Junior Cycle Maths is a busy course that seeks to turn you into an all-round mathematician, one that can deal with mathematical ideas and concepts and then apply these to solving problems. Its goal is to teach you to work with the main concepts of algebra, geometry, numbers, functions, probability and statistics and then push you to use these ideas to find the solutions to problems. The exam is dynamic and varied, meaning you will get some very direct and straightforward questions (where you apply mathematical procedures) as well as some busy problems for you to apply your knowledge to and tackle. It can be a tricky course but there is no need to stress. This guide will highlight everything you need to know and do in order to succeed in maths.
How to get a Distinction in Junior Cycle Maths
By Stephen Begley - 12 minute readStephen, an experienced teacher and state examiner for Junior Cycle Maths, shares his top tips on how to get a distinction.
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Introduction
Assessment information
You will be assessed in four main ways throughout Junior Cycle (these will be explained below). You will also complete two CBAs (one in 2nd year and one in 3rd year) with each CBA graded by your class teacher who will give you one of the following descriptors for your work:
Exceptional
Above expectations
In line with expectations
Yet to meet expectations
The Assessment Task and final exam are corrected by an examiner for the State Examinations Commission (SEC). Your overall grade will then appear on your Junior Cycle Profile of Achievement, along with your two CBA grade descriptors. You will be awarded one of the following grades: distinction, higher merit, merit, achieved or partially achieved.
Classroom-Based Assessment (CBA) breakdown
For Junior Cycle Maths, you are asked to carry out two investigations: a mathematical investigation (CBA 1) in 2nd year and a statistical investigation (CBA 2) in 3rd year. These are broad projects and can sometimes appear daunting but both investigations can be nicely broken down into simple steps that you can follow in order to complete your CBA.
CBA 1: mathematical investigation
For this CBA, you will be asked to carry out a mathematical investigation by following the problem-solving cycle (outlined below). You are asked to come up with a mathematical problem, question or investigation that you will work on over a three-week period in class. Then, you will create a report in a format of your choice to present your project. Your report should be approximately 400-600 words and you will complete this CBA in 2nd year.
The problem-solving cycle
In a nutshell, here are the steps for the problem-solving cycle used for CBA 1:
- 1
Define a maths problem.
- 2
Break it down into manageable parts and steps.
- 3
Translate the problem into maths.
- 4
Follow your steps in order to work with the problem and try to solve it.
- 5
Explain your findings and solutions.
Some examples:
Investigate the cheapest box design/layout for 24 golf balls.
How much would it cost to complete a bedroom/kitchen makeover?
What’s the quickest route to my locker?
Is there a relationship between the area and perimeter of a particular shape?
CBA 2: statistical investigation
This CBA is a statistical investigation where you follow the statistical enquiry cycle (outlined below) to try and answer a statistical question. Over a three-week period in class, you will come up with a statistical question and use statistical methods to try and answer it. You must create a report for your CBA in a format of your choice, in roughly 650-800 words. This CBA is completed during the first term of 3rd year and will act as the basis of the Assessment Task which you will complete in class after you finish CBA 2.
The statistical enquiry cycle
Here's a snapshot of the steps involved in using the statistical enquiry cycle in CBA 2:
- 1
Come up with a statistical question.
- 2
Plan and collect your data.
- 3
Organise and manage your data.
- 4
Analyse your data using graphs.
- 5
Analyse your data using numerical summaries.
- 6
Answer your statistical question based on the above analyses.
- 7
Write a conclusion for your investigation.
Some examples:
Who can run faster, boys or girls?
Do rural or urban students have longer screen time?
Do boys or girls have more pets?
An analysis of the distance people travel in a car per week.
