All Junior Cert Mathematics posts
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    Things to remember for Paper 2 HL SryanBruen

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

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      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.

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      Relative frequency = Number of successful trials / number of trials

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      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.

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

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      are you going for straight A's Syran?

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      If the line is rising, the slope is positive.

      If the line is falling, the slope is negative.

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      Silly Old Harry (son)

      Caught A Herring (cah)

      Trawling Off Africa (toa)

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      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?

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      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.

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

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      The probability of something NOT happening :

      1 - the probability of it happening

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      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.

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      to find the intersection of two lines - use simultaneous equations

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      Oh yeah I forgot about that ^. Thank you.

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      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.

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

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      Which one is theorem 19?

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      To find missing sides or angles in a right-angled 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 right-angled 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|.

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      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

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      what constructions will come up do you think?

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      sound these notes are great

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      Sin 25° = Cos x

      90-25= 65

      Sin 25° = Cos 65°

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      Theorem 19 answer for anybody here

      Given: Circle, centre 0, containing points A, B and C

      To prove: |BOC (triangle)| = 2|BAC (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| = 2|5|

      |1| + |4| = 2|2| + 2|5|

      Therefore |BOC (triangle)| = 2|BAC (triangle)|

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      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.

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

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

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      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.

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

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      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.

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

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      thanks for posting so much advice throughout the year :)

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      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.

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      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

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      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.

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      Soh cah to

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

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

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      any geometry rules please

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      constructions predictions??

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

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      What is the definition of a corollary?

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      corollary - a statement that follows from a previous thereom

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

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      Have you an example of one?

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

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      Corollary 3: Each angle in a semi-circle is a right angle.

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      Have you got definitions and examples for those please?

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      Just for theorem and axiom

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

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      An axiom is a statement accepted without any proof

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

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      No problem:)

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      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)

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

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      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

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      Know how to prove congruency

      E.g. ASA




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      Well here's past constructions Danielle:

      Bisector of a line segment - 2015, 2013

      Constructing a right-angled triangle - 2014, 2012

      Drawing line segments, 2014

      Maybe constructing a right-angle triangle... but also maybe one of the other 12 constructions..

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      (Sin) Oh Hell (Cos) Another Hour (Tan) Of Algebra

      Sin= O/H

      Cos= A/H

      Tan= O/A

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

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      how many constructions are there in total?

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

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      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)

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      you're litch my saviour not even messing

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      Theorem 14

      Given: A right-angled triangle

      To prove: a(squared) + b(squared) = c(squared)

      Construction: Draw a square PQRS with sides of length a + b.

      Draw four congruent right-angled 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)

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      Ur lucky u have a short and easy one.

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      carolinaaplasencia 67

      all important theorems

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      Are these good theorem answers?

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      Carolina these ^^ are the ones in my book

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

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      19 did not come up last year Oisin

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

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

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      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

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

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

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

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      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.

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      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?!

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

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      Okay great thanks :)

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      @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 !

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      @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 !

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      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.

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      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

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      I just drew it with a ruler....

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      you will probs still get marks

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      Same, except for the triangles.

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

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      I measured with a ruler....

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

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      Nevermind, I think it was.

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

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      I'm sure they'll give you some marks

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

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      It did say show all construction lines clearly though

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

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      @SryanBruen you're very welcome :)

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      I drew the net using constructions

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

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

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

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      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..

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      ok good thanks

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      any tips on business tomorrow?

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