LEAVING CERT HIGHER LEVEL · MATHS

2023 — Paper 1

300 marks · fully worked video solutions

📄 View exam paper ☑ Marking scheme

Section A · Concepts & Skills

Q130 marks

Algebra

📚 3 relevant video tutorials

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

Q230 marks

DifferentiationSequences & SeriesFunctions & Graphs

📚 3 relevant video tutorials

Functions and Graphs 10 — Limits, convergence, divergence, continuity Functions and Graphs 2 — Shapes of Quadratic Functions Differentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)

Q330 marks

ProofsNumber TheoryIndices & Logs

📚 3 relevant video tutorials

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

Q430 marks

Complex Numbers

📚 4 relevant video tutorials

Complex Numbers 7 — Rotations on the Argand Plane (multiplying by ±i, collinearity, parallelogram rule)Complex Numbers 14 — Using De Moivre's theorem to find more than one answer Complex Numbers 4 — Argand Plane and Modulus Complex Numbers 8 — Quadratic Equations with Complex Roots (conjugate-pair theorem, sum-and-product, non-real coefficients)

Q530 marks

DifferentiationFunctions & Graphs

📚 6 relevant video tutorials

Differentiation 6 — Product Rule Differentiation 7 — Quotient Rule Differentiation 8 — Chain Rule Functions and Graphs 4 — Composite functions Functions and Graphs 5 — Injective Functions Functions and Graphs 6 — Surjective Functions

Q630 marks

AlgebraIntegrationIndices & Logs

📚 4 relevant video tutorials

Algebra 2 — Factorising Quadratic Equations Integration 12 — Area between a curve and the x-axis Integration 3 — Exponentials Integration 7 — Integration with Limits

Section B · Contexts & Applications

Q750 marks

DifferentiationAlgebraIntegration

📚 4 relevant video tutorials

Differentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)Differentiation 17 — Points of Inflection Differentiation 18 — Rates of Change (Distance/Displacement → Speed/Velocity → Acceleration; physics-flavoured first-and-second-derivative application)Integration 11 — Average Value

Q850 marks

Financial MathsSequences & SeriesProbability

📚 5 relevant video tutorials

Financial Maths 3 — Time Value of Money Financial Maths 5 — Annuities (Saving Money) — geometric-series application of compound interest across multiple periodic investments Financial Maths 2 — Compound Interest Financial Maths 4 — Converting Interest Rates from Monthly to Yearly etc.Probability 9 — Relative Frequency And Expected Value

Q950 marks

Number TheoryFunctions & GraphsDifferentiation

📚 3 relevant video tutorials

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

Q1050 marks

IntegrationSequences & SeriesAlgebraDifferentiation

📚 4 relevant video tutorials

Differentiation 20 — Rate Problems Integration 1 — Algebra Integration 7 — Integration with Limits Sequences and Series 1 — Arithmetic Sequences 1