Joe’s Jotter: What Maths You Should Know for Higher Level Paper 2 2023

/in /by

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)

or

  1. 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.

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/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

*****

*****

Joe’s Jotter: Final Thoughts on Exam Prep Including Parental Support 2023

/in , /by

Parental Support for Students at Home

Parents, your new role is one of increasing influence, given that your child is now at home revising for their exams all the time. Strangely enough, students actually like the structure of school and seeing their friends there every day. Being at home is not something they are used to and may require some time to bed down into a pattern of revision and rest. You are not a teacher, so it’s important to remember that if you are doing your best, you are doing enough. Here are my twenty recommendations to help you be the best you can for your child currently revising in the home environment:

  1. Help them establish a revision routine in a quiet, clean, and comfortable area.
  2. Plan your day a little around them, so you can be there to support their efforts.
  3. Provide the quiet support: school materials , healthy dinners & encouragement.
  4. Be realistic about the amount of revision they may do each day.
  5. Encourage family time including walks & drives to keep communication open.
  6. Show interest by requesting that they discuss or come and teach topics to you.
  7. Be calm, tolerant, and patient with their moods as best you can.
  8. Try praise their efforts (no matter how small) even if you feel they don’t deserve it.
  9. Remind them to communicate with their teachers and friends if they have queries.
  10. If they are disorganised or scatty, sit down & brainstorm to help them get organised.
  11. Empower them to help you around the house, i.e. Cooking/Cleaning/Gardening etc
  12. Trust them to take responsibility for their own learning.
  13. Encourage them to talk to you if they feel anxious about anything.
  14. Endeavour to maintain balance. Nothing is ever as bad or as good as it seems.
  15. Don’t be afraid to get stuck in academically. Impart your knowledge to them.
  16. Examine them on subjects, questions, and texts they may need help with.
  17. Try not to pass any anxiety you have on to them; Just let them breathe.
  18. Try to cook substantial nutritious meals, so that they aren’t constantly ‘grazing’.
  19. Intervene in all cases if you feel they are overwhelmed or struggling mentally.
  20. Parent.

ACE’ing Your Prep at Home – Some Final Thoughts

Students,

Your best bet now is to make the most of this challenge set down for you. You now have more freedom than ever to create your own study blocks and breaks; effectively you can control the pace of your learning. If your revision blocks are short (i.e. thirty minutes), you are less likely to daydream and waste time in them. You can now allocate time to various subjects and tasks unlike before; embrace it. It is an opportunity to take responsibility for your own learning and with this you are preparing yourself for third level education or whatever route you choose after school.

Create a good solid routine, especially to start the day. Having a good morning can often be the key to a productive day. Keep your social media stint to a limited time in the morning, otherwise it may become an endless scroll, with well laid out plans being scuppered. Every morning, commence your Lifestyle (Study) Timetable or the list of ten to twelve tasks you have set yourself from the night before. Be sure to make everyone in the house aware of your revision times, so that they can try to be as quiet as possible during these periods.

Be Honest and Realistic with Yourself

Keeping your timetable or task list simple and realistic will allow you to get through the day’s work and make it easier to get started also. Maybe setup four tasks in the morning, three after lunch and three in the evening if you find creating a timetable for the full day too daunting. Sample tasks may include revising a short chapter in your Maths book and completing ten test questions based on it, or note taking on a certain period in History, or summarising one aspect of your Biology or Home Economics course. How do you eat an elephant? Answer: Break it up into small pieces and eat it bit by bit. Treat your daily task list or timetable the same.

Be honest with yourself (as best you can) about how you are going to use the Internet, social media, and phone during revision times. The best way to control this is to set out the exact times you will use devices and where they will be located during revision blocks. If you struggle to separate yourself from your phone, request the help of your parents to find a solution. If you find your eyes are getting sore from ‘screen time’, whether that be on a PC or phone, this is your body telling you to give it a break and it is wise to listen to the voice within in these cases. Along with reasonable tech time, ensure you enjoy and inbuild fun, phone calls to friends, exercise, music, and relaxation into each day’s revision timetable. These types of breaks are essential for productivity; but ensure to keep an eye on time away, as short breaks can easily turn into longer wasteful ones.

