What topics are covered in Transition Year Maths?

Our TY Maths course covers algebra, geometry, statistics, trigonometry, and number systems aligned with the Irish curriculum.

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Is StudyPug aligned with the Irish curriculum?

Yes, our Transition Year Maths content follows Irish curriculum standards so you learn exactly what's covered in your TY programme.

Can I use StudyPug to prepare for TY maths exams?

Absolutely! Practice with unlimited problems, use diagnostic tests to find weak spots, and review video lessons before your exams.

How do I know which maths topics to focus on?

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Are the video lessons taught by real teachers?

Yes, all lessons are taught by certified maths teachers who explain concepts step-by-step in a clear, easy-to-understand way.

Can I practice TY maths problems at my own level?

Yes! Our adaptive practice problems adjust to your skill level, getting progressively harder as you improve and master concepts.

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Transition 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. 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

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

ax^2 + bx + c

12.8

Factorising polynomials:

ax^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 =

\frac{o}{h}

)

25.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

)

25.3

Use tangent ratio to calculate angles and sides (Tan =

\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

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