!! OL Maths 2015 predictions, discussion etc

leavingcert15

What theorems do we need to know?

skippy1977

leavingcert15 wrote: »

What theorems do we need to know?

You need to know and understand (but not prove) all of them!

Theorem 1 (Vertically-opposite Angles)
Vertically opposite angles are equal in measure.
Theorem 2 (Isosceles Triangles)
In an isosceles triangle the angles opposite the equal sides are equal.
Conversely, if two angles are equal, then the triangle is isosceles.
Theorem 3 (Alternate Angles)
If a transversal makes equal alternate angles on two lines, then the lines are parallel.
Conversely, if two lines are parallel, then any transversal will make equal alternate angles with them.
Theorem 4 (Angle Sum 180)
The angles in any triangle add to 180°.
Theorem 5 (Corresponding Angles)
Two lines are parallel if and only if for any transversal, corresponding angles are equal.
Theorem 6 (Exterior Angle)
Each exterior angle of a triangle is equal to the sum of the interior opposite angles.
Theorem 7
The angle opposite the greater of two sides is greater than the angle opposite the lesser side.
Conversely, the side opposite the greater of two angles is greater than the side opposite the lesser angle.
Theorem 8 (Triangle Inequality)
Two sides of a triangle are together greater than the third.
Theorem 9
In a parallelogram, opposite sides are equal, and opposite angles are equal.
Converse 1 to Theorem 9:
If the opposite angles of a convex quadrilateral are equal, then it is a parallelogram.
Converse 2 to Theorem 9:
If the opposite sides of a convex quadrilateral are equal, then it is a parallelogram.
Theorem 10
The diagonals of a parallelogram bisect one another.
Theorem 11
If three parallel lines cut off equal segments on some transversal line, then they will cut off equal segments on any other transversal.
Theorem 12
Let ∆ABC be a triangle. If a line l is parallel to BC and cuts [AB] in the ratio s:t, then it also cuts [AC] in the same ratio.
Theorem 13
If two triangles ∆ABC and ∆A' B' C' are similar, then their sides are proportional, in order.
Theorem 14 (Pythagoras)
In a right-angle triangle the square of the hypotenuse is the sum of the squares of the other two sides.
Theorem 15 (Converse to Pythagoras)
If the square of one side of a triangle is the sum of the squares of the other two, then the angle opposite the first side is a right angle.
Theorem 16
For a triangle, base times height does not depend on the choice of base.
Theorem 17
A diagonal of a parallelogram bisects the area.
Theorem 18
The area of a parallelogram is the base by the height.
Theorem 19
The angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.
Theorem 20
Each tangent is perpendicular to the radius that goes to the point of contact.
If P lies on the circle, s, and a line l through P is perpendicular to the radius to P, then l is tangent to s.
Theorem 21
The perpendicular from the centre to a chord bisects the chord.
The perpendicular bisector of a chord passes through the centre.

hooked96

skippy1977 wrote: »

Hi there, exactly. That was a geometry question and geometry is still being tested. Nothing has been dropped from the syllabus and you still need to know how to apply your theorems.

Thanks so much for clearing things up Skippy

Kremin wrote: »

You don't know... the proof of a theorem doesnt have to come up either, they could just ask us to do both now, neither, or one or the other... no more choices and you MUST know everything

Thanks, I'm a little more clear headed now

KatieGhomie

Tet2015 wrote: »

Hypothesis Testing:

1.

H0 (zero is supposed to be small and lowered to ground of H, like an inverse H^0) = null hypothesis e.g. Coin not biased
H1 = alternative hypothesis e.g. Coin is biased

2. Write down / calculate sample proportion (p -with an arrow on its head-)

3. Find margin of error (1/-root sign-n)

4. Write down confidence interval for p using:

sample proportion - margin of error < p < sample proportion + margin of error

5. If population proportion is within confidence interval, accept H0. If outside, reject H0 and accept H1.

EXPLANATIONS:
A sample proportion is the number of targeted people examined. Let's say "the results of a survey finds that 112 of 400 households keep a condom in their sock", in this case the targeted people are 112, so the sample proportion is 112/400.

The sample size is total amount of people, which is 400 in the case of households that don't keep condoms in their socks. So sample size (n) = 400

The null hypothesis or H0 is the assumption or statement made, e.g. "KatieG spends 45% of her day in the closet".
The alternative hypothesis or H1 is a change in null hypothesis, it shows that H0 is wrong e.g. "KatieG does not spend 45%....."

