Joe’s Jotter: Performing Well in Difficult Subjects (Case Study – Maths)

As you settle into the new year, teachers and parents totally understand that even though you are making great strides, you still have plenty of fears. From speaking with students over the years, I find it’s not the full set of exams that cause concern, it is usually only one or two subjects. Naturally everyone has their own talents and subjects they prefer. Personally, I was better at the Sciences than the languages, but I persevered and got the grades I wanted in the languages I chose.

Sometimes subjects you are not looking forward to are the ones that have you on guard and you end up doing better in; A paper on the day can go well in an exam you were dreading. I regularly hear welcome surprise coming from students on results day, with comments such as “I didn’t expect that result in xxxxx”. The moral of the story here is that too much concern about a subject could end in false worry and be draining you of energy; energy you need for revising all subjects and getting your head space right.

Preparing for one of your less favoured subjects is a blatant case of having to ‘get on with it’. Of course, it is easier to revise and work on subjects you enjoy and are good at, but you must not ignore the others. Studying and preparing the ‘frog subjects’ is probably the biggest challenge you will face in school. You must prioritise these subjects on your weekly ‘Lifestyle Study Timetable’. I will detail how to setup this timetable in a later blog feature. Author and reconstructive surgeon, Jack Penn, once said:

“One of the secrets in life is making steppingstones out of stumbling blocks”.

Building Confidence in Maths

Maths is one of those subjects that many students find difficult. To me Maths is about grafting to understand the basics, building your confidence, and not being prepared to give up easy. Always start by attempting the easier topic questions (usually the part a’s and b’s) and subsequently graduating to the part c’s and d’s. You should check your work as you go against a good quality solutions book and thus be constantly ‘learning by doing’. Here are some of my top tips to improve your performance in Maths (and its exam) at any level.

Joe’s Top Tips for Success in Maths

  1. Put formulas, explanation of words and keynotes into a little pocket notebook.
  2. Practice as many past exam questions as you can and check your answers against a fully developed and explained solutions book.
  3. Challenge yourself to try and come up with a second method of doing questions.
  4. Try to approach each question from different angles. Always write down something. Do not be afraid of making a mistake.
  5. Draw a diagram (if possible) and label it to simplify a question.
  6. Be familiar with what is and what is not in your log tables.
  7. When studying, exhaust all attempts to answer an exam question before referring to your solutions book. Do not give up easily.
  8. Read each question in Maths carefully underlining the key words and phrases.
  9. At all levels, if you feel overwhelmed by the length and difficulty of the course – start with basic Algebra
  10. Find yourself a study buddy to share questions and resources with. Discuss problems with each other and encourage.
  11. Use various Internet sites as a companion to improve your Maths skills.
  12. Consult your teacher about problems with topics or specific Maths questions during and after class.
  13. Start by attempting basic questions for each Maths topic, building up to a full exam question. Answer the exact question being asked.
  14. The word FAIL in Maths for me means First Attempt In Learning
  15. Do not be afraid to explain a solution to a question with words if you cannot do so with numbers and symbols.
  16. Spend five to ten minutes daily going over what you have learned in class that day.
  17. Every time you write down a formula, draw a box around it to help you remember it. Check if this formula is in your log tables. If not, you need to memorise it.
  18. Anything that you type into your calculator (related to a question) must be written on your answer book/copy also.
  19. Have all resources present when doing Maths questions i.e. Full Maths set, pencil, calculator, and log tables.
  20. 3rd and 6th Years, practice as many previous exam questions as you possibly can.
  21. Rewrite sample questions given in your textbook to get an understanding of the basics.
  22. It is ok to look at a solution to a question if you have tried your best to solve it alone. Use the answer to figure out the exact method for the question. Re-do it without help.
  23. Work with groups of friends on harder Maths questions. Bounce ideas off each other in order to understand and learn from their thinking.
  24. Always write out every single step of your answer. This will be easy to look back, revise and follow later.
  25. Talk positive about subjects you find difficult. Don’t throw away your shot at success by talking your way into failure.

In next week’s Joe’s Jotter, I will advise 2nd and 3rd year students on how to restart their revision routine. Don’t miss it. To view last week’s feature article on ‘How to Efficiently Review your Exam Scripts’, click here. Get in touch if I can help you in any way. Joe.

‘Sail on the Seas of ambition and land on the shore of success.’

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

*****

*****
Photo:@ZhangChaosheng

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

 

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: Tips to ACE the Transition into First Year (Part 1)

 

There are so many genuine concerns for students as they make the leap into the big pond that is secondary school. Over the next few weeks, I will provide Information and direction to help you as a parent to reduce the stress of this unique transition. This feature article comes in two parts. Firstly, i will analyse the differences between Primary and Secondary School followed by my Top twenty tips for Transitioning from one to the other. A further instalment of this feature will follow online in two weeks’ time. There will also be a feature article to aid Parents (of Secondary School students) who have children with a Special Educational Need (SEN) published soon.

