CSAT Sample Paper Answers and Discussion
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Original post by jameshyland29
Can you explain your proof? I've only studied statistics for about half an hour of my life and I can't understand how you arrived at 1/3, I'd have thought it'd just be 0.5x0.5=0.25 for {1,2,3} at the beginning and when the recursion is activated it resets the whole game? No?
I'm wondering whether I've arrived at a valid alternative by altering A...
By the way here is the question:
9. Using a fair coin we can generate random integers in{1,2,3,4}with equal probability by doing:
(a) toss coin, if heads go to (b) otherwise go to (c)
(b) toss coin, if heads output 1 otherwise output 2
(c) toss coin, if heads output 3 otherwise output 4
By altering just one of the lines (a), (b) or (c), we can generate random integers in{1,2,3}with equal probability. Identify which line and give the new version. Prove that it is correct.
So I altered (a) to "toss coin, if heads go to (b), otherwise toss coin, if heads output three, otherwise restart (a)"
I'm wondering whether I've arrived at a valid alternative by altering A...
By the way here is the question:
9. Using a fair coin we can generate random integers in{1,2,3,4}with equal probability by doing:
(a) toss coin, if heads go to (b) otherwise go to (c)
(b) toss coin, if heads output 1 otherwise output 2
(c) toss coin, if heads output 3 otherwise output 4
By altering just one of the lines (a), (b) or (c), we can generate random integers in{1,2,3}with equal probability. Identify which line and give the new version. Prove that it is correct.
So I altered (a) to "toss coin, if heads go to (b), otherwise toss coin, if heads output three, otherwise restart (a)"
this should work, you've got a 0.25 probability of each option still. When you recursively apply the probabilities, you get a geometric sequence with initial value 0.25, and common ratio of 0.25. You can then use the formula for sum to infinity of a geometric series to discover that the final probability is 1/3rd for each option:
Sum to infinity = a/(1 - r) where a = initial value, r = common ratio
S = 0.25/0.75 = 1/3
Minimal statistics knowledge required, except recognising that the recursion doesn't reset the game, it adds an additional probability of getting one of the options again (which you can visualise with a probability tree if you want)
(edited 6 years ago)
Original post by uponthyhorse
this should work, you've got a 0.25 probability of each option still. When you recursively apply the probabilities, you get a geometric sequence with initial value 0.25, and common ratio of 0.25. You can then use the formula for sum to infinity of a geometric series to discover that the final probability is 1/3rd for each option:
Sum to infinity = a/(1 - r) where a = initial value, r = common ratio
S = 0.25/0.75 = 1/3
Minimal statistics knowledge required, except recognising that the recursion doesn't reset the game, it adds an additional probability of getting one of the options again (which you can visualise with a probability tree if you want)
Sum to infinity = a/(1 - r) where a = initial value, r = common ratio
S = 0.25/0.75 = 1/3
Minimal statistics knowledge required, except recognising that the recursion doesn't reset the game, it adds an additional probability of getting one of the options again (which you can visualise with a probability tree if you want)
Thanks, I think I remember coming across something like that where a probability is supposedly altered by something that happened previously, as if the previous action is having a mysterious residual effect, but it was quite controversial and loads of PHD students protested against its validity. Not sure if that's something completely different though haha! Also, I'm currently contemplating further maths modules for next year, could you suggest which would be most helpful with the CSAT, further pure or stats?
Cheers!
Original post by Peractio
Hi jameshyland, your method appears to be the same as mine.
You say that you "altered (a) to 'toss coin, if heads go to (b), otherwise toss coin, if heads output three, otherwise restart (a)'"
Your answer can be rewritten as:
- (a) unchanged i.e. if heads go to (b), if tails go to (c)
- (c) changed to: if heads output three, otherwise restart/go to (a)
Our answers are essentially the same!
You say that you "altered (a) to 'toss coin, if heads go to (b), otherwise toss coin, if heads output three, otherwise restart (a)'"
Your answer can be rewritten as:
- (a) unchanged i.e. if heads go to (b), if tails go to (c)
- (c) changed to: if heads output three, otherwise restart/go to (a)
Our answers are essentially the same!
