I will post things that you should remember for Paper 2  HL. Feel free to post your own stuff also.

SryanBruen
Remember
Soh Cah Toa
Sin = O / H (Opposite / Hypotenuse)
Cos = A / H (Adjacent / Hypotenuse)
Tan = O / A (Opposite / Adjacent)
You MUST know Soh Cah Toa as it is not in the tables book.

SryanBruen
Relative frequency = Number of successful trials / number of trials

SryanBruen
Pythagoras' Theorem = a(squared) + b(squared) = c(squared)
This is in the tables book but you must know that a and b are the opposite and adjacent sides of the triangle whilst c is the hypotenuse.

SryanBruen
To show that lines are perpendicular to each other, the answer should be 1.

mathswhiz101
are you going for straight A's Syran?

SryanBruen
If the line is rising, the slope is positive.
If the line is falling, the slope is negative.

Whackojacko
Silly Old Harry (son)
Caught A Herring (cah)
Trawling Off Africa (toa)

Elisha447
I'm not able to understand when to use sin cos and tan. Like if you put it as a fraction or how to know when to use second function. Any advice?

SryanBruen
Instead of using the slope formula, on a diagram, you can find the slope by doing the rise / run. So make a right angled triangle on the diagram between the two points, then count the number of squares rising and running. It don't matter if the squares are not full.

SryanBruen
No mathswhiz101, after all it's only the JC.

Danielle1358
The probability of something NOT happening :
1  the probability of it happening

SryanBruen
When given equations of lines, always remember that the number in front of the x is the slope. So for example,
y = 8  2x. The slope is 2.
y = x + 5. The slope is 1.

Danielle1358
to find the intersection of two lines  use simultaneous equations

SryanBruen
Oh yeah I forgot about that ^. Thank you.

mathswhiz101
Also syran, i see where your prediction come from for theorom 19 but i dont think maths will be that predictable. As paper 1 was easy i imagine they might ask an awkward variation of the theorom rather than just it straight.

SryanBruen
The question would be with that ^, how could they make it anymore awkward? hahaha (the original is awkward already LOL).

Aoife_9776
Which one is theorem 19?

SryanBruen
To find missing sides or angles in a rightangled triangle, we use Sin, Cos or Tan. Follow these steps whilst doing so:
1. Label the sides of the triangle with all the information you're given.
2. Select which formula to use.
3. Substitute values into the formula.
4. Solve the resulting equation to find the missing value.
So for example of a past question,
ABC is a rightangled triangle
ACB (triangle) = 50 degrees and AC = 10cm
Calculate the length of [AB], correct to two decimal places.
Label the sides first!
We have the hypotenuse and we want the opposite.
Which formula has H and O in it? Soh Cah or Toa? Soh has. So you use Sin's formula.
Sin 50 degrees = AB / 10
Bring the ten over and multiply (because it was dividing before you brought it over) with Sin of 50 degrees.
Fill it into your calculator and you should get:
7.66044 = AB
Correct to two decimal places, 7.66 = AB.

SryanBruen
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 Aoife

Danielle1358
what constructions will come up do you think?

Name
sound these notes are great

Danielle1358
Sin 25° = Cos x
9025= 65
Sin 25° = Cos 65°

SryanBruen
Theorem 19 answer for anybody here
Given: Circle, centre 0, containing points A, B and C
To prove: BOC (triangle) = 2BAC (triangle)
Construction: Join A to 0 and continue to D
Label angles 1, 2, 3, 4 and 5
Proof: Consider AOB (triangle):
1 = 2 + 3
But 2 = 3
Similarly, 4 = 25
1 + 4 = 22 + 25
Therefore BOC (triangle) = 2BAC (triangle)

SryanBruen
When it asks you for the probability of something, DO NOT answer in words unless they specifically say to. If they ask probability, it has to be a fraction. Like what's the probability of getting a King out of a 52 card pack:
The probability is 4/52 which simplifies to 2/26 which simplifies to 1/13.
Unless they specifically say to, it is not advised to simplify probabilities. You should keep it as the original probability, in this case, 4/52 but there is NO HARM in simplifying it.

Study2000
Actually sometimes u lose marks if u do not simplify ur answer, so it is better to simplify.

SryanBruen
My teacher even told us to not simplify unless they say to.

Study2000
In some of the marking schemes, for probability questions if u leave ur answer as it is, u are deducted 1 mark. Even in my mock i was deducted one mark for it.

