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Joe’s Jotter: What Maths You Should Know for Higher Level Paper 2 2024

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Joe’s Jotter: What Maths You Should Know for Higher Level Paper 2 2024

 

 

Joe’s Jotter: What Maths You Should Know for Higher Level Paper 2 2024

 

Paper 2 usually contains Probability and Stats, Trig, Geometry, Inferential Statistics and Co-ordinate Geometry, Area and Volume.

•    Your Paper 2 is on the Monday so you will have some time to look over at the weekend.
•    Paper 2 is more about the formula’s so use them if you are stuck
•    Label your diagrams and Label co-ordinates (x1, y1)
•    Do not get caught up in one or two topics – cover all your topics
•    Note that Financial Maths came up on P2 2018 – Be careful..
•    Proofs can be mixed between the two papers


What do you need to learn off for Paper 2?

•    Constructions Numbered 1-22
•    JCH Theorems 4, 6, 9, 14 and 19
•    LCH Theorems 11-13
•    Eight Trigonometric Identities 1-7 and 9
•    Some Statistics Terms (explain the words….‘population’, ‘sample’ etc)
•    Some Geometry Terms (explain the words…‘axiom’, ‘theorem’ etc )

See your textbook for all of these


Geometry

•    Geometry and Trigonometry often come up together
•    This idea of Similar Triangles is quite popular lately
•    There’s a bit of learning here:
•    Students need to Learn Constructions and Learn Theorems off by heart
•    Practice these and know all the steps
•    The best way to learn your proofs and constructions is to keep writing them out. Pin the ones you find difficult to remember up onto your wall. Repeat this process.
•    This could well be mixed with Trigonometry or Area and Volume
•    This is usually one short question on the paper (Section A)
•    In order to learn your proofs and constructions, keep writing them out. Pin the ones you find difficult to remember up onto your wall. Repeat this process.


Trigonometry

•    3d Shapes are popular. The advice here is to break the shape into 2/3 triangles and solve using SOH/CAH/TOA, Pythagoras, Sin or Cosine Rule. 
       [Sin and Cosine Rule is in the Log Tables]
•    Be able to read the period and the range from a Periodic graph or a Periodic function
•    Be able to solve Trig Equations (this also may appear on P1 also)
•    You need to be able to prove 8 trig identities – these are listed in your textbook
•    The advice here is go over the questions from 2014-2019 as practice
•    This can be mixed with an Area and Volume Diagram or Co-ordinate Geometry
•    Triangles and Circles linked
•    Understand Trigonometric graphs including Periodic functions (period. Range etc)
•    Go over the questions from 2014-2020 as practice here


Area and Volume

•    Started to get popular from 2017 onwards
•    We sometimes see combined shapes here so it’s a good idea to redraw diagrams
•    Have a look at Q7 2018 and Q7 2017 as practice
•    Can appear on Paper 1


Co-ordinate Geometry of the Line and the Circle

•    They can come up together or on their own
•    They tend to be more in Section A and could be two short questions
•    All the Important formula for these topics is on Page 18 and 19 of the log tables
•          I feel the ‘Big 3 formulas’ are Important (always have a great chance of appearing)
1.    Perpendicular distance between a point and a line
2.    Dividing a line in a given ratio
3.    Finding the angle between two lines using the Tan Formula
                 [ALL THREE OF THESE ARE IN THE LT]
•    Know the idea of slopes well.  Slope formula (LT), m = -x/y & rise/run
•    Know the method for finding the equation of a tangent to the circle. This will involve    the slope and maybe the radius of a circle
•    Be able to find the centre and radius of any circle given its equation.. 
         Note that the equation can appear in different formats….
•    This tends to be more in Section A of Paper 2 
•    Mixed with Geometry


Probability

            100% chance of prob appearing…
•    Know the following three formula’s off by heart (Not in LT)…………… There is a great chance one of these will appear…..

1.    Formula for Conditional Probability – Probability of an event A occurring given that event B occurs.
2.    Formula to show that two events are independent
3.    Formula to show that two events are mutually exclusive

•    One of the following topics usually comes up every year:
1.    Bernoulli Trials (Know how to spot this & apply formula)
or
2.    Expected value of an event
•    e.g. Expected profit from A GAA club lottery

•    It doesn’t tend to be a long question (Section B) except in 2015 when it was mixed with patterns. It could be too short questions on Section A however
•    There isn’t really any help from Log Tables here so learn the above


Statistics

•    Be able to understand z scores for the normal curve
•    The Empirical rule can also appear. Symmetry is the secret to solving. Learn and practice this:
1.    98% of the population falls within one standard deviation of the mean
2.    95% of the population is within two standard deviations of the mean
3.    68% of the population is within three standard deviations of the mean

•    Inferential Statistics. This is where we use the data from a small sample to assume something is true or not for the full population
1.    Know Confidence Intervals for a Sample Proportion
2.    And Know Hypothesis Testing

Both could well appear on Section A but more likely on Section B. Try and understand these as opposed to just learning off the methods like a robot.

•    Know how to analyse data by measuring its middle – Mean, Median and Mode. Know about data spread – range, inter-quartile range and standard deviation.
•    Know how to analyse data by measuring its middle – Mean, Median and Mode, as well as its spread – range, inter-quartile range and standard deviation.
•    Correlation and correlation co-efficient do pop up the odd time
•    The Empirical rule does also appear every so often. See the diagram in the Log tables on Page 36. Symmetry is the secret here. Learn and practice this:
1.    98% of the population falls within one standard deviation of the mean
2.    95% of the population is within two standard deviations of the mean
3.    68% of the population is within three standard deviations of the mean
•    Inferential Statistics. This is where we use the data from a small sample to assume something is true or not for the full population
1.    This is a mix of Probability and Stats
2.    This has a good chance of appearing
3.    Confidence Intervals/Hypothesis Testing or both could well appear
4.    It could appear on Section A but more likely on Section B
•    Try and understand confidence interval and hypothesis testing as best you can as opposed to just learning off the methods like a robot.

More details about Joe as a Maths Tutor for Leaving Certificate (Sept 2024) and his Award Winning ACE Maths Solution Books can be found via the links below.

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition
ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

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