Joe’s Jotter: How to Study Smart (2023) – Key Tips for 2nd & 3rd Years.

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Spending a short amount of quality time with someone is better than spending hours paying very little attention to them at all. Revising for an exam is similar. You must hit revision in small intense bursts where you give it your 100% attention. The following are three useful efficiencies that will help you construct good study sessions.

Rotate your Place of Study

It is good practice to rotate where you study. The main reason for this is that if you start to get bored or listless there, you’ll associate boredom with learning. Try other places such as the kitchen table, the park, the back garden, the library or just a different room; anywhere you want to really. Try revising certain topics in unusual locations. An example of this could be to learn English drama quotes on your lawn in the sun. When you need to remember these quotes in the exam hall, you can visualise yourself being back there in the sun, recalling the day you learned them and hopefully triggering your mind to recall that information. Experiment to see if music or TV helps you concentrate. Some subjects will be more suited to this than others. I believe some Maths topics do not require one hundred percent attention, an example being adding words or formula’s to your hardback notebook. This, however, may be associated with my aptitude for the subject. You may be able to listen to some low level music in subjects you are more tuned into. This varies from person to person obviously and definitely won’t work for every subject.

Leaving Material Out

Come the next few weeks, as regular as a clock ticks, the rumour mill kicks into action. Comments like “Oh, this is coming up this year”, “I heard this is expected to come up”, “There’s no way that will be on the paper” or even ‘I’m leaving that out’ are common both online and offline. Please be aware that if a topic is listed on the syllabus for your subject, it can appear on the paper, even if it came up last year. Your teacher will source you a copy of the syllabus document if you wish to view it, or alternatively you can download it online. The syllabus document will tell you exactly what can be examined in the subject and is useful when you are creating a list of topics to be covered for each subject.

In relation to exam preparation, I know you all will try to cut corners, predict, throw topics away and ignore information. I would not recommend leaving out big chunks of the course. The State Exams Commission (SEC), who set the exam papers each year, state that they do not want any element of predictability in them. In general my advice is to cover your bases well and be as sensible as you can.

The plan should be to continue to reduce the volume of your keynotes. Summarising is the core idea here. I am convinced that summarising information will help you assimilate it better and your final content will be something more manageable and far less scary. Keep re-writing summaries into something clear that you can read and understand. As exams approach, be careful who you listen to. Teachers with many years’ experience (whether that’s your subject teacher or someone you know well) won’t put you far wrong. Having seen many exam papers, I think you can certainly place a good level of trust in them. The newspaper revision supplements written by experienced professionals, can be a useful revision aid also. However, too many notes are a bad thing and may overwhelm you.

Implement a Workable Revision Plan Now

Now that you are aware and have listed out all the topics on a sheet (per subject), it is time to make a robust yet practical revision plan that you can follow. Here are twenty practical study tips you can start using today:

  • Divide your revision time into small sessions
  • Take a break of five or ten minutes after each session
  • At weekends and holidays, revise during the hours when you feel most productive
  • Each student has their own method of studying, so figure yours out and use it
  • Divide study time proportional to effort needed. Difficult topics = More time
  • Underlining the key points for each topic is a great revision habit to start now
  • Make a practical study plan you can follow. A plan that is not doable is a big ‘NO’
  • Short notes should be just that – short and concise. This makes revision easier later
  • Use abbreviations and note down the key points only. No waffle or padding
  • Do not skip a topic because it seems difficult. Revise it a few times to let it sink in
  • Use revision breaks for something productive such as music, exercise, or activities
  • Always set a target score you are aiming towards in each subject
  • Take tests regularly. Your test scores are a regular reminder of your target score
  • Maintain test records so that you know which subtopics you need to work on
  • Sleep 7-8 hours daily. Losing sleep will affect your ability to concentrate and retain
  • Stay as healthy as you possibly can. Exercise
  • You cannot change the amount of revision you did yesterday. Start today
  • Be kind to yourself. Use positive self-talk each day. Example, ‘ I will do …… today’
  • Reflect on the amount of revision you did today, instead of what you didn’t do
  • If today’s plan didn’t go well, revisit it and tweak tomorrows one. Never give up

and remember..

“It is never too late to step into your own greatness”

Joe McCormack.

More details about Joe’s Maths Tuition for 5th & 6th Year 2023 (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/

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Joe’s Jotter: How to become a Specialist at Maths Exams (Act 1)

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Surprisingly, thousands of top students over the years have struggled when it comes to performing to their ability in Maths exams. In my experience, there is now a disconnect between how teachers teach a Maths class, and the skills students use during a Maths test.

For some students, a fear almost overcomes them with the thought of a Maths test upcoming.  Similarly, a fair percentage of students that breeze through other subject exams freeze during Maths ones. A significant aspect of Teaching Maths now is helping students overcome their anxieties, while teaching them the key techniques to retain that calmness and confidence.

Sitting a Maths exam is a skill, but it is something that if you practice and apply a defined strategy to, you can get quite good at it. Every day, I work closely with students to teach them these vital skills to excel in all kinds of Maths assessments.  Below are my insights into how to ACE any Maths exam – from the five minute class test to the ‘full on’ final state examination.

Make Changes to How You Revise and Prepare for Maths Exams

Below are some clipits of advice to help you get set for a Maths exam. Applying these practical guidelines in your revision plan and during exams will 100% improve your grades.