The Main Differences Between Primary and Secondary School

Subjects and Settling into Secondary School

  • All first year students will take Irish, English, Maths, Science, History and Wellbeing (excluding exemptions).
  • Students may get a chance to sample subjects in first year before committing to them.
  • Extra-curricular activities such as debating, drama, science club etc may be available.
  • It is a great idea for students to join clubs and make new friends. Remind them about some of the skills of making friends; good eye-contact, smiling, showing interest in other children and reciprocal conversational skills. Making friends is a key element to settling into any secondary school.
  • Encourage your child to enjoy many school activities. I did a study of a panel of footballers I coached previously, and they performed better on average academically compared to their peers. This suggests a link between activity, socialisation, and performance.
  • If your child enjoys a specific sport or activity, it is a good idea to get to know the teacher who co-ordinates it.
  • It will be exciting for your child to start new subjects if the school offers them. For example: wood technology, home economics, engineering, business studies etc.
  • Students should give each subject an equal amount of homework time for the first few weeks to give each one a chance.
  • It is wise for students to complete the homework of their less favoured subjects first each evening. This will ensure their concentration is at its maximum for these subjects.
  • The better your child’s teachers know them, the better working relationship in class they will have with them. This also feeds back into what extra-curricular activities they sign up to. Personally, I find that the better I know my students, the more I am able to help them in the classroom. Encourage your child to build positive relationships with their teachers, even if they aren’t crazy about their personality or teaching style.
  • Advise your child to enjoy their secondary school experiences. This takes any early pressure off them.

The Secondary School Structure

  • The Subject Teacher – most teachers teach two subjects and may spend up to six classes per week with your child.
  • The Tutor/Form/Home Room Teacher – involved in attendance, day to day and possibly some pastoral care or disciplinary work.
  • The Year Head – Home room teachers report to this person. They usually deal with serious discipline and pastoral care issues etc.
  • Deputy Principal and Principal – Admin, School Organisation, Events, Final decisions etc.
  • First Year Students – Students are usually divided into 4 or 5 class groups of around 25 to 30 people (depending on the size of the school). They will remain with this base class for core subjects: Irish, English, Maths, Wellbeing etc. The majority of schools have mixed ability classes in first year. This tends to help with socialisation.

‘Mixed-ability groupings in first Year leads to improved progress in literacy and numeracy and can give students more confidence as learners’

(Moving Up -ESRI/NCCA 2004).

  • Students are usually mixed in their base classes based on Information from their Education Passport (provided by their primary school) and performance in their entrance tests.
  • Streaming may occur in some subjects in second year. This is where students are grouped by their ability – Higher and Ordinary. e.g. Maths
  • The student council body suggests ideas and raises student related issues with school management. Usually one student is nominated from each class or year. This is the students’ vehicle for discussion and influencing change. The schools’ head girl/boy and deputy head girl/boy are usually elected by the school’s student council.

The Day to Day School Routines

  1. It’s important for students to have a substantial breakfast each morning e.g. Porridge, fruit, yoghurt, or a wholesome cereal. Students will need something ample to sustain them until little break when they can have a snack. Advise them on the sensibility of not eating their packed lunch at the first small break and being hungry for the afternoon then as a result.
  2. Roll call, locker access and lunch are at certain times. If your child tends to be dis-organised, make sure to advise and help them to plan ahead for these situations. Ask them to speak to their class tutor or mentor/buddy if any early issues emerge here.
  3. Get them to copy out their timetable into their journal in order to get familiar with it. Colour coding subjects on this timetable can help them track their progress for the week.
  4. In some schools, the students travel to the teacher’s base rooms. In other schools, the teachers move around, and each class group has their own base. Having the correct materials for each class every day is Important. Checklists can help here. Being efficient at having these materials will greatly help the transition into secondary school and keep your child’s stress levels down. Colour coding or identifying belongings with a unique mark also works well.
  5. Moving around a new building can be disconcerting for a child. They can get lost which can be upsetting for them. Advise them to tag on to one person from the class for the first few days or weeks until they get their bearings.
  6. Many schools have gone to hour long classes to facilitate recent Junior Cycle changes. During the first few weeks settling in, they will be tired each evening. It may be an idea to plan ahead so that extra-curricular activities outside school are minimised during this period. After this ‘fitting in’ period is over, plough on with these important pastimes as normal.

