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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. Adding and Subtracting Integers

2.1 Introduction to integer addition
2.2 Adding integers
2.3 Introduction to integer subtraction
2.4 Subtracting integers
2.5 Application of integer operations

3. Multiplying and Dividing Integers

3.1 Understanding integer multiplication
3.2 Multiplying integers
3.3 Understanding integer division
3.4 Dividing integers
3.5 Applications of integer operations

4. Rational Numbers

4.1 Comparing and ordering rational numbers
4.2 Solving problems with rational numbers in decimal form
4.3 Solving problems with rational numbers in fraction form
4.4 Determine square roots of rational numbers

5. Solving Linear Equations

5.1 Solving linear equations using multiplication and division
5.2 Solving two-step linear equations: ax + b = c, x/a + b = c
5.3 Solving linear equations using distributive property: a(x + b) = c
5.4 Solving linear equations with variables on both sides
5.5 Solving literal equations

6. Linear Inequalities

6.1 Express linear inequalities graphically and algebraically
6.2 Solving one-step linear inequalities
6.3 Solving multi-step linear inequalities
6.4 Compound inequalities

7. Solving Simultaneous Equations

7.1 Determining number of solutions to linear equations
7.2 Solving simultaneous linear equations by graphing
7.3 Solving simultaneous linear equations by elimination
7.4 Solving simultaneous linear equations by substitution
7.5 Money related questions in linear equations
7.6 Unknown number related questions in linear equations
7.7 Distance and time related questions in linear equations
7.8 Rectangular shape related questions in linear equations

8. Exponents

8.1 Product rule of exponents
8.2 Quotient rule of exponents
8.3 Power of a product rule
8.4 Power of a quotient rule
8.5 Power of a power rule
8.6 Negative exponent rule
8.7 Combining the exponent rules
8.8 Scientific notation
8.9 Convert between radicals and rational exponents
8.10 Solving for exponents

9. Exponential Functions

9.1 Exponents: Product rule (a^x)(a^y) = a^(x+y)
9.2 Exponents: Division rule (a^x / a^y) = a^(x-y)
9.3 Exponents: Power rule (a^x)^y = a^(x * y)
9.4 Exponents: Negative exponents
9.5 Exponents: Zero exponent: a^0 = 1
9.6 Exponents: Rational exponents
9.7 Solving exponential equations using exponent rules
9.8 Graphing exponential functions
9.9 Graphing transformations of exponential functions
9.10 Finding an exponential function given its graph

10. Exponential Growth and Decay

10.1 Exponential growth and decay by a factor
10.2 Exponential decay: Half-life
10.3 Exponential growth and decay by percentage
10.4 Continuous growth and decay

11. Operations of Polynomials

11.1 What is a polynomial?
11.2 Polynomial components
11.3 Multiplying monomial by monomial
11.4 Multiplying monomial by binomial
11.5 Multiplying binomial by binomial
11.6 Multiplying polynomial by polynomial
11.7 Applications of polynomials

12. Factorising Polynomial expressions

12.1 Common factors of polynomials
12.2 Factorising polynomials by grouping
12.3 Solving polynomials with the unknown "b" from x^2 + bx + c
12.4 Solving polynomials with the unknown "c" from x^2 + bx + c
12.5 Factorising polynomials: x^2 + bx + c
12.6 Applications of polynomials: x^2 + bx + c
12.7 Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
12.8 Factorising polynomials: ax2+bx+cax^2 + bx + c
12.9 Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
12.10 Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
12.11 Evaluating polynomials
12.12 Using algebra tiles to factorise polynomials
12.13 Solving polynomial equations
12.14 Word problems of polynomials

13. Factorising Quadratic Functions

13.1 Factorise by taking out the greatest common factor
13.2 Factorise by grouping
13.3 Factorising difference of squares: x^2 - y^2
13.4 Factorising trinomials
13.5 Factoring difference of cubes
13.6 Factoring sum of cubes

