After 3 years of secondary education, the annual Junior Certificate (JC) examination takes place in June. **Due to the pandemic, the Junior Cert was cancelled for two years, but it’s finally back for 2022!!**

That’s why in this article, we will break down the Junior Cert Maths courses for you. We will also show you the difference in Foundation, Ordinary, and Higher Level Maths syllabuses so that you can choose your course level accordingly.

The Junior 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.

**Junior Cert Maths is designed as a 3-years course and can be studied at 3 levels:**

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

Each level follows a separate Maths syllabus that matches each level’s difficulty. We have classes for each year in our Junior Cert Maths Grinds!

In this article, I’ll describe:

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

## Junior Cert Maths Syllabus

At the Foundation level of Junior Certificate Mathematics, there is only one examination paper. But there are two examination papers at the Ordinary level and the Higher level. They are referred to as:

- Paper 1
- Paper 2

The syllabus of the Junior 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 them 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 them as the
**‘Long questions’**as they take longer to complete.

## Contents Of Section A

In this section, the JC 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.

*Materials for Higher level only are shown in bold text.*

### 1. Statistics and Probability

Work in this strand focus on engaging learners in this process of data investigation: posing questions, collecting data, analyzing and interpreting this data in order to answer questions.

#### Course Content And Descriptions

Topics | What Will Students Learn(Bold text is for Higher Level only) |
---|---|

1. Counting | • Listing outcomes of experiments in a systematic way, such as in a table, using sample spaces, tree diagrams. |

2. Concepts of Probability | • Predicting and determining probabilities. • Difference between experimental and theoretical probability |

3. Outcomes of simple random processes | • Finding the probability of equally likely outcomes. |

4. Statistical reasoning to become a statistically aware consumer | • Situation where statistics are misused • Learn to evaluate the reliability and quality of data • Different types of data sources |

5. Finding, collecting, and organizing data | • Gathering information from a selection of the population • Formulating a statistics question based on data that vary • Distinction between different types of data. |

6. Representing data graphically and numerically | • Methods of representing data • Organizing data in different ways • Using proportions and measures of center to describe the data. • Mean of a grouped frequency distribution. |

7. Analysing, interpreting, and drawing conclusions from Data | • Drawing conclusions from data • Identifying limitations of conclusions. |

### 2. Geometry and Trigonometry

The synthetic geometry covered in Junior Certificate Mathematics is selected from section B, including terms, definitions, axioms, propositions, theorems, converses, and corollaries.

#### Course Content And Descriptions

Topics | What Will Students Learn(Bold text is for Higher Level only) |
---|---|

1. Synthetic geometry | • Concepts and Axioms (see section B) 1. [Two points axiom] There is exactly one line through any two given points. 2. [Ruler axiom] The properties of the distance between points 3. [Protractor Axiom] The properties of the degree measure of an angle 4. Congruent triangles (SAS, ASA, and SSS) 5. [Axiom of Parallels] Given any line l and a point P, there is exactly one line through P that is parallel to l.• Theorems (Formal proofs are not examinable at OL). Formal proofs of theorems (see section B) 4, 6, 9, 14, and 19 are examinable at HL.1. Vertically opposite angles are equal in measure. 2. In an isosceles triangle, the angles opposite the equal sides are equal. Conversely, if two angles are equal, then the triangle is isosceles. 3. If a transversal makes equal alternate angles on two lines then the lines are parallel, (and converse). 4. The angles in any triangle add to 180˚. 5. Two lines are parallel if and only if, for any transversal, the corresponding angles are equal. 6. Each exterior angle of a triangle is equal to the sum of the interior opposite angles. 9. In a parallelogram, opposite sides are equal, and opposite angles are equal (and converses). 10. The diagonals of a parallelogram bisect each other. 11. If three parallel lines cut off equal segments on some transversal line, they will cut off equal segments on any other transversal. 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 (and converse). 13. If two triangles are similar, their sides are proportional, in order (and converse). 14. [Theorem of Pythagoras] In a right-angled triangle, the square of the hypotenuse is the sum of the squares of the other two sides. 15. If the square of one side of a triangle is the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. 19. The angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.• Corollaries 1. A diagonal divides a parallelogram into 2 congruent triangles. 2. All angles at points of a circle, standing on the same arc, are equal. (and converse). 3. Each angle in a semi-circle is a right angle. 4. If the angle standing on a chord [BC] at some point of the circle is a right-angle, then [BC] is a diameter. 5. If ABCD is a cyclic quadrilateral, then opposite angles sum to 180˚, (and converse).• Constructions: 1. Bisector of a given angle, using only compass and straight edge. 2. Perpendicular bisector of a segment, using only compass and straight edge. 3. Line perpendicular to a given line l, passing through a given point, not on l. 4. Line perpendicular to a given line l, passing through a given point on l. 5. Line parallel to a given line through a given point. 6. Division of a line segment into 2 or 3 equal segments without measuring it. 7. Division of a line segment into any number of equal segments without measuring it. 8. A line segment of a given length on a given ray. 9. Angle of a given number of degrees with a given ray as one arm. 10. Triangle, given lengths of three sides 11. Triangle, given SAS data 12. Triangle, given ASA data 13. Right-angled triangle, given the length of the hypotenuse and one other side. 14. Right-angled triangle, given one side and one of the acute angles (several cases). 15. Rectangle, given side lengths |

