In this article, we will break down the Leaving Cert Maths syllabus for you. This article will also show you **the difference in Foundation, Ordinary and Higher Level syllabuses** of leaving certificate maths. This will help you to decide on your appropriate level and help you to study!

The Leaving Cert Timetable 2022 has been published! And we’ve prepared a 2-hour maths crash course which is the final boost your child needs to be prepped, ready, and confident as they walk into their exams.

Leaving Cert Maths is designed as a 2-year course and can be studied at three levels:

- Higher Level (HL)
- Ordinary Level (OL)
- Foundation level (FL)

Each level follows a separate syllabus that matches each level’s difficulty. We have classes for each level in our leaving cert maths grinds!

In this article, I’ll describe:

- Sections of the LC Maths Syllabus
- Contents Of Section A
- Statistics and Probability
- Geometry and Trigonometry
- Number
- Algebra
- Functions
- Contents Of Section B
- For Foundation Level
- For Ordinary Level
- For Higher Level

## LC Maths Syllabus Sections

The syllabus of the Leaving Cert Maths for all three levels contains two sections –** Section A and Section B. **

- Section A includes core mathematics topics, focusing on concepts and skills. We refer to it as the
**‘Short questions’**as they take a shorter time to complete. - Section B includes questions that require more context-based applications. We refer to it as the
**‘Long questions’**as they take a longer time to complete.

## Leaving Cert Maths Syllabus: Contents Of Section A

In this section, the LC Maths syllabus is comprised of five strands. They are

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

Each strand and its course topics are given below.

### 1. Statistics and Probability

The aim of the Probability unit is to provide a certain understanding of patterns that will help you to naturally solve problems. The Statistics unit will help you to collect and analyze mathematical data.

#### Course Content And Descriptions

Topics | What Will Students Learn (Foundation Level) | What Will Students Learn (Ordinary And Higher Level) |
---|---|---|

1. Counting | • You’ll discover the outcomes of experiments in a systematic way | • Count the arrangements of n distinct objects (n!)• Count the number of ways of arranging r objects from n distinct objects |

2. Concepts of probability | • You’ll learn the probability of an event occurring • Informal to formal descriptions of probability • Predicting and determining probabilities | • Discuss basic rules of probability (AND/ OR, mutually exclusive) through the use of Venn diagrams • Calculate the expected value • Recognize the role of expected value in decision making and explore the issue of fair games |

3. Outcomes of simple random processes | • You’ll find the probability of equally likely outcomes | • Find the probability that two independent events both occur • Apply an understanding of Bernoulli trials • Solve problems involving up to 3 Bernoulli trials • Calculate the probability that the 1st success occurs on the nth Bernoulli trial where n is specified |

4. Statistical reasoning with an aim to becoming a statistically aware consumer | • You’ll learn about situations where statistics are misused • Learn to evaluate the reliability and quality of data and data sources. • You’ll learn about different types of data. | • Discuss populations and samples decide to what extent conclusions can be generalized • Work with different types of bivariate data |

5. Finding, collecting, and organising data | • Gathering information from a selection of the population • Formulating a statistics question based on data that vary • Distinction between different types of data. | • Select a sample (Simple Random Sample) • Understanding Bias • Discuss different types of studies |

6. Representing data graphically and numerically | • Methods of representing data. • Organizing data in different ways • Using proportions and measures of centre to describe the data. | Graphical • Describe the sample (both univariate and bivariate data) by selecting appropriate graphical or numerical methods • Explore the distribution of data, including concepts of symmetry and skewness • Compare data sets using appropriate displays including back-to-back stem and leaf plots Determine the relationship between variables using scatterplot • Recognise that correlation is a value from -1 to +1 and that it measures the extent of the linear relationship between two variables • Match correlation coefficient values to appropriate scatterplots understand that correlation does not imply causality Numerical • Recognise standard deviation and interquartile range • Use a calculator to calculate the standard deviation • Use the interquartile range appropriately when analysing Data • Recognise the existence of outliers |

7. Analysing, interpreting and drawing conclusions from Data | • Drawing conclusions from data • Identifying limitations of conclusions. | • Understand variability of sampling • Make conclusions from Data. • Understand the distribution of Data • Empirical rule • Hypothesis testing • Use Margins of Error |

### 2. Geometry and Trigonometry

The Geometry and Trigonometry section is examined in Paper 2 of Leaving Cert. It accounts for around 20-25% of the questions on Paper 2 in the Leaving Cert.