Twenty ACE Tips for Transitioning into First Year

  1. Talk with your child, listen to their views and concerns and answer any questions they may have about the planned move. Talk to them about individual subjects. Help them plan their evenings and the fact that each one will now be different.
  2. Many students get anxious about tests. You can explain that they are to help the school to learn more about the supports that they may need. Advise them to speak with the individual subject teacher if they are concerned in any way about a subject or an upcoming test.
  3. Try and bring them inside the school building before term starts. This is to familiarise them with the school at a time when there are fewer people in the building. They can learn about the layout of the school and maybe get to know some of their new teachers. They can become familiar with the operation of the school including the frequency of bells, the location of lockers, where their base room is, and the location of other key practical rooms.
  4. Involve your child in buying schoolbooks, uniform, P.E. gear, materials etc. Involve them in more decision making from now on. Empowerment fosters ‘buy in’ from them and works.
  5. Talk to your child about the length of the school day, how a timetable works and travelling to school. Trial runs are good. Leaving early for school each morning will minimise any anxiety caused by rushing. Anticipate where they may get anxious during the day.
  6. Talk regularly over the next few weeks about the new school rules, P.E. arrangements, the canteen, lunch breaks, uniform, and the timetable. Make yourself familiar with the policies of the school. Regularly check the school’s website for any news or policy updates.
  7. Ensure that as many of their subject teachers know about your child’s exact strengths and difficulties. i.e. Some of this information is on their ‘Education Passport’.
  8. During term one, if possible, visit the school every so often to meet their subject teachers, the tutor, and their year head. Check their journals regularly for any notes sent home.
  9. Get your hands on or draw up a map of the school to promote familiarisation.
  10. Consider that it may take your child time to adapt to a new classroom, new teachers, new activities, and new subjects. Ensure they build in down time each evening to maintain freshness and enthusiasm for the next set of daily challenges ahead. Unlike Primary School, every week differs, and things can be more unpredictable for them.
  11. Organising Issues: Be sure to plan ahead by purchasing additional materials for each subject. School booklists and stationary lists are your first port of call here.
  12. If possible, show them a few little skills around note-taking. Most of their subject teachers may not get the opportunity to work on this vital skill due to the focus mainly being on content.
  13. Talk about and help clarify the Locker process. Many kids get bogged down with this.
  14. Advise them to use their mentor or buddy, and class tutor as best they can.
  15. Getting clever at knowing what equipment is required for each class is important: i.e. protractors, setsquares, colours, stencil sets, rulers, pens, calculators etc. A good tip is to remind them to write down each teachers’ instructions during week one about what is required in each subject. There is no need to carry all of their books all of the time. Put their Class Timetable and School Calendar on the fridge at home as a reminder to all.
  16. Encourage them to sign up to a few clubs and society’s on ‘club’s day’ in September.
  17. Re-enforce the key habit of recording Information, especially in relation to homework. Check their Journal weekly to ensure homework is being recorded and completed properly.
  18. Get the 3-way communication lines going i.e. Teachers-Parent-Student. In primary school, it was more about the Teacher-Parent link. Start including your child in more appropriate conversations from now on. This allows them to feel more important and take more ownership of their school day, and ultimately their learning.
  19. Do as much preparation for each school day the night before as you can. Get your child into the habit of having the uniform out, bag correctly packed by the door, lunch ready etc. This again will reduce stress levels for all involved in the morning madness. Again, consider using a checklist with your child if they struggle to organise themselves in the mornings.
  20. At secondary school, the days tend to be longer. Encourage them to start their day with nutritious food. They should grab something and eat it in the car on hectic mornings. Of course, this isn’t ideal but is certainly better than going without as another busy day starts for them.

To view last week’s feature article on ‘Anticipating Better Revision for 2022/23’, click here.

Part 2 of transitioning Insights into First Year will be published online in two weeks’ time. Don’t miss it. Do contact me if I can advise you in any way. Joe

**Leaders are made. Heroes earn their status**

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

 

Leaving Higher Maths Paper 2 usually contains Probability and Stats, Trig, Geometry, Inferential Statistics and Co-ordinate Geometry, Area and Volume.

  • Your Paper 2 is on the Monday so you will have some time to look over. Again watch out for topics appearing here that should appear on Paper 2.
  • Paper 2 is more about the formula’s so use them if you are stuck
  • Label your diagrams and Label co-ordinates (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: Shorthand Best Practice for LC Maths Paper 1

 

General Guidance for Leaving Cert Higher Maths Paper 1

  • Leaving Cert Paper 1 in Maths is on Friday 10th June so you may have two/three papers done already (Eng/Engin/Home Ec).. i.e. The bulk of the prep for Maths Paper 1 needs to be done from the week before as a result of this.
  • Paper 2 material can come up on Paper 1 and vice versa – i.e. 2015/2017 Trig Functions appeared. Financial Maths appeared on P2 in 2018 even though it’s more of a P1 topic. A&V can appear on both
  • There is no specific layout to the paper year to year – Any topic can appear anywhere.
  • Topics tend to mix together into one question. So….I wouldn’t leave any topics out
    • Example Prob/Stats and Geom/Trig
  • I wouldn’t do extra questions on the paper as you will run out of time
  • Night before exam – Check…Maths set, pencils, two alarms, your usual calculator etc
  • Only answer the question that’s being asked. Read it three times.
  • Often the answer can be hidden somewhere inside the Information given in question
  • Do not scribble or tippex out any writing and make it unreadable. Draw an X through it and make sure it is readable – this could be worth marks and will be corrected.
  • Always give your answer in the form requested in the question e.g. surd form
  • Always use the correct units.. e.g. m2 for the area of a rectangular field etc
  • Only round off your answer at the very end of the sum. Retain as much of the decimal as you can through the question to ensure accuracy and full marks.
  • If you don’t give your answer in the correct form, round off decimal places or leave out the units, you will more than likely lose one marks
  • Exams are scanned in and are then corrected by a person (examiner)
  • When revising, break the course into sections and break each section into sub-topics in order to make it more manageable to tackle. Practice loads of past exam questions.

Sample Marking Scheme Scale for LC Maths

This is an example of how the paper is marked and shows the opportunities to pick up marks depending on how many marks is allocated to each question.

LC Maths Exam Paper Layout [Red Text – 2022 only] – Paper 1 and 2

The layout is normally 6 short questions (150 marks) and 3 or 4 long questions (150 marks). This is not the layout in 2022.

