = 2\]
Give your answers to three significant figures. [2 marks]
Mark scheme (a)
Scheme
Marks
AO
Draws the correct shape, approximately symmetrical about the \(y\)-axis and above the \(x\)-axis
B1
1.1b
Indicates one \(y\)-axis intercept at \((0, 1)\) Accept 1 clearly labelled on the \(y\)-axis.
B1
1.1b
(2)
Typical solution
Mark scheme (b)
Scheme
Marks
AO
Obtains at least one correct solution. Accept \(\ln\left(2 + \sqrt{3}\right)\) or \(\ln\left(2 - \sqrt{3}\right)\) or equivalent ln expression. Accept AWRT 1.32 or \(-1.32\) Do not accept \(\cosh^{-1} 2\)
M1
1.1a
Obtains AWRT \(\pm 1.32\) with no other solutions given.