Strength Based Learning

As above, vary the different ways you study and indeed your revision location also. Keep your study area clean and organised in order to be more productive. Find out which ways of learning that work for you and repeat them. If you are finding a specific revision method worthless, come at it from a different angle. Manage your revision effectively by using the best methods suitable to you and appropriate to that subject. Always play to your strengths!

Winston Churchill once said that ‘Perfection is the enemy of progress’. In subjects we find difficult, we often learn more by making mistakes as opposed to getting everything perfectly right at the beginning. If you always think your notes and revision blocks aren’t of a high enough standard, you will soon loose heart by your perceived lack of excellence. Failure and Imperfection should be viewed as a positive, as it encourages us to try harder and continually better ourselves. This was one of my keys to success. I always wanted to improve and ultimately be the best at whatever I did. You will never actually reach perfection, so be contented with progress and don’t be too hard on yourself.

Write Down Your Goals

Finally, write down both your short and long term goals and re-read and update them regularly to remind yourself why you are putting in such an effort right now. Goals should be used to motivate and drive you to achieve great things. Focus always on the work you have completed, not what you haven’t done. The quicker you settle down into a routine and discover study techniques that work for you, the better you will feel. Right now, you are effectively searching for the best possible home routine that facilitates an increased accumulation of knowledge. Don’t be afraid to try new learning methods as part of this new phase. These might give you the edge on topics you have struggled to understand so far.

I wish you luck and good health going forward and feel free to contact me through the channels below if I can help you in any way. Joe

More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books for all students can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

*****

*****

Joe’s Jotter: The ACE Exam Day Reference Guide 2023

/in /by

As we reach the start this year’s exams and work our way through each subject, here is a little checklist that you can have a glance at before setting off each morning. It is important to get your brain into ‘exam mode’ in order to exact the maximum out of each paper. The below pointers will help you get organised and put you in the right head space:

  • Do your best – that is all that is expected of you.
  • Get to the exam hall at least fifteen minutes before each exam.
  • Be fully aware of the start and finish time of each exam.
  • Read the instructions carefully on every single page.
  • You cannot leave during the first thirty or the last ten minutes of each exam.
  • Prepare for a longer exam paper than any of the ones you have sat during school
  • Make sure you have plenty of pens, pencils, rulers, etc.
  • Phones, books and notes are all forbidden in the exam hall.
  • Use the toilet before entering the exam hall.
  • Answer your best question first to settle the nerves.
  • Take your time when reading each question.
  • Attempt all parts of every question asked.
  • If you make a mistake, draw a line through, so it is still readable.
  • Questions answered, even if cancelled out, must be corrected by the examiner.
  • Check that you have answered all parts of all questions.
  • Make sure to include all extra pages used e.g. graph paper etc
  • Place twice as much emphasis on ten markers than fives etc (twice as much time also)
  • Carefully label any diagrams you draw or use.
  • Layout your paper well. You can save the trees in later life.
  • Do not repeat yourself in a question.
  • Skip a line or two after each full question.
  • Remember that any reasonable attempt will get you some marks.
  • Bring some sweets and water into the exam hall.
  • Focus on your own exam paper not your friends efforts beside you.
  • Don’t panic if you don’t understand a question at first.
  • Eat good meals before and after each exam.
  • If you run out of paper, ask for more from the superintendent.
  • Think how your answers will sound to someone else reading it.
  • Spend appropriate time on a question depending on marks allocated.
  • Try and write clearly especially in subjects with a lot of writing.
  • Answer the exact question that you are being asked on the paper.
  • Go into each exam with a positive and determined attitude.
  • Put a ‘*’ on questions you didn’t finish and revisit at the end.
  • Show all rough work for each question on your answer book.
  • A labelled picture/diagram can explain better than words.
  • Scribble down notes if you happen to run out of time.
  • You are ready. Leave all doubt outside the exam hall.
  • Stay until the end of all your exams.
  • Do your best!