  1. Apply the skills you have learned from practicing past exam questions under time pressure at home. A time budget plan is a key part to success in any Maths exam.
  2. Keep a hardback of Maths notes. Being familiar with words that appear on Maths papers are vital to aid understanding of the questions you are being quizzed on.
  3. Find multiple-choice questions online or ask your teacher if they have some. These are like ‘speed-studying’ and require less time to work through and test yourself on.
  4. Attempt past exam questions. After completing each past exam question, be sure to view its exact and fully developed solution to see how your work stacks up against it.
  5. Stay alert for key words and phrases to guide you through a question. For example, the volume of an object should allow you to find measurements on it by working backwards.
  6. Use familiar mathematics to guide you. Think back to relate the test question to a concept, topic, or technique your teacher did with you in class.
  7. Formulas are key in Maths. Reflect on what formula you know that may help you solve the problem. This formula may in fact be printed on the test paper or in your log tables.
  8. Can the diagram in the question help? Writing relevant information on a given diagram may prompt relevant thoughts and connections to help you start a maths question.
  9. Show all workings. Always show how to get from one step to the next. Provide all your workings out to support your answer. At the end of each question, always ask yourself ‘Is this a realistic answer or solution to the question being asked?’ Example: Ten metres would never be an acceptable answer for the height of a pencil. You get the Idea.
  10. Read the entire question… twice. Check what the question is asking and in what form you need to present the answer. For example, you might need to round the final answer (decimal places, significant figures, scientific notation) or convert to an annual amount.
  11. Note the key Information given in the question onto your answer book. Subsequently, note the Information that isn’t present. Link these two to help complete the full jigsaw.
  12. Don’t be afraid to utilise diagrams or tables in your solution. This will clarify your understanding of the information in the question and support your workings out.
  13. Show all relevant substitution (subbing in). This shows the examiner that correct maths processes are being used (e.g. showing the substitution of an x-value into a function).

‘Act 2’ of this two part drama will follow in a few weeks… 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 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/

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Joe’s Jotter: The Importance of Getting that Extra Support in Maths.

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As a Maths teacher of the last 20 years, I understand the struggles students have with Maths on a day to day basis.  They are frustrated with not being able to understand methods in class, their friends progressing quicker than them, not being able to get maths questions started and either spending too much time or not being able to attempt homework at all.

The key to having more success in Maths is being open to new methods and using each night to practice questions that the teacher has shown that day. Maths requires a higher level of dedication and persistence than most other subjects. When I was in school in the 1990’s, only those with a strong aptitude for the subject were successful in it. I feel that today it is more important to stick the course, ride out the storms, work hard and not give up; as opposed to being a natural Maths talent.

The reality is that many students will need extra support outside the mainstream classroom, and it is important to find a teacher or tutor they can relate to and has the ability to explain concepts in simple terms. Looking for extra support in Maths is not a sign of weakness, the opposite in fact. It is often no fault of the student when they seek this extra help to try, and both boost their confidence and grades in the subject.

How an External Maths Tutor Could Benefit Your Child

That extra bit of support in Maths can make all the difference.  From a short term point of view, students need someone who can be there for them should they get stuck a question. They also need someone who can see the bigger picture, allowing them to work towards their longer term goal. Here are some of the benefits and subtle advantages of having a tutor in Maths:

  1. Parents can contact your tutor directly and keep up to date with specific progress.
  2. It is a more relaxed atmosphere where your child is more likely to ask questions.
  3. Tutors tend to focus on helping your child be an expert on ‘tackling’ exam paper questions.
  4. The tutor will hopefully give your child a more positive outlook towards the subject.
  5. The tutor will give your child insights on how to revise Maths (compared to other subjects).
  6. Most tutors will set the foundations with core work in Algebra, Functions and Equations.
  7. Your child’s confidence will grow as they rebuild core aspects of Maths they missed out on.
  8. Your child will be less anxious about keeping up in class and with their friends.
  9. It will give your child the organisational skills to plan for upcoming exams.
  10. Your child’s weaknesses in Maths will be identified and fixed quicker.
  11. Those who struggle in school usually try to hide in Maths. Tutors can tease this out.
  12. Most tutors will be contactable when students run into ‘Maths trouble’ at home.
  13. The advent of Online Maths tuition saves wasted time in the car each week.
  14. Maths tuition often shows a student’s real ability, which may not be apparent in school.
  15. Better engagement with the subject gives students that ‘can do’ attitude to work alone.
  16. Tutors can focus more on revision of key topics and ensuring core skills are enhanced.
  17. Increased help in Maths allows students to relax more and focus on other subjects.
  18. Students often move up two or three grades with that extra bit of reassurance & guidance.
  19. Students can request extra notes for topics they may be finding difficult in school.
  20. With many 3rd level courses having a Maths module, this support ‘invests in their future’.

‘It is never too late to step into your own greatness.’

 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/

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Joe’s Jotter: How to Choose Your 5th Year Subjects

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Choosing subjects for 5th Year can be daunting enough, and soon many 3rd and all Transition (4th) year students will be faced with that task in school. A 4th year student will have had more time to contemplate options, and so sometimes make more considered choices than those coming straight from the Junior Cycle (3rd year), and this is something Parents need to be aware of. It is important to put some thought into how subject choices may influence career options later. Students should now consult with all their teachers and ask them about the level of work that’s required for success in a given subject at a specific level.

Third Level Considerations

Students, if you have a third level course or career in mind, it is important now to do a little research into its content and investigate if there are any ‘minimum entry requirement’ to gain access to it. All courses now have detailed descriptions of each module online, listing out exactly what you will be required to study on a year by year basis. It is important to note that no matter what points you achieve; you will not be allowed onto a course unless you achieve its minimum entry requirement (if it has one). This may guide you to choose particular subjects. In the case of compulsory exam subjects (which you will be studying anyway), obviously there is no choice to make there. However, if there is a requirement on your desired course to score a certain grade in a foreign language or other subject, you will need to opt for this subject if your heart is set on that course. However, to this tune, I would strongly recommend you have a plan B and C in place when choosing courses and will discuss the importance of this in articles later in the year.

