# CSAT Sample Paper Answers and Discussion

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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

Question 1 by Forecast

Question 2 by Forecast

Question 3 by uponthyhorse

Question 4 by Forecast

Question 5 by uponthyhorse

Question 6 ???

Question 7 by Lelanor

Question 8 by irishapplicant

Question 9 by uponthyhorse

Question 10 by Squiidsquid

Question 11 by Forecast

Question 12 by Integer123

Question 13 by Squiidsquid (beware, also links to answers for 14 and 19)

Question 14 by uponthyhorse + Squiidsquid (No method)

Question 15 by Forecast

Question 16 by Forecast

Question 17 by irishapplicant

Question 18 by uponthyhorse

Question 19 by uponthyhorse + Squiidsquid

Question 20 by TTTRRee

Solutions to Sample Paper 2

Question 1 by uponthyhorse

Question 2 by kishen111

Question 3 by uponthyhorse

Question 4 by southpacific

Question 5 by uponthyhorse

Question 6 by Sirlamb

Question 7 by Sirlamb

Question 8 by kishen111

Question 9 by Peractio

Question 10 by Sirlamb

Question 11 by LaiFuShi (and loads of other people, I just kept forgetting to put this on the original post! Sorry guys!)

Question 12 by mayanksharma318

Question 13 by Integer123

Question 14 by uponthyhorse

Question 15 by uponthyhorse

Question 16 by southpacific

Question 17 by Peractio

Question 19 by uponthyhorse + kishen111

Question 20 by uponthyhorse

Post solutions with spoiler blocks so anyone looking for an answer to another question doesn't read yours by accident, and please specify the paper and question number. Thanks!

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

Question 6 ???

Question 7 by Lelanor

Question 8 by irishapplicant

**Section B**Question 9 by uponthyhorse

Question 10 by Squiidsquid

Question 11 by Forecast

Question 12 by Integer123

Question 13 by Squiidsquid (beware, also links to answers for 14 and 19)

Question 14 by uponthyhorse + Squiidsquid (No method)

Question 15 by Forecast

Question 16 by Forecast

Question 17 by irishapplicant

Question 18 by uponthyhorse

Question 19 by uponthyhorse + Squiidsquid

Question 20 by TTTRRee

Solutions to Sample Paper 2

**Section A**Question 1 by uponthyhorse

Question 2 by kishen111

Question 3 by uponthyhorse

Question 4 by southpacific

Question 5 by uponthyhorse

Question 6 by Sirlamb

Question 7 by Sirlamb

Question 8 by kishen111

**Section B**Question 9 by Peractio

Question 10 by Sirlamb

Question 11 by LaiFuShi (and loads of other people, I just kept forgetting to put this on the original post! Sorry guys!)

Question 12 by mayanksharma318

Question 13 by Integer123

Question 14 by uponthyhorse

Question 15 by uponthyhorse

Question 16 by southpacific

Question 17 by Peractio

Question 19 by uponthyhorse + kishen111

Question 20 by uponthyhorse

Post solutions with spoiler blocks so anyone looking for an answer to another question doesn't read yours by accident, and please specify the paper and question number. Thanks!

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Sample Paper 1, Q3:

Spoiler:

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

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

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Sample Paper 1, Q5 (Not sure about this one)

Spoiler:

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.

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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.

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#9

Sample Paper 1, Q15:

Spoiler:

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 .

Show

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 .

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#10

Sample Paper 1, Q16:

Spoiler:

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 .

Further reading: https://en.wikipedia.org/wiki/Rule_of_72

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.

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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 .

Further reading: https://en.wikipedia.org/wiki/Rule_of_72

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.

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#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???

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#12

(Original post by

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???

**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???

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(Original post by

Has anyone done questions from Sample Paper 2?

**kishen111**)Has anyone done questions from Sample Paper 2?

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#15

(Original post by

Yes I'll try and type them up, are there any questions in particular you wanted to discuss?

**uponthyhorse**)Yes I'll try and type them up, are there any questions in particular you wanted to discuss?

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#16

(Original post by

1, 2 and 3 of Section A please. I've done 2 and 3, but I don't even understand question 1.

**kishen111**)1, 2 and 3 of Section A please. I've done 2 and 3, but I don't even understand question 1.

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#17

(Original post by

I got 8 for question 2 sample paper 2

**fp1washard**)I got 8 for question 2 sample paper 2

My answer:

Spoiler:

12 hmm...

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12 hmm...

Spoiler:

CEDAB,CADEB,AECDB,EACDB,ACEDB,EC ADB,ACDEB,ECDAB,CDEAB,CDAEB,CAED B,CEADB

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CEDAB,CADEB,AECDB,EACDB,ACEDB,EC ADB,ACDEB,ECDAB,CDEAB,CDAEB,CAED B,CEADB

Are these correct?

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(Original post by

My answer:

Are these correct?

**kishen111**)My answer:

Spoiler:

12 hmm...

Show

12 hmm...

Spoiler:

CEDAB,CADEB,AECDB,EACDB,ACEDB,EC ADB,ACDEB,ECDAB,CDEAB,CDAEB,CAED B,CEADB

Show

CEDAB,CADEB,AECDB,EACDB,ACEDB,EC ADB,ACDEB,ECDAB,CDEAB,CDAEB,CAED B,CEADB

Are these correct?

(Original post by

I got 8 for question 2 sample paper 2

**fp1washard**)I got 8 for question 2 sample paper 2

For a more in depth explanation:

Spoiler:

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.

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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.

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**kishen111**)

1, 2 and 3 of Section A please. I've done 2 and 3, but I don't even understand question 1.

Spoiler:

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.

Show

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.

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Sample Paper 2, Question 3:

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