 Ten Admin checks to do before entering the Exam Hall

If you are getting ready to sit your Leaving Certificate examinations this week, the following administration information is certainly worth a quick read. The more familiar you are with exam hall procedures, the more you can focus on your own game plan:

  1. Be very clear on the timing of each exam.
  2. Get there early on the first day of your exams to find out where to put your school bag and what centre (exam hall) you are sitting in.
  3. When you sit down each day, double check you have the correct paper and label in front of you. At Leaving Cert level, you can change from one level to another on the morning of the exam, but this does not come recommended, as you have spent considerable time preparing for a specific level.
  4. You cannot bring any notes, school bags, phones, or materials into the exam hall with you. You should just bring in your pens, instruments, and some water/sweets.
  5. Listen to the superintendents’ instructions carefully at the start of each exam, as there may be corrections to be made to the exam paper or other announcements.
  6. Be aware that Higher, Ordinary and Foundation Papers may finish at different times.
  7. You will not be allowed enter the exam hall once thirty minutes from the official start time of the exam has elapsed.
  8. If you take paper one at higher level for a subject, you must take paper two at higher level also. The same obviously applies to Ordinary and Foundation levels.
  9. You can obtain a copy of the exam paper from the school authorities after the exam. Each exam paper will be uploaded to the examinations.ie website soon after each exam.
  10. Ensure you write your exam number on each booklet you use and be sure to hand up all your writing material. Good Luck to you. Joe. (www.acesolutionbooks.com)

*****

*****

Joe’s Jotter: What Maths You Should know for Higher Level Paper 1 2023

/in /by

Paper 1 usually contains Algebra, Complex numbers, Functions and graphs, Indices and Logs, Financial Maths, Numbers, Proof by induction.

What do you need to learn off for Paper 1?

  • Prove that Root 2 is irrational
  • Construct Root 2 and Root 3
  • Derive the amortisation formula
  • Derive De-Moivres theorem
  • Derive Sum to Infinity of a Geometric Series
  • Use differentiation from first principles method on a:
  1. Linear Function
  2. Quadratic Function
  • Learn Proof by Induction methods for:
    1. Divisibility
    2. Series
    3. Inequality

See your textbook for full details all of these

Algebra

  • This is the most important topic on the course, and it is very hard to score well unless you know it. It is a massive part of Paper 1 and Paper 2, but more so Paper 1
  • Know solving, simplifying terms, multiplying terms, dividing terms, quadratic equations, inequalities, simultaneous equations, modulus equations etc…

Logs

  • Logs seem to be appearing more lately -> Know how to use the basic rules of logs from page 21 of your log tables (LT) – These are well worth practicing finding out when to use which rule.. do some basic examples from your book to get started here.
  • Logs appear when you get an unknown as a power (5 to the power of p and we are trying to solve for p) e.g. 5p

Complex Numbers

  • Multiplying and dividing complex numbers is really important
  • Convert a complex number into polar form
  • De-Moivres theory is always worth learning

Proof by Induction

  • You need to practice this technique and just know what the three basic steps are here
    • Prove true for n=1, Assume true for n=k and prove is true for n=k+1

Sequences and Series (Patterns)

  • This could be a number pattern or a picture pattern
  • You will need to be able to predict future patterns and come up with a formula to describe the pattern presented
  • Big Emphasis on the formula’s here for the Arithmetic sequence and the Geometric Sequence – Page 22 of the Log tables
  • The Sum to infinity of a geometric series is a popular question
  • The best way to prepare for this question is to practice past exam questions..