In relation to specific college requirements, it is useful to know that the NUI colleges (UCD, UCG, UCC, Maynooth etc) require a pass in a third language [excluding English and Gaeilge] for many of their courses. However there are now exceptions to this: UCD has dropped this requirement for Engineering and Agricultural Science, and Maynooth has removed it for Business, Accounting, Finance and Law. Trinity, UL, DCU and the Institutes of Technology don’t have this third language requirement, except for language courses. Again, the advice here is to double check the requirements online for each individual course and college.

There are also ‘Subject requirements’ on courses. Examples include: to study Primary teaching, you need a H4 in Irish, Engineering courses may require honours Maths and sometimes a science subject, Medicine may require two science subjects (one being chemistry) and Nursing may also require a science subject. The savvy student will do some research on websites like Qualifax and Careers portal to get a handle on the exact requirements of courses they are Interested in. Be fully informed prior to CAO time.

The Eight ACE ‘Do’s’ for choosing Subjects

All in all, when it comes to subject choice, students should think a little about their futures, talk to teachers, look at courses they may have an Interest in and discuss with their peers gone ahead how they found studying the subject. Take your time and choose well. It may be wiser to choose subjects you have an interest in, as opposed to ones you feel you must choose in order to get into a certain career later. It is definitely a balancing act. Here are my eight ACE do’s for subject choice for 3rd and 4th year students:

  • Do…Choose subjects you enjoy learning about
  • Do…Discuss it with as many people as you can including teachers and peers etc
  • Do…Try and keep your options open as much as possible
  • Do…Choose subjects you have some kind of a flair for or Interest In
  • Do…Research each subject’s content on www.curriculumonline.ie
  • Do…Choose subjects linked to a possible future career you are considering
  • Do…Write down the Pro’s/Con’s when trying to decide between two subjects
  • Do…Make the final decision yourself (not your friends, teachers, or parents)

Final Choice Advice

The best advice I can give about subjects is to select ones that keep your options open.

You can best do this by choosing one foreign language and ensuring that at least two of the other three subjects picked are ones you have an interest in or flair for. Remember that you will be spending a lot of time studying your chosen subjects over the next two years and the nightmare scenario would be dreading going into that class each day. I myself selected a subject I regretted taking in 5th year, but luckily was allowed switch later. You may not be as fortunate in your school, so try and get it right the first time to save any unnecessary anxiety. I also have a degree in a subject that I didn’t study for my Leaving Cert. Life can be funny, so my advice is ‘rule nothing out’ and keep as many doors open as possible.

In choosing subjects, always play to your strengths. For example, if business is something you are really interested in, you could choose Business and Accounting (assuming they don’t clash on the school timetable). Similarly, if Science is your area of passion, you could opt for two of the Science subjects i.e. Biology, Chemistry or Physics. Applied Maths or Agricultural Science may also be other options here.

Enthusiasm for any subject will foster a desire to learn more about it and studying these subjects in Senior Cycle won’t even feel like learning. If you are struggling with this decision, put all the information and swaying factors out on the kitchen table. Usually, your heart will guide you one way or the other at that stage. I wish you every success with your decision. Joe

‘Compare yourself against yourself, not how much work your friend is doing.’

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/

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Joe’s Jotter: Preparing for a Mock Paper in Maths (3rd & 6th Yrs)

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As third and sixth years prepare for their Mock Paper in Maths, here are some quick pointers to help them be ready. Some students get quite anxious about the Mock examinations, but I always feel the focus should be on preparing and being ready for the final June exams. Here are my ACE tips for the Mocks 2023:

  1. Focus on getting the timing right for each question on the day. This is one of the main ‘learnings’ to take from the Mocks. You should come away with better timing skills.
  2. Practice easier past exam question that you feel confident on beforehand. I wouldn’t take on ‘rock hard’ or new content that may actually sway your existing confidence.
  3. Write down all the formula’s that you need to know for the exam (those that are not in your Log Tables). Be very familiar with what formulas are in your Log Tables.
  4. I would give the textbook a break for a short period. Know the core skills and use your notes from class to help you tackle more straightforward questions in preparation.
  5. Do Maths revision in short bursts. Maths can be quite intense, especially if you take on longer past exam questions. Forty mins max and then take a break. Stay fresh!
  6. Rotate your Maths revision between topics over the next few weeks. This will keep your brain more tuned and aid motivation. Note all the key points into a hard back.
  7. Target three main topics on both Paper 1 and Paper 2 (Leaving Certs) as opposed to trying to cover the whole course. It isn’t possible in two weeks. Sensibility rules!
  8. Get advice from a Maths teacher. Ask your teacher ‘how should you best prepare for the Maths mock?’ Each teacher will have their own take on best to prep for this exam.
  9. Invest in a good Maths Solutions book. This will allow you to check your solutions to questions in a step-by-step manner at home. ACE Maths Solution Books will help here.
  10. Be realistic with your Maths Mock exam. You have still so much more to cover in class and haven’t actually sat down to do a full exam paper yet. Time is still on your side. 

To find out more about how to approach the Mock examinations for all subjects (among other topics), there is a full chapter with advice and guidance on it in my ACE Study Guidebook entitled ‘How to ACE the Leaving Certificate’ for all subjects. This textbook is suitable for all students from second year to sixth.

