Chapters

Since 2014, the Leaving Cert Maths exams have been exclusively based on the Project Maths Syllabus. This Syllabus is based more on real-life maths and the understanding of the subject, what is expected from students in the exams is a demonstration of their understanding of the questions whereas the old syllabus was largely focused on the more mechanical steps of a calculation.

"Maths is like learning a language: you need to learn the basics to get going, but a lot of adults go into blind panic about numbers and switch off."

Rachel Riley

## Project Maths - Syllabus Breakdown

The Leaving Certificate Mathematics syllabus comprises five strands, in each strand of this syllabus, there are separate learning outcomes specific to that strand.

The Foundation level learning outcomes are distinct from the Ordinary level and Higher level outcomes and are listed separately.

The 5 strands in the Project Maths are as follows:

- Statistics and Probability
- Geometry and Trigonometry
- Number
- Algebra
- Functions

As mentioned different things are expected from students studying at different levels, the main difference is for those taking Foundation level maths. Students at this level are not required to deal with abstract mathematics meaning the Leaving Cert exam for Foundation maths is largely based on 'practical maths', they will be expected to solve the types of problems they may encounter in their daily lives.

Foundation level Mathematics is intended to equip learners with the knowledge and skills required in everyday life, and it is also intended to help learners proceed on to Further Education.

## Strand 1 - Statistics and Probability

Below is a simplified breakdown of Strand 1:

**Counting**- Listing outcomes of experiments in a systematic way.**Concepts of probability**- The probability of an event occurring: students progress from informal to formal descriptions of probability.**Outcomes of random processes**- Finding the probability of equally likely outcomes.**Statistical reasoning**- Situations where statistics are misused and learn to evaluate the reliability and quality of data and data sources.**Finding, collecting and organising data**- The use of statistics to gather information from a selection of the population with

the intention of making generalisations about the whole population.**Representing data graphically and numerically**- Methods of representing data. Students develop a sense that data can convey information and that organising data in different ways.**Analysing, interpreting and drawing conclusions from data**- Drawing conclusions from data; limitations of conclusions.

## Strand 2 - Geometry and Trigonometry

Below is a breakdown of strand 2:

**Synthetic geometry**- Dynamic geometry software.**Co-ordinate geometry**- Linear relationships in real-life contexts and representing these relationships in tabular and graphical form.**Trigonometry**- Right-angled triangles. Trigonometric ratios.**Transformation geometry, enlargements**- Translations, central symmetry, axial symmetry and rotations.

## Strand 3 - Number

In Strand 3, learners continue their understanding of addition, subtraction, multiplication and division of whole and rational numbers and extend this sense-making to complex numbers.

Strand 3 is broken down as follows:

**Number systems**- develop a unified understanding of numbers, recognising fractions, decimals.**Indices**- Representing numbers as squares, cubes, square roots, and reciprocals**Arithmetic****Length, area and volume**- solve problems involving the length of the perimeter, solve problems involving surface area and volume.

## Strand 4 - Algebra

In Strand 4, learners build on their proficiency in moving among equations, tables and graphs and become more adept at solving real-world problems.

**Expressions**- Evaluating expressions derived from real-life contexts.**Solving equations**- Solving linear equations set.**Inequalities**- Solving linear inequalities.**Complex Numbers**- work with complex numbers to solve quadratic and other equations.

## Strand 5: Functions

Students are introduced to calculus as the study of how things change and use derivatives to solve various kinds of real-world problems. They learn how to go from the derivative of a function back to the function itself. The relationship between functions and algebra is further emphasised and learners continue to connect graphical and symbolic representations of functions.

This strand may cover fewer topics than the other 4 strands but it is equally as important that you complete this section of the Project Maths syllabus. Strand 5 is broken down into the following topics:

**Functions**- Recognise functions, composite functions, investigate functions.**Calculus**- find first and second derivatives of linear, quadratic and cubic functions, associate derivatives with slopes and tangent lines, apply differentiation to rates of change, maxima and minima, curve sketching.

Now that we've taken a brief look at the Leaving Cert, Project Maths Syllabus, it makes sense that we take a quick look at things you might need to aid you in your studies.

## Useful Tools to Aid Leaving Cert Maths Study

"It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment."

Carl Friedrich Gauss

There are quite a few useful tools to help you study the Project Maths Leaving Cert Syllabus. I have compiled a list of what I feel to be the 3 absolute essentials tips below:

**A Scientific Calculator**- Yes this one really is quite obvious, however, I would recommend getting 2. One for school and one for home. I always left a calculator in my school locker, that way I could never accidentally leave it at home.**Formulae & Tables (Log Tables)**- I know a lot of the time teachers hand these out in class and before exams, but my advice is to get your own copy, that way you have it for home revision and if you're taking grinds you won't need to borrow one.**Past Exam Papers**- Again some teachers hand copies out in class or project them on a screen, but having your own access to as many past questions as possible can be really beneficial, buying the books of exam papers for every subject can work out very expensive but don't worry, there are alternatives. For past maths exam papers and marking schemes, across all three Leaving Cert Levels, you can visit The Leaving Cert.

Another set of useful tools for Leaving Cert Maths, although it may not be essential for everyone, are Revision Courses and Grinds. At Superprof there are several tutors offering grinds in Maths. You can choose your tutor from a large selection, you can also pick times that suit you and take as many or as few revision/preparation classes as you need. No matter what the subject, if you choose to take grinds with Superprof, you will see they are affordable, as they start from just €10 and they are flexible to suit your study timetable.

The Superprof homepage is really easy to navigate, which means you can find the perfect Maths Tutor for you within minutes! All you have to do is select the subject you would like to take lessons in, and add your area then search for a full list of tutors and their fees. A lot of the time you even get your first lesson free, which makes Superprof even better value!

For more help and guidance when it comes to Leaving Cert Maths, visit the following article:

The platform that connects tutors and students