Calculus (Differentiation and Integration)

Differentiation

  • Diff (80%) Integ (20%) That 20% integration comes up every year so it’s worth knowing
  • Differentiation appears on Section A, but can also appear with functions on Section B
  • ‘Max’/’Min’ or similar words used – Differentiate the function…let equal to zero and solve
  • Practice Product, Quotient, and chain rules here from log tables
  • Again you could be asked to differentiate a trig function (sin, cos, or tan). Page 26 of the Log tables will help you here. Indices links in here.
  • Rates of change…Rate is always something over dt as it’s how an object changes over time e.g. of this might be how an area change over time da/dt…
    • Again practice past questions here…
  • ‘Slope of a line or a tangent’ also means differentiation. This can appear on either paper…
  • Can appear on Paper 2

Integration

  • Integration is the opposite of Differentiation

Know..

  1. How to use the rules of Integration (Log Tables Page 26)
  2. Find the area underneath a curve. (The Trapezoidal rule from the Ordinary level course could appear here with this)
  3. Find the average value of a function [Learn this formula – Not in LT]

Financial Maths

  • Students get a little hung up on this topic given it is only one section of many in P1..
  • There is way more in the books than is needed in my opinion
  • Know how to deal with Taking out money (Loans) and Depositing money
  • Know how to use your Sn Formula from P22 of log Tables
  • Know how to use your Amortisation Formula from P31 of log tables

Question types include…

  • A person needs to have 100,000 in an account by 2050.. Work back, how much should he deposit in his account each month. These are a bit trickier than the loan questions
  • Use the amortisation formula to calculate equal payments on a loan. i.e. how much I have to pay back each month? These payments are always the same each month. You need to able to derive the proof of this formula also
  • Know how to convert between monthly rate ‘i’ & the Annual rate (APR) & vice versa.

Functions

  • This involves a link between Algebra and graphs.
  • This often appears on Section B and is what I call ‘Equations representing reality’.
  • g. The amount of fish in a lake or the path taken by a basketball in motion
  • e can be popular here..
  • You need to be able to recognise a graph of a function and also answer questions on it
  • Trig functions can appear here even though Trig is mainly a Paper 2 topic

More details about Joe’s Maths Tuition Classes for September 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books for all students can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

*****

*****

Joe’s Jotter: The Importance of Nutrition at Exam Time

/in , /by

Food provides all the essential nutrients that we require for healthy living and to fuel our daily activity. A car can work well, but if it doesn’t have any fuel it can’t go anywhere. Unfortunately for us, no single food provides all the nutrients required, so a mixture and range of different foods must be consumed in our diet. Research has shown that the healthier we eat, the better we feel and the more we can focus on tasks at hand.

When studying for exams, some students tend to stay up late and forget to eat and drink properly or maybe worse, they eat too much of the bad stuff. The following are five short exam nutrition recommendations for the next few weeks and beyond (in depth discussions about added sugar have been omitted here, with it being the obvious heralded evil).

  1. Eat something in the morning

Parents, if your child skips breakfast before school, they are more likely to be tired throughout the day and will have reduced concentration levels. If breakfast is a busy time of day in your house, then feeding your children what they need quickly might be a daunting experience, but it doesn’t have to be. By stocking up on all the ingredients you need beforehand, you can deliver quick healthy breakfasts that they will enjoy.

Alternatively, if your kids aren’t hungry or everyone is in a rush out the door, make sure there are plenty of easy-to-grab pieces of fruit, yoghurt, smoothies, and muesli bars (sugar free) that can be eaten quickly on the go. In an ideal world, everyone should sit down at the same time and share food together, although I do realise that this isn’t always possible. I feel strongly that sugary cereals are a ‘no no’. Some of these cereals can contain up to one-third added sugar. Maybe check the ingredients on cereal boxes before bringing them to the checkout and ultimately the breakfast table. 

  1. Increase ‘brain food’ intake

Proteins from lean meat, fish, eggs, fruit, nuts, and whole grains are foods that help keep the brain mentally alert. Snacking on nuts and dried fruit will help prevent concentration levels dipping. Keep in mind that fruit like bananas, blueberries, and oranges all have natural sugars that will give a lift when feeling tired. Brain food is the fuel that helps us think clearly, make good decisions, and maintain concentration when fatigue sets in during critical periods, that is, during the last half an hour of an exam.

