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# MAT Prep Thread - 2nd November 2016 watch

1. Prove that x+Square root(1-x) <= 5/4
2. (Original post by Mystery.)
yes that's the type I meant. Like this question :https://www.imperial.ac.uk/media/imp...tions-2010.pdf
Q3 I
No, that's really not what I'm talking about, this is what algebraic geometry is: https://www.dpmms.cam.ac.uk/study/II...5-2016/HW1.pdf

(Original post by RuairiMorrissey)
I don't fully understand how you got that last term?
Do you mean how I got ? If so: what's the value of .
3. (Original post by GrungeGirl)
Can someone please explain to how to do this? It is from 2011, Q3.
Attachment 589816
Put the RHS under a common denominator i.e. 3b^2 -1 .
4. Also How would you sketch the below? I did algebraic division and got 1-2/x^2-5x+6 and drew a parabola but when I put it into wolfram alpha it looks different

((x-1)(x-4))/((x-2)(x-3))

(Original post by Zacken)
No, that's really not what I'm talking about, this is what algebraic geometry is: https://www.dpmms.cam.ac.uk/study/II...5-2016/HW1.pdf

ohh looks like fun.
5. nevermind i got it
6. Edit: Also this;
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Is this question correct, the mark scheme shows a different answer
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7. I think I am being really stupid here but I tried to do a graph because the standard way doesn't work
Attached Images

8. Could anyone explain q3 2013 pls. I dont understand the last two bits at all.
https://www.maths.ox.ac.uk/system/fi...nts/test13.pdf
9. stuck on part ii
Attached Images

10. (Original post by Mystery.)
stuck on part ii
Lad are these MAT questions? where are you finding them?
11. (Original post by joodaa)
Lad are these MAT questions? where are you finding them?
yeah man like 2000s
12. (Original post by Mystery.)
stuck on part ii
a^3x + a^-3x is a sum of cubes so equals (a^x + a^-x)(a^2x -1 + a^-2x)

a^2x + a^-2x = 4y^2-2 which is just squaring a^x + a^-x = 2y

so equals 2z=(2y)(4y^2-3) then just expand
13. (Original post by 11234)
Could anyone explain q3 2013 pls. I dont understand the last two bits at all.
https://www.maths.ox.ac.uk/system/fi...nts/test13.pdf
pls help im so confused with this one
14. (Original post by 11234)
a^3x + a^-3x is a sum of cubes so equals (a^x + a^-x)(a^2x -1 + a^-2x)

a^2x + a^-2x = 4y^2-2 which is just squaring a^x + a^-x = 2y

so equals 2z=(2y)(4y^2-3) then just expand
Thanks!
What's the way to spot a sum of cubes ?
15. (Original post by Mystery.)
Thanks!
What's the way to spot a sum of cubes ?
i just learnt the identities so x^3 + y^3 = (x+y)(x^2-xy+y^2)

x^3-y^3= (x-y)(x^2 + xy + y^2)
16. (Original post by Mystery.)
yeah man like 2000s
i found that the old ones are much easier than the new ones
17. (Original post by 11234)
i found that the old ones are much easier than the new ones
yeah they are.
18. (Original post by 11234)
pls help im so confused with this one
if you look at part iii, the f(k)...=-f(2-k)... so it has been reflected in the x-axis
then it also changes from (1+t) to (1-t) essentially this is a reflection the line x=1 because for example if you sub t=0 you get the same function so that is the axis of symmetry
when you reflect or move a graph the area stays the same
19. I got it, I think anyway. Could you take a look at what I did please?

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20. (Original post by KloppOClock)
Edit: Also this;
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Is this question correct, the mark scheme shows a different answer
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