Higher Level Maths Paper 2 2023

Paper 2 at Leaving Cert Higher Level Maths 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. 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 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 2014-2019 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)

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:

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.

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