2. Co-ordinate geometry | • Co-ordinating the plane. • Properties of lines and line segments include midpoint, slope, distance, and the equation of a line in the form. y – y1 = m(x – x1 ). y = mx + c. • ax + by + c = 0 where a, b, c, are integers and m is the slope of the line. • The intersection of lines. • Parallel and perpendicular lines and the relationships between the slopes. |

3. Trigonometry | • Right-angled triangles. • Trigonometric ratios. • Working with trigonometric ratios in surd form for angles of 30˚, 45˚ and 60˚.• Right-angled triangles. • Decimal and DMS values of angles. |

4. Transformation geometry | • Translations, central symmetry, axial symmetry and rotations. |

### 3. Number

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

#### Course Content And Descriptions

Topics | What Will Students Learn(Bold text is for Higher Level only) |
---|---|

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 R: the set of real numbers R/Q: the set of irrational numbers | • Binary operations of addition, subtraction, multiplication, and division and the relationships between these operations, beginning with whole numbers and integers. • Revisit these operations in the context of rational and irrational numbers (R/Q) and refine, revise and consolidate their ideas.• Articulate the generalization that underlies their strategy, firstly in the vernacular and then in symbolic language • Algorithms used to solve problems involving fractional amounts. |

2. Indices | • Binary operations of addition, subtraction, multiplication and division in the context of numbers in index form. |

3. Applied Arithmetic | • Solving problems involving, e.g., mobile phone tariffs, currency transactions, shopping, VAT, and meter readings. • Making value for money calculations and judgments. • Using ratio and proportionality |

4. Applied Measures | • Measure and time. • 2D shapes and 3D solids, including nets of solids (two-dimensional representations of three-dimensional objects). • Using nets to analyze figures and to distinguish between surface area and volume. • Problems involving perimeter, surface area, and volume. Modelling real-world situations and solving a variety of problems (including multi-step problems) involving surface areas and volumes of cylinders and prisms. The circle and develop an understanding of the relationship between its circumference, diameter, and π |

5. Sets | • Set language as an international symbolic mathematical tool; the concept of a set as being a well-defined collection of objects or elements. • They are introduced to the concept of the universal set, null set, subset, cardinal number; the union, intersection, set difference operators, and Venn diagrams. |

### 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 Junior Cert questions.

#### Course Content And Descriptions

Topics | What Will Students Learn(Bold text is for Higher Level only) |
---|---|

1. Generating arithmetic expressions from repeating patterns | • Patterns and the rules that govern them; • Students construct an understanding of a relationship as that which involves a set of inputs, a set of outputs, and a correspondence from each input to each output |

2. Representing situations with tables, diagrams and graphs | • Relations derived from some kind of context – familiar, everyday situations, imaginary contexts, or arrangements of tiles or blocks. • Students look at various patterns and make predictions about what comes next. |

3. Finding formulae | • Ways to express a general relationship arising from a pattern or context. |

4. Examining algebraic relationships | • Features of a relationship and how these features appear in the different representations. • Constant rate of change: linear relationships. • Non-constant rate of change: quadratic relationships. Proportional relationships. |

5. Relations without formulae | • Using graphs to represent phenomena quantitatively. |

6. Expressions | • Using letters to represent quantities that are variable. • Arithmetic operations on expressions; applications to real-life contexts. • Transformational activities: collecting like terms, simplifying expressions, substituting, expanding, and factoring. |

7. Equations and inequalities | • Selecting and using suitable strategies (graphic, numeric, algebraic, mental) for finding solutions to equations and inequalities. • They identify the necessary information, represent problems mathematically, making correct use of symbols, words, diagrams, tables, and graphs. |

### 5. Functions

This strand seeks to make explicit the connections and relationships already encountered in strands 3 and strand 4. 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(Bold text is for Higher Level only) |
---|---|