  • In 2022, we have Section A: 6 short questions of thirty marks (Do 4 of these).
  • Section B: These are the more practical real life scenario Questions..4 long questions on the paper (Do 2 of these) (fifty marks each). [Both Higher and Ordinary level]
  • Even though there is a choice on both papers, I would NOT attempt an extra question in either Section A or Section B
  • My proposed Timing for 2022: (Apply the 20:30 rule for Exams 2022)
    • 10 mins to read paper and carefully choose questions at the start
    • Short Question (4) (30 marks) – Max of 20 minutes each
    • Long Questions (2) (50 marks) – Max of 30 minutes each
  • Set out a time budget plan before your exam and stick to it.

How do attempt marks (Low Partial Credit) work in Maths?

You can pick up 2/5 and 4 or 5 out of 10 for just getting one step in the right direction. This is called Low Partial Credit

  • This could just be writing down line one

OR

Writing down the correct formula and subbing a relevant value into it [‘Relevant substitution’]

OR

Bringing down the last answer and doing something sensible with it

  • Write down everything – a formula from your Log tables, a step, a piece of English, a diagram, a table anything at all. If you type something into your Calculator, write it down. The examiner will be desperate to give you 2/5 or 3/10 or 6/20 or whatever Low partial credit is for each part. They will take no pleasure at all in giving you zero.
  • You may use a different way to solve a question (with success) that’s not written on the examiners marking scheme – this is full marks.
  • If you make more than one attempt on a question, make sure to leave both visible on the paper.. Never scribble out anything. Never write a ‘?’ on your paper.
  • Draw a single line through a method you feel is incorrect, it will be checked and may be allocated marks

What if I need an answer from the previous part to answer the next part?

There are two possible scenarios’ here. If you got an answer you think may be wrong and need to use it further down the question, carry it down anyway. If you didn’t get an answer at all and need one further down, explain in a note to the examiner that you are going to guess the answer needed and use it. You might word it something like:

“I didn’t get a value for x in part a so I’m going to assume that x=10 here.”

Do this and continue on…You can still get high marks for this question

What do you do if you mind goes blank?

  1. Fill in something you have done in class related to the question being asked.
  2. Use all the Information given in the question in some way.
  3. Use a formula you think that may be relevant to the question.
  4. Any correct element to a question will give you low partial credit.

What are the core skills I cannot live without for LC Higher Maths?

  • Solving a linear and quadratic equation
  • Solve a simultaneous equation (Basic JC Method or by substitution)
  • Subbing into a formula
  • Being familiar with Log Table Formulas (See below)

Why are Log Tables so important..?

Each student will have a set of log tables on their desk when they go into the exam hall. You will not be allowed to bring in your own set of log tables. Know whats in your log tables but more importantly whats not in your log tables. Be familiar with roughly where each formula is in the tables, so you are not in a mild tizzy trying to find one. Learn off the formula’s not in your Log tables. Enter these into a hardback notebook now and start memorising them. Guidance and advice for Maths Paper 2 will follow very soon. Stay tuned to Joe’s Jotter Blog for updates. Joe

To view last week’s feature article on ‘The ACE Exam Day Quick Ref Guide’, 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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Joe’s Jotter: The ACE Guide to Exam Preparation from Home (Parental Support and Final Thoughts)

 

 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

To view last week’s feature article on the ‘Importance of Nutrition around exam time’, 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

*****

*****

Photo:@ZhangChaosheng

Joe’s Jotter: Nifty Tricks to Remember Maths Formulas

 

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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Joe’s Jotter: Guiding your Child Through Exams 2022

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’.

To view last week’s feature article on ‘Why Practicing Past Exam Questions in Maths is Crucial’, 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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Joe’s Jotter: Why Practicing Past Exam Questions in Maths is Crucial

 

Practicing past exam questions is essential if you’re looking to score highly in either Higher or Ordinary level Maths this June. Similar question types come up regularly; but you still need to revise all the topics on your course, as the Maths exam isn’t predictable anymore. Both sections (A and B) at Leaving Cert higher and ordinary levels are important and the correct amount of time must be left for the longer questions in Section B, as they tend to require more thought.

The new Maths syllabus at both Junior and Leaving Certificate level is quite crowded with a lot of material to get through, not to mention trying to link up topics in true Project Maths style. Incidentally ‘Project Maths’ was the name given to the subject ‘Mathematics’ when it was rebranded in 2008. It has now reverted to ‘Maths’ after this bedding in period.

Why Past Exam Questions are Key!

With so much to cover during class time, it is difficult for teachers to expose their students to any substantial level of past exam questions during term time. The reality is that many teachers will only fully complete the course after Easter, through no fault of their own. It is up to each individual student to dust off their book of past exam papers and start by initially attempting the part (a)’s and (b)’s of as many exam questions as they can. Initially focus on topics you have covered yourself in class in order to build up your competence. My advice is to work on the last six or seven years past papers to get a grasp on what comes up in certain topics. If your exam paper book is filling up, re-print the papers in it. These are free to download on the examinations website. Set your stopwatch and test to see can you really do a question against the clock without your notes.

‘Do an exam question a day, and start today’

Doctor Maths, the Poet.

