# Extra MAT 2023

How did you guys do on the MAT 😭😭?

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it went ok, the questions were easier than the last one imo.
Original post by annieelhm
How did you guys do on the MAT 😭😭?

Went better than I expected, I think this one was easier than the other additional MCQs.
What did u guys get for the sequence for the sum of k^3?
Original post by harvey_specterx
Went better than I expected, I think this one was easier than the other additional MCQs.
What did u guys get for the sequence for the sum of k^3?

19900 i think
What did you guys get for the first question i think i picked c or whatever option had a 3 at the end.
For the second q i picked the logarithm with the 10 in it and stuff.
For the sum of k^3 i think 19900-I can't remember the question
For that product of roots question i got 2- I used further maths and did e/a. pretty sure for the quartic we were given we had 1 as a and e as 2.Cus they don't care about workings for this test.
For the last question I got graph d which i checked on desmos is correct.Since it was (x+y)^4=x^2 in disguise.
For the vector question i said there were two vectors.(1,-1) and. (-1,1)
For the question involving triangle nums in it i said it can represent all positive integers except the triangle numbers which i think was e.
For the question with x^2+3y^2=4442 i guessed at the end there were 3 pairs of solutions but that was dumb cause there's probably 0 most likely got that one wrong.
I can't remember the other questions if anyone can and share answers that would be helpful.
(edited 1 week ago)
Original post by TheOneRing19
What did you guys get for the first question i think i picked c or whatever option had a 3 at the end.
For the second q i picked the logarithm with the 10 in it and stuff.
For the sum of k^3 i think 19900-I can't remember the question
For that product of roots question i got 2- I used further maths and did e/a. pretty sure for the quartic we were given we had 1 as a and e as 2.Cus they don't care about workings for this test.
For the last question I got graph d which i checked on desmos is correct.Since it was (x+y)^4=x^2 in disguise.
For the vector question i said there were two vectors.(1,-1) and. (-1,1)
For the question involving triangle nums in it i said it can represent all positive integers except the triangle numbers which i think was e.
For the question with x^2+3y^2=4442 i guessed at the end there were 3 pairs of solutions but that was dumb cause there's probably 0 most likely got that one wrong.
I can't remember the other questions if anyone can and share answers that would be helpful.

There was the lines one (I put 15) but I think the answer is 13. There was the sum of 20^-d(n) which was 9/10
Original post by TheOneRing19
What did you guys get for the first question i think i picked c or whatever option had a 3 at the end.
For the second q i picked the logarithm with the 10 in it and stuff.
For the sum of k^3 i think 19900-I can't remember the question
For that product of roots question i got 2- I used further maths and did e/a. pretty sure for the quartic we were given we had 1 as a and e as 2.Cus they don't care about workings for this test.
For the last question I got graph d which i checked on desmos is correct.Since it was (x+y)^4=x^2 in disguise.
For the vector question i said there were two vectors.(1,-1) and. (-1,1)
For the question involving triangle nums in it i said it can represent all positive integers except the triangle numbers which i think was e.
For the question with x^2+3y^2=4442 i guessed at the end there were 3 pairs of solutions but that was dumb cause there's probably 0 most likely got that one wrong.
I can't remember the other questions if anyone can and share answers that would be helpful.

How confident are you in the quartic question? I half guessed 2 but was very uncertain
Original post by TheOneRing19
What did you guys get for the first question i think i picked c or whatever option had a 3 at the end.
For the second q i picked the logarithm with the 10 in it and stuff.
For the sum of k^3 i think 19900-I can't remember the question
For that product of roots question i got 2- I used further maths and did e/a. pretty sure for the quartic we were given we had 1 as a and e as 2.Cus they don't care about workings for this test.
For the last question I got graph d which i checked on desmos is correct.Since it was (x+y)^4=x^2 in disguise.
For the vector question i said there were two vectors.(1,-1) and. (-1,1)
For the question involving triangle nums in it i said it can represent all positive integers except the triangle numbers which i think was e.
For the question with x^2+3y^2=4442 i guessed at the end there were 3 pairs of solutions but that was dumb cause there's probably 0 most likely got that one wrong.
I can't remember the other questions if anyone can and share answers that would be helpful.