SryanBruen
Yeah I'm just saying what I have been told. I do agree with you.

needhelp101
I'm lost with some of the volume questions. The way that sometimes they ask you about surface area's or something of shapes but the formula's aren't in the log tables. And how do you learn off the formula's? Thanks.

needhelp101
Whoops. I meant how to you learn off the proofs of theorems.

aisling31
thanks for posting so much advice throughout the year :)

SryanBruen
Volume is always something cubed whether it's cm or m etc.
So if the output is something cubed, then there are 3 inputs that you multiply to make it. This is the clue I do <
Volume (not Cylinder, Sphere & Cone which you're given in the tables book) = Length x Base x Height (which you could also write as lbh or l (cubed)
Surface area (not Cylinder, Sphere & Cone which you're given in the tables book) = All the sides added with Base and Height (Otherwise: 6l (squared) (squared because it's area)
You MUST KNOW these formulae as they are not in the tables book.

SryanBruen
You MUST REMEMBER the following conversions:
1 litre = 1,000 cm (cubed)
To convert litres to cubic centimetres (cm cubed), multiply by 1,000.
1 litre = 1,000 ml > 1cm (cubed) = 1 ml

SryanBruen
When the question has multiple units of measurement, make sure to convert each one all to the same unit as it will make the question 10x easier for you to understand.

nms2001
Soh cah to

nms2001
Ignore my last comment soh cah toa is in the log tables

belle1234
will you ever get question asking to explain or define collaries and theorems, etc

naoise123
any geometry rules please

Danielle1358
constructions predictions??

SryanBruen
I double it Belle but EXPLAIN THE TERM COROLLARY came up on my mock.

Aoife_9776
What is the definition of a corollary?

eveen
corollary  a statement that follows from a previous thereom

SryanBruen
A corollary follows after a theorem and is a statement which must be true because of that theorem. More or less what eveen said ^.

Aoife_9776
Have you an example of one?

Study2000
Know the Converse of a theorem, an axiom and especially corollary 3.

Study2000
Corollary 3: Each angle in a semicircle is a right angle.

Aoife_9776
Have you got definitions and examples for those please?

Aoife_9776
Just for theorem and axiom

Study2000
Axiom 1: There is exactly one line through any two given points

Study2000
An axiom is a statement accepted without any proof

Study2000
A theorem is a statement deduced from the axioms by logical argument e.g Pythagoras Theorem.

Aoife_9776
Thanks!

Study2000
No problem:)

rocky123
To find an angle if you know the sin,cos or tan of it you use the inverse of it
Eg Sin X =3/4
X=Sin^1 (3/4)

rocky123
In an equation of a line in the format y=mx+c , m is the slope and c the y intercept

rocky123
Know the different geometry statements that apply to junior cert geometry
E.g 3 sums of a triangle =180 degrees
In a cyclic quadrilateral opposite angles sum to 180 degrees

rocky123
Know how to prove congruency
E.g. ASA
SSS
SAS
RHS

SryanBruen
Well here's past constructions Danielle:
Bisector of a line segment  2015, 2013
Constructing a rightangled triangle  2014, 2012
Drawing line segments, 2014
Maybe constructing a rightangle triangle... but also maybe one of the other 12 constructions..

Danielle1358
thanks

ST@1
(Sin) Oh Hell (Cos) Another Hour (Tan) Of Algebra
Sin= O/H
Cos= A/H
Tan= O/A

Elisha447
For 2015 paper 2 question 5 how do you know which equation matches with each?? :)

123HOLOPER456
how many constructions are there in total?

123HOLOPER456
@SryanBruen could u post the theorem 14 asnwer as u did above for theorem 19 thanks!

Aoife_9776
To remember sin, tan and cos there's also Silly old Harry (sin= opp /hyp ) caught a herring (cos= adj/hyp ) trawling off America (tan=opp/adj)

Kristine_5238
you're litch my saviour not even messing

SryanBruen
Theorem 14
Given: A rightangled triangle
To prove: a(squared) + b(squared) = c(squared)
Construction: Draw a square PQRS with sides of length a + b.
Draw four congruent rightangled triangles in the square with sides of length a and b and hypotenuse c.
Label angles 1, 2, 3 and 4
Proof: Each of the four inscribed triangles is congruent to the original triangle.
Each side of the inner quadrilateral has length c.
1 + 2 = 90 degrees (Remaining angles in the triangle)
1 = 3 (Corresponding angles in congruent triangles)
2 + 3 = 90 degrees
4 = 90 degrees (Straight angle)
The inscribed quadrilateral is a square.
Area of square PQRS = 4
(a + b) (squared) = 4(half x ab) + c(squared)
a(squared) + 2ab + 2b(squared) = 2ab + c(squared)
a(squared) + b(squared) = c(squared)

Study2000
Ur lucky u have a short and easy one.

carolinaaplasencia
http://www.projectmathsbooks.com/wpcontent/uploads/2014/02/Theorems121.pdf 67
all important theorems

SryanBruen
Are these good theorem answers?

