Leaving Cert Higher Level Maths

LCHL Maths

226 tutorials covering the LCHL Maths course.

Try out our FREE Algebra course and if you like what you see, sign up for the entire course today. Exam solutions for each topic are available for FREE below.

Our tutorials are available to help you every step of the way on your LCHL Maths journey. Additionally you can Contact us for advice today.

Additionally, for reference see the LCHL Maths Syllabus here. Our content is specifically tailored to ensure students are prepared for exam questions.

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Paper 1

LCHL Maths – Algebra 23 Lessons Sample Topic

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Algebra 1 – Revision of Junior Cert factorising

Algebra 2 – Factorising quadratic equations

Algebra 3 – Factorising the sum of two cubes and difference of two cubes

Algebra 4 – Revision of Junior Cert fractions

Algebra 5 – Fractions Part 2

Algebra 6 – Inequalities

Algebra 7 – Rational Inequalities

Algebra 8 – Quadratic graphs

Algebra 9 – Nature of quadratic graphs

Algebra 10 – Generating a cubic equation given the roots

Algebra 11 – Solving cubic equations

Algebra 12 – Nature of cubic roots

Algebra 13 – Long division

Algebra 14 – Manipulation of formula

Algebra 15 – Modulus Equations

Algebra 16 – Modulus graphs

Algebra 17 – Surd equations

Algebra 18 – Simultaneous equations in three variables

Algebra 19 – Simultaneous Equations by substitution

Algebra 20 – Pascal’s triangle

Algebra 21 – Binomial Theorem

Algebra 22 – Abstract Inequalities

Algebra 23 – Iterative equations

LCHL Maths – Algebra Exam Questions 1 Lesson Sample Topic

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Algebra Exam Questions

LCHL Maths – Number Theory 5 Lessons

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Number Theory 1 – Types of numbers

Number Theory 2 – Prime Factorisation

Number Theory 3 Proof by contradiction: Prove root 2 is irrational

Number Theory 4 Construct √2

Number Theory 5 – Construct √3

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Number Theory Exam Questions

LCHL Maths – Indices and Logs 8 Lessons

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Indices and Logs 1 – JC revision

Indices and Logs 2 – Rules of logs Part 1

Indices and Logs 3 – Rules of logs part 2

Indices and Logs 4 – Changing the base

Indices and Logs 5 – Unknown in the power/ the natural log

Indices and Logs 6 – Quadratic Equations 1

Indices and Logs 7 – Quadratic Equations 2

Indices and Logs 8: Log Problems

LCHL Maths – Indices and Logs Exam Questions 1 Lesson Sample Topic

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Indices and Logs Exam Questions

LCHL Maths – Functions and Graphs 10 Lessons

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Functions and Graphs 1: JC Revision

Functions and Graphs 2: Shapes of Quadratic Functions

Functions and Graphs 3 – Vertex form/Completing the square

Functions and Graphs 4: Composite functions

Functions and Graphs 5: Injective Functions

Functions and Graphs 6: Surjective Functions

Functions and Graphs 7 – Bijective Functions

Functions and Graphs 8: Inverse functions

Functions and Graphs 9: Drawing Graphs

Functions and Graphs 10: Limits, convergence, divergence, continuity

LCHL Maths – Functions and Graphs Exam Questions 1 Lesson Sample Topic

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Functions and Graphs Exam Questions

LCHL Maths – Sequences and Series, Patterns and Limits 15 Lessons

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Introduction

Patterns 1: Quadratic Patterns

Patterns 2: Cubic patterns

Sequences and Series 1: Arithmetic Sequences 1

Sequences and Series 2: Arithmetic Sequences 2

Sequences and Series 3: Arithmetic sequences 3

Sequences and Series 4: Arithmetic Sequences 4

Sequences and Series 5: Geometric Sequences 1

Sequences and Series 6: Geometric Sequences 2

Sequences and Series 7: Geometric Sequences 3

Sequences and Series 8 : Geometric Sequences 4

Sequences and series 9: Geometric Sequences 5

Sequences and Series 10: Prove the Sum of Geometric Series by induction

Convergence, Divergence, Continuity and Limits

Proof of Sum to infinity of Geometric sequences

LCHL Maths – Sequences and Series, Patterns and Limits Exam Questions 1 Lesson Sample Topic

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Sequences and Series, Patterns, and Limits Exam Questions

LCHL Maths – Differentiation 21 Lessons

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Differentiation 1 – Introduction

Differentiation 2 – First Principles

Differentiation 3 – Trigonometric Functions

Differentiation 4 – PTA

Differentiation 5 – Exponentials

Differentiation 6 – Product Rule

Differentiation 7 – Quotient Rule

Differentiation 8 – Chain Rule

Differentiation 9 – Logs

Differentiation 10 – Implicit Differentiation

Differentiation 11 – Inverse Trig

Differentiation 12 – Substitution

Differentiation 13 – The Second Derivative

Differentiation 14 – Slopes

Differentiation 15 – Turning points/Maximum and Minimum points

Differentiation 16 – Increasing/ Decreasing Curves

Differentiation 17 – Points of Inflection

Differentiation 18 – Rates of Change (Displacement, Velocity, Acceleration)

Differentiation 19 – Tan of the angle made with the horizontal

Differentiation 20 – Rate Problems

Differentiation 21 – Shapes of derivatives

LCHL Maths – Differentiation Exam Questions 1 Lesson Sample Topic

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Differentiation Exam Questions

LCHL Maths – Integration 13 Lessons

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Integration 1 – Algebra

Integration 2 – Integrating 1/x

Integration 3 – Exponentials

Integration 4 – Integrating a constant to the power of an unknown

Integration 5 – Trigonometry 1

Integration 6 – Trigonometry (II)

Integration 7- Integration with limits

Integration 8 – Finding f(x) when given the slope

Integration 9 – Distance, Speed, Acceleration

Integration 10 – Anti- Derivatives

Integration 11 – Average value

Integration 12 – Area between a curve and the x- axis

Integration 13 – Area between a curve and the y-axis

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Integration Exam Questions

LCHL Maths – Financial Maths 8 Lessons

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Financial Maths 1 – Simple Interest

Financial Maths 2 – Compound Interest

Financial Maths 3 – Time value of money

Financial Maths 4 – Converting interest rates from monthly to yearly etc.

