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Prove by induction that 2^(6n)+3^(2n-2) is divsible by 5. (AS Further pure)

For this question I would heavily emphasise layout as these questions are very strict. Base n=1 simply plug n=1 into the equation and you will find you end up with 65 which is divisble by 5 Assumption n=k pl...
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How does speciation occur?

A barrier separates the original population into two groups. Due to the different environmental conditions (selection pressures) either side of the barrier, different alleles are selected that better adapt t...
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Answered by Hasna B. • Biology tutor
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Can you teach me how to rationalise the denominator of an algebraic expression?

You may be asked to rationalise the denominator of an algebraic expression if it contains a surd in the denominator - such as a 1/2 . They can get slightly more complex than this though! What it is asking fo...
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Solve the differential equations dx/dt=2x+y+1 and dy/dt=4x-y+1 given that when t=0 x=20 and y=60. (A2 Further pure)

These questions are really mean but if given in the exam give ALOT of marks and whilst scary at first follow a very general pattern. First I would take either equation and re-arrange for the lone variable. T...
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Given that y = 4x^3 -1 + 2x^1/2 (where x>0) find dy/dx.

This is an example of a common AS differentiation Q. To find dy/dx simply apply the power rule to each term in the equation. The power rule is if you have a term x^n then dy/dx will be n times x^(n-1). e.g. ...
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