Apologies for not being clearer, LINK TO RESOURCE HERE: [
Thank you thank you will have a look at it tmro just seen ur link there

Tet2015 wrote: »

Updated post, check and np!

THANK YOU,thank you will check it out tmro. Wrecked after today.Must sleep haah

IrishLoriii

Does anybody remember the table for Standard deviation by any chance??

gracew

Can someone list the chapters from paper 2 for me please? They're all mixed up in my book and am afraid I'll miss one after yesterday!

IrishLoriii

Guys if anyone had an awful teacher like me all of the CONSTRUCTIONS are on youtube done out in perfect detail on how to DRAW them Seriously use it!!

gracew wrote: »

Can someone list the chapters from paper 2 for me please? They're all mixed up in my book and am afraid I'll miss one after yesterday!

Im going by my book 2 but I know that some stuff is taken from paper 1 like the trap rule and all so cover all bases-
Probability
Statistics
Counting and Permutations
Geometry
Constructions
Length, Area and Volume
Co-Ordinate Gemoetry- The line
Co-Ordinate Geometry- The Circle
Transformations and Enlargements
Trigonometry

Famoso

skippy1977 wrote: »

You need to know and understand (but not prove) all of them!

Theorem 1 (Vertically-opposite Angles)
Vertically opposite angles are equal in measure.
Theorem 2 (Isosceles Triangles)
In an isosceles triangle the angles opposite the equal sides are equal.
Conversely, if two angles are equal, then the triangle is isosceles.
Theorem 3 (Alternate Angles)
If a transversal makes equal alternate angles on two lines, then the lines are parallel.
Conversely, if two lines are parallel, then any transversal will make equal alternate angles with them.
Theorem 4 (Angle Sum 180)
The angles in any triangle add to 180°.
Theorem 5 (Corresponding Angles)
Two lines are parallel if and only if for any transversal, corresponding angles are equal.
Theorem 6 (Exterior Angle)
Each exterior angle of a triangle is equal to the sum of the interior opposite angles.
Theorem 7
The angle opposite the greater of two sides is greater than the angle opposite the lesser side.
Conversely, the side opposite the greater of two angles is greater than the side opposite the lesser angle.
Theorem 8 (Triangle Inequality)
Two sides of a triangle are together greater than the third.
Theorem 9
In a parallelogram, opposite sides are equal, and opposite angles are equal.
Converse 1 to Theorem 9:
If the opposite angles of a convex quadrilateral are equal, then it is a parallelogram.
Converse 2 to Theorem 9:
If the opposite sides of a convex quadrilateral are equal, then it is a parallelogram.
Theorem 10

Well, there goes my D3.

Kremin

Famoso wrote: »

Well, there goes my D3.

You realise max one of these will come up? Even if you dont know it worst case scenario is you lose 25 marks.

IrishLoriii

This is a really stupid question but remember I am really really bad at maths..is a theorem the same as a construction?? These chapters are just a blur to me Ive spent all morning going through probability and statistics

Kremin

IrishLoriii wrote: »

This is a really stupid question but remember I am really really bad at maths..is a theorem the same as a construction?? These chapters are just a blur to me Ive spent all morning going through probability and statistics

No. A geometry theorem proof is proving for example, the angles in a triangle add to 180*, Pythagoras' theorem etc..
Constructions are where you use geometry sets and have to draw a circle inside a triangle etc.

Theorems= require proving things.
Constructions: draw something.

theLuggage

You should be able to work this out on your calculator. Calculator instructions for the Casio Natural Display and for one the Sharp models is on the project maths site:

http://www.projectmaths.ie/for-students/learn-to-use-calculators/

There is a link there for calculating standard deviation.

KatieGhomie

IrishLoriii wrote: »

Does anybody remember the table for Standard deviation by any chance??

no sorry does anyone if so explain????? god I am so screwed for paper two spend more time studying for the first one

theLuggage wrote: »

You should be able to work this out on your calculator. Calculator instructions for the Casio Natural Display and for one the Sharp models is on the project maths site:



There is a link there for calculating standard deviation.

