**HL Maths Paper 2 before/after**

outnumbered

Slow Show wrote: »

We don't have to prove them though, just apply them, right?

Yeah we do have to prove them.... unfortunately
Well i don't see it happening, They don't want us learning off stuff sure!

Slow Show

outnumbered wrote: »

Yeah we do have to prove them.... unfortunately
Well i don't see it happening, They don't want us learning off stuff sure!

Erm...does anyone have a source of this as I've heard nothing of the sort? Bearing in mind I haven't a notion of touching 6B so if that's where they crop up then I'm not fussed.

yournerd

whats mean median deviattion?

outnumbered

Slow Show wrote: »

Erm...does anyone have a source of this as I've heard nothing of the sort? Bearing in mind I haven't a notion of touching 6B so if that's where they crop up then I'm not fussed.

Source: Page 382 Active Maths and My Teacher.
"Students must be able to give formal proofs of the following in examination: 4,6,14,19,11,12,13.
Theorem 4,6,14 and 19 are JC but may also be examined at LC level."

EDIT NB::: Pythagoras theorem is not included in them. apologies.

Slow Show

outnumbered wrote: »

Source: Page 382 Active Maths and My Teacher.
"Students must be able to give formal proofs of the following in examination: 4,6,14,19,11,12,13.
Theorem 4,6,14 and 19 are JC but may also be examined at LC level."

Heh that's not good. :L Ah 4 and 6 I could make up on the spot I think, I'm not likely to ever forget how to prove Pythagoras after JC, and hmmm 19, I'll have to give that one a look over.

I doubt they'll come up either but I guess it's worth giving them a quick look over.

Lukeyy

http://www.ncca.ie/en/Curriculum_and_Assessment/Post-Primary_Education/Project_Maths/Syllabuses_and_Assessment/Leaving_Cert_Maths_syllabus_for_examination_in_2013.pdf
Page 24 of that shows the Higher Level syllabus for this year. We've only to know how to prove 11, 12, 13 formally.

DarkDusk

Solution to problem above:

Constuct line perpendicular to tangent at P. Point S is where perpendicular hits circle at top. This is the diameter of the circle, because it is perpendicular the diameter.

Therefore PQS = 90, and TPS = PQS = 90. Mark SPQ as "A" and PSQ as 90-A.

Since TPS is 90, TPQ = 90-A. Therefore TPQ = PSQ.

PSQ and PRQ are lying on same arc, so they are equal. We now see that PRQ = TPQ. And so, triangle PQR is isosceles because it was two equal angles, which means that QP = QR

outnumbered

The letters of the word EUCLID are arranged at random. Find the prob that the three vowels are together? Anyone know hoe to do it?

Slow Show

outnumbered wrote: »

The letters of the word EUCLID are arranged at random. Find the prob that the three vowels are together? Anyone know hoe to do it?

EUI are always together as one unit, which means there are four possible spaces to be filled (EUI/C/L/D in any order), which is 4!. Then you have to remember EUI can be arranged in any order which is 3!. Multiply 4! x 3! and that's the answer.

Monsieur Folie

outnumbered wrote: »

The letters of the word EUCLID are arranged at random. Find the prob that the three vowels are together? Anyone know hoe to do it?

Okay, this is it I think:

There are 3! different ways the 3 vowels could be arranged together, that's 6. Treat the 3 vowels as one letter now, so you have 4 things to arrange (the 3 vowels as one thing, the consonants as the other 3 things) so there are 4! ways (24) of doing that, times the 3! ways of ordering the vowels themselves. 4! times 3! = 144

Now you have to get the probability, so you need the total number of ways the letters can be arranged with no restrictions, which is simply 6! or 720.

144/720 = 0.2 or 20% probability. (a fifth :P)

Can someone confirm that I've done this right?

outnumbered

Slow Show wrote: »

EUI are always together as one unit, which means there are four possible spaces to be filled (EUI/C/L/D in any order), which is 4!. Then you have to remember EUI can be arranged in any order which is 3!. Multiply 4! x 3! and that's the answer.

yeah that is what i did first. but it's the "probablity" not the number of ways.

outnumbered

Monsieur Folie wrote: »

Okay, this is it I think:

There are 3! different ways the 3 vowels could be arranged together, that's 6. Treat the 3 vowels as one letter now, so you have 4 things to arrange (the 3 vowels as one thing, the consonants as the other 3 things) so there are 4! ways (24) of doing that, times the 3! ways of ordering the vowels themselves. That gives you 30 ways in total that the letters can be arranged, keeping the 3 vowels together.