The Assessment Task
The Assessment Task is based on CBA 2 and will be completed across two single classes. This task is worth 10% (30 marks) of your overall Junior Cycle Maths grade so it’s worth your while to put a big effort into your CBA 2 and know your project inside out. Remember that the main work in CBA 2 is to complete a statistical investigation (posing a question and then gathering, analysing and interpreting your data) and that the idea of the statistical enquiry cycle is the basis for the CBA so it’s a good idea to familiarise yourself with this because the Assessment Task will ask you to:
Review a statistical investigation
This includes the design, validity, structure, analysis and conclusions. With this, you will need to know what a good investigation looks like so you can comment on it appropriately.
Apply your learning
This includes completing your own statistical investigation of an unseen
statistical situation and data. With that, you will need to brush up on different types of graphs and statistical calculations (mean, mode, median and range).Reflect
You will need to reflect on the skills you have learned and developed while completing CBA 2. The ball is in your court for this part to know what skills you used and learned throughout the process. You certainly can prepare for and study this before you complete the Assessment Task.
The final exam
The final exam is worth 90% (270 marks) of your overall grade and it will take place on the first Friday afternoon of the timetabled Junior Cycle exams. It takes place over a 2-hour period and has no fixed number of questions. You will be given log tables at the start of the exam by the examiner.
Common questions
How many questions are there?
There are usually around 14 questions and they cover the entire course. The questions are of varying length with some of them having a single part to them and others having up to 4 or 5 parts. Usually, if a question has many parts, each part will get increasingly difficult.
How long should I spend on each question?
Each question will have a ‘suggested maximum time' which I recommend you try your best to stick to. If you follow these times, it will leave you with an extra 10 minutes at the end to check over your work and spend more time on parts that may need it.
What will my exam paper look like?
Each part will have an answer box for your solution and your answer to the question. Every topic covered between 1st and 3rd year can come up in the exam so my advice is to study them all.
Will I know how many marks a question is worth?
The exam paper will not state the marks awarded for each question but it is worth knowing that a single part of a question can range between 5 and 20 marks. The exam paper will have questions based on individual and mixed topics. Some questions may be straightforward while others will be trickier and focused on problem-solving.
How to study for maths
Make a plan
Narrow down the topics and sections you need to work on and build your plan around these. Use your chapter tests, Christmas tests and summer tests to see what needs work. Instead of saying you’re going to study ‘algebra’ tonight, narrow it down to something specific like ‘factorising quadratics’ or ‘adding algebraic fractions' and work specifically on that area. Each study session should focus on one idea or subtopic, don’t try and bite off more than you can chew. Small, targeted bursts of revision done often are the key to success.
Practice questions
The most effective way to study a section is to practice questions on it. Now I don’t mean do all the easy questions on a section and build a false sense of security, I mean for you to start on the basic questions and then quickly progress onto the more difficult ones. When you struggle with a question and you push/work through it to the end, the learning will happen. Start with questions in your textbook and then move on to the exam paper questions. Regularly practicing exam-style questions will get you into the habit of their layout and the level of the challenge expected.
Don’t over-rely on the marking scheme
When practicing questions, don’t over-rely on the marking scheme. I often see students just copy from a marking scheme to complete a question and this is a poor study habit. As you are copying a solution and not thinking of it yourself, you are losing out on the important learning in between. The best way to utilise a marking scheme is to first attempt the question yourself and if you reach a point where you cannot go forward, then look at the marking scheme to get to the next step. That way, you identify the exact step you don’t understand and will learn from there. Continue the question without the marking scheme and repeat the above steps if necessary.
Avoid over-reading notes
Reading pages of notes is not a very effective way to study. In my years of studying, I found that just reading notes doesn’t equip you to fully solve a question. While you may need to read over an example first to help you work on a question, your focus should be on getting stuck into working on questions.
Start by looking at worked examples
Unsure of how to start studying a section you know nothing about? Here is some advice: start by looking at a worked example in your textbook or notes, read through the question and solution and try to make sense of it and then cover the solution and write out the question. After doing this, try the question on your own. If you get stuck, look at the next step in the example and proceed from there. Repeat if necessary and then move on to the questions after the example which will be similar in style. If you run into difficulty and can’t figure it out, make sure to ask your teacher, a friend or the internet. The main thing is not to give up because maths is full of challenging parts and it’s all about keeping going, pushing forward and asking for help when you need to.