Wishing you all the luck,

Joe.
ACE Maths Tuition
W: acesolutionbooks.com

Joe’s Jotter: Practical Tips to Equip Yourself for any Exam

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Most students realise at this stage of the year that it is time to settle down into a proper homework and revision routine. If you’re unsure about how to get the best out of yourself, here are some simple but practical recommendations to get you on track. This guidance applies to all Secondary School students, no matter what exam you are preparing for.

  1. Structure your Day.

If tomorrow is a non-school day, it is important to have a plan written down from the night before as to what tomorrow will look like. Having a somewhat set routine will keep you grounded and help you be organised. Waking and going to bed on a routine, eating a proper breakfast, showering, dressing yourself, knowing what topics you will tackle and indeed knowing when break times are –  will all greatly help.

  1. Be Aware of You.

Be aware of how you are feeling and ensure you get plenty of rest and healthy food. Make sure and keep in touch with friends and family to keep you sane and maintain motivation levels.

  1. Short Revision Bursts.

Oscar winning actors wing it. But that’s not you. Research has shown that you need to keep revisiting Information regularly for it to stick in your head. Limit revision bursts on a topic to thirty minutes. This is where short summaries are key. Using postits, summaries, flashcards and mind maps are all tools you should have in your revision toolbox. There are so many different ways to revise, so be sure to utilise them as much as you can. Reading from a book is a very small part of preparing for any exam in 2023.

  1. Write Down your Goals.

At the start of each week, write down how much/what you would like to revise and complete. Ensure you know what sub-topics need covering for each subject by consulting each subject teacher. Set realistic goals that you can achieve in seven days. If you find you are having success and a certain approach is working for you: keep repeating that process. Use common sense by playing to your strengths.

  1. Start Today.

By the law of averages, you may not be super motivated about exams right now. Motivation will increase as you see subtopics being ticked off and completed in front of you. Just get started and then keep going as best you can.

  1. Sleep is always Important.

Sleep refreshes brain cells allowing you to wake up refreshed and begin storing more Information in both your short and long term memory. If you are feeling too tired at your study desk, stop. Time spent in ‘Zzz’ land will actually be more productive at that stage.

  1. Compare Yourself against Yourself.

Always try to compare yourself against yourself, not others. How can I improve my last test result? How can I be more efficient with my revision this week compared to last? etc

  1. Limit Time on your Phone.

Limit social media and phone time over the next few weeks. The only way to do this is to leave the phone out of the bedroom and check in on it during breaks. Any time I take a snap survey in my classroom, 90% of students admit that their phone is a distraction. Students have already acknowledged this as a big problem, but still ignore it.

  1. Take it One Small Step at a Time

Remember that a big mountain hike starts with the first small step. Get on the first rung of the ladder by planning out the topics and subjects you will revise tomorrow, remembering that you can only reach your goal of success by taking it step by step, hour by hour and day by day.

  1. Think About Being Finished

Picture yourself walking out of the exam (you are preparing for) and meeting up with your friends. Picture the weight that will be lifted off your shoulders when it is all over. Use these thoughts to provide you with extra motivation and focus for each task.

Did you find this article Interesting? My two hundred page Study Guide Book entitled ‘How to ACE the Leaving Certificate’ for all subjects is packed with an abundance of guidance for any kind of exam preparation from Second Year upwards. Click here for more details. Joe.

‘Listen to your body. Rest or sleep if you are tired.’

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/

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Joe’s Jotter: Two Underused Revision Hacks for Success

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Students,

As Christmas exam time draws closer, here are two under-rated hacks that might just give you the edge as you try to get the most out of upcoming revision time.

  1. Record yourself

With so many portable digital devices to play content on now, recording audio is a great option being availed of now by many students. This is an excellent revision hack if you have long commutes or spend a lot of time in the car. Playing back notes you have recorded is a very successful method of retaining information. I have recorded questions and answers for job interviews previously, where I called out a possible interview question and then proceeded to answer it as best I could. Recording information on various subjects has been helpful during my career, when different jobs and challenges emerged. The great thing about recorded audio is that it will always be at your fingertips and is easily accessed from multiple devices. You can also barter this material with your study buddy i.e. swap it for other audio content or even for a great set of their written notes.

Bullet points, facts, and lists are ideal revision components that can be recorded to your phone and replayed repeatedly. Remember, you will need to repeat any learning process regularly to achieve success. Having a portable learning tool like your phone or a small hardback in your pocket is great to keep you tuned in when opportunities to catch up arise.

  1. Rotate your learning

I feel it is important to rotate the type of learning you do in order to keep the brain fresh and interested. When you sit down at the start of the week to plan your Lifestyle (Study) Timetable, rotate your learning in each study block. This rotation tricks the brain into going longer. You should even rotate your place of study: for example, study a specific topic in the garden, it will make it easier to recall what you revised there, since you have created an association with this part of your home. Rotation could also involve going down the road to your grandparents or your local library to write some essays or update your hardback. Initiatives like this maintain freshness in your preparation. These ensure each homework or revision session gets the attention it deserves. A change is as good as a rest!

Rotating your learning is achieved by using multiple ways to take in and understand material and notes. There are so many ways you can acquire Information these days. Rotate your learning between reading, writing notes, developing summaries, listening to podcasts, recording something you have learned into your phone, playing back lists through your headphones, searching the Internet, reading out loud, getting someone to examine you, watching educational YouTube videos, watching educational tv programmes, watching ted talks, creating flashcards, summary hardbacks, using postits, sticking key notes up on your wall, underlining and highlighting or discussing a sub-topic with your friends in a study group etc. These are just some of the learning options available to you, which you could and should be using. Select and practice a number of these in order to try and find out what works for you. After that, rinse and repeat the winning formula. Good luck. Joe

‘Don’t let what you cannot do interfere with what you can do.’

