# Leaving Cert Maths Syllabus Simplified 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:

1. Higher Level (HL)
2. Ordinary Level (OL)
3. 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!

## LC Maths Syllabus Sections

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

1. 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.
2. 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

1. Statistics and Probability
2. Geometry and Trigonometry
3. Number
4. Algebra
5. 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.

### 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.

### 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.

### 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.

### 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.

## 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:

1. Terms
2. The Theory
• Length and Distance
• Angles
• Degrees
• Congruent Triangles
• Parallels
• Perpendicular Lines
• Ratios And Similarly
• Trigonometry
• Area
• Circles
3. Constructions To Study

### Section B Syllabus For Foundation Level

1. 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

1. 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.
2. Students will be expected to understand the meaning of the following terms: Theorem, Proof, Axiom, Corollary, Converse, Implies.
3. Knowledge of the Axioms, concepts, Theorems and Corollaries prescribed for JC-OL will be assumed.
4. Students will be examined using problems that can be attacked using the theory.
5. 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!

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