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Will this prepare my child for the Leaving Certificate?

Yes! Third Year Maths builds essential foundations for Leaving Certificate Higher Level mathematics success.

How does this align with the Irish curriculum?

Our content follows the Irish Junior Cycle specifications exactly and prepares students for Leaving Certificate requirements.

What maths topics are covered in Third Year?

Linear equations, coordinate geometry, functions, trigonometry, statistics, and algebraic reasoning - all essential for Leaving Cert preparation.

Third Year Maths Help for Leaving Cert Prep

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Third Year Maths Topics

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1. Number System and Radicals

1.1

Understanding the number systems

1.2

Prime factorisation

1.3

Greatest Common Factors (GCF)

1.4

Least Common Multiple (LCM)

1.5

Rational vs. Irrational numbers

1.6

Converting repeating decimals to fractions

2. Ratios, Rates, and Proportions

2.1

Ratios

2.2

Rates

2.3

Proportions

3. Percents

3.1

Representing percents

3.2

Percents, fractions, and decimals

3.3

Percent of a number

3.4

Adding and multiplying percents

3.5

Taxes, discounts, tips and more

3.6

Simple interest

4. Measuring Systems

4.1

Metric systems

4.2

Imperial systems

4.3

Conversions between metric and imperial systems

4.4

Conversions involve squares and cubic

5. Coordinates, Quadrants, and Transformations

5.1

Cartesian plane

5.2

Draw on coordinate planes

5.3

Introduction to transformations

5.4

Horizontal and vertical distances

6. Angles, Lines, and Transversals

6.1

Pairs of lines and angles

6.2

Parallel lines and transversals

6.3

Parallel line proofs

6.4

Perpendicular line proofs

7. Properties of Triangles

7.1

Classifying triangles

7.2

Isosceles and equilateral triangles

8. Circles

8.1

Circles and circumference

8.2

Angles in a circle

8.3

Arcs of a circle

8.4

Areas and sectors of circles

9. Congruent Triangles

9.1

Congruence and congruent triangles

9.2

Triangles congruent by SSS proofs

9.3

Triangles congruent by SAS and HL proofs

9.4

Triangles congruent by ASA and AAS proofs

10. Symmetry and Surface Area

10.1

Line symmetry

10.2

Rotational symmetry and transformations

10.3

Surface area of 3-dimensional shapes

11. Scale Factors and Similarity

11.1

Enlargements and reductions with scale factors

11.2

Scale diagrams

11.3

Similar triangles

11.4

Similar polygons

12. Pythagorean Theorem

12.1

Squares and square roots

12.2

Pythagorean theorem

12.3

Estimating square roots

12.4

Using the pythagorean relationship

12.5

Applications of pythagorean theorem

13. Introduction to 3-Dimensional Figures

13.1

Introduction to surface area of 3-dimensional shapes

13.2

Nets of 3-dimensional shapes

13.3

Surface area of prisms

13.4

Surface area of cylinders

14. Volume

14.1

Introduction to volume

14.2

Volume of prisms

14.3

Volume of cylinders

14.4

Word problems relating volume of prisms and cylinders

15. Introduction to Trigonometry

15.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

)

15.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

)

15.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

)

15.4

Combination of SohCahToa questions

15.5

Solving expressions using 45-45-90 special right triangles

15.6

Solving expressions using 30-60-90 special right triangles

15.7

Word problems relating ladder in trigonometry

15.8

Word problems relating guy wire in trigonometry

15.9

Other word problems relating angles in trigonometry

16. Patterns and Solving Equations

16.1

Patterns

16.2

Evaluating algebraic expressions

16.3

Solving one - step equations: x + a = b

16.4

Graphing linear relations

17. Introduction to Linear Relations

17.1

Representing patterns in linear relations

17.2

Reading linear relation graphs

17.3

Solving linear equations by graphing

18. Linear Inequalities

18.1

Express linear inequalities graphically and algebraically

18.2

Solving one-step linear inequalities

18.3

Solving multi-step linear inequalities

18.4

Compound inequalities

19. Introduction to Relations and Functions

19.1

Relationship between two variables

19.2

Understand relations between x- and y-intercepts

19.3

Domain and range of a function

19.4

Identifying functions

19.5

Function notation

20. Data and Graphs

20.1

Reading and drawing bar graphs

20.2

Reading and drawing histograms

20.3

Reading and drawing line graphs

20.4

Box-and-whisker plots and scatter plots

20.5

Stem-and-leaf plots

20.6

Circle graphs

20.7

Reading and drawing Venn diagrams

20.8

Frequency tables and dot plots

21. Linear Functions

21.1

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

21.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

21.3

Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

21.4

Gradient intercept form: y = mx + b

21.5

General form: Ax + By + C = 0

21.6

Gradient-point form:

y - y_1 = m (x - x_1)