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

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

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

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Joe’s Jotter: RIGHT it out by WRITING it out

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With a lot of schools switching to iPads and tablets as a mode of Education, the debate rages about which type of notes is best to have from a classroom lecture i.e., typed or handwritten ones. I still think there is a question mark about learning content in digital format, with it being more suitable in some subjects than others. If a student has the possibility of printing something out, in my opinion they should do. With decent printers just over €50, I feel this is a great long-term investment for parents of children at Secondary School.

From listening to students, I think many of them still like to hold a hard copy book in their hand when learning. Even as an ICT teacher myself, I believe that the old-fashioned way of taking notes by hand is still best. Since we now can type faster than we write, students are tending to type notes verbatim (exactly to the word) as they try to keep up with their teacher. We are copying down a lot of the teacher’s language directly. There would be more of our own language than the teacher’s used in a handwritten set of notes, which makes them easier to understand and ultimately, of better quality. The following case for handwritten notes applies to both Secondary and Third level education…

Why handwritten notes are still the market leader…

  • With handwritten notes, we spend more time thinking about the Information before the actual physical act of writing occurs. If we are attempting to type everything exactly as spoken, there is less thinking time about that same information. In essence, I believe that slightly more learning takes place during the actual handwriting process.
  • Keywords are valuable in any content. When you are taking down notes by hand in a lecture/class, you are listening out for the keywords to ensure you are grasping the bones of the sentence. Again, while typing you are trying to get everything down and so your brain misses out on this ‘essential keyword focus’.
  • When handwriting notes, you are putting your own special stamp on them, making it easier to recall information you have translated into your own words.
  • During class, you can link handwritten notes quicker with bubbles and arrows. While doing this, you are learning what the connections are in the teachers’ content.
  • Above all, writing your own notes engages the mind and prompts new ideas and thoughts. It enables your brain to switch to ‘background learning’ mode while you prepare and enhance your notes.

Learning in a variety of ways is the key to success. Working with a study buddy or group is another way that many don’t consider. Students can swap essays and notes, and indeed even teach each other. Upon swapping these notes with friends, they should rewrite them into understandable Information, in order to be able to revise them better later. I am a big believer in summarising your own notes. By all means you can work in a group or with a ‘study buddy’, but once you get their essays or interpretation of topics; highlight and underline their key points. The final piece of the puzzle is summing their content into your own words, to ensure that you really understand it. In my experience, there is a much higher chance of Information sticking with personal and individualised handwritten notes – the old ways are still the best. Try it and see! Good luck, Joe

‘Work hard, dream big, never give up’

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

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

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

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Joe’s Jotter: How to Prepare for Exams ‘Home Alone’ (Episode 1)

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Being able to work alone is becoming an even more important skill, as third level institutions increasingly develop their online learning platforms. Getting used to notetaking and revising at home, however, is proving challenging for many students. In school, your subject teachers are present to keep you on task, class-by-class each day. This contrasts sharply with the number of distractions and ‘extra-curricular’ activities vying for our attention at home.

Episode one of this feature article contains recommendations and practical advice to get a revision routine going at home. Preparing notes and revising at home is alien to most students unless they have been home-schooled. These guidance articles, which come in six parts spread over the year, will provide you with tools and ideas to help you get organised, advise on motivation and explore the role your parents may have during ‘home revision’ periods.

Next Day’s Plan

From an exam student’s point of view, the first thing you need to look at each night is your plan for the next day. If your plan is to ‘do a bit of study’, a large part of the day could well pass you by. At this stage you need to develop your own workable home routine. To do this, I would recommend getting up at the same time, showering and having a structured plan for revision, meals and breaks to facilitate that pattern you need. Organising yourself the night before is key. Knowing what to expect the next day will increase your productivity.

Learning Successfully at Home

To learn successfully at home, you need to investigate new ways of finding and using material online, including being familiar with new software and websites. You will definitely need to be more self-disciplined and more efficient at managing your time than ever before. Planning next day’s ‘Revision timetable’ each night with thirty-minute blocks for each sub-topic will certainly help. Use breaks and little rewards to motivate yourself. With your teachers not around, you will need to challenge and motivate yourself minute-by-minute, hour-by-hour. Hopefully you will look back later and view these changes you have made at home as a positive period in your life. Without knowing it, you will effectively be turning yourself into independent thinkers and learners, and these skills will stand to you at third level and in the world of work to come. Even during term time, there is only so much your teachers can do for you. You must do the bulk of summaries, testing and revision at home.

Your Study Area

Ask yourself the following questions: Is my revision area free from distractions, comfortable, and spacious? Is there natural light in the room and is the desk and chair I am using the right height for me? Is my study desk full of ‘non educational material’ or is it clutter free? Is this a place to prepare notes and learn? Your answers to these questions will indicate if you need to make changes to this area or not.  Up to now, your study area was only used for three to four hours each evening, but now it may be required more, and you need to ensure you are happy with how it is setup. Ideally, I would locate my revision area outside the bedroom, in order to disassociate revision with sleep. Depending on your circumstances, all of the above may not even be possible – but just do what you can. Link in with your parents to try and get as many of these elements in place as possible. I will publish the five subsequent parts of this feature at Christmas, February Mid-term, Easter and just prior to June’s State Exams. Stay tuned for more useful Insights on ‘Revising at home’ as time progresses. Joe

‘Check the plan the night before for tomorrow. Adjust and make it achievable.’