Hi Peractio,
Thank you, I thought so!
This year's sample paper has been published on the website: https://www.cl.cam.ac.uk/admissions/undergraduate/admissions-test/sample-test-3.pdf
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test
@ImprobableCacti @uponthyhorse
I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test
@ImprobableCacti @uponthyhorse I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
(edited 6 years ago)
Original post by CompSciCat
This year's sample paper has been published on the website: https://www.cl.cam.ac.uk/admissions/undergraduate/admissions-test/sample-test-3.pdf
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test @ImprobableCacti @uponthyhorse
I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test
@ImprobableCacti @uponthyhorse I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
The 2017 past papers for the courses with a pre-interview assessment are available too, eg ENGAA for Engineering. I don't know how long they've been available but I hadn't noticed them before.
Posted from TSR Mobile
Original post by CompSciCat
This year's sample paper has been published on the website: https://www.cl.cam.ac.uk/admissions/undergraduate/admissions-test/sample-test-3.pdf
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test @ImprobableCacti @uponthyhorse
I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test
@ImprobableCacti @uponthyhorse I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
Oh damn this gives me flashbacks
Some of those questions I now recognise as very simple STEP style questions but others I still don't know what to do. Will definitely do them out of curiosity EDIT: Good luck for your exams! My first one is in 4 weeks But the rest are in 7 weeks.
(edited 6 years ago)
Original post by uponthyhorse
Oh damn this gives me flashbacks Some of those questions I now recognise as very simple STEP style questions but others I still don't know what to do. Will definitely do them out of curiosity
EDIT: Good luck for your exams! My first one is in 4 weeks But the rest are in 7 weeks.
Some of those questions I now recognise as very simple STEP style questions but others I still don't know what to do. Will definitely do them out of curiosity EDIT: Good luck for your exams! My first one is in 4 weeks But the rest are in 7 weeks.
Yup, the difficulty seems to vary significantly between questions
Good luck to you too!
I have 3 at at the beginning of May, but then a 3-4 week break until my last 2 in June, so still quite a while until I finish as well
Original post by CompSciCat
This year's sample paper has been published on the website: https://www.cl.cam.ac.uk/admissions/undergraduate/admissions-test/sample-test-3.pdf
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test @ImprobableCacti @uponthyhorse
I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test
@ImprobableCacti @uponthyhorse I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
After learning FP2 (further maths module) half of this paper suddenly seems a million times easier...
Original post by CompSciCat
This year's sample paper has been published on the website: https://www.cl.cam.ac.uk/admissions/undergraduate/admissions-test/sample-test-3.pdf
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test @ImprobableCacti @uponthyhorse
I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
For 2019 entry prospective applicants or if any of this year's applicants want to relive the pain of sitting the test
@ImprobableCacti @uponthyhorse I will probably go through the questions out of interest after I'm done with my final exams (first one in 11 days rip). I've gotta say some of the questions definitely seemed harder under exam stress than they seem now haha (though I've also got better at maths since then so that is probably also a factor). However I would generally still say that test is harder than the other sample tests and kinda different.
Phwoar, this looks ridiculously hard! Think I'll stick to being good at NatSci maths...
Original post by ImprobableCacti
After learning FP2 (further maths module) half of this paper suddenly seems a million times easier...
I did fp2 before the interview and I still didn't get them
Original post by uponthyhorse
I did fp2 before the interview and I still didn't get them
Hahahaha 😄
We can add the new paper to the original post if anyone wants to do it for fun, I imagine it will still be useful for the applicants of THE FUTURE
Original post by uponthyhorse
We can add the new paper to the original post if anyone wants to do it for fun, I imagine it will still be useful for the applicants of THE FUTURE
Sample paper 3 which they've added to the website is the exact one that was administered this year, quite a tough one.
