"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding." -William Paul Thurston
Not everyone studying maths likes it and that's fine, but since it's a mandatory subject for the Leaving Cert, there's not much point in complaining about it.
Instead, it's better to accept that you have to do it, learn what's on the exams, and do your best. This is easier said than done, but having a plan based on the topics on the exams is a good place to start.
Before you even start worrying about the problems and mathematics you have to learn, you should find out what it is that you'll be tested on. To effectively study Leaving Cert Maths, you need to study the topics on the exam and the exam format itself.
After all, you don't get any marks for how well you do in class or how much you know about each topic on the syllabus, but rather how close your answers are to the marking scheme for each of the exams.
With that in mind, here's our guide to the Leaving Cert Maths Exams and syllabus.
The Structure of the Leaving Cert Maths Exams
For the Leaving Cert Maths exams, there are several areas of study that students will be tested on through the exams they take.
The Leaving Certificate (Leaving Cert) is Ireland's final secondary school qualification and it takes at least 2 years of study. Students between the ages of 16 and 20 will prepare for several Leaving Cert subjects.
The core subjects are Irish, English, maths, and European languages and subjects can be further classified into higher, ordinary, or foundation levels.
Only Irish and Mathematics are available at the foundation level and every other subject must be taken at ordinary or higher level. These levels affect a student's final results with better marks being awarded for the higher levels.
The topics covered by Leaving Cert Maths are called "strands" in the syllabus. They are:
- Strand 1: Statistics and Probability
- Strand 2: Geometry and Trigonometry
- Strand 3: Number
- Strand 4: Algebra
- Strand 5: Functions
Students will spend two or three years studying these strands in preparation for their Leaving Cert Maths exams. Each year, the exams change slightly, but in recent years, the overall structure has remained largely the same.
The Leaving Cert Maths is divided into two papers, aptly named Paper 1 and Paper 2. Students are given two and a half hours for each paper.
Both papers are divided into two sections of equal weighting: Section A and Section B. You should keep this in mind for your time management during the exam. With the same number of marks available, you should consider spending a similar amount of time on each section.
Section A includes 6 shorter questions while Section B has longer questions based on applying mathematical concepts to real-world problems. There are 3 questions in Section B.
We highly recommend that every student practise regularly with past papers to get better at their time management and understanding what two and a half hours feel like when under exam conditions.
The Mathematical Topics on the Leaving Cert Maths Paper 1 and Paper 2
The five aforementioned strands for maths should be studied extensively by Leaving Cert students by the time they sit each of the exams.
Let's dive into each of the five strands of the Leaving Cert Maths syllabus to see exactly what they entail and what you should know before you take your Leaving Cert Maths exams.
Strand 1: Statistics and Probability
The first strand is statistics and probability, which mainly deals with:
- Finding, collecting, and organising data
- Representing data graphically and numerically
- Analysing, interpreting, and drawing conclusions from data
In statistics, students are expected to understand:
As for statistics, the following aspects should be well learnt by students to succeed during the final examination:
- Sampling
- Pie Charts
- Bar Charts
- Stem & Leaf Plots
- Histograms
- Scatter Plots
- Line of Best Fit
- Mean, Median & Mode
- Frequency Distribution Table
- Range & Interquartile Range
- Standard Deviation
- Percentiles
- Central Limit Theorem
- Population Proportion
Strand 2: Geometry and Trigonometry
While related, geometry and trigonometry aren't the same thing. For this strand of the Leaving Cert Maths syllabus, however, they're put together.
Over 2 or more years of studying Leaving Cert Maths, students will cover these topics in the geometry part of strand 2:
- Lines & Angles
- Triangles
- Congruent Triangles
- Parallelograms
- Ratio & Parallel Lines
- Similar Triangles
- Circles
- Transformations
- Enlargements
Geometry for Leaving Cert Maths also covered synthetic geometry, coordinate geometry, and transformation geometry.
Trigonometry or trig for Leaving Cert Maths should leave learners with a solid foundation if they wish to continue their mathematical studies in this area after secondary education.
The areas of the trigonometry covered for the Leaving Cert are:
- Sin, Cos & Tan
- Sine Rule
- Cosine Rule
- Radians
- Uses of Radians
- Graphs of Sin, Cos & Tan
- Unit Circle
- Trigonometric Identities
- Pythagoras
Strand 3: Number
You might think that "number" refers to every part of mathematics, but for the Leaving Cert, this involves manipulating and understand ing complex numbers.
The topics taught in this strand include:
- Number systems
- Indices
- Arithmetic
- Length, area, and volume
During the number section, the purpose is to expand on your knowledge of calculating complex numbers.
Strand 4: Algebra
Algebra covers a lot of things in the world of mathematics, but it's essentially studying mathematical symbols and the rules for manipulating said symbols.
Secondary school students will likely spend a fair amount of time covering algebraic concepts before they start studying algebra for Leaving Cert Maths.
Quite a few questions and problems on Leaving Cert Maths exams may cover the following areas of algebra and students should be aware of them:
- Multiplying Brackets
- Algebraic Fractions
- Factorisation
- Quadratic Formula
- Simplifying Algebraic Fractions
- Manipulating Formulas
- Solving Simultaneous Equations
- Solving Quadratic Equations
- Roots of Quadratics
- Simultaneous Equations, Linear & Quadratic
- Surds
- Algebraic Long Division
- Factor Theorem
- Polynomials
- Solving Cubic Equations
- Verifying Roots in Cubic Equations
- Finding Unknown Values
- Completing the Square
- Number Line
- Linear Inequalities
- Quadratic Inequalities
- Modulus
With so much to study across algebra and the other strands that make up the Leaving Cert Maths syllabus, we recommend that you regularly take notes during your class and review them as part of your study and revision schedule.
We remarkably suggest paying attention, taking notes, and asking questions during class when any of the previously mentioned aspects of algebra are brought up since there will 100% be questions that refer to these topics on the final exam.
Strand 5: Functions
Last but not least, we have functions, which are how maths is used to create outputs from inputs. Leaving Cert Maths students should be aware of the following:
- Graph cubic, exponential, logarithmic, and trigonometric functions
- Injective, Surjective, and Bijective Functions
- Limits and continuity of operations
The functions strand also includes aspects of calculus like limits, calculating the slope, differentiation, points of inflexion, and turning points.
Get Help Studying for Leaving Cert Maths with a Private Tutor
If you're struggling with any part of the Leaving Cert or are afraid of failing, it can help to get tutoring from a private tutor. On the Superprof website, you just need to search for maths tutors in your local area.
You can find local tutors offering face-to-face tutoring on Leaving Cert Maths, browse their profiles, see how much they charge, and find out what their other students have to say about them.
Even if you can't find any local tutors, you can always broaden your search to include online private tutors. There are tutors all over Ireland and around the world who can help you get to grips with trigonometry, functions, or any other of the topics you need to know for your exam.
If you find one-on-one tutors too pricey, you can always save some money by opting for group tutoring. While group tutoring doesn't come with all the benefits of one-on-one tutoring, some students really enjoy learning in small groups with others and there's something to be said for the benefits of peer learning.
To search more effectively, we recommend that you have a clear idea of your requirements before starting your search and shortlisting the potential tutors that meet your requirements.
Many of the tutors on the Superprof website offer the first session for free so consider trying a few out before choosing the one that's the best fit for you, what you want to learn, and how you like to study.
Once you've found a handful of potential tutors that you'd consider studying with, you can start getting in touch with them and arranging free sessions.
If you need more than just help in Leaving Cert Maths, you might want to look for tutors offering study skills, help with revision, or general Leaving Cert tutoring.
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