CSAT For Computer Science Undergrad Admissions 2016 Entry

Has anyone tried Question 8 (aka Question 2 from the Open Days questions)? It looks to be pretty logical and it's in Section A, so it should be too hard, right? RIGHT?
I got 108, not a clue if it's right.. :/

Here's my answer to Q20. I didn't think the solution should be this simple, but I checked on my calculator and the given sum does converge to my answer as n -> infinity.

I am pretty certain the answer is 516. This is quite a fun question.

Hi everyone, I've been lurking on this forum for a while after they released the sample paper, and since no one yet has posted a complete set of solutions (the Cambridge guy took his down), I'm posting mine. The list is missing 3 questions, but I'm convinced that the rest are all correct, but if anyone disagrees then feel free to call me out.

You should be able, with some clever cancelling, to get $P_k$ as an expression without pi notation.

I have been trying to get the expression for it. I found that there is an expression for k!k however I can't derive it from first principles, could you give me some hints please?

Question 15 factorises as (n)(n^4-1 ) which is also (n)(n^2+1)(n^2-1)=n(n+1)(n-1)(n^2+1.) You notice that it is (n-1)(n)(n+1) this means that it its a product of 3 consecutive integers. Factors of 30 are 2,3,5. In any 3 consecutive integer there will always be a multiple of 2 and a multiple of 3. which means that only a factor of 5 is left to prove. I have seen several ways of proving it is a factor of 5 but I personally did Fermats little theorem, n^p-n is always a multiple of p as long as p is a prime. n^5-n, 5 is a prime, therefore by Fermats little theorem we see that it is always going to be a multiple of 5. Therefore n^5-n is always going to be a multiple of 30 as it is a multiple of 2,3 and 5.

Anyone know if you can take a calculator into the CSAT. The website says no calculators for the CS with Maths test but not specifically the CSAT.

Anyone know if you can take a calculator into the CSAT. The website says no calculators for the CS with Maths test but not specifically the CSAT.

Number 12 is wrong the question says to give it in terms of n. I made the same mistake when I did it first haha
Number 6 is also wrong, I got corrected by ILoveCS. I also did what you did
I don't think number 17 is correct either that would have been true if zeros can be adjacent to each other. On a second that is correct I think
I need some help with number 18

I'm not sure how 6 could be wrong, i've checked the graphs and it seems -4/3 is the upper limit. In response to 18, notice how the longitudinal lines of the earth are going to range in length from 2πR to 0 (equator to poles). Therefore there must be a longitudinal line which is exactly n miles in length (or in this case the one we're looking for is n/2 miles). With this just take a cross section of the earth and calculate the arc length.

For question 6 I am guessing you dy/dx 2 times and then made it equal to 0 and all that. I did that too and I was hinted by ILoveCS to try to sub in x=-1 then any values of K, you should realise it is a trick question

But isn't the question asking for the maximum, its clear that for all f(-1) remains constant, so you would have to take that second derivative?

But isn't the question asking for the maximum, its clear that for all f(-1) remains constant, so you would have to take that second derivative?

But isn't the question asking for the maximum, its clear that for all f(-1) remains constant, so you would have to take that second derivative?

if it remains constant throughout, that means there is only 1 possible point. meaning the answer is any values of k :P

I see your point. But I think this question was looking for something else...
Some of these questions have unfortunate wording.