I went over some questions during a free I had today at school (chemistry revision? what chemistry revision?), so here are some (hopefully correct) answers:
section A, question 2:
section A, question 3
section A, question 4
section A, question 6
Question 3 and 4 I did in the exam, the other two I didn't do back then. I am also pretty sure I have a solution for question 8, and some from B, but I'm going to have another look over them before typing them up
(Please point out any stupid mistakes if I made them)
section A, question 2:
Spoiler
section A, question 3
Spoiler
section A, question 4
Spoiler
section A, question 6
Spoiler
Question 3 and 4 I did in the exam, the other two I didn't do back then. I am also pretty sure I have a solution for question 8, and some from B, but I'm going to have another look over them before typing them up
(Please point out any stupid mistakes if I made them
)(edited 6 years ago)
Original post by CompSciCat
I went over some questions during a free I had today at school (chemistry revision? what chemistry revision?), so here are some (hopefully correct) answers:
section A, question 2:
section A, question 3
section A, question 4
section A, question 6
Question 3 and 4 I did in the exam, the other two I didn't do back then. I am also pretty sure I have a solution for question 8, and some from B, but I'm going to have another look over them before typing them up
(Please point out any stupid mistakes if I made them)
section A, question 2:
Spoiler
section A, question 3
Spoiler
section A, question 4
Spoiler
section A, question 6
Spoiler
Question 3 and 4 I did in the exam, the other two I didn't do back then. I am also pretty sure I have a solution for question 8, and some from B, but I'm going to have another look over them before typing them up
(Please point out any stupid mistakes if I made them
)In the exam I also tried to do question 6 by assuming it was triangular but I think you can't do this, because you don't know if it's an "if and only if" scenario (to use STEP terminology). I realized I'd done it wrong as soon as I finished the exam. Your solution is the right one I'm pretty sure.
edit: what I'm trying to say is I think you can't assume what you're trying to prove because there could be other scenarios if that makes sense. Like if you're proving that all squares are rectangles you can't prove it by the reverse argument, because only a certain set of rectangles are squares.
(edited 6 years ago)
Original post by uponthyhorse
In the exam I also tried to do question 6 by assuming it was triangular but I think you can't do this, because you don't know if it's an "if and only if" scenario (to use STEP terminology). I realized I'd done it wrong as soon as I finished the exam. Your solution is the right one I'm pretty sure.
yeah that's what I thought, you can't assume the thing you're trying to prove, though isn't what I wrote basically the same just in reverse order?
Original post by CompSciCat
I went over some questions during a free I had today at school (chemistry revision? what chemistry revision?), so here are some (hopefully correct) answers:
section A, question 2:
section A, question 3
section A, question 4
section A, question 6
Question 3 and 4 I did in the exam, the other two I didn't do back then. I am also pretty sure I have a solution for question 8, and some from B, but I'm going to have another look over them before typing them up
(Please point out any stupid mistakes if I made them)
section A, question 2:
Spoiler
section A, question 3
Spoiler
section A, question 4
Spoiler
section A, question 6
Spoiler
Question 3 and 4 I did in the exam, the other two I didn't do back then. I am also pretty sure I have a solution for question 8, and some from B, but I'm going to have another look over them before typing them up
(Please point out any stupid mistakes if I made them
)I’m pretty sure that out of these I only attempted q3. *facepalm*.
God knows how I got an offer.
(edited 6 years ago)
Some more attempts (this totally counts as studying for my maths exam on Wednesday )
section B, question 15
section B, questions 16:
)section B, question 15
Spoiler
section B, questions 16:
Spoiler
btw just noticed that the department website now states that "starting with 2018, the duration of the CSAT will be 120 minutes, an increase from 100 minutes (this does not imply that difficulty must also increase)"
Good change in my opinion Also in line with the fact that even though my feedback stated that I was around average in the CSAT, the more questions I do the more I realised how wrong many of my attempts are, so the average must've been pretty bad this year...
Good change in my opinion
Also in line with the fact that even though my feedback stated that I was around average in the CSAT, the more questions I do the more I realised how wrong many of my attempts are, so the average must've been pretty bad this year...Quick Reply
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