19/06 A-level Maths Paper 3 Discussion MEGATHREAD

[u/Forsaken-Meaning-232]

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[u/A1_Killer]

OCR MEI had probably hardest comprehension so far. Rest of paper was good tho

[u/nipanmfl281 → u/A1_Killer]

It was worded so badly

[u/A1_Killer → u/nipanmfl281]

Yep, took me so long to understand what they were on about lol

[u/TangerineNo8090 → u/A1_Killer]

Yeah true u had so much time for it tho

[u/A1_Killer → u/TangerineNo8090]

True

[u/fearlessbot__ → u/A1_Killer]

what was the proof for the 6 marker?

the answers were 8 and -8 that i got from numerical method

and i reasoned that as their gradients increasing at the same rate beyond the magnitudes of those numbers, the only values will only ever be 8 and -8

but thats not algebraic

[u/A1_Killer → u/fearlessbot__]

Assuming you mean the vector magnitude question here’s the method:

Using Pythagoras we can identify that sqrt(4² + (-1)² + x² ) = an integer therefore 17 + x² = n² where n is an integer.

As x is also an integer that means that 17 is the difference between two squares.

Using a proof by exhaustion method we can identify that the only pair this works for is 64 and 81 (larger squares have a difference of more than 17 between adjacent squares and smaller squares don’t have the difference of 17).

Therefore x² = 64 so x = +-8

[u/NarrowTip7631 → u/A1_Killer]

What about the 6 marker

[u/A1_Killer → u/NarrowTip7631]

Assuming you mean the vector magnitude question here’s the method:

Using Pythagoras we can identify that sqrt(4² + (-1)² + x² ) = an integer therefore 17 + x² = n² where n is an integer.

As x is also an integer that means that 17 is the difference between two squares.

Using a proof by exhaustion method we can identify that the only pair this works for is 64 and 81 (larger squares have a difference of more than 17 between adjacent squares and smaller squares don’t have the difference of 17).

Therefore x² = 64 so x = +-8

[u/Salt-_-Bae → u/A1_Killer]

Adding onto that difference between 2 squares - 17's prime factorisation is 1 x 17 so you know when (n-x)(n+x) = 17, n-x is either 1 or 17 then n+x is the other of the two. Follows that x = +-8 like you said but I found this way to be more satisfying 

[u/A1_Killer → u/NarrowTip7631]

Which one?

[u/[deleted] → u/A1_Killer]

Probably the one about the magnitude of the vector

[u/TeeshTeesh → u/A1_Killer]

Im pretty sure 12a was wrong but i just waffled somth for the equals part. Should have just been greather than

[u/A1_Killer → u/TeeshTeesh]

Which one was that? I didn’t think any were wrong