LEAVING CERT HIGHER LEVEL · MATHS

2023 — Paper 1

300 marks · full worked video solutions by Paul

📄 View exam paper ☑ Marking scheme

Section A · Concepts & Skills

Q130 marks

Algebra

📚 3 tutorials for this question

Algebra 15 — Modulus Equations Algebra 14 — Manipulation of Formula Algebra 13 — Long Division

Q230 marks

DifferentiationSequences & SeriesFunctions & Graphs

📚 5 tutorials for this question

Differentiation 15 — Turning Points / Max & Min Points Differentiation 1 — Introduction Sequences & Series 14 — Convergence, Divergence, Continuity and Limits Functions and Graphs 10 — Limits Functions and Graphs 3 — Vertex Form / Completing the Square

Q330 marks

ProofsNumber TheoryIndices & Logs

📚 4 tutorials for this question

Paper 1 Proofs §1 — Prove √2 is irrational Number Theory 3 — Proof by Contradiction: √2 is Irrational Indices and Logs 4 — Changing the Base Indices and Logs 2 — Rules of Logs Part 1

Q430 marks

Complex Numbers

📚 7 tutorials for this question

Complex Numbers 8 — Quadratic Equations with Complex Roots Complex Numbers 2 — Addition, Subtraction, Multiplication Complex Numbers 14 — Using De Moivre’s Theorem to Find More Than One Answer Complex Numbers 13 — Converting to Polar Form and Applying De Moivre’s Theorem Complex Numbers 10 — Introduction to Polar Form Complex Numbers 7 — Rotations on the Argand Plane Complex Numbers 5 — Modulus and Conjugates

Q530 marks

DifferentiationFunctions & Graphs

📚 9 tutorials for this question

Differentiation 8 — Chain Rule Differentiation 1 — Introduction Differentiation 7 — Quotient Rule Differentiation 6 — Product Rule Differentiation 3 — Trigonometric Functions Differentiation 9 — Logs Functions and Graphs 4 — Composite Functions Functions and Graphs 5 — Injective Functions Functions and Graphs 6 — Surjective Functions

Q630 marks

AlgebraIntegrationIndices & Logs

📚 6 tutorials for this question

Algebra 2 — Factorising Quadratics Integration 12 — Area between a curve and the x-axis Integration 7 — Integration with Limits Integration 1 — Algebra Integration 3 — Exponentials Indices and Logs 5 — Unknown in the Power / Natural Log

Section B · Contexts & Applications

Q750 marks

DifferentiationAlgebraIntegration

📚 9 tutorials for this question

Differentiation 18 — Rates of Change Differentiation 1 — Introduction Differentiation 15 — Turning Points / Max & Min Points Algebra 9 — Nature of Quadratic Graphs Differentiation 13 — Second Derivative Integration 11 — Average Value Integration 7 — Integration with Limits Integration 1 — Algebra Differentiation 14 — Slopes

Q850 marks

Financial MathsSequences & SeriesProbability

📚 6 tutorials for this question

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)Sequences and Series 5 — Geometric Sequences 1 Probability 9 — Relative Frequency and Expected Value

Q950 marks

Number TheoryFunctions & GraphsDifferentiation

📚 4 tutorials for this question

Number Theory 2 — Prime Factorisation Functions and Graphs 9 — Drawing Graphs Differentiation 14 — Slopes Differentiation 8 — Chain Rule

Q1050 marks

IntegrationSequences & SeriesAlgebraDifferentiation

📚 8 tutorials for this question

Integration 12 — Area between a curve and the x-axis Sequences and Series 1 — Arithmetic Sequences 1 Algebra 6 — Inequalities Integration 7 — Integration with Limits Integration 1 — Algebra Differentiation 20 — Rate Problems Differentiation 8 — Chain Rule Differentiation 18 — Rates of Change