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

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

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

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Joe’s Jotter: How 2nd and 3rd Years Can Make the Most of their Evenings

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Students, as we come towards the end of the first few weeks back in Secondary School, it is important now that you get into a routine of homework and revision, both during the week and at the weekend. Breaks are important for all students who are putting effort in at home each night, as well as giving yourself some wind down time before bed also. Over the next few months, try and improve the standard of your homework. Always take pride in how you complete written homework. Doing homework like a mini exam is the best form of preparation for your any upcoming tests. Here are four more practical tips you can try to get the more out of your evenings.

Be positive

Being positive will vastly improve your attitude towards study and therefore its quality. You should always focus on what you have studied, what you have learned or what you know as opposed to continually looking at what needs to be done. When you come across an awkward question, you need to box it off properly in your mind. Instead of thinking, “we haven’t covered this!” or “how is this relevant to what I know?”, you need to reflect on how it links into your subject, topics within the subject and what your teacher has taught you in class.

The same goes for studying prior to the exam. Take control by changing the way you speak about your preparation. Instead of saying “I should be studying more”; be good to yourself and say, “Well I did a solid two hours this morning and will go back to it tonight”. Change “I should be…” to “I’m going to…” Research has shown that positive language can lead to more positive results. If you say: “I can’t climb that wall”, you are less likely to succeed in the task, as your brain has almost been auto programmed to fail. As a Maths teacher, I love this equation of positivity:

Positive attitude + Positive actions = Powerful results

Look after your eyes

You will be doing plenty of reading from textbooks, summary notes, post-its, flashcards and the likes over the next few years, so it is important to look after your eyes during this period. The expert’s advice on reducing eye strain is to apply the twenty-twenty-twenty rule. That is to take twenty seconds to look at something twenty feet away and repeat this every twenty minutes. Going outside on your breaks will get some fresh air to the eyes. Another good exercise is to simply rest your eyes in the palm of your hands for a few minutes, making sure that no light gets through. Too much time on devices wouldn’t be great for keeping your eyes fresh. Just saying!

Rotate your learning

The brain can only concentrate on a subject matter for a certain time period. At times, when I was penning my ACE Study Guidebook, I needed to get away and come back to it in order to maintain my focus. Rotate your work between memorising content, writing, oral work, audio, Internet research and watching documentaries etc. Most importantly, rotate your subjects. We all enjoy discovering about subjects we find interesting, but it is so important not to forget the subjects you find difficult or the ones you are just not as interested in. Rotation of stimulus will trick the brain into performing better and going for longer.

Become an active learner

During study sessions, always have a pen and a highlighter to hand. You should mark the key points onto your textbook, write brief comments at the side of the page or underline the important sentences. This information should then be transferred to a summary page later. I really like this method of revision as it reduces the quantity (amount) of notes you have to analyse and there shouldn’t be a need to revisit that part of your textbook again. Active learning is a great way to keep yourself tuned into what you are studying. Spend time thinking about how you can use your life experiences and places visited to enhance essays or answers with a few extra bells and whistles. Individuality and drawing on your personal experiences are what every Teacher and examiner is looking out for in your answers. You need to try and stand out a bit from your fellow students.

Next weeks ‘Joe’s Jotter’ will provide students with six ACE pointers to settle them back into revision. Don’t miss it. To view last week’s feature article on ‘How to Perform Well in Subjects you Find Difficult’, click here. Get in touch if I can help you in any way. Joe.

‘Record all revision done so you can track whats what later.’

More details about Joe’s Maths Tuition Classes for Junior Cycle and Leaving Certificate (2023) and his Award Winning ACE Maths Solution Books can be found via the links below.

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

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

Joe’s Facebook Page: https://www.facebook.com/JoeMcCormackEducationalExpert

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Photo:@ZhangChaosheng

Joe’s Jotter: Useful Insights for Parents on…Secondary School Maths

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I think it may be interesting for both students and parents to consider the following observations I have become aware of in Maths over the last number of years. Maths is a very emotive subject, and everyone has their own way of understanding and practicing it. This presents its own set of difficulties. The below insights and observations should help you as a parent to reach out and help your child with Maths in a more positive way. Read on…

The Second Year Maths Dip

Firstly, in general, I have noticed that some of my students (and those of my colleagues) experience a slight dip in performance in Maths during their second year in secondary school. This is partly due to workload and the fact that the first-year common course is quite basic. This dip for girls is not as pronounced as for boys. There is also a drop off in fifth year, but it isn’t as extreme as the second year one. If your child is heading into second year, you need to be aware that this could be the case for them. I believe that working diligently on their algebra, fractions, and general numeracy (external to the calculator) are the key elements to overcoming barriers. These topics are the three main pillars of Junior Cycle Maths and underpin and are linked to every other topic on the course.

We all need to keep in mind that online learning has not suited some students and that they have missed out on that key face-to-face contact with teachers, especially in Maths. As a parent, it is important that you encourage positivity around this subject and remind them that every student in the country is in the same boat. From a personal point of view, I noticed that last year’s Junior Cycle class did struggle (more than usual) with a variety of topics, but it did eventually come together for them in the end. I expect that the incoming third year cohort will take a while to settle back (through no fault of their own) this year. In fairness, it may take many of them until after Christmas before they settle down into a pattern of revision and work across all subjects. It is understandable that they may not hit the ground running this year and we all need to be cognisant of this.

Girls – Go for it!

From the students I have taught since the Project Maths syllabus was introduced in 2008, I have noticed another trend in my classes. I have spotted that female students are less likely to take risks when attempting past exam questions. The new phrasing of questions on Maths papers suit boys better, as they are less conscious of what they are writing down and are less afraid of being wrong. In my opinion, it is important for girls to express their opinions freely and openly and we, as teachers, need to help them develop this skill. I think it is important for all students not to get unduly perturbed if they cannot get a certain part of a question out perfectly. In Maths now, it is more important to go onto another question (within the allotted time), instead of looking to complete every single question part absolutely perfect.  I feel that Churchill’s (not the dog) quote is quite apt for our modern day Maths syllabus.