Thank you,seriously love people on boards.ie everyone is so helpful
Could I ask what are you focusing on for paper two I am scared I won't be able to even attempt half the q's on it .

brickeyvalley

From a teachers perspective it was a nice, varied paper that made students think, normally the (a) and (b) were easy in the short 1 - 6, E.g. Q1 the (a) (b) were easy but then you needed to know how to get the i or something. The point of this being so difficult is because now the SEC have decided that Project Maths works and now have to upper the standard to that of other European countries (hence the development of project mats, less a memory test of slotting numbers in formulas and more making students think as the maths standard in Ireland was lower than other EU countries). It was predicted by some teachers on studyclixs and other teacher websites that it was going to be tough at OL. However the problem is for some of you is what constitutes a difficult paper? Some of my own students who were logical, and were able to think found it easy, other less logical students panicked and found it difficult. The point of them making it more difficult and unpredictable was to make it unpredictable as maths, English, engineering, History and more are so predictable it's sinful. The good news however is that if you attempted all of the paper your in the money, as they say. Because facts remain when correcting, if you do a formula and you do the question out right you will get attempt marks, If you go Into an English exam and write anything and don't make a simple spelling mistake you have to get atleast 10% for Spelling and Grammar, etc). Now the thing about the marking scheme is an interesting one. Does who studied a good good bit or dropped from HL to OL probably found it an easy paper, they'll get the B's and A's atleast. But however nobody knows yet the X amount that dropped to OL on the day and too FL, so unfortunately it's a game of chance in that area. If the results overall calculate a lower average result then the marking scheme will be made easier to an extent. All subjects must apply to the Bell cure which means there must X amount of NG's, X amount of E's, X amount of D, C, B & A's meet quotas and then there will be a tolerance of + or - X, now any maths teacher, or logical thinker can follow that train of thought. And if your a student who followed the explanation of the bell curve and studied chances are you did well in the paper cause if you understand that train if thought you shouldn't of had problems. The same amount of ABCDEFNG must be given the thing ye need to hope for, for those who struggled, is the overall country sitting OL maths experienced similar problems but like saying that some will find it hard, others found it easy, some grand.

Unfortunately this paper is done and cannot be influenced, don't alter CAO courses, don't panic, they do realise ye are students. Normally the papers reflect each other and I now wouldn't be surprised if something like differentiation appeared in paper 2 seeing as elements of paper 2 appeared in paper 1, I don't think they would just do it to one paper and not the other. I would not study anything on paper 1 if you think it may come up as it will be only worth, 10-15 marks at max. I do think that if you feel you did well on (a) and (b) on the Q1 - Q6 on paper 1 and fine the long questions Q7 - Q9 on (a) - (c) or (d) then you probably did far better than expected. Paper 2 is generally harder so I would suggest doing two or three full exam papers between now and Monday. Lastly, attempt EVERYTHING, write any formula of relevance, it doesn't matter if your completely wrong, do it your way and doing it right your way and then you'll get attempt marks. For time, I saw recommended by a teacher online to see the amount of marks the question is worth, divided it by 2, and that's how long to spend on that question, e.g. 25 marks - 12. 5minutes, 50 marks - 25 minutes, 70 marks - 35minutes, 40 marks - 20 marks and so on. There's a famous saying, how do you get to Carnegie Hall? Practice, Practice, Practice.

ecoste

brickeyvalley wrote: »

From a teachers perspective it was a nice, varied paper that made students think, normally the (a) and (b) were easy in the short 1 - 6, E.g. Q1 the (a) (b) were easy but then you needed to know how to get the i or something. The point of this being so difficult is because now the SEC have decided that Project Maths works and now have to upper the standard to that of other European countries (hence the development of project mats, less a memory test of slotting numbers in formulas and more making students think as the maths standard in Ireland was lower than other EU countries). It was predicted by some teachers on studyclixs and other teacher websites that it was going to be tough at OL. However the problem is for some of you is what constitutes a difficult paper? Some of my own students who were logical, and were able to think found it easy, other less logical students panicked and found it difficult. The point of them making it more difficult and unpredictable was to make it unpredictable as maths, English, engineering, History and more are so predictable it's sinful. The good news however is that if you attempted all of the paper your in the money, as they say. Because facts remain when correcting, if you do a formula and you do the question out right you will get attempt marks, If you go Into an English exam and write anything and don't make a simple spelling mistake you have to get atleast 10% for Spelling and Grammar, etc). Now the thing about the marking scheme is an interesting one. Does who studied a good good bit or dropped from HL to OL probably found it an easy paper, they'll get the B's and A's atleast. But however nobody knows yet the X amount that dropped to OL on the day and too FL, so unfortunately it's a game of chance in that area. If the results overall calculate a lower average result then the marking scheme will be made easier to an extent. All subjects must apply to the Bell cure which means there must X amount of NG's, X amount of E's, X amount of D, C, B & A's meet quotas and then there will be a tolerance of + or - X, now any maths teacher, or logical thinker can follow that train of thought. And if your a student who followed the explanation of the bell curve and studied chances are you did well in the paper cause if you understand that train if thought you shouldn't of had problems. The same amount of ABCDEFNG must be given the thing ye need to hope for, for those who struggled, is the overall country sitting OL maths experienced similar problems but like saying that some will find it hard, others found it easy, some grand.