1. Functions | • The meaning and notation associated with functions. |

2. Graphic Functions | • Interpreting and representing linear, quadratic, and exponential functions in graphical form |

## Contents Of Section B

Section B of the Junior Cert Maths Syllabus is based on 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
- Pythagoras
- Area
- Circles
- Special Triangle Points

- Constructions To Study

## Section B Syllabus For Junior Cert Ordinary Level (JCOL)

### 1. Concepts

The concepts that students at the Ordinary level are going to learn for Junior Cert Maths are:

Set, plane, point, line, ray, angle, real number, length, degree, triangle, rightangle, congruent triangles, similar triangles, parallel lines, parallelogram, area, tangent to a circle, subset, segment, collinear points, distance, midpoint of a segment, reflex angle, ordinary angle, straight angle, null angle, full angle, supplementary angles, vertically-opposite angles, acute angle, obtuse angle, angle bisector, perpendicular lines, the perpendicular bisector of a segment, ratio, isosceles triangle, equilateral triangle, scalene triangle, right-angled triangle, exterior angles of a triangle, interior opposite angles, hypotenuse, alternate angles, corresponding angles, polygon, quadrilateral, convex quadrilateral, 80 rectangle, square, rhombus, base and corresponding apex and height of triangle or parallelogram, transversal line, circle, radius, diameter, chord, arc, sector, circumference of a circle, disc, area of a disc, circumcircle, point of contact of a tangent, vertex, vertices (of angle, triangle, polygon), endpoints of segment, arms of an angle, equal segments, equal angles, adjacent sides, angles, or vertices of triangles or quadrilaterals, the side opposite an angle of a triangle, opposite sides or angles of a quadrilateral, centre of a circle.

### 2. Construction

Students revisit the following constructions and learn how to apply these in real-life contexts:

**Constructions 1:**Bisector of a given angle, using only compass and straight edge.**Constructions 2:**Perpendicular bisector of a segment, using only compass and straight edge.**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 6:**Division of a segment into 2, 3 equal segments without measuring it.**Constructions 8:**Line segment of a given length on a given ray.**Constructions 9:**Angle of a given number of degrees with a given ray as one arm.**Constructions 10:**Triangle, given lengths of three sides.**Constructions 11:**Triangle, given SAS data.**Constructions 12:**Triangle, given SAS data.**Constructions 13:**Right-angled triangle, given the length of the hypotenuse and one other side.**Constructions 14:**Right-angled triangle, given one side and one of the acute angles (several cases).**Constructions 15:**Rectangle, given side lengths.

### 3. Axioms

The students should be exposed to some formal proof. **They will not be examined on these.**

**Axiom 1: (Two Points Axiom)**

There is exactly one line through any two given points. (We denote the line through A and B by AB.)

**Axiom 2: (Ruler Axiom10)**

The distance between points has the following properties:

- The distance |AB| is never negative;
- |AB| = |BA|;
- If C lies on AB, between A and B, then |AB| = |AC| + |CB|;
- (Marking off a distance) given any ray from A, and given any real number k ≥ 0, there is a unique point B on the ray whose distance from A is k.

**Axiom 3: (Protractor Axiom)**

The number of degrees in an angle (also known as its degree-measure) is always a number between 0◦ and 360◦ . The number of degrees of an ordinary angle is less than 180◦ . It has these properties:

- A straight angle has 180◦ .
- Given a ray [AB, and a number d between 0 and 180, there is exactly one ray from A on each side of the line AB that makes an (ordinary) angle having d degrees with the ray [AB].
- If D is a point inside an angle ∠BAC, then |∠BAC| = |∠BAD| + |∠DAC|.

**Axiom 5: (Axiom of Parallels)**

Given any line *l* and a point P, there is exactly one line through P that is parallel to *l*.

### 4. Proofs of Theorems (Statement only)

**Theorem 1:(Vertically-opposite Angles)**

Vertically opposite angles are equal in measure.

**Theorem 2: (Isosceles Triangles)**

(1) In an isosceles triangle, the angles opposite the equal sides are equal.

(2) Conversely, If two angles are equal, then the triangle is isosceles.

**Theorem 3: (Alternate Angles)**

Suppose that A and D are on opposite sides of the line BC.

(1) If |∠ABC| = |∠BCD|, then AB||CD. In other words, if a transversal makes equal alternate angles on two lines, then the lines are parallel.

(2) Conversely, if AB||CD, then |∠ABC| = |∠BCD|. In other words, if two lines are parallel, then any transversal will make equal alternate angles with them.

