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# CSAT Sample Paper Answers and Discussion watch

1. Hello all, I haven't seen a thread on this anywhere (not sure why) during my travels so I thought I'd make one. Discussing the answers and solutions might help since it seems Cambridge haven't provided any answers to the sample questions.

What is the CSAT?
Information on the Computer Science Admissions Test can be found on the Cambridge Website. The Cambridge CST department has also started the CSAT practice platform to aid CSAT preparation based on the sample papers. Also see the official FAQ.

CSAT Sample Papers
These are the sample papers provided by Cambridge, based on some real questions. There have been reports that the real exam last year was noticeably harder than these but it should be a good start.
Solutions to Sample Paper 1
Section A
Question 1 by Forecast
Question 2 by Forecast
Question 3 by uponthyhorse
Question 4 by Forecast
Question 5 by uponthyhorse
2. Sample Paper 1, Q1:

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and so . To maximise , set and solve for , giving and . Clearly gives the minimum volume of 0, and thus the maximum volume that can be achieved is .

3. Sample Paper 1, Q2:

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Repeatedly applying to gives . So, . So .

4. Sample Paper 1, Q4:

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. Note that all terms after contain a factor of 10 and thus their units digits are 0. The units digit of the first four terms are 1, 6, 6, 6 respectively. Thus the units digit of the sum is .

5. Sample Paper 1, Q3:

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It's much easier to explain if I include a diagram

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I can probably go into more detail about why I think it's this if anyone wants to know but an analysis of the various possibilities for the overlaps of two intervals will yield the first formula, . The outer formula is there to ensure that if there is no overlap, then we output 0 as the first formula will give a negative number.

7. Sample Paper 1, Q11:

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On day , the organism produces new cells, which simplifies to give . The total number of cells produced by the end of day is therefore .

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, using the method of differences.

8. (Original post by Forecast)
Sample Paper 1, Q11:

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Arghh I managed to crack the first half of it but couldn't simplify it further like you went on to do within the second spoiler tag. I've never been taught the method of differences but I feel like I could have gotten there by some other route. I'll add it to the OP
9. Sample Paper 1, Q15:

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Note that and . The factors of , and ensure that will always be divisible by 2 and 3. If is one more than a multiple of 5 then will be divisible by 5; if is two more than a multiple of 5 then , and thus will be divisible by 5; if is three more than a multiple of 5 then , and again will be divisible by 5; if is four more than a multiple of 5 then will be divisible by 5. So always has factors of 2, 3 and 5, and thus 30 does divide for all positive integers .

10. Sample Paper 1, Q16:

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Let be the initial value of the investment. After years, the total value of the investment is . For the investment to have doubled, . Using the definition from Q7, . If is sufficiently small, we can ignore the term and all subsequent terms, giving and so .

Additional note: in an earlier version of Sample Paper 1 (plus the actual 2015 test I believe), the value of was given. I'm not sure why it was removed.

11. For question 1, by Forecast... Isn't it should be 10-2x instead of 10-x? because we are cutting out 4 squares from the card....If we do, for one width and length we must subtract 2 x from the length and width each???
12. (Original post by GimmeRice)
For question 1, by Forecast... Isn't it should be 10-2x instead of 10-x? because we are cutting out 4 squares from the card....If we do, for one width and length we must subtract 2 x from the length and width each???
You're right. Amended.
13. Has anyone done questions from Sample Paper 2?
14. (Original post by kishen111)
Has anyone done questions from Sample Paper 2?
Yes I'll try and type them up, are there any questions in particular you wanted to discuss?
15. (Original post by uponthyhorse)
Yes I'll try and type them up, are there any questions in particular you wanted to discuss?
1, 2 and 3 of Section A please. I've done 2 and 3, but I don't even understand question 1.
16. (Original post by kishen111)
1, 2 and 3 of Section A please. I've done 2 and 3, but I don't even understand question 1.
I got 8 for question 2 sample paper 2
17. (Original post by fp1washard)
I got 8 for question 2 sample paper 2

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12 hmm...

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Are these correct?
18. (Original post by kishen111)

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12 hmm...

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Are these correct?
(Original post by fp1washard)
I got 8 for question 2 sample paper 2
I am agreeing with kishen here for that question, those are the combinations I came up with as well.

For a more in depth explanation:

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B always has to be at the end as all other scores are bigger. Only A, C and E can be at the front. Notice that even though C > D, it could be the case that C > E > D, or even C > A > E > D. There are 12 combinations as listed by kishen.
19. (Original post by kishen111)
1, 2 and 3 of Section A please. I've done 2 and 3, but I don't even understand question 1.
I'm not sure I understand Question 1 either but here's what I interpreted it as

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The function f(x) = min t^2 for all real x where t < x plots the smallest squared value below a certain x value. Where x is negative, t^2 > x^2 and hence the smallest squared value would be x^2. So for x < 0, the function takes the shape of the regular x^2 parabola. For x > 0, the smallest t^2 is just where t = 0. So for x > 0 the curve is always 0.
20. Sample Paper 2, Question 3:

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is just over 1 and hence . Subtract this from to get .

With the remaining fractions, create a common denominator repeatedly to obtain

Equate the numerators and the denominators to get :

so c = 3 or 1 or d = 1 or 3.

d = 3 gives b = 2, so the solution is a = 1, b = 2, c = 1, d = 3

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