LEAVING CERT HIGHER LEVEL · MATHS

2021 — Paper 1

COVID-adjusted sitting · 220 marks · fully worked video solutions

📄 View exam paper
☑ Marking scheme

Section A · Concepts & Skills — answer any 4

Q130 marks

Complex Numbers

Complex NumbersAlgebra

📚 3 relevant video tutorials

Complex Numbers 14 — Using De Moivre's theorem to find more than one answer Complex Numbers 3 — Division and Conjugates Complex Numbers 6 — Equating Coefficients (🎯 LOAD-BEARING TECHNIQUE; one complex equation becomes two real equations; first corpus instance of treat-as-quadratic-in-substitution + first explicit anti-pattern directive)

Q230 marks

Algebra

Solution coming soon

📚 3 relevant video tutorials

Algebra 11 — Solving Cubic Equations Algebra 13 — Long Division Algebra 15 — Modulus Equations

Q330 marks

Cuboid Volume + Logs Quadratic

AlgebraIndices & Logs

📚 3 relevant video tutorials

AVM 1.1 — Area, Volume & Measurement JC Revision (🏁 §10 Measurement strand-opener: comprehensive shape-formula recap for the LCHL course. 🚨 LOAD-BEARING — Paul opens with the framing that AVM is NOT a stand-alone topic at LCHL: 'it pops up in differentiation, it pops up in integration, it pops up in different parts of the course.' Treat this lesson as a FORMULA TOOLKIT to be applied wherever shape calculations appear elsewhere. Covers the full inventory: 🎯 2D shapes (square, rectangle, triangle, circle — page 8 log tables) and 🎯 3D shapes (cube, rectangular block, cylinder, cone, sphere — page 10 log tables), with 🚨 LOAD-BEARING insights: (1) 'consistent-cross-section' rule — Volume = (area of base) × height works for cylinder/rectangular block/triangular prism BUT NOT for cone (because the cross-section shrinks); (2) cone has THREE dimensions (radius R, perpendicular height h, slant height L) related by Pythagoras (R² + h² = L²) — if you know two you can find the third; (3) sphere has only ONE dimension (R). Three worked questions: Q1 cylinder (V → R → CSA), Q2 cone (CSA + L → R → h via Pythagoras → V), Q3 sphere (A → R → V). All three reduce to the same skeleton: use one formula to find a missing dimension, then sub into another formula.)Algebra 2 — Factorising Quadratic Equations Indices and Logs 6 — Quadratic Equations 1

Q430 marks

