## Joe’s Jotter: What Maths You Should Know for Higher Level Paper 2 2022

Leaving Higher Maths 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. 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 (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 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 past exam 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)

- 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 probability 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
- 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:

- 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, 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 does 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.

To view my recent feature article on ‘Best Practice for LC Higher Maths Paper 1’, click here.

More details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022) 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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