  1. Snack as healthy as you can

Students, when your head is in the books and time is ticking by, you might be tempted to skip a meal to keep up momentum. Your brain needs food and water to keep working. Mental fatigue can cloud your brain, especially if an exam is close by. I would recommend the following healthy snacks to get you through study bumps: Whole wheat toast with peanut butter, fruit smoothies, berries, honey, dried fruit and nuts, hard boiled eggs, low fat chocolate milk or vegetables with a homemade dip. Graze away on the Guilt Free Good Stuff (GFGS) as you revise and move towards exam time.

  1. Minimise caffeine

Caffeine is a stimulant that is present in coffee and many energy drinks. Stay away from Energy drinks as they provide a false high followed by a sugar crash. Sleep can also be affected by caffeine, and I know a good few adults who abstain from caffeine after four p.m. as it disturbs their sleep. I would recommend water, peppermint tea or even a small glass of milk to aid sleep and as a healthy replacement for caffeine. 

  1. Consume ‘good’ fats

Fats are an important component of the diet and have received an enormous amount of bad publicity over the last twenty-five years. As a rough guide, saturated (bad) fats are generally solid at room temperature and tend to be animal fats (such as the fats found in butter or margarine). Unsaturated (good) fats are liquid at room temperature and are usually vegetable fats (such as olive oil, rapeseed oil, oily fish (sardines, tuna, mackerel, or salmon)). Unsaturated fats or good fats are an important nutrient for you to intake as a student. The following are other sources of Unsaturated fats: cheese, dark chocolate, eggs, nuts, coconut and coconut oil, peanut butter, pistachios, and walnuts.

Eating well and drinking plenty of water in the lead up to exams is as important as the quality of the notes you prepare prior to them. ‘You are what you eat’! Good luck. Joe

‘If you always do the same thing, you will always get what you have always got.’

More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books for all students can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

*****

*****

Joe’s Jotter: Sterling Tricks to Remember Maths Formulas

/in , , , , , , /by

Maths Students,

Knowing how to use formulas correctly is still as important as it was back in the 80’s and 90’s when you parents were young. Formulas help us understand questions better and assist us in converting the theoretical wording of a question into something useable. Often subbing in any correct value into the appropriate formula will yield low partial credit in an exam e.g. 4/10.

Formulas also enhance our understanding of practical scenarios. For example, the Quadratic Formula is used to find the location and value of various unknowns, trigonometric formulas are used to find distances and heights of real world objects in architecture and aviation, and Statistics and Probability formulas are used in insurance and mortgage calculations. A student’s problem is that not all Formulas they need to be familiar with are present in the Log Tables provided. So, what is the best way to remember the ones that aren’t? 

The Six Best Ways to Make Maths Formulas Stick. 

  1. Link the formula to something fun or interesting in your life.

Build a song or a rhyme around a given formula. The sequence of the song or rhyme can be the different parts of the formula. Look up an example on the Internet, or better again invent your own one which will make it easier for you to recall. Examples include: BOMDAS for order of operations and SOH CAH TOA for Trigonometric ratios in a right angled triangle.

  1. Understand each part of the formula.

When you understand a formula and whats its parts are, it is much easier to memorise it. Take time to understand the rules, variables, logic, and symbols in the formulas you use in Maths classes every day. Be very clear on what each letter represents.

  1. Put it on your wall.

Write each formula on its own A4 page and put it up on your bedroom wall to allow it to sink in. This is the best way to memorise formulas, as they will be seeping into your brain without you even knowing it. Wall summaries regularly catch ones eye, forcing the brain to take pictures of them. This is definitely an underused trick in revision and exam preparation. 

  1. Let formula’s sit before learning them.

In my experience, it takes time to learn formula’s; it isn’t like a set of French verbs or physics definitions that you may be able to cram. Every time you use a formula in class, be sure to write it down in your copy. The more times you write it, the easier it will be to remember it later. I would recommend buying a little A5 hardback and note all formulas from the Maths course into it, even the ones that appear in the Log Tables. This hardback is something you can flick through on journeys or even while keeping an eye on a bit of TV. It’s all learning!

