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.

    1. avatar image

      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.

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      SryanBruen

      Relative frequency = Number of successful trials / number of trials

    3. avatar image

      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.

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      SryanBruen

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

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      mathswhiz101

      are you going for straight A's Syran?

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      SryanBruen

      If the line is rising, the slope is positive.

      If the line is falling, the slope is negative.

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      Whackojacko

      Silly Old Harry (son)

      Caught A Herring (cah)

      Trawling Off Africa (toa)

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      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?

    9. avatar image

      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.

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      SryanBruen

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

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      Danielle1358

      The probability of something NOT happening :

      1 - the probability of it happening

    12. avatar image

      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.

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      Danielle1358

      to find the intersection of two lines - use simultaneous equations

    14. avatar image

      SryanBruen

      Oh yeah I forgot about that ^. Thank you.

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      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.

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      SryanBruen

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

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      Aoife_9776

      Which one is theorem 19?

    18. avatar image

      SryanBruen

      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|.

    19. avatar image

      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

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      Danielle1358

      what constructions will come up do you think?

    21. avatar image

      Name

      sound these notes are great

    22. avatar image

      Danielle1358

      Sin 25° = Cos x

      90-25= 65

      Sin 25° = Cos 65°

    23. avatar image

      SryanBruen

      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)|

    24. avatar image

      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.

    25. avatar image

      Study2000

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

    26. avatar image

      SryanBruen

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

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      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.

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      SryanBruen

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

    29. avatar image

      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.

    30. avatar image

      needhelp101

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

    31. avatar image

      aisling31

      thanks for posting so much advice throughout the year :)

    32. avatar image

      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.

    33. avatar image

      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

    34. avatar image

      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.

    35. avatar image

      nms2001

      Soh cah to

    36. avatar image

      nms2001

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

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      belle1234

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

    38. avatar image

      naoise123

      any geometry rules please

    39. avatar image

      Danielle1358

      constructions predictions??

    40. avatar image

      SryanBruen

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

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      Aoife_9776

      What is the definition of a corollary?

    42. avatar image

      eveen

      corollary - a statement that follows from a previous thereom

    43. avatar image

      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 ^.

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      Aoife_9776

      Have you an example of one?

    45. avatar image

      Study2000

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

    46. avatar image

      Study2000

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

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      Aoife_9776

      Have you got definitions and examples for those please?

    48. avatar image

      Aoife_9776

      Just for theorem and axiom

    49. avatar image

      Study2000

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

    50. avatar image

      Study2000

      An axiom is a statement accepted without any proof

    51. avatar image

      Study2000

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

    52. avatar image

      Aoife_9776

      Thanks!

    53. avatar image

      Study2000

      No problem:)

    54. avatar image

      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)

    55. avatar image

      rocky123

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

    56. avatar image

      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

    57. avatar image

      rocky123

      Know how to prove congruency

      E.g. ASA

      SSS

      SAS

      RHS

    58. avatar image

      SryanBruen

      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..

    59. avatar image

      Danielle1358

      thanks

    60. avatar image

      ST@1

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

      Sin= O/H

      Cos= A/H

      Tan= O/A

    61. avatar image

      Elisha447

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

    62. avatar image

      123HOLOPER456

      how many constructions are there in total?

    63. avatar image

      123HOLOPER456

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

    64. avatar image

      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)

    65. avatar image

      Kristine_5238

      you're litch my saviour not even messing

    66. avatar image

      SryanBruen

      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)

    67. avatar image

      Study2000

      Ur lucky u have a short and easy one.

    68. avatar image

      carolinaaplasencia

      http://www.projectmathsbooks.com/wp-content/uploads/2014/02/Theorems-1-21.pdf 67

      all important theorems

    69. avatar image

      SryanBruen

      Are these good theorem answers?

    70. avatar image

      Study2000

      Carolina these ^^ are the ones in my book

    71. avatar image

      OisinR

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

    72. avatar image

      SryanBruen

      19 did not come up last year Oisin

    73. avatar image

      123HOLOPER456

      thanks

    74. avatar image

      123HOLOPER456

      thanks

    75. avatar image

      123HOLOPER456

      thanks

    76. avatar image

      123HOLOPER456

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

    77. avatar image

      carolinaaplasencia

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

    78. avatar image

      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/wp-content/uploads/2014/02/Theorems-1-21.pdf

    79. avatar image

      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.

    80. avatar image

      Elisha447

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

    81. avatar image

      SryanBruen

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

    82. avatar image

      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.

    83. avatar image

      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?!

    84. avatar image

      SryanBruen

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

    85. avatar image

      Elisha447

      Okay great thanks :)

    86. avatar image

      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 !

    87. avatar image

      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 !

    88. avatar image

      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.

    89. avatar image

      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

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      SryanBruen

      I just drew it with a ruler....

    91. avatar image

      jenny_1000

      you will probs still get marks

    92. avatar image

      Theresa_3825

      Same, except for the triangles.

    93. avatar image

      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? 😌

    94. avatar image

      SryanBruen

      I measured with a ruler....

    95. avatar image

      Theresa_3825

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

    96. avatar image

      Theresa_3825

      Nevermind, I think it was.

    97. avatar image

      Elisha447

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

    98. avatar image

      Aoife_9776

      I'm sure they'll give you some marks

    99. avatar image

      barcelona

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

    100. avatar image

      Aoife_9776

      It did say show all construction lines clearly though

    101. avatar image

      Danielle1358

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

    102. avatar image

      Danielle1358

      @SryanBruen you're very welcome :)

    103. avatar image

      Aoife_9776

      I drew the net using constructions

    104. avatar image

      Danielle1358

      how?

    105. avatar image

      SryanBruen

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

    106. avatar image

      Aoife_9776

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

    107. avatar image

      Danielle1358

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

    108. avatar image

      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..

    109. avatar image

      Danielle1358

      ok good thanks

    110. avatar image

      Danielle1358

      any tips on business tomorrow?

    111. avatar image

      SryanBruen

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

    112. avatar image

      Me

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