#### Course Content And Descriptions

Topics | What Will Students Learn (Foundation Level) | What Will Students Learn (Ordinary And Higher Level) |
---|---|---|

1. Synthetic geometry | • Constructions and how to apply these in real-life situations. • Dynamic geometry software. • The instruments that are used to perform constructions | • Perform constructions 16-21 (see section B) • Understand: theorem, proof, axiom, corollary, converse, implies • Investigate theorems 7, 8, 11, 12, 13, 16, 17, 18, 20, 21 and corollary 6 (see section B) |

2. Co-ordinate geometry | • Co-ordinating the plane • Linear relationships • The Slope of a graph • Comparing linear relationships in real-life contexts. • The significance of the point of intersection of two linear relationships. | • Use slopes to show that two lines are parallel or perpendicular • Calculate the Area of a Triangle • Solve Circle and line problems |

3. Trigonometry | • Right-angled triangles. • Trigonometric ratios | • Pythagoras Theorem • Area of a triangle • Sine and Cosine Rules • Understand Sin Cos Tan • Area of a Circle • Work with trigonometric ratios in surd form |

4. Transformation geometry, enlargements | • Translations, central symmetry, axial symmetry and rotations. • Enlargements. | • Understand Enlargements • Solve problems involving enlargements |

#### Trigonometric Formulae

### 3. Number

The Number section is at the core of our Maths understanding in the Leaving Cert. Almost all of the questions are shown in Paper 1 of the Leaving Cert. It accounts for around 10-15% of the questions on Paper 1 in the Leaving Cert.

#### Course Content And Descriptions

Topics | What Will Students Learn (Foundation Level) | What Will Students Learn (Ordinary And Higher Level) |
---|---|---|

1. Number systems N: the set of natural numbers, N = {1,2,3,4…} Z: the set of integers, including 0 Q: the set of rational numbers | • Understand fractions, decimals and percentages • Addition, subtraction, multiplication, and division • Understand the rules for adding, subtracting and dividing negative numbers • Solve problems with fractions | • Recognise irrational numbers • Work with irrational numbers • Operations with complex numbers • Illustrate complex numbers on an Argand diagram • Interpreting the Modulus • Working with decimals • Factors, multiples and prime numbers • Express numbers in terms of their prime factors • Express non-zero positive rational numbers • Apply Patterns • Recognise whether a sequence is arithmetic, geometric or neither • Find the sum to n terms of an arithmetic series |

2. Indices | • Representing numbers as squares, cubes, square roots, and reciprocals | • Solving problems using the rules for indices |

3. Arithmetic | • Solving everyday problems • Making value for money calculations and judgments • Using ratio and proportion | • Accumulate error • Calculate percentage error • Calculate average rates of change • Calculating cost price, selling price, loss, discount, mark up • Compound interest, depreciation, income tax and net pay • Costing: materials, labour and wastage • Metric system and imperial units • Make estimates of measures in the real world |

4. Length, area and volume | • 2D shapes and 3D solids • Using nets to distinguish between surface area and volume. • Problems involving perimeter, surface area and volume • The Circle | • Investigate the nets of prisms, cylinders and cones • Solve problems involving the surface area and volume of 3D figures • Understand the Trapezoidal rule |

### 4. Algebra

Algebra is the foundation of both Higher, Ordinary and Foundation levels. It comes up right across paper 1 and paper 2. It accounts for about 30% of the overall Leaving Cert questions.

#### Course Content And Descriptions

Topics | What Will Students Learn (Foundation Level) | What Will Students Learn (Ordinary And Higher Level) |
---|---|---|

1. Expressions | • Generating arithmetic expressions from repeating patterns • Using Tables, graphs and diagrams • Finding formulae • Examining algebraic relationships • Relations without formulae • Expressions | • Evaluate expressions • Expand and re-group expressions • Factorize expressions • Adding and subtracting equations • Simplifying equations • Rearrange formulae |

2. Solving equations | • Solving linear equations | • Inteprepreting linear equations using algebra • Form quadratic equations given whole number roots |

3. Inequalities | • Solving linear inequalities | • Solving linear inequalities |

4. Complex numbers | • See strand 3, Numbers |

### 5. Functions

The function section is built on the student’s understanding of Algebra. Functions questions account for around 10-15% of Paper 1. Understanding functions plays a key role in completing differentiation.

#### Course Content And Descriptions

Topics | What Will Students Learn (Foundation Level) | What Will Students Learn (Ordinary And Higher Level) |
---|---|---|

1. Functions | • Functions as a special type of relationship. Representing linear functions graphically | • Understand how functions work • Form composite functions • Graph functions of the form • Finding roots of a function • Understand the limit of a function |

2. Calculus | • Find first and second derivatives of different function types • Associate derivatives with slopes and tangent lines • Apply differentiation to: a. rates of change b. maxima and minima c. curve sketching |

## Leaving Cert Maths Syllabus: Contents Of Section B

Section B of the Leaving Cert Maths Syllabus is based around problem-solving. Questions are longer and more complex. Section B questions have more words and students have to solve real-life scenarios with Maths. It is worth 150 marks, the same as Section A. It includes the following topics:

- Terms
- The Theory
- Length and Distance
- Angles
- Degrees
- Congruent Triangles
- Parallels
- Perpendicular Lines
- Quadrilaterals and Parallelograms
- Ratios And Similarly
- Trigonometry
- Area
- Circles

- Constructions To Study

### Section B Syllabus For Foundation Level

- Students revisit the following constructions and learn how to apply these in real-life contexts:
**Constructions 4:**Line perpendicular to a given line*l*, passing through a given point on*l.***Constructions 5:**Line parallel to a given line, through a given point.**Constructions 10:**Triangle, given lengths of three sides.**Constructions 13:**Right-angled triangle, given the length of the hypotenuse and one other side.**Constructions 15:**Rectangle, given side lengths.

### Section B Syllabus For Ordinary Level

- Students will study the following constructions:
**Constructions 16:**Circumcentre and circumcircle of a given triangle, using only straight-edge and compass.**Constructions 17:**Incentre and incircle of a given triangle, using only straight-edge and compass.**Constructions 18:**Angle of 60०, without using a protractor or set square.**Constructions 19:**Tangent to a given circle at a given point on it.**Constructions 20:**Parallelogram, given the length of the sides and the measure of the angles.**Constructions 21:**Centroid of a triangle.

- Students will be expected to understand the meaning of the following terms:
**Theorem**,**Proof**,**Axiom**,**Corollary**,**Converse**,**Implies**. - Knowledge of the Axioms, concepts, Theorems and Corollaries prescribed for JC-OL will be assumed.
- Students will be examined using problems that can be attacked using the theory.
- Students will study proofs of the following Theorems and Corollary (No proofs are examinable):

**Theorem 7**

(a) In ABC, suppose that jACj > jABj. Then j\ABCj > j\ACBj. In other words, the angle opposite the greater of two sides is greater than the angle opposite the lesser side.

(b) Conversely, if j\ABCj > j\ACBj, then jACj > jABj. In other words, the side opposite the greater of two angles is greater than the side opposite the lesser angle.

**Theorem 8 (Triangle Inequality)**

Two sides of a triangle are together greater than the third.

**Theorem 11**

If three parallel lines are cut to equal segments on some transversal line, then they will cut to equal segments on any other transversal.

**Theorem 12**

Let ABC be a triangle. If a line l is parallel to BC and cuts [AB] in the ratio s: t, then it also cuts [AC] in the same ratio.

**Theorem 13**

If two triangles ABC and A՛B՛C՛ are similar, then their sides are proportional, in order:

|AB|/|A'B'| = |BC|/|B'C'| = |CA|/|C'A'|

**Theorem 16**

For a triangle, base times height does not depend on the choice of base.

**Theorem 17**

A diagonal of a parallelogram bisects the area.

**Theorem 18**

The area of a parallelogram is the base by the height.

**Theorem 20**

(a) Each tangent is perpendicular to the radius that goes to the point of contact.

(b) If P lies on the circle s, and a line l through P is perpendicular to the radius to P, then l is tangent to s.

**Theorem 21**

(a) The perpendicular from the centre to a chord bisects the chord.

(b) The perpendicular bisector of a chord passes through the centre.

**Corollary 6**

If two circles share a common tangent line at one point, then the two centres and that point are collinear.

### Section B Syllabus For Higher Level

- Students will study the constructions prescribed for Leaving Cert Ordinary Level (16-21), and
**Construction 22**: Orthocentre of a triangle. - Students will be expected to understand the meaning of the following terms related to logic and deductive reasoning:
**Theorem, Proof, Axiom, Corollary, Converse, Implies, Is equivalent to, If and only if, Proof by contradiction.** - Knowledge of the Axioms, concepts, Theorems and Corollaries prescribed for JC-HL will be assumed.
- Students will study all the theorems and corollaries prescribed for LC-OL, but will not, in general, be asked to reproduce their proofs in the examination.
- However, they may be asked to give proofs of the Theorems 11, 12, 13 (mentioned in “Section B Syllabus For Ordinary level”) concerning ratios, which lay the proper foundation for the proof of Pythagoras studied at JC, and for trigonometry.
- They will be asked to solve geometrical problems (so-called “cuts”) and write reasoned accounts of the solutions. These problems will be such that they can be attacked using the given theory. The study of the propositions may be a useful way to prepare for such examination questions.

## Conclusion

In summary of the leaving cert maths syllabus, Paper 1 is primarily based around Algebra and Differentiation. Most of the 5th year curriculum is covered in Paper 1.

Paper 2 is primarily based on Statistics and Probability. Most of what students learned in their 6th year is covered in Paper 2.

If you need extra help with your Leaving Cert Maths, you can join our** **Online LC Maths Grinds for a FREE trial lesson!

Good Luck