Give any valid solution to a second order ODE with general solution Ae^x+Bcosh(x)+Csinh(x)

Quiz designed as summary test for MAST resource: Hyperbolic Functions (A Level Further Maths content)

Use defintions of the hyperbolic functions to integrate by considering exponentials.

Rearrange and make a substitution to integrate a quotient to a function in terms of arsinh.

Rearrange and make a substitution to integrate a quotient to a function in terms of arsinh.

Use double angle an pythagorean identities to manipulate before integrating.

Using double angle and pythagorean identities (2 parts)

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Multiple choice of hyperbolic functions (image of graph given).

Compute the inverse of a linear or hyperbolic function. Part of HELM book 2.3.

Students are given a hyperbolic graph and asked to select the correct equation from 4 choices.

Students are shown a hyperbola and asked to identify it as such.

Students are given the equation of a hyperbola and asked to identify the hyperbolic graph out of a set of 4 graphs.

Students are shown an exponential curve and asked to identify it as either linear, parabolic, hyperbolic or exponential.

Solve for $x$: $a\cosh(x)+b\sinh(x)=c$. There are two solutions for this example.

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$.

Advice tidied up.

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Express $f(z)$ in real-imaginary form, given that $z=x+iy$, where $f(z)$ involves hyperbolic functions.

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Express $f(z)$ in real-imaginary form, given that $z=x+iy$, where $f(z)$ involves hyperbolic functions.

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

4 questions involving hyperbolic functions.