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