  1. Take them to bed with you.

At the end of each day, have a quick glance at any new formulas you learned that day. Check how well you memorised them by trying to write them down without looking. I would estimate that knowing which formula to use where in Maths is worth at least 25% in exams.

  1. Most Formulas are in your Log Tables.

It is crucial to learn the formulas that are not in your log tables and be familiar with the ones that are in there. Try and get used to using the index on Page 1 of the Log tables in order to access the formulas you need quickly. The main formulas we use in the log tables are on Pages 8, 9, 10, 13, 14, 15, 16, 18, 19, 20, 21, 22, 25, 30, 31, 34 and 36. Good luck. Joe.

More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Years including upcoming ‘Live’ Online revision blitz’s and his Award Winning ACE Maths Solution Books can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

*****

*****

Joe’s Jotter: The Best Strategy for the 2023 Maths Exams (incl Marking & Timing)

/in /by

What is the best Strategy for tackling both Maths Exam Papers 2023?

Just for the 2023 LC Maths papers only, I would spend 10-12 minutes reading the paper and tick off the parts of the questions that look familiar making a few notes at the side. Ring or e-mail me if you would like more Information on the best way to choose your questions. You should then know by the amount of ticks and positive notes which questions that you fancy taking on. Start a short question (you like the look of) first to settle the nerves. You don’t have to do Question 1 first!

For each paper, I would have a clear plan in my head on how I would tackle the questions. My reasoning for this is that students tend not to get the long questions done if they are left until the end. Personally I wouldn’t take on any extra questions  – Do five short and three long questions well.

Recommended Paper Plan

  1. Read and select questions really carefully – 10-12 mins
  2. Do your favourite short question – (12.5 mins each for short)
  3. Alternate between long and short questions – (25 mins each for long)
  4. Be sure you have done five short questions and three long questions.
  5. Check, recalculate and tidy – Use any extra time at the end of the exam for this…

Total Time 2023 (Both for Paper 1 and 2)  = 150 mins  (2.5 hours) [Higher & Ordinary Level]

Read each question twice highlighting and underlining the key words and numbers with your red or green pen. Highlight the key words. Think what those words might trigger from a Maths point of view. e.g. The word ‘indefinitely’ in a pattern indicates to use the sum to infinity formula. Be very clear and what you are being asked to find before commencing.

Marking and Timing on the LC Maths Exam Papers 2023

50 markers [LONG Qs] -spend at most 25 minutes per Q [2023 Only].

30 markers [SHORT Qs]-spend at most 12.5 minutes per Q. [2023 Only]. Stick rigidly to time.

I have noticed that the first parts of most questions are carrying 10 marks, so it is really Important to make a big effort to attempt them really well.

I was giving an exam recently and my student submitted her work by email. She explained how she ran out of time on Q1. I was delighted. She had stuck to the time and moved on. Often you need the first part of each question for attempt further parts. You will only know how much marks each full question is worth – you will not know how many marks per part.

I would say it is easy get the first 60% of any question part but more difficult to get the last few percent. Trying to get that last few percent can cost you between five and ten minutes and may not be worth it. This could mean that you don’t get to even see the last question on the paper i.e. there is a knock on effect. Stick to your time budget plan at all levels.

It is better to know a little about loads of topics than an in-depth knowledge of one topic. Algebra is the exception to this and really worth learning in-depth for all levels. Algebra is the language of Maths and effectively appears inside every question. Also…

  • Incorrect answer and no workings out = No Marks
  • Incorrect answer with a step in the right direction = Some Marks
  • SHOW YOUR WORKINGS OUT CLEARLY IN A STEP BY STEP FORMAT
  • Show exactly what you are thinking on the page. i.e. Write it down clearly. If you think you should multiply/divide/subtract/add and aren’t sure, show it on the page anyway.
  • Take risks and go for it. Never be afraid of being wrong!