Study2000
Carolina these ^^ are the ones in my book

OisinR
What theorem do you think will come up? 19 came up last year!

SryanBruen
19 did not come up last year Oisin

123HOLOPER456
thanks

123HOLOPER456
thanks

123HOLOPER456
thanks

123HOLOPER456
@carolinaaplasencia you only need to know theorems 4,6,9,14 and 19 for the exam

carolinaaplasencia
yeah but ppl wanted the link to them online 123HOLOPER456 and Study2000 yeah Ikr active maths?

rocky123
The only acceptable form of the theorem of pythagaros is where you divide a right angled triangle in 2 then use similar triangles to prove the theorem
The one that sryan bruen has posted above isn't acceptable as far as i know as we did that one but after the mocks we were told we had to learn the version project maths wants
The correct version is in this link
http://www.projectmathsbooks.com/wpcontent/uploads/2014/02/Theorems121.pdf

SryanBruen
Neither theorems appeared hahaha. But the one that did was so easy to proof and explain. I loved paper 2. It was so easy.

Elisha447
How did you get the diagonal in the two cubes in square root form??

SryanBruen
Oh I meant to also say that only 2 questions caught me out, that ^ and the spinner 8 euro back thing.

SryanBruen
Point of intersection came up and I wouldn't have a clue how to do it if it weren't for the person who posted how to do it on this thread. Thank you very much  sorry I cannot see your post right now. Plus, Rocky how? Less Stress More Success and my teacher told me to learn off the theorem that way? And yeah my Less Stress More Success book says PROJECT MATHS on it, not just Maths. And no constructions came up after all that Danielle haha.

Elisha447
For making equations in the co ord geometry question I used to slope formula to get slopes but the slope of a and b didn't work out which affected other questions will I loose many marks?!

SryanBruen
No I got the same Elisha (negative fractions). It won't!

Elisha447
Okay great thanks :)

jenny_1000
@sryanbruen constructions did come up when you had to draw the net of the prism you had to CLEARLY show construction lines. But its all g cause loads ofpeople didn't get it !

jenny_1000
@sryanbruen constructions did come up when you had to draw the net of the prism you had to CLEARLY show construction lines. But its all g cause loads ofpeople didn't get it !

SryanBruen
I don't really consider that a construction (the 15 ones that you study I do) but I did get it! I'm not normally great with nets but I got it.

Aoife_9776
It was a combination of the rectangle and triangle constructions. I realised that 5 mins before the end (and then I was frantically rubbing out lol). I just drew it with a ruler the first time but the second time I used the constructions methods

SryanBruen
I just drew it with a ruler....

jenny_1000
you will probs still get marks

Theresa_3825
Same, except for the triangles.

Theresa_3825
I used the boxes on the page as a guide and I didn't measure with a ruler. Will I be okay though? 😌

SryanBruen
I measured with a ruler....

Theresa_3825
Or is 1cm equal to the length of one of the boxes?

Theresa_3825
Nevermind, I think it was.

Elisha447
Ya it was I did the same! I measured the box afterwards!

Aoife_9776
I'm sure they'll give you some marks

barcelona
all the squares were 1cm by 1cm so it would be the same with a ruler!!!!!

Aoife_9776
It did say show all construction lines clearly though

Danielle1358
oh no i just drew a net?? no constructions or anything?

Danielle1358
@SryanBruen you're very welcome :)

Aoife_9776
I drew the net using constructions

Danielle1358
how?

SryanBruen
Higher Level Maths paper 2 is up now! Just thought I'd let you know.

Aoife_9776
I used the triangle construction for each end and the rectangle one for the sides

Danielle1358
i dont think i ever learnt those constructions! will i still get marks for just drawing with a ruler?

SryanBruen
Well I did Danielle... I don't see why not. I have exactly constructed as they told me to with the exact cm they instructed..

Danielle1358
ok good thanks

Danielle1358
any tips on business tomorrow?

SryanBruen
People, remember these things for your JC. (Obviously I'm not talking to the ones who already commented here haha)

Me
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