Now you have to get the probability, so you need the total number of ways the letters can be arranged with no restrictions, which is simply 6! or 720.

30/720 = 0.04167 or 4.167% probability.

Can someone confirm that I've done this right?

seems correct but the answer is actually 1/5

Monsieur Folie

outnumbered wrote: »

seems correct but the answer is actually 1/5

Crap.

I did it in a hurry, I'll repeat on paper now and see if I can spot an error.

Yep, spotted it! I added 24 and 6, instead of multiplying. Silly mistake. The answer indeed works out at a fifth, I'll fix that now. :P

outnumbered

Monsieur Folie wrote: »

Crap.

I did it in a hurry, I'll repeat on paper now and see if I can spot an error.

Yep, spotted it! I added 24 and 6, instead of multiplying. Silly mistake. The answer indeed works out at a fifth, I'll fix that now. :P

Brilliant! you're a beaut!

catherinek12

hey
i cant get an answer from anyone i know doing LC HL maths but is area on volume on paper 2 , sitting the exam tommorow and i dont wanna go in and open the paper to find it staring back at me, but i also dont wanna waste time studying it if its not even coming up ... HELP me please !:eek:

yournerd

How do I get Cos ^-1 (81/480) to be 99.72angle.

My calculator is being a nuthead.

outnumbered

yournerd wrote: »

How do I get Cos ^-1 (81/480) to be 99.72angle.

My calculator is being a nuthead.

it's 80.28 degrees
Just go mode 1 and try again.

catherinek12

dont forget trig identities and definitions for statistics

catherinek12

but no 1st principles came up on friday so ive a feeling they wont be making an apperance

catherinek12

and does area and volume come up on paper 2?

outnumbered

catherinek12 wrote: »

and does area and volume come up on paper 2?

no ,mybe area of triangle though

catherinek12

can proofs come up on paper one that under atopic that on paper two for example de moivre from complex numbers make an apperance on paper 2 because its a proof?

Slow Show

I think area and volume is Paper 2, in the sample the last question is a tetrahedron. It'd make sense for them to mix it in with trig, the two are pretty closely related after all.

Lukeyy

catherinek12 wrote: »

can proofs come up on paper one that under atopic that on paper two for example de moivre from complex numbers make an apperance on paper 2 because its a proof?

There's a DeMoivre trigonometric proof type question that could be asked I think

catherinek12

thanks have you anyclue about my other question though

catherinek12

so any of those proofs could come upComplex Numbers
• De Moivre’s Theorem
• De Moivre’s Theorem to Prove Trigonometric Identities
Differentiation
• 1st Principles

• General Rule
• Sum Rule
• Product Rule
• Quotient Rule
Integration
• Volume of Cone
• Volume of Sphere
Proof By Contradiction
• Proof that √2 is irrational
Trig identities

Lukeyy

catherinek12 wrote: »

so any of those proofs could come upComplex Numbers
• De Moivre’s Theorem
• De Moivre’s Theorem to Prove Trigonometric Identities
Differentiation
• 1st Principles

• General Rule
• Sum Rule
• Product Rule
• Quotient Rule
Integration
• Volume of Cone
• Volume of Sphere
Proof By Contradiction
• Proof that √2 is irrational
Trig identities

Diff and Integ ones won't come up on this paper but yeah everything else is possible.

Correct me if I'm wrong but isn't the Root 2 thing optional this year? You could use a simpler proof by contradiction.

I could be completely wrong about that though.

Acciaccatura

Area and volume is generally paper 1, but they might throw up one or two basic bits that'd involve the formulae in the log book. If you've studied it for paper 1 you should be ok

catherinek12

http://www.educate.ie/solutions/HL%20Solutions/HL%20SPC%20Solutions/HLSPCSoln(P2Q2).pdf
heres the answer to that q most answer are on educate.ie

catherinek12

thanks :P