More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

*****

*****

Joe’s Jotter: Your Role as a Parent in Exams 2023

/in , /by

Your Role as a Parent as Exams Approach


One of your main roles, as parents, around exam time is to create a good atmosphere at home. It will be important to remain calm and try not to transfer additional pressure on to your child in the lead up. This applies whether they are sitting a state exam or an end of year summer test. I would be wary of placing any extra emphasis on them achieving certain grades or points. Allowing them to talk without judgment, actively listening to them and keeping career options and results in perspective are other ways that you can be there for them at this time. Be sure to check that they have a plan ‘B’ in place for further education/training, as this will help greatly to regulate their stress levels.

Try not to let uncertainties or worries you had in school, especially any negative vibes you had around exams or certain subjects influence how your child deals with their exam year. I don’t think conversations beginning with “When I was doing the Leaving Cert…” are really that helpful or relevant to their situation now. Similarly, never compare your child’s performance or study ethic to that of their peers or siblings, as this will just add to the stress. Complaining about the unfairness of the exam process is also airing unhelpful negativity. Keep it all on a positive plane and let them breathe. If you have any concerns at all about your child, you should contact their school, as teachers and management are usually more than happy to help. If you meet a roadblock, I would be delighted to help and advise you in some small way; so don’t hesitate to reach out to me.

More than any other time in their life, it is important to help your child manage their feelings, as they may struggle with overwhelming emotions and pressures placed on them by exams. There are lots of great techniques you can show them, like slowing their breathing down or helping them become aware of their feelings. Maybe, look up one or two of these online, so that you can pass on something practical to use during intense situations. Exercise and involvement in activities right up to exam start are brilliant stress reducing techniques and should be strongly encouraged.

Practical Insights to Really Support Your Exam Student

The following are some real and practical insights into how your support can really help your son or daughter be their best around exam time. This advice applies to all types of examinations, not just the Junior and Leaving Certificate.

  • It’s an obvious one to start but ensure that your child is present in the exam hall for each exam. For parents who are working and leaving home early, avoid the ultimate disaster of your child missing an exam. This advice applies on days they have important class tests also. Ensure they are up and dressed before you leave home for work each morning. A small number of students regularly fail to turn up for morning exam papers.
  • Making them a healthy and substantial breakfast will greatly help their focus and concentration all the way to the end of an exam, especially if they have an afternoon paper to sit also.
  • Help them to draw up a check list of daily requirements based on each day’s exams. Make a final check with them each morning, so that your child is fully prepared for the day’s exams. The amount of guidance required will obviously depend on how organised your child is. Writing instruments along with the other requirements such as rulers, erasers, calculators, water, and any non-intrusive nourishment such as sweets, or fruit should be checked off for inclusion.
  • When your child arrives home after their exam, listen to their experience carefully and then move on. After each day’s exams allow them to recount their daily story to you. Do not be tempted to review in detail with them any errors or omissions on the paper. Such a process achieves absolutely nothing, other than to again increase anxiety levels. Simply allow them the time and space to tell their tale and move on to the next challenge (i.e. the subsequent paper) is the best policy.
  • Know the exam schedule. Pin the exam timetable prominently up at home; highlight each exam to be taken. This applies to house exams also. Diary the date and time of each paper your child must take. In the stress of the whole exam period, you need to be continuously aware of whats going on and when. Investigate which days or subjects your child isn’t looking forward to so that you can be there for them in a real and practical way.
  • It can help them greatly if you have a little knowledge of each exam paper or at least show some interest in it. Simple questions such as, “What is up next?”, “Are there any compulsory sections?” or “Are there any predictable questions?” can be asked. The best open question to ask is “How are you feeling about …? “. This will allow them to express themselves more freely if they wish. This also ensures they won’t feel alone and that you really care about how they get on. If they will allow you, work with them on devising a short but efficient revision schedule, as this is something I have noticed that students struggle to do alone. How all students manage their time from now on is key. Wishing you luck, especially if you are a ‘first time exam parent’.

‘Life is about dancing in the rain, not waiting for the storm to pass’

More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books for all students can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

*****

*****