Financial Maths 5 – Annuities ( Saving Money)

Financial Maths 6 – Annuities (Paying Money Back)

Financial Maths 7 – Proof of Amortization formula

Financial Maths 8 – Pensions

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Financial Maths Exam Questions

LCHL Maths – Complex Numbers 17 Lessons

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Complex Numbers 1 – Introduction

Complex Numbers 2 – Addition, Subtraction, Multiplication

Complex Numbers 3 – Division and Conjugates

Complex Numbers 4 – Argand Plane and Modulus

Complex Numbers 5 – Modulus and conjugates

Complex Numbers 6 – Equating Co-efficients

Complex Numbers 7 – Rotations

Complex Numbers 8 – Quadratic equations

Complex Numbers 9 – Cubic equations

Complex Numbers 10: Introduction to Polar Form

Complex Numbers 11 – Rules for Polar Form

Complex Numbers 12 – Introduction to De Moivres theorem

Complex Numbers 13 – Converting to polar form and applying De Moivres theorem

Complex Numbers 14 – Using De Moivres theorem to find more than one answer

Complex Numbers 15: Polar form, De Moivres theorem and fraction in the power

Complex Numbers 16 Proof of De Moivres Theorem by Induction

Complex Numbers 17 – Proof of Sin(3A) and Cos(3A)

LCHL Maths – Complex Numbers Exam Questions 1 Lesson Sample Topic

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Complex Numbers Exam Questions

LCHL Maths – Induction 7 Lessons

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Induction 1 – Introduction

Induction 2 – Inequalities

Induction 3- Factorials

Induction 4 – Divisibility

Induction 5 – Series

Induction 6 – Proof of De Moivre’s Theorem by induction

Induction 7 Proof by induction of the Sum of a geometric series

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Induction Exam Questions

LCHL Maths – Paper 1 Proofs 5 Lessons

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Proof 1 – Prove root 2 is irrational (Number theory)

Proof 2 – Prove by induction the sum of a geometric series

Proof 3 – Prove De Moivres theorem by induction

Proof 4 – Prove the Amortization formula (Financial maths)

Proof 5 – Prove Sum to Infinity formula (Geometric Sequences)

Paper 2

LCHL Maths – Statistics 21 Lessons

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Statistics 1 – Types of Data

Statistics 2 – Types of Sampling

Statistics 3 – Mean, Mode, Median, Range, Interquartile range, Standard Deviation, Percentiles

Statistics 4 – Basic Graphs

Statistics 5 – Scatter Graphs, correlation coefficient, line of best fit

Statistics 6 – Correlation versus causality

Statistics 7 – Skewed data

Statistics 8 – Empirical Rule

Statistics 9 – z-scores 1

Statistics 10 – z-scores 2

Statistics 11 z-scores 3

Statistics 12 z-scores 4

Statistics 13 z scores 5 (standardising formula)

Statistics 14 z scores 6 (standardising sample means)

Statistics 15- z scores 7

Statistics 16 – Margin of error

Statistics 17 – Confidence Intervals

Statistics 18 Central Limit Theorem, trends in population proportion

Statistics 19 – Hypothesis testing

Statistics 20 p-values and critical regions

Statistics 21 – Hypothesis testing and confidence intervals

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Statistics Exam Questions

LCHL Maths – Probability 9 Lessons

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Probability 1 – JC Revision

Probability 2 Mutually Exclusive and Not-Mutually Exclusive events

Probability 3 – Independent events and Conditional probability

Probability 4 – Factorials

Probability 5 – Permutations

Probability 6 – Combinations

Probability 7 – Twin Rule

Probability 8 – Bernoulli Trials

Probability 9 – Relative frequency and Expected value

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€199.99

Gain access to the entire Leaving Cert Higher Level Maths course until 1st July 2025 for only €199.99

Buy Now

About the tutor

Paul has a B.Sc in Pharmacy from Trinity College Dublin. After graduating, Paul made a Career change by completing his Masters in Education and has been teaching the current Maths course since its introduction.

In conjunction with his Teaching Career, Paul is a former Paralympic Athlete and volunteers as an Ambassador for the Gaisce President’s Award, motivating students and inspiring them to overcome obstacles along their journey towards adulthood.

Contact Paul:

paul@gktuition.ie 087-214 93 48

LCHL Maths

226 tutorials covering the LCHL Maths course.

Try out our FREE Algebra course and if you like what you see, sign up for the entire course today. Exam solutions for each topic are available for FREE below.

Our tutorials are available to help you every step of the way on your LCHL Maths journey. Additionally you can Contact us for advice today.

Additionally, for reference see the LCHL Maths Syllabus here. Our content is specifically tailored to ensure students are prepared for exam questions.

For reference see the LCHL Maths Syllabus here

€199.99

Gain access to the entire Leaving Cert Higher Level Maths course until 1st July 2025 for only €199.99

Buy Now

About the tutor

Paul has a B.Sc in Pharmacy from Trinity College Dublin. After graduating, Paul made a Career change by completing his Masters in Education and has been teaching Project Maths since its induction.

Contact Paul:

paul@gktuition.ie 087-214 93 48