**Theorem 4: (Angle Sum 180)**

The angles in any triangle add to 180◦ .

**Theorem 5: (Corresponding Angles)**

Two lines are parallel if and only if for any transversal, corresponding angles are equal.

**Theorem 6: (Exterior Angle)**

Each exterior angle of a triangle is equal to the sum of the interior opposite angles.

**Theorem 9:**

In a parallelogram, opposite sides are equal, and opposite angles are equal.

**Theorem 10:**

The diagonals of a parallelogram bisect one another.

**Theorem 13:**

If two triangles ∆ABC and ∆A0B0C 0 are similar, then their sides are proportional, in order:

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

**Theorem 14: (Pythagoras)**

In a right-angled triangle, the square of the hypotenuse is the sum of the squares of the other two sides.

**Theorem 15: (Converse to Pythagoras)**

If the square of one side of a triangle is the sum of the squares of the other two, then the angle opposite the first side is a right angle.

### 5. Corollary

**Corollary 3:**Each angle in a semicircle is a right angle. In symbols, if BC is a diameter of a circle, and A is any other point of the circle, then ∠BAC = 90◦ .**Corollary 4:**If the angle standing on a chord [BC] at some point of the circle is a right angle, then [BC] is a diameter.

## Section B Syllabus For Junior Cert Higher Level (JCHL)

### 1. Concepts

Same as JCOL and concurrent lines.

### 2. Construction

Students will study all the constructions prescribed for JCOL, and also:

**Constructions 3: **Line perpendicular to a given line *l*, passing through a given point, not on *l.*

**Constructions 7: **Division of a segment into any number of equal segments without measuring it.

### 3. Logics

Students will be expected to understand the meaning of the following terms related to logic and deductive reasoning:** Theorem, proof, axiom, corollary, converse,** and** implies.**

### 4. Axioms

They will study Axioms 1, 2, 3, 4, 5 (mentioned in JCOL)

### 5. Proofs of Theorems

They will study the proofs of Theorems 1, 2, 3, 4*, 5, 6*, 9*, 10, 13, 14*, 15 (mentioned in JCOL) and,

**Theorem 11:**

If three parallel lines are cut off equal segments on some transversal line, then they will cut off 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 19*:**

The angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.

### 6. Corollary

Corollary 3, 4 (mentioned in JCOL) and,

**Corollary 1:**A diagonal divides a parallelogram into two congruent triangles.**Corollary 2:**All angles at points of the circle, standing on the same arc, are equal. In symbols, if A, A′, B, and C lie on a circle, and both A and A′ are on the same side of the line BC, then ∠BAC = ∠BA′C.**Corollary 5:**If ABCD is a cyclic quadrilateral, then opposite angles sum to 180◦ .

Those marked with a * may be asked in the examination. Students will deal with Area only as part of the material on arithmetic and mensuration.

## Conclusion

In summary, Paper 1 is primarily based on Algebra and Differentiation. Most of the 1st year curriculum is covered in Paper 1.

Paper 2 is primarily based on Statistics and Probability. Most of what students learned in their 3rd year is covered in Paper 2.

You can join our junior cert maths grinds for FREE to get the best possible online maths help and prepare for your exams!

Good Luck!

**Recommended Reading:** Junior Cycle Grading System

## Frequently Ask Questions

### 1. What is a Strand?

A strand is a broad topic. You can compare it with chapters of different topics. For example, the broad topics or chapters or strands of JC maths are: Statistics and Probability, Geometry and Trigonometry, Numbers, Algebra, and Functions.

### 2. What is the difference between sections A and B of JC?

**Section A** focuses on concepts and topics. It also consists of shorter questions, and usually, it takes less time to complete.

On the other hand, **section B** focuses on context-based applications. Students apply the concepts they have learned in their answers. It also takes more time to complete than section A.

### 3. What are Axioms?

**Axioms are essentially mathematical truths that are accepted without proof.** They lay a foundation for the study of more complicated geometry. **Axioms are generally statements made about real numbers.** Often what they say about real numbers holds true for geometric figures, and since real numbers are an important part of geometry when it comes to measuring figures, axioms are very useful.

### 4. What is Construction?

Construction in geometry refers to drawing lines, angles, and other geometric shapes and figures using only a compass and a straightedge (usually a ruler without measurements), without the use of specific measurements of length, angle, etc.

### 5. What is a Corollary?

**A corollary is a theorem that can be proved from another theorem.** It is a statement that follows with little or no proof required from an already proven statement. Often said that “this is a corollary of Theorem A”.