For the ellipse (if its integer x,y)
x^2+3y^2=4442
there are no solutions
Original post by abc1234!
There was the lines one (I put 15) but I think the answer is 13. There was the sum of 20^-d(n) which was 9/10

Same I also put 15 ,explain a bit on why you think it was 13 because i think thats probably true now that i started thinking about it more.I also got 9/10 for the sum things.
(edited 1 week ago)
Original post by mqb2766
For the ellipse (if its integer x,y)
x^2+3y^2=4442
there are no solutions

How'd you know that the ellipse had no integer points on it tho?It's clear to see from desmos of course but how'd you find that out in the exam? Did you just assume it was super unlikely?
Original post by abc1234!
How confident are you in the quartic question? I half guessed 2 but was very uncertain

If you tell me the full equation we had to find the product of the roots of i can tell you I'm sure since i don't clearly remember but i do seem to remember it being e=2 and a=1 so 2/1=2.In further maths the topic is called roots of polynomials.Where in a quartic ax^4+bx^3+cx^2+dx+e we use e/a to get the product of polynomial roots.
(edited 1 week ago)
Original post by TheOneRing19
How'd you know that the ellipse had no integer points on it tho?It's clear to see from desmos of course but how'd you find that out in the exam? Did you just assume it was super unlikely?

The 3 coefficient is a bit of a hint.
*4442 is 2 mod 3
*squares are 0,1 mod 3 and 3y^2 is 0 mod 3,
so the left hand side is 0,1 mod 3 but the right hand side is 2 mod 3 so no solutions.
Original post by TheOneRing19
If you tell me the full equation we had to find the product of the roots of i can tell you I'm sure since i don't clearly remember but i do seem to remember it being e=2 and a=1 so 2/1=2.In further maths the topic is called roots of polynomials.Where in a quartic ax^4+bx^3+cx^2+dx+e we use e/a to get the product of polynomial roots.

I think that a was 2, I knew this but completely forgot to use roots of polynomials
Original post by Anonymous
I think that a was 2, I knew this but completely forgot to use roots of polynomials

Are you sure? I can't remember it being 2. I remember e being 2 and a being 1.If not then i've screwed up massively despite literally knowing how to get the answer.
Original post by mqb2766
The 3 coefficient is a bit of a hint.
*4442 is 2 mod 3
*squares are 0,1 mod 3 and 3y^2 is 0 mod 3,
so the left hand side is 0,1 mod 3 but the right hand side is 2 mod 3 so no solutions.

Ngl that's clever your probably gonna get in.Also did you get 15 for the lines question?And 2 for that product of roots question?
(edited 1 week ago)
Original post by TheOneRing19
Ngl that's clever your probably gonna get in.

The mod stuff is just another way of talking about remainders so its just saying
y^2 = (4442-x^2)/3 = 4442/3 - x^2/3
so the first term 4442/3 is remainder 2 and the only way for the right hand side to be an integer (nevermind a square) is if x^2/3 is remainder 2 which never happens.

The squares and 3 (divisor) were the hint and the fact that 4442 isnt a square so there wasnt going to be a nice factorisation.
Original post by mqb2766
The mod stuff is just another way of talking about remainders so its just saying
y^2 = (4442-x^2)/3 = 4442/3 - x^2/3
so the first term 4442/3 is remainder 2 and the only way for the right hand side to be an integer (nevermind a square) is if x^2/3 is remainder 2 which never happens.

The squares and 3 (divisor) were the hint and the fact that 4442 isnt a square so there wasnt going to be a nice factorisation.

Also did you get 15 for the lines question?And 2 for that product of roots question?
Original post by TheOneRing19
Also did you get 15 for the lines question?And 2 for that product of roots question?

I didnt do it, what were the questions?
Original post by mqb2766
I didnt do it, what were the questions?

Oh sorry lol, i realise you meant you haven't done the test
(edited 1 week ago)
Original post by TheOneRing19
Oh sorry lol, i realise you meant you haven't done the test

product of roots was 1 (constant term was 2, and coefficient on x^4 term was 2)
lines question was 13 as there were 16 lines in total, so its clear that y = 1 - 10x is gonna 'touch' all 16, but take away 3 from 16 as 3 points are intersections between all three graphs (namely at y = 0, -1/3, -2/3 if i remember correctly)