21.7

Rate of change

21.8

Graphing linear functions using table of values

21.9

Graphing linear functions using x- and y-intercepts

21.10

Graphing from gradient-intercept form y=mx+b

21.11

Graphing linear functions using a single point and gradient

21.12

Word problems of graphing linear functions

21.13

Parallel and perpendicular lines in linear functions

21.14

Applications of linear relations

22. Linear Equations

22.1

Introduction to linear equations

22.2

Introduction to nonlinear equations

22.3

Special case of linear equations: Horizontal lines

22.4

Special case of linear equations: Vertical lines

22.5

Parallel line equation

22.6

Perpendicular line equation

22.7

Combination of both parallel and perpendicular line equations

22.8

Applications of linear equations

23. Solving Simultaneous Equations

23.1

Determining number of solutions to linear equations

23.2

Solving simultaneous equations by graphing

23.3

Solving simultaneous equations by elimination

23.4

Solving simultaneous equations by substitution

23.5

23.6

Unknown number related questions in linear equations

23.7

Distance and time related questions in linear equations

23.8

Rectangular shape related questions in linear equations

24. Exponents

24.1

Product rule of exponents

24.2

Quotient rule of exponents

24.3

Power of a product rule

24.4

Power of a quotient rule

24.5

Power of a power rule

24.6

Negative exponent rule

24.7

Combining the exponent rules

24.8

Scientific notation

24.9

Convert between radicals and rational exponents

24.10

Solving for exponents

25. Quadratic Functions

25.1

Characteristics of quadratic functions

25.2

Transformations of quadratic functions

25.3

Quadratic function in general form: y = ax^2 + bx + c

25.4

Quadratic function in vertex form: y = a(x-p)^2 + q

25.5

Completing the square

25.6

Converting from general to vertex form by completing the square

25.7

Shortcut: Vertex formula

25.8

Graphing parabolas for given quadratic functions

25.9

Finding the quadratic functions for given parabolas

25.10

Applications of quadratic functions

26. Polynomials

26.1

Characteristics of polynomials

26.2

Equivalent expressions of polynomials

26.3

Adding and subtracting polynomials

27. Operations of Polynomials

27.1

What is a polynomial?

27.2

Using algebra tiles to factorise polynomials

28. Factorising Polynomial expressions

28.1

Common factors of polynomials

28.2

Factorising polynomials by grouping

28.3

Solving polynomials with the unknown "b" from x^2 + bx + c

28.4

Solving polynomials with the unknown "c" from x^2 + bx + c

28.5

Factorising polynomials: x^2 + bx + c

28.6

Applications of polynomials: x^2 + bx + c

28.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

28.8

Factorising polynomials:

ax^2 + bx + c

28.9

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

28.10

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

28.11

Evaluating polynomials

28.12

Solving polynomial equations

28.13

Word problems of polynomials

29. Radicals

29.1

Square and square roots

29.2

Cubic and cube roots

29.3

Evaluating and simplifying radicals

29.4

Converting radicals to mixed radicals

29.5

Converting radicals to entire radicals

29.6

Adding and subtracting radicals

29.7

Multiplying and dividing radicals

29.8

Rationalize the denominator

30. Rational Expressions

30.1

Simplifying rational expressions and restrictions

30.2

Adding and subtracting rational expressions

30.3

Multiplying rational expressions

30.4

Dividing rational expressions

30.5

Solving rational equations

30.6

Applications of rational equations

30.7

Simplifying complex fractions

30.8

Partial fraction decomposition

31. Reciprocal Functions

31.1

Graphing reciprocals of linear functions

31.2

Graphing reciprocals of quadratic functions

32. Probability

32.1

Determining probabilities using tree diagrams and tables

32.2

Probability of independent events

32.3

Probability with Venn diagrams

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