“Perfection is the enemy of Progress”.

Winston Churchill (Former Prime Minister of the UK)

One does not really have time for 100% perfection on a Maths paper as they tend to be ‘question packed’, and unlike other subjects, there isn’t time for admiring your work. Students should apply this principle across the board to all their Maths tests in 2022/23.

The New Practical Style Questions

Thirdly, girls especially need to practice more exam questions involving engineering and mechanical parts. My reasoning for this is that, in general, most of the student cohort studying Engineering, Construction studies and Design/Communication Graphics (DCG) at Leaving Certificate are boys, and girls are not being exposed to this specific type of learning. With more everyday life practical questions being the order of the day in Maths, it is inevitable that more technical and mechanical questions will appear in years to come, and girls and parents of girls need to be aware of this. This trend will slowly become more pronounced if the Governments’ promotion and focus on the Science, Technology, Engineering and Maths (STEM) subjects continues and I expect it will.

Always Follow Your Passion

Lastly, in a survey conducted a few years ago, twenty-nine percent of Irish parents surveyed thought that technology subjects weren’t suitable for girls and fifty-three percent of girls in secondary school dropped STEM subjects due to pressure from their parents. These statistics may be contributing to the lack of representation of females working in STEM. Students and parents need to be aware of the excellent third level courses and future career opportunities available in these areas for both genders. Students need to be encouraged to explore all avenues of interest and follow their passions. Pursuing a spinoff of the subjects that a student enjoys each day in school wont set them too far wrong. Joe

**You can achieve more than you actually expect.**

 

To view last weeks feature article on ‘Transitioning into 1st Year or back to school’, click here.

More details about Joe’s Maths Tuition Classes for Junior Cycle and Leaving Certificate (2023) and his Award Winning ACE Maths Solution Books can be found via the links below.

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

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

 

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Joe’s Jotter: Anticipating Better Revision Methods in 2022/23

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The key to doing well in exams is continually trying to improve the quality of your preparation. An hour of good quality revision is equivalent to three hours wastefulness. Was your revision productive and fruitful in the school year just gone? Here are some reflections to help you assess this and also to contemplate what changes you can make to be more effective in the upcoming academic year:

  1. Assess your study area: The ideal study space is somewhere where external distractions are kept to a minimum and has an organisation about it. It should be a quiet area where you can concentrate, allow yourself to think and effectively listen to those notes on the page.
  2. Sort out a study routine: You should plan revision for the same time each day, especially during the school week. On these days, I would recommend that you commence study thirty minutes after completing your homework. This will eventually become routine as your mind and body adjusts. Our bodies like routine, as they learn to anticipate events better and become more familiar with them.
  3. Organise your materials/notes: Have all the materials you need to hand for revision. Having to search for materials will lead to frustration. Develop a system that works for you. There is no excuse for not having your notes organised and close at hand. A suggested system is to have a large ring binder for each subject. In each binder, divide off each topic for the subject using card dividers. Subsequently, put the content for each sub-topic into plastic poly pockets between these card dividers. This is just one suggested method. It is never too late to get yourself organised. It is never too late to start studying.
  4. List out the topics: For each subject, list out the topics that need to be revised. Show the list to your teacher to make sure you haven’t excluded anything. You need to be realistic in not expecting to cover them all over a short period; it will take time. Make a second list of the sub-topics inside each main topic. The full listing for each subject should fit onto an A3 landscape page, giving you a quick reference summary of a subject at a glance. Each time you complete and understand a sub-topic, tick it off. I always find that ticking off lists and seeing them shrink gives a great sense of satisfaction.
  5. Mirror exam hall challenges: I would recommend during the days leading up to the first exam that you get up at eight-fifteen a.m., have your breakfast and complete a full past exam paper from nine-thirty to twelve similar to the time the real exam will actually be taking place. This prepares the mind, body and even the arm for the process of rising, eating, and focusing on the task ahead. This serves to mirror upcoming challenges you are about to face and is a little known and under used technique.
  6. Use clever ways to remember content: You need to use your imagination when revising – this includes constructing summaries and lists in different parts of your house to help you remember them. Over my educational career, I based a lot of my preparation around summarising notes. Set yourself a target to summarise a full chapter onto one A4 page and then summarise this page into bullet points using post-its or flash cards. You will then have a shortened summary (written in a language you understand) of a topic, instead of fifteen pages of text in a textbook to trawl over. It’s so simple and it works. Effective study is based on working smarter not harder or longer.
  7. Set short term goals: Setting goals will help you monitor your revision and will give you something to work towards. For example, if you under perform in a test, set a mini goal for your next test to improve by a certain percentage. In your school journal, write down all your goals and check them off as you complete them – call it an ‘Exam bucket list’. If we do not set some goals in our lives, we tend to just plod along aimlessly in more hope than expectation.
  8. Eat your frog: We all put off things we dislike, like going to the dentist for example. Start by studying the subject or topic which isn’t your favourite. Look at the subjects you are struggling with, and then consider the topics within these subjects that you need to tackle. Do not avoid a subject if you don’t enjoy it, as it will eventually catch up with you. Similarly, don’t invest all your time and energy into subjects and content that you enjoy. You need to find a balance that works here.
  9. Attend school and listen: Make sure to attend school every day and be fully present in class, paying attention and taking notes as best you can. Remember that your teachers have been through exams with hundreds (maybe thousands) of students before you, so they are well worth listening to, especially during the last six to eight weeks of term time.
  10. Live in the present: Writer T.S. Elliot once said: “Time past and time future are all contained in time present”. Try not to give yourself a hard time about the lack of revision done in ‘time past’. Conversely, it is also not a good idea to be looking too far ahead into the future as this can cause anxiety and tension about your upcoming tasks and workload. Plan your revision strategy week-by-week and review it as you go along. Joe

**Don’t ever sell yourself short – you are worth more than gold.**

 

More details about Joe’s Maths Tuition Classes for Junior Cycle and Leaving Certificate (2023) and his Award Winning ACE Maths Solution Books are available below.

