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Further Mathematics

A Level

By Differentiating from first principles, find the gradient of the curve f(x) = x^2 at the point where x = 2

This qustion can be solved easily using the gradient formular, m = ∆y/∆x, and some simple algrebra.

The gradient at the point x = 2 is calculated by find the gradient of a tangent at x = 2. To find...

Answered by Hugo F. • Further Mathematics tutor

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Find the determinant of a 3x3 square matrix

We can expand following any row or column we want. A wise choice would be to use a row/column in which we have one or more zero entries to reduce the calculations. From this, we pick the first entry on th...

Answered by Stefano Z. • Further Mathematics tutor

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Prove by induction that (n^3)-n is divisible by 3 for all integers n>0 (typical fp1 problem)

Let P(n) be the statement “(n^3)-n is divisible by 3”

First we’ll examine the base case: P(1)

(n^3)-n=1^3-1=1-1=0

0=3*0, so is divisible by 3, and so P(1) is true

Now assume fo...

Answered by Tom N. • Further Mathematics tutor

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How do I sketch accurate graphs for rational functions in a short amount of time? (I.e. A step by step guide of sketching graphs)

Often in Further Pure modules for various exam boards a common question in the exam paper will be to sketch a graph for a rational function. The step by step aproach I used is as follows:

Answered by Darshan H. • Further Mathematics tutor
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solve the equation 4cos^2(x) -15sin(x) = 13

We first want to get every term in terms of the same variable, namely sin(x). to do so, we will use the identity sin^2(x) +cos^2(x) = 1 to get: 4(1-sin^2(x)) -15sin(x) -13 = 0. which we can then rewrite a...

Answered by Max G. • Further Mathematics tutor

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