AEA Prep Thread - 25th June 2015 (Edexcel)

Boundary thoughts?


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Why wouldn't they put a logo...

Why wouldn't they put a logo...

Some people might not want to blatantly tag their logo on a flagrant copyright violation.

I mean, yeah, we all know that exam papers get copied left right and center, but actually removing copyright notices (*) and putting your own logo on just might (**) get you to the point where someone at Edexcel says "we really can't ignore this guy, call the lawyers".

(*) I'm assuming this paper had the standard "This publication may be reproduced only in accordance with Pearson Education Ltd copyright policy. ©201X Pearson Education Ltd" notice that previous years have had.

(**) Yes, I realise it's still very unlikely this will actually happen. Still.

Quick question.
what does the mean value theorem show and how could I use it to solve problems. I know what it is but what can it show

There are lots of different ways of looking at it, but perhaps the most intuitive is the integral form:

We can find $\xi \in (a, b)$ such that $\int_a^b f(x) \, dx = (b-a)f'(\xi)$.

Since $\frac{1}{b-a} \int_a^b f(x)\,dx$ is the mean value of f(x) between a and b, this is the same as saying that f(x) equals its mean value for some x between a and b.

There are lots of different ways of looking at it, but perhaps the most intuitive is the integral form:

We can find $\xi \in (a, b)$ such that $\int_a^b f(x) \, dx = (b-a)f'(\xi)$.

Since $\frac{1}{b-a} \int_a^b f(x)\,dx$ is the mean value of f(x) between a and b, this is the same as saying that f(x) equals its mean value for some x between a and b.

There are lots of different ways of looking at it, but perhaps the most intuitive is the integral form:

We can find $\xi \in (a, b)$ such that $\int_a^b f(x) \, dx = (b-a)f'(\xi)$.

Since $\frac{1}{b-a} \int_a^b f(x)\,dx$ is the mean value of f(x) between a and b, this is the same as saying that f(x) equals its mean value for some x between a and b.

My pure is not great but there is a differentiation mean value theorem which I remember pictorially and says if a function is continuous between 2 points A and B, the there is at least one point on the function with the same gradient as the gradient of the chord AB. (I think Rolle is a special case where the chord is horizontal)

(I think Rolle is a special case where the chord is horizontal.

I think the f on the RHS is not dashed ...

$\int_a^b f(x) \, dx = (b-a)f(\xi)$, unless I'm getting confused in my sleep deprivation?

My pure is not great but there is a differentiation mean value theorem which I remember pictorially and says if a function is continuous between 2 points A and B, the there is at least one point on the function with the same gradient as the gradient of the chord AB. (I think Rolle is a special case where the chord is horizontal)

The one with the integral is used often by engineers to find the mean value of a function (sometimes the integrand is squared then the answer is square rooted).
I think the f on the RHS is not dashed ...

could you recommend any further reading for maths over the holidays. Many thanks

could you recommend any further reading for maths over the holidays. Many thanks

I assume you've applied to warwick as you sat the aea. If so: http://www2.warwick.ac.uk/fac/sci/maths/admissions/ug/read_list2/
Or, https://www0.maths.ox.ac.uk/courses/material , click on a topic and select course synopsis, there are reading lists there

Morally I could not help anybody who has an intention of going to Warwick, supports Arsenal or dislikes cats ...

Morally I could not help anybody who has an intention of going to Warwick, supports Arsenal or dislikes cats ...

Why is that?

Clearly I strongly indicate my personal likes and dislikes.

Clearly I strongly indicate my personal likes and dislikes.

That really does not answer my question.

Why do hate warwick? We know they are better then UCL for maths 👀🌝.


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Only for pure and simply I have no interest in Pure.

However UCL in terms of institutional prestige makes mince meat of Warwick.