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Prove by contradiction that there is an infinite number of prime numbers.

The 'by contradiction' tells us we need to assume the opposite to begin with: 1) Let's assume there is a finite number of prime numbers2) Let P be the largest prime number (the last one) 3) if we multiply al...
CL
Answered by Charlotte L. • Maths tutor
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What are the necessary conditions for a random variable to have a binomial distribution?

There can only be two possible outcomes, 'success' and 'fail' (e.g heads or tails) There is a fixed number of trialsThe probabilities of 'success' and 'fail' are constant and stay the same in each trial (e.g...
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Answered by Julie T. • Maths tutor
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Find the integral of ln(x)

The best way to approach this question is to solve it using integration by parts.First, recognise that ln(x) = 1 x ln(x), and set du/dx = 1 and v = ln(x). We then find that u = x, and dv/dx = 1/x.With this w...
FG
Answered by Finn G. • Maths tutor
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Find the solution of the differential equation: dy/dx = (xy^2 + x)/y. There is no need to rearrange the solution to be in terms of y.

This is a separable differential equation, so the first step is to separate the two variables. Factorise out the x from the top bracket so that the equation becomes: dy/dx = x(y^2+1)/yThe next step is to mul...
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Answered by Thomas S. • Maths tutor
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A-level circle question

Answer will be provided during session (easier to write maths than to type)
Answered by • Maths tutor
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