14. Quadratic Functions

14.1 Characteristics of quadratic functions
14.2 Transformations of quadratic functions
14.3 Quadratic function in general form: y = ax^2 + bx + c
14.4 Quadratic function in vertex form: y = a(x-p)^2 + q
14.5 Completing the square
14.6 Converting from general to vertex form by completing the square
14.7 Shortcut: Vertex formula
14.8 Graphing parabolas for given quadratic functions
14.9 Finding the quadratic functions for given parabolas
14.10 Applications of quadratic functions

15. Radicals

15.1 Square and square roots
15.2 Cubic and cube roots
15.3 Evaluating and simplifying radicals
15.4 Converting radicals to mixed radicals
15.5 Converting radicals to entire radicals
15.6 Adding and subtracting radicals
15.7 Multiplying and dividing radicals
15.8 Rationalize the denominator

16. Rational Expressions

16.1 Simplifying rational expressions and restrictions
16.2 Adding and subtracting rational expressions
16.3 Multiplying rational expressions
16.4 Dividing rational expressions
16.5 Solving rational equations
16.6 Applications of rational equations
16.7 Simplifying complex fractions
16.8 Partial fraction decomposition

17. Reciprocal Functions

17.1 Graphing reciprocals of linear functions
17.2 Graphing reciprocals of quadratic functions

18. Coordinates, Quadrants, and Transformations

18.1 Cartesian plane
18.2 Draw on coordinate planes
18.3 Introduction to transformations
18.4 Horizontal and vertical distances

19. Angles, Lines and Transversals

19.1 Pairs of lines and angles
19.2 Parallel lines and transversals
19.3 Parallel line proofs
19.4 Perpendicular line proofs

20. Properties of Triangles

20.1 Classifying triangles
20.2 Isosceles and equilateral triangles

21. Circles

21.1 Circles and circumference
21.2 Angles in a circle
21.3 Arcs of a circle
21.4 Areas and sectors of circles

22. Congruent Triangles

22.1 Congruence and congruent triangles
22.2 Triangles congruent by SSS proofs
22.3 Triangles congruent by SAS and HL proofs
22.4 Triangles congruent by ASA and AAS proofs

23. Scale Factors and Similarity

23.1 Enlargements and reductions with scale factors
23.2 Scale diagrams
23.3 Similar triangles
23.4 Similar polygons

24. Pythagorean Theorem

24.1 Squares and square roots
24.2 Pythagorean theorem
24.3 Estimating square roots
24.4 Using the pythagorean relationship
24.5 Applications of pythagorean theorem

25. Introduction to Trigonometry

25.1 Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
25.2 Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
25.3 Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
25.4 Combination of SohCahToa questions
25.5 Solving expressions using 45-45-90 special right triangles
25.6 Solving expressions using 30-60-90 special right triangles
25.7 Word problems relating ladder in trigonometry
25.8 Word problems relating guy wire in trigonometry
25.9 Other word problems relating angles in trigonometry

26. Surface Area and Volume

26.1 Surface area and volume of prisms
26.2 Surface area and volume of pyramids
26.3 Surface area and volume of cylinders
26.4 Surface area and volume of cones
26.5 Surface area and volume of spheres

27. Probability

27.1 Determining probabilities using tree diagrams and tables
27.2 Probability of independent events
27.3 Fundamental counting principle
27.4 Factorial notation
27.5 Probability with Venn diagrams

28. Data and Graphs

28.1 Reading and drawing bar graphs
28.2 Reading and drawing histograms
28.3 Reading and drawing line graphs
28.4 Box-and-whisker plots and scatter plots
28.5 Stem-and-leaf plots
28.6 Pie charts
28.7 Reading and drawing Venn diagrams
28.8 Frequency tables and dot plots

29. Statistics

29.1 Median and mode
29.2 Mean
29.3 Range and outliers
29.4 Application of averages

29 Chapters · 174 Topics · 1240 Videos

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Yes — our Transition Year Maths content covers all major topics regardless of textbook, aligned to standard Irish secondary school curriculum.

What topics are covered in Transition Year Maths?

We cover algebra, geometry, statistics, trigonometry, number systems, and all core topics in the Irish Transition Year programme.

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