Joe’s Jotter: What Maths You Should Know for Higher Level Paper 2 2023
Paper 2 at Leaving Cert Higher Level Maths usually contains Probability and Stats, Trig, Geometry, Inferential Statistics and Coordinate Geometry, Area and Volume.
 Your Paper 2 is on the Monday so you will have some time to look over. Again watch out for topics appearing here that should appear on Paper 2.
 Paper 2 is more about the formula’s so use them if you are stuck
 Label your diagrams and Label coordinates (x_{1}, y_{1})
 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 122
 JCH Theorems 4, 6, 9, 14 and 19
 LCH Theorems 1113
 Eight Trigonometric Identities 17 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 20142019 as practice
 This can be mixed with an Area and Volume Diagram or Coordinate Geometry
 Triangles and Circles linked
 Understand Trigonometric graphs including Periodic functions (period. Range etc)
 Go over the questions from 20142019 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
Coordinate 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)

 Perpendicular distance between a point and a line
 Dividing a line in a given ratio
 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…..
 Formula for Conditional Probability – Probability of an event A occurring given that event B occurs.
 Formula to show that two events are independent
 Formula to show that two events are mutually exclusive
 One of the following topics usually comes up every year:
 Bernoulli Trials (Know how to spot this & apply formula)
or
 Expected value of an event
 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:

 98% of the population falls within one standard deviation of the mean
 95% of the population is within two standard deviations of the mean
 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

 Know Confidence Intervals for a Sample Proportion
 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, interquartile range and standard deviation.
 Know how to analyse data by measuring its middle – Mean, Median and Mode, as well as its spread – range, interquartile range and standard deviation.
 Correlation and correlation coefficient 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:

 98% of the population falls within one standard deviation of the mean
 95% of the population is within two standard deviations of the mean
 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

 This is a mix of Probability and Stats
 This has a good chance of appearing
 Confidence Intervals/Hypothesis Testing or both could well appear
 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 (2023) and his Award Winning ACE Maths Solution Books can be found via the links below.
ACE Maths Classes: acesolutionbooks.com/acemathstuition
ACE Maths Solution Books: acesolutionbooks.com/buymybooks
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