To commence, attempt all past exam questions to the best of your ability with guidance from your textbook and class notes. This allows you an access route into questions you are unable to start. Subsequently, refer to a good solutions book to see how accurately you are progressing. With an unprecedented level of detail, my exam paper solutions (ACE Maths Solution Books) at both Junior and Leaving Certificate levels are an ideal companion to revise Maths effectively for this year’s exams. You should start by practicing and familiarising yourself with the language used on past papers. 5th Years also need to start planning ahead. Most Maths teachers will put past exam questions on a 5th Yr Summer Maths Paper.

Your exam paper focus should always be on practicing previous official state exam questions under time pressure. Replicating exam hall pressure is a brilliant way to hone your skills and really check if you can complete the question asked within the time limit allocated. I would start by taking on a short question or two against the clock, and then a longer question, until eventually you feel confident enough to take on a full paper. Constantly doing questions out from your textbook will never fully prepare you for a full sit down test paper in Maths. This is where a lot of students are going wrong.

 

 Using Past Exam Questions to your Advantage

Knowing how to work with past papers and making the most of them is a skill in itself. Some key preparation tips to keep in mind while tackling past papers are:

  • Start with questions you can do in order to build confidence and reduce anxiety as you commence your revision routine.
  • Solve as many past exam questions as possible from every topic on the course. This will help you understand the type of questions that are asked and also how much work you still need to do to reach your target score in the subject.
  • Estimate how an examiner would have graded your work by comparing your solution against a detailed Maths solution book. Using a solutions book to mark your own questions will allow you to see how your percentages are stacking up.
  • Maintain an error-log on mistakes you keep making. This will help you get to know your weak points and what traps you are regularly are falling into.
  • Everyone has deficiencies in Maths. To overcome these, attempt extra questions from topics you are struggling with.
  • When solving past questions, make a habit of always timing yourself with a stopwatch. This will help you improve speed and manage your timing better during the actual exam. Practice makes perfect. Treat your revision work at home as the training sessions before the actual matches in the exam hall.

Doing an exam question trial at home every week will greatly improve your performance in the final exam. After some time, you will cut out silly errors and feel calmer about tackling a full paper. This process will give you the belief that you can get the awkward question started or tackle the unseen graph or diagram on the day.

  Commence a Strict Diet of Past ‘Exam Questions’ Today

If I was in 6th year, i would move quickly now onto the strict but ultimately rewarding ‘Past Exam Question’ diet. Here are some directions to consider as you trawl through good quality past exam questions and their solutions over the next few months:

  • You need to get practicing multiple real life application questions (Section B)
  • You need to get familiar with marking schemes and how marks are allocated
  • You need to practice exam questions under time pressure
  • Constantly strive to get used to the wording, layout, and style of past questions
  • Get accustomed to how the examiners are phrasing exam questions now
  • Be conscious of the fact that there is extra text and less numbers on the papers now
  • You need to be aware that you could now be asked to ‘explain your answer’
  • Be familiar with justifying your answers using Maths calculations
  • Practice different strategies for starting unseen or unexpected questions
  • Be familiar with the exact meaning of each word that appears on past papers. Joe.

To view last week’s feature article on ‘How to ACE any Maths Exam’, 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

*****

*****

Joe’s Jotter: How to ACE Any Maths Exam

 

No matter how intelligent you are or how well you prepare, if you are not exam smart, you will underachieve in any Maths exam. It is also vital to have a plan in place for the content that can appear on your Maths paper. This involves going in there with your eyes wide open and being tactically aware in case things go a little bit wrong on the day. The following are my ACE tips to effectively deal with a Maths exam paper. These apply to both the Junior and Leaving Certs, as well as being relevant to the summer tests for 1st, 2nd TY, and 5th Years.

