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Further Mathematics

A Level

Find the inverse of the general 2x2 matrix A= ([a, b],[c, d]) when does this inverse exist?

This is a typical further maths question, doing it correctly is a matter of carrying out a two-step process.

Start by finding the determinant of the matrix,

det(A)=ad-bc

Answered by Larry R. • Further Mathematics tutor

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The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

Tangent is parallel, therefore (dy/dx)=0.

Find y:

y = r sin(x) = 3a(1 + cos(x))(sin(x))

Differentiate y with respect to x

dy/dx = 3a[(2cos(x) - 1...

Answered by Salah S. • Further Mathematics tutor

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Given that f(x)=2sinhx+3coshx, solve the equation f(x)=5 giving your answers exactly.

Firstly set 2sinhx+3coshx=5Now using the exponential definitions of sinhx and coshx rewrite the equation to give:2(1/2(e^x-e^-x))+3(1/2(e^x+e^-x))=5Simplify the equation by expanding out the brackets, mul...

Answered by Emily-Louisa S. • Further Mathematics tutor

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How do I use proof by induction?

Induction is an incredibly powerful form of proof. As such, it is essential to be able to call upon such a tool if you want to study any higher form of mathematics.
The basic structure of the method ...

Answered by Andrew D. • Further Mathematics tutor

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What are polar coordinates?

People doing mathematics at A-Level will be familiar with the concept of using x and y coordinates in the cartesian coordinate system. But introducing the idea of the polar coordinate system can be confus...

Answered by Alex W. • Further Mathematics tutor

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