Utilise study resources
If you don’t understand something and can’t figure it out, don’t just leave it, we want to leave no stone unturned in our study. So, if you need help you can check if your textbook has a worked example on it, ask your teacher (they will only be delighted to help you with any questions), ask a friend (they might be able to explain it to you) or search online for the question or section you’re struggling with. There are millions of maths videos out there that can help as well.
You can give multiple answers to a single question in the exam. For example, say you have two possible solutions for a question and you're not sure which one is correct, leave both and the examiner will give you marks for the correct one.
How to prepare for maths
Algebra is your new best friend
Whether you know it or not, algebra is one of the most important chapters to have on your side as it can seep into several questions on the exam. Algebra comes into almost every chapter of the course so it really is unavoidable. I recommend prioritising algebra in your study.
Get to know your calculator
While there are lots of brands of calculators, I am personally on team Casio because its features are clear and easy to use. Make sure you know the ins and outs of your calculator such as fractions, decimals, degrees, minutes, seconds, mixed/improper fractions, function tables and so on. Being confident in using your calculator will mean no time lost in the exam inputting calculations or trying to figure things out.
Rounding is important
You could potentially lose out on a distinction if your rounding game is
weak. Highlight when a question asks you to round so you don’t forget to. Know how to round to the nearest whole number, to one and two decimal places and to different significant figures. Finally, know scientific notation in case a question wants an answer in this format.Leave no stone unturned
As the exam has no set structure or sections, that means everything on the course is examinable. Start your study by focusing on the main chapters and then move on to the smaller nitty gritty bits.
Use the log tables in your study
Familiarise yourself with finding the relevant formulas in your log tables. When you are working on a topic, have this section of the log tables open and ready to go. Many people don’t know how to effectively use log tables so to build your confidence with them and to save time in the exam, get to know what is in there and use them in your study.
Log tables
Noteworthy sections in the log tables include:
Area and volume
Co-ordinate geometry
Sequences and series
Trigonometry
Financial maths
Sets and number systems
Final exam tips
Don’t forget your units
Make sure you know the units for any lengths, areas, volumes, distances, speeds, angles and times. The examiner can take marks from you for not having the correct units.
Show your work
The examiner can deduct marks from you if correct workings are not shown. You have ample time to show your workings so make sure you do.
Formulas
You don’t get marks for just writing down a formula; you must substitute at least some correct values into it to get some marks.
Use your log tables
Double-check the formula you are using to make sure you have it taken down correctly. I’ve seen it happen many times where students take down something wrong in a formula which potentially leads to a dock in marks.
Presentation is important
Present your work in a neat, well-laid-out format. While you won’t gain any extra marks for having tidy work, the examiner will certainly be in good form correcting clear and well-presented work.
Some final tips
for Junior Cycle Maths.
Don’t forget your units
Make sure you know the units for any lengths, areas, volumes, distances, speeds, angles and times. The examiner can take marks from you for not having the correct units.
Show your work
The examiner can deduct marks from you if correct workings are not shown. You have ample time to show your workings so make sure you do.
Formulas
You don’t get marks for just writing down a formula; you must substitute at least some correct values into it to get some marks.
Use your log tables
Double-check the formula you are using to make sure you have it taken down correctly. I’ve seen it happen many times where students take down something wrong in a formula which potentially leads to a dock in marks.
Presentation is important
Present your work in a neat, well-laid-out format. While you won’t gain any extra marks for having tidy work, the examiner will certainly be in good form correcting clear and well-presented work.
Hope these help - happy studying!
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Best of luck! You'll be great.
Stephen is a Mathematics & Coding teacher at Dundalk Grammar School. Stephen tutors maths at Maynooth University’s Mathematics Support Centre and is also an examiner. Having a huge passion for teaching maths, Stephen believes that with the right guidance and attitude, everyone can enjoy and succeed in maths.