Oxford MAT Test - 5th Nov 2014

The bit that starts 'hence we see the desired integral equals...'

Will Imperial look for a similar MAT score as oxford does, or lower? eg. if oxford was looking for say, 65, what do you think Imperial would want? Thanks

I was under the impression their STEP offers were subject to a borderline MAT performance? I'm sure their usual is A*A*A, same as Cambridge?

Not usually, I don't think.

Will Imperial look for a similar MAT score as oxford does, or lower? eg. if oxford was looking for say, 65, what do you think Imperial would want? Thanks

In the range $\log_2 k \leq x < \log_2 ( k+1)$ the integrand ($\lfloor 2^x \rfloor$) = k.

So $\displaystyle \int_{\log_2 k}^{\log_2 ( k+1)} \lfloor 2^x \rfloor \,dx = \int_{\log_2 k}^{\log_2 (k+1)} k \,dx = k ( {\log_2 (k+1)} - \log_2 k)$.

Then add up the integrals for k = 1, 2, ..., 2^n - 1.

Guys! quick question, in exam situation how are we meant to draw the sin(x)/x graph (referrnig to the 2010 paper question 3 part ii) it just gave me some trouble

They explicitly say not to determine turning points.

In this case, I'd worry about behaviour when x = 0, x goes to infinity, and the points where y = 0. I don't expect they will care that much about anything else here.

It is impossible to a numerical estimate, only that it would be lower, perhaps by a fair degree. Again, I refer back to what the head of maths admissions said at the open day, they made an offer to someone in the low 40s, yet the average was 44.8.

Guys! quick question, in exam situation how are we meant to draw the sin(x)/x graph (referrnig to the 2010 paper question 3 part ii) it just gave me some trouble

That's not a use of "critical values" I'm familiar with; from Wiki:

"A critical point or stationary point of a differentiable function of a single real variable, f(x), is a value x0 in the domain of f where its derivative is 0: f′(x0) = 0. A critical value is the image under f of a critical point."

(I kind of hate the term myself, to be honest).

Is that a typo? 44.8 being the average offer seems quite low! I thought it would be quite similar to Oxford's average, seeing as there would be loads of Cambridge and Oxford applicants applying to Imperial as well. No complaints though, that's a massive load off my shoulders!

Was the 44.8 the average applicant / offer holder / successful applicant?

Use L'Hopital's rule to work out at x=0, Sin(x)/x = 1, though obviously it's not = but lim as x->0.

Use L'Hopital's rule to work out at x=0, Sin(x)/x = 1, though obviously it's not = but lim as x->0.

ah. no but theyre known for giving hard offers thats probably why they gve 700 offers for around 250 places cause they know most people wont make them!


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