Unfortunately this paper is done and cannot be influenced, don't alter CAO courses, don't panic, they do realise ye are students. Normally the papers reflect each other and I now wouldn't be surprised if something like differentiation appeared in paper 2 seeing as elements of paper 2 appeared in paper 1, I don't think they would just do it to one paper and not the other. I would not study anything on paper 1 if you think it may come up as it will be only worth, 10-15 marks at max. I do think that if you feel you did well on (a) and (b) on the Q1 - Q6 on paper 1 and fine the long questions Q7 - Q9 on (a) - (c) or (d) then you probably did far better than expected. Paper 2 is generally harder so I would suggest doing two or three full exam papers between now and Monday. Lastly, attempt EVERYTHING, write any formula of relevance, it doesn't matter if your completely wrong, do it your way and doing it right your way and then you'll get attempt marks. For time, I saw recommended by a teacher online to see the amount of marks the question is worth, divided it by 2, and that's how long to spend on that question, e.g. 25 marks - 12. 5minutes, 50 marks - 25 minutes, 70 marks - 35minutes, 40 marks - 20 marks and so on. There's a famous saying, how do you get to Carnegie Hall? Practice, Practice, Practice.

"it doesn't matter if your completely wrong"

I'll give you some attempt marks for that sentence, professor.

Gooners

ecoste wrote: »

"it doesn't matter if your completely wrong"

I'll give you some attempt marks for that sentence, professor.

How many attempt marks for "does of you"......

OriginV

I felt a bit prepared for paper 1 but it crushed my hope for even scraping a pass and I know paper 2 will be much worse..

leavingcert15

Does anyone know when there's a number over another number without any line like
(3)
(4)
But the brackets just all one on each side. What is it and is there any links to show me how to do it?

Peregrine

leavingcert15 wrote: »

Does anyone know when there's a number over another number without any line like
(3)
(4)
But the brackets just all one on each side. What is it and is there any links to show me how to do it?

Sounds like combinations (probability chapter).

spl99

Firstly, the the guy who posted the project maths link to using the calculator to answer standard deviation etc. Why the fudge do we not get shown that in school?! :O

Secondly, it's gonna be a long day, lets just buckle down and do what we have to do. We shall shed no tears till we are safely home and tucked a way in a dark corner!

Kermin

Any advice on studying for this paper. 2 weeks ago i was pretty prepared with the exception of inferential statistics and trigonometry. Going through the papers today im ****** . If its anything like paper 1 ill fail

Rozada

What topics from paper 1 could appear on this paper? So so worried

Kremin

Kermin wrote: »

Any advice on studying for this paper. 2 weeks ago i was pretty prepared with the exception of inferential statistics and trigonometry. Going through the papers today im ****** . If its anything like paper 1 ill fail

I saw this post and was like Hmm I never posted this.. and then noticed the difference in our names haha.

Kermin

Kremin wrote: »

I saw this post and was like Hmm I never posted this.. and then noticed the difference in our names haha.

I noticed the same thing on the history (I think) thread yesterday we were right after each other

cab15

sarah_97 wrote: »

Hi guys, what proofs and constructions do we need to learn?

Our teacher has given us work sheets with Constructions 16-21 marked as *NB*

Dr..

Anyone know the list of definitions needed to be known for paper 2??

Tet2015

Dr.. wrote: »

Anyone know the list of definitions needed to be known for paper 2??

So far from what I've found, Converse theorems has come up once or twice, also things like range, median and interquartile range come up. I think it really depends on the topic they decide to examine on the day.

Fortunately if you skim over your book you will be able to get a grasp on a majority of definitions and on the day if they ask you for a definition you don't know, you can surely come up with something.

Leitrim96

For the g(x) question in paper one where it said (x-2)x g(x) or something along those lines is that long division or something

skippy1977

leavingcert15 wrote: »

Is the interquartile range the difference between the 3rd and 1st quarter?

Yep

skippy1977

Leitrim96 wrote: »

For the g(x) question in paper one where it said (x-2)x g(x) or something along those lines is that long division or something

Yeah you could do long division for it