MAT Prep Thread - 2nd November 2016

And does anyone rmb what Q1 G for the summation one was about? The acc question

and what Q1J-b acc was

There was some kind of recurrence relation like
a1 = 1; a(n+1) = Σak [from 1 to n]
and the question was to find Σ(1/an) [from 1 to infinity]

Sorry about the bad formatting; in words:

There was a sequence where each term was the sum of every previous term in the sequence, starting with 1. So it goes 1, 1, 2, 4, 8, ... Find the sum of the reciprocals of this series. The sum was 1 + 1 + 1/2 + 1/4 + 1/8 + ..., which you could use the GP formula on, or 1+1 = 2 and the rest is a fairly famous infinite sequence which sums to 1. So the answer was 3.

MCQ,H: The area for x^4-a is negative right? (Provided a>0) Or does that not matter somehow?

Looking at the answers, I reckon I got somewhere between 65 and 70.

Should that be enough to get an offer from Imperial that's solid?

The summation question I think you're talking about, to quote myself:



1J: Might have messed up some of the options in particular because I spent more time analysing some of them than others. But this was roughly it:

Let ∏(n) denote the number of unique prime factors in n; for example, ∏(8) = 1 and ∏(6) = 2. Let x(n) equal the last digit of n. Which of the following statements is false?

(a) If ∏(n) = 1, there are some values of x(n) for which n must not be prime.
(b) If ∏(n) = 1, there are some values of x(n) for which n must be prime.
(c) If ∏(n) = 1, there are some values of x(n) which are not possible to obtain.
(d) If ∏(n) + x(n) = 2, it is not possible to determine whether n is prime.
(e) If ∏(n) = 2, there are some values of x(n) which are not possible to obtain.

[I think the TSR consensus is (b), which is what I put. Although "Which is false?" instead of "Which is true?" nearly caught me out.]

hmm... (c) seems correct - if ∏(n) = 1, x(n) cannot be equal to zero. If the last digit of a number is zero, we can always factor out 10 and therefore 2 and 5, rendering ∏(n)>1.

Yes, but the question is which option is false. Your logic is correct so (c) is not the right answer.

Anybody remembers the answer to the MCQ about the graph of （x^2-1）+（cospix）

answer a.
it was the one through the origin with 4 x-intercepts:

Do you remember what answer b looks like? I think there are two looks quite similar but I forgot which one I choose.

ah yeah they were pretty similar - i got a bit hung up between the two
answer a had four x-intercepts, while answer b had 6
if you set y=0 then you get (x-1)^2 = cos(pi*x)
drawing y=(x-1)^2 and y=cos(pi*x), you get four intersections
hence the four x-intercepts and answer a.

Anybody remembers the answer to the MCQ about the graph of （x^2-1）+（cospix）

Thanks then I think I have chosen the more complex one which is b.. sad for losing another 4 marks... btw what do you think of this year's grade boundary, greater or lower than last year??