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

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

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Joe’s Jotter: Improving our Exam System 2022

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The debate is ongoing in relation to continuous assessment at Secondary school, with a keen focus currently on the percentage and type of allocation taking place for the new Junior Cycle. Many subjects at Junior Cycle level now have Classroom Based Assessments (CBA’s) incorporated into them. With a review of the Leaving Certificate (likely to be rebranded the ‘Leaving Cycle’) taking place, I am wondering what is on the horizon? As with any change to an assessment model, we need to ensure there are transparent procedures in place and a clear sense of fairness is preserved.

Preserving Fairness

With the above in mind, firstly I feel that any continuous assessment introduced needs to be completed during school time. If students take work home, it may become an unfair competition depending on the socio-economic background of their parents and other extrinsic factors. i.e. I feel we can’t take the chance of having any external interference in projects or tasks that students are required to complete alone. We need to make sure a level playing field is retained for all students and that we don’t allow potential changes to tarnish or unbalance our currently solid exam system.

Should Teachers assess their own Students?

I strongly feel that projects and practical’s should not be corrected by the student’s own teacher. The department needs to hire suitably qualified personnel for these posts. They also need to properly resource schools for these assessments and allocate proper time on the timetable for students and teachers to prepare for them.

Teachers are clear that they don’t want to assess their own pupils. A teacher correcting their pupils’ work for any kind of state certification would leave our existing robust system open to all kinds of accusations. When I read articles from around the world and hear of exam papers being leaked and scandals over corruption in education, it’s clear to me that our exam system here in Ireland actually works pretty well. People need to be careful what they wish for. ‘The law of unintended consequences’ and ‘baby and bath water’ come to mind here. The SEC and our Department of Education and Skills have a great record of always acting professionally and with the utmost integrity when it comes to the exam process. These principles need to be maintained at all costs.

According to a January 2019 report from the National Association of Principals and Deputy Principals (NAPD) entitled ‘Senior Cycle Reform – What do we want?’, the responses are varied in relation to the question of exam assessment. For example, only 22% of principals, deputy principals and teachers support the practice of correcting their own students’ work, with many having concerns that a teacher would be biased against or for a student. That number increases to 30% of parents who would support such a change, with a slight majority of 51% of students wanting it. Not major numbers in favour there are they?

How can we Improve our Current Exam System?

In order to further improve the exam system, I would propose that we have a week of continuous assessment before Easter to take the pressure off the June bottleneck. Each student could still then enjoy their Easter holidays and return refreshed for the last push towards June’s finals. I think by spreading the load more, it would mean that all the focus for the student isn’t placed on one part of the academic year. This would greatly reduce the intensity levels for those two weeks in June.

Would studying a reduced amount of subjects (five for example) be an option?  I think the benefit of having less subjects would mean that students could spend more time exploring and even enjoying their selected ones. It might also take away the focus on how many CAO points a subject can yield and allow them to investigate topics (in these subjects) they genuinely have an interest in. Third level courses are usually made up of quite specific content compared to our current broad based Leaving Cert. Is our second level system too broad?  Are our students ‘Jack’s and Jill’s of all trades and masters of none’?

Another potential option might be a compulsory Transition year (TY) and implementing a form of continuous assessment at the end of that year. This would ensure the majority of students would be eighteen years old upon sitting their final exams and therefore be in a better position to decide on their third level/further education options also. The students could still enjoy their trips, experiences, and work placement in tandem with assessment in certain subjects. In addition to this, I would also like to see a system where all TY’s have the opportunity to sample leaving cert subjects. This would give them a deeper understanding of subject content, prior to making subject choices at the end of 4th year.

I am for some form of continuous assessment, but still feel the final exam is the best way to differentiate the students academically. I would be in favour of students having around 30% (approximately one-third) continuous assessment finalised in each subject, before sitting down to do their final exam papers at the end of 6th year. This would reduce current exam anxiety, especially if the student was made aware of what their score was out of 30 prior to the final exam. This is the way many third level modules operate now.

There are improvements we can make to our exam system, but I feel a lot is still right with it. We need initiatives that would take some pressure off our students, while maintaining the core integrity of the process. Indeed, there are many changes the department could make, and it seems some are afoot. Ultimately, I still firmly believe that sitting down to final exam papers should be retained as the main and fairest judgement. Joe

**Today is a new day. I can try yesterday’s unfinished task again.**

More details about Joe’s Maths Tuition Classes for Junior Cycle and Leaving Certificate (2023) and his Award Winning ACE Maths Solution Books can be found via the links below.

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

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

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Photo:@ZhangChaosheng

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

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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 (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 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)
  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 probability 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
    • 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 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:
  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.

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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Joe’s Jotter: Nifty Tricks to Remember Maths Formulas

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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.

 

To view last week’s feature article on ‘Guiding Your Child Through Exams 2022’, click here.

 

More details about Joe’s Maths Tuition Classes 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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