Sensible Tips When Dealing with a Maths Exam Paper

  • Units matter. If they are present in your question, they are required in your answer.
  • Do not type anything into the calculator that you have not already written down in your answer book.
  • You can get almost full marks (high partial credit) with just one slip/mistake in your solution. High partial credit could gain you as much as seven or eight marks out of ten.
  • If you make two attempts at a question, they will all be corrected and the highest marks from your efforts will be counted. Don’t be afraid to have a proper go.
  • Marks will be given for any work done on diagrams that have been printed on the paper.
  • Be careful when dealing with minus signs.
  • You must show your full workings out for all questions.
  • Write down every single step until you arrive at the solution.
  • If your answer is ‘off the wall’, it is probably incorrect.
  • If there are many steps required in a solution, continually double check completed steps for accuracy; otherwise, you may need to re-write the whole solution. In that case, watch the clock very closely.
  • Never rub/tippex out any work done even if you think it isn’t neat. Draw a single line through any part of the solution you are unsure about. The examiner must correct it.
  • When asked for your opinion, give it, and refer to any numbers or statistics given in the question if available.
  • Algebra is the bedrock of all Maths courses and is the main area that students struggle with. You need to become a master of Algebra to achieve high grades.
  • Get used to attempting questions involving real life statistics.
  • Estimating the heights of larger objects outside in nature is now an important part of Geometry and Trigonometry.
  • In Co-ordinate Geometry, the slope of a line is very important in practical questions.
  • More recent Maths exam questions tend to contain an increased number of words. The reason for this is the examiners need more English to describe real life Maths scenarios. You need to be able to separate the important keywords in the text from the padding that surrounds them. Use your highlighter or green pen to mark the significant words.
  • Look through the wording of each question and pick out the Maths related information. In all subjects, but especially Maths, identify exactly what you are given and what you are looking for. Watch out for numbers written as words, for example “thirty” instead of “30”.
  • If no diagram is presented, draw one yourself to give a clearer picture of what is being asked. This is especially important in Geometry, Trigonometry, and Area and Volume.
  • If given a diagram on the paper, mark in the numerical information given in the text of the question onto it. Re-drawing sections of more complicated diagrams into your answer book can help to simplify question parts for you.
  • Do not leave any blanks, ensuring that every question is fully attempted. If you leave a blank, the examiner can give you at most zero marks for that question part. If you attempt the question; you may get some marks and perhaps more than you think. In summary: No attempt = No marks.
  • If you are dealing with a Trigonometric problem at Leaving Cert level, know how to apply the three basic Trigonometric ratios (SOH, CAH, TOA) , Pythagoras’ theorem, the Sin rule, and the Cosine rule. In these, you have all you need to solve most right-angled and non-right-angled triangle problems.
  • Relate the information you have in the exam question to the theory and equations you have worked on in class. In Geometry, have you got two right-angled triangles that need to be solved separately? Again, if you are unable to start a question, there is nearly always something you have learned from your teacher or hopefully from my ACE Maths Solution Books that you can draw on to help you. Don’t give up. Be persistent.
  • The relationship between two data sets is important. At LC Level, this concept links ‘slope of a line’ in Co-ordinate Geometry to that of ‘correlation’ in Statistics. Other examples of where topics overlap in Maths at Leaving Cert level include Co-ordinate Geometry of the line and the Circle, and of course Geometry and Trigonometry. Across all levels of Maths, there are many links between topics that you need to keep an eye out for.
  • Do out a ‘time budget’ plan before sitting any Maths paper and be sure to stick to it.

Most importantly, remember that you are not alone and there are tens of thousands of other students in the same position as you on exam day, many of whom have had their various struggles with Maths. Above all, practice your Algebra and be familiar with what formulas are available to you in the log tables on the day. If you are familiar with the main equations and some theory on your course, you have a solid base for giving any exam your best shot. Joe.

To view last week’s feature article on ‘How to Prepare for an Exam Efficiently at Home’, 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

*****

*****

Photo: @ZhangChaosheng

Joe’s Jotter: How to Improve Homework at Secondary School

 

 

Is Homework Useful?

Students, Time spent at homework each night serves two purposes. Firstly, it is a reminder of what you did that day in school. In my opinion, the first five minutes of homework you do in each subject should be to go back over what the teacher did in class that day. Secondly, it also allows you to test yourself to see if you now understand information about a topic, and maybe how you may need to explore it further. Students should take care over each piece of homework and complete it as best they can. Personally, I really see the value of homework as a key tool in re-enforcing learning that has taken place during each day.

The Best Way to Tackle Homework

 How you approach homework after a long day is the secret to being more efficient with it. Firstly, I would make sure to rest a little when you get home and get a good solid meal into you, especially if you have plenty to do. Clever students ‘eat their frog’ and do the difficult homework or subjects they struggle with first. This allows them to feel better as the evening goes on. As I see it, this make total sense, as your concentration levels, later in the evening, do not need to be as high for subjects you are good at or enjoy as tiredness creeps in.

On a similar note, attempt the type of learning you do not particularly enjoy first. In other words, if you aren’t fond of reading or learning off, do that first as opposed to writing or note taking. Homework and revision are about playing to your strengths and working smarter. It is better to write short key jottings as opposed to spending hours mindlessly reading. Fact!

No Homework Tonight!

 If your daily homework has been completed during ‘free periods’ during the day, it is still important to use those few hours in the evening to revise material from last week or the week before. You need to take these opportunities, if they arise, to catch up. For students in Senior cycle, you cannot really afford to take a full night off. Am I saying you should work from 5 – 11pm every night? No, and you certainly should take a short break every thirty minutes. Even on weeknights, take some exercise or go do that little activity you enjoy that keeps you sane – whatever works for you to get your mind off things.

Homework is the Best Form of Study

 Homework done to a high standard is a brilliant form of study. Reviewing work done in class via mini test questions or checking what’s coming up tomorrow can be included as part of your homework if time allows. Homework teaches you to analyse the information your teacher has given to you. Always take pride in the homework you produce, as it will stand to you in the long term. Time spent doing homework should be counted as part of ‘exam preparation’ time and you shouldn’t feel in anyway guilty when there are nights you do ‘all homework’ and ‘no revision’. Judge each night on its merits and how important each task is.

Super Organisation

Being super organised with homework and your journal are important aspects to kick-start your success. In my opinion, homework is the best form of study, and you need to be disciplined with it. Write homework diligently into your journal each day and complete each piece of homework like you are doing an exam question. Being ‘smart’ with how to tackle homework is a skill, which could take months to refine. Ensure each subject gets a fair amount of ‘homework time’, depending on what you schedule is like for the next day.

Every day, I make a list of tasks on my phone that I need to complete. At the end of the day, I review this list to see how many of them I have actually fully completed. Tasks unfinished are then moved to another day so that each task eventually gets dealt with. At times, tasks are postponed (put off into the future), but ultimately they always get completed unless I deem them unimportant. Apply this technique to your revision, ensuring that everything gets completed eventually in the most efficient manner. Task monitoring, homework discipline and dedication are all attributes of the ‘Super Organised’ H1 student.

Student Survey: The Importance of Homework

 I completed a survey of students previously and asked them to think about the importance of homework to them and how its benefits helped them achieve their goals. Here are some of the more interesting observations they made in their surveys:

“Record your homework carefully in your journal every day.”

“Use class time well if teachers allot it to homework.“

“Set the same time aside every evening for homework.“

“Do your homework after dinner and soon after arriving home.“

“Try to complete your homework before nine p.m.“

“Try to be honest with your teachers in relation to homework.“

“Tick off your homework for each subject as it gets done.“

“When doing your homework, do not lounge on a bed or sofa.“

“Ask your parents or teachers if you cannot understand your homework.“

“Have a quiet study area with a desk, fresh air, and good lighting.“

“As well as written work, browse over what was covered in class that day.“

“Do not let homework affect sleep time, but don’t leave it until the next morning.“

“Plan ahead on assignments if you are expecting a busy week.“

“Get the phone numbers of classmates for queries on homework.“

 

To view last weeks feature article on ‘How to become a Specialist at Maths Exams (Part 2)’, click here. Joe

 

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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Photo:@ZhangChaosheng

Joe’s Jotter: How to become a Specialist at Maths Exams (Part 2)

 

Thousands of students have gone through the exam system having achieved their dreams, so be sure to aim high and keep believing in yourself. Put a plan in place today, so that you can revise effectively for all your upcoming Maths exams. Here are my top twelve tips to ACE any Maths Exam – both in preparation and tackling an exam paper on the day.

Top Twelve ACE Tips to Success in Maths

  1. Do out a weekly study timetable ensuring Maths is prominent on it. Make sure there are loads of topic variety with Algebra and Functions being the Initial cornerstones of learning.
  2. Buy a hardback and enter all keynotes, new information learned, and formulae’s that are not in your log tables into it. Divide it into topics to find Information easier.
  3. Note all new words you learn each day. If you don’t understand the meaning of them, ask your teacher or google them. Write down their meaning in your own words when you find out. One of the biggest issues in Maths is not understanding the words used on the paper.
  4. Practice past exams questions to get used to the wording, layout, and style of them.
  5. “Homework is study”, so approach all Maths homework as an exam hall question.
  6. Practice challenging questions at home. Time yourself on each question to get used to ‘Exam Hall’ pressure. Stick rigidly to the timing for each question.
  7. Get a “study buddy” that will complete past exam questions for you and with you. You can then meet up regularly and share Information and exam solutions with each other.
  8. On the day of the exam, read the wordy questions three or four times and then step through them word by word, line by line, underlining the key words as you go.
  9. Prepare for each exam the night before by checking you have all the materials you need for it. This is especially important in Maths.
  10. Don’t be afraid to express yourself in simple English if you are not sure what Maths to use to solve a problem. The State Exams Commission (SEC) encourages this type of creativity.
  11. Buy yourself an Exam Paper Solutions Book. You can use this book to check the work you are doing and to help you get started on the more challenging exam questions.
  12. Start today.

The Importance of the Words and the Formulas

Lastly, the language of Maths is extremely important especially since the birth of ‘Project Maths’ in 2008. The State Exams Commission (SEC) now place more of an emphasis on students knowing and understanding concepts and topics, as opposed to just been able to do numerical calculations. There are more words than ever on our Junior and Leaving Cert Maths exam papers, and it is crucial that you start familiarising yourself with them.

If you are not familiar with the words and phrases that appear on the paper, you may not be even able to get a question started. This would be an awful shame given the amount of time you have spent learning the mathematical skills. You need to be aware that different words have a different meaning depending on the subject. For example, the word “Evaluate” in Maths is quite different to what it means in English. I believe that knowing the key words and phrases is now a key component of “Ace-ing” a Maths exam. Apply the principles that I have outlined in this feature article to ACE any Maths exam you take on in 2022. Wishing you good luck students. Joe

To view last week’s feature article on ‘Maximising Your Junior and Leaving Cert Results’, 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

*****

*****
Photo:@ZhangChaosheng

Joe’s Jotter: How to Revise more Effectively

 

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 cutting corners; you will predict, throw topics away and ignore information. I would not recommend leaving out big chunks of the course. The State Exams Commission, 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 now should be to continue to whittle down and reduce the volume of your keynotes. I am convinced that summarising information helps assimilate it better and leaves one with a more concise set of notes. Keep re-writing summaries into something manageable 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 much notes are a bad thing and may overwhelm you. Summarise, Summarise, Summarise!

Implement a Solid Study 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 study plan that you can follow. Here are twenty practical study tips you can start using today:

  • Divide your study time into small sessions
  • Take a break of five or ten minutes after every session
  • 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 times as per topics and effort needed. Difficult topics = More time
  • Underlining the key points for each topic is a great 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
  • Reflect on the amount of revision you did today, instead of what you didn’t do
  • If today’s study plan didn’t go well, revisit it and tweak tomorrows one

and remember..

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

Joe McCormack

To view last weeks article on ‘How to become a Specialist at Maths Exams (Part 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

*****

*****

Photo: @ZhangChaosheng

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


Surprisingly, thousands of top Maths 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 their 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). Joe

To view last weeks article on ‘The ACE Guide to Exam Prep from Home”, 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

*****

*****

Photo:@ZhangChaosheng

Joe’s Jotter: The ACE Guide to Exam Preparation from Home (Part 3 of 6)


Dealing with Motivation Issues – ‘I Don’t Know Where to Start’

Students, if you are struggling for motivation at home right now, put a half day’s timetable in place tonight and give it a go tomorrow. Set each revision block to just thirty minutes and time will fly. As you begin to see progress, your motivation will grow. An alternative approach to developing a timetable would be to create a task list. Each night you could write down a list of ten to twelve challenges you would like to achieve in various subjects the next day. Tick them off then as you get them completed. If you currently feel you are swamped with work and worry, this is now your ‘get out of jail’ card, so try it.

Set Measurable Targets

It is so important to set targets, otherwise timetables and lists are just ‘drive bys’ and ‘hopeful’ preparations that you will never be answerable to. We all need targets to help us achieve things. It is also a fact that we are more likely to reach them if they are written down.

Once you set a measurable target (example: eight pages from a textbook to be summarised into your own words), assess how much progress you have made. On completion, tick it off from your full sub-topic list for the subject. A short term target could be as simple as ‘understanding emotions’ from two English poems or practicing writing letters to an imaginary pen pal in whatever modern foreign language you study. Remember if you don’t know where to start, commence with the basics of a topic. i.e. view the first few chapters of your textbook or the first set of notes your teacher gave you on it. Start small and then when you get up and running and notice progress, you will be encouraged by your own efforts. Just get a routine going somehow, and then rinse and repeat. Information about setting up a full ‘Lifestyle Study Timetable’ is detailed in my textbook ‘How to ACE the Leaving Certificate’ for all subjects.

Write out a List of Motivations in Your Journal

Another tip to improve motivation is to write out a list of medium and long term targets in your Journal and then write ten reasons underneath explaining your motivation to ACE them. On lazy days, open that page and read your ‘motivational list’,  thinking about how you felt when you wrote them. This will inspire you to get started on revision and keep going when days get tough. Revising and preparing may seem like it is solely for your upcoming exam, but you will discover that learning is a lifelong process. Try to enjoy the challenge of getting that timetable completed or ticking off those tasks; you have nothing to lose and all to gain. It doesn’t have to be perfect, just give it your all.

For those of you who continue to struggle to get started on revision, start by writing down the activities you lean towards to dodge study. Put this list on your wall and be fully aware of the times you drift towards them. Being aware of this ‘distraction list’ will remind you of what you really should be putting your mind to at any given moment. Any effort or movement towards starting a short revision block should motivate you to commence a second one i.e. The hardest part of being successful with any task is often just getting it started. Imagine yourself, on your side, rolling down a steep hill. You will gain momentum as you go…and it could even be fun. Give yourself plenty of breaks as a reward for your hard work.

The Many and Best Ways to Learn

The key to any successful Lifestyle (Study) Timetable is keeping your brain fresh by completing different tasks every thirty minutes. Rotate your learning between different subjects but also within subjects. What I mean by this is: Revise in all the different ways possible. You only need a few repeatable methods that work for you, but you won’t know which ones suit until you actually road test them yourself. The below is a sample list of the many ways we learn. I am sure you could add even more creative and interesting ones to this list matching your personality. Pick out four or five of the below approaches and give them a try today.

  1. Write a bulleted list to explain and summarise a short book extract.
  2. Summarise a chapter of your textbook into your own words.
  3. Create flash cards with a list of facts. Limit each card to seven key points.
  4. Record a summary using the voice memo function on your phone. Replay back.
  5. Put keywords and their definition for each subject (per topic) into a hardback.
  6. View a YouTube video of an expert or listen to audio/podcasts on topics.
  7. Teach or discuss what you have learned with a member of your family.
  8. Get your parents/siblings to ask you questions on a topic you have just revised.
  9. Read a summary out loud to yourself.
  10. Rotate your place of study to retain freshness. e.g. the garden or kitchen table.
  11. Create Bubble diagrams with Microsoft PowerPoint to illustrate topic linkages.
  12. Create a visual Mind Map for a sub-topic you are struggling with.
  13. Stick nine postits onto an A4 sheet. Write a summary with keywords onto them.
  14. Use different coloured pens (red and green) to draw attention to key points.
  15. Use different coloured highlighters to mark relevant dates and details of note.
  16. Chat to friends to find out how they are approaching certain subjects/topics.
  17. Stick stickies/sheets on your wall for memory. Rotate this content every five days.
  18. Research topics on the Internet to give yourself extra pieces of information.
  19. Continually test yourself with sample tests, online quizzes & past exam papers.
  20. Use Graphic Organisers to create a more visual set of notes (samples below).
Sample Graphic Organisers*

*Source: Using Graphic Organisers in Teaching and Learning (SLSS)

To read last weeks article on ‘The Core Skills required to Revise Maths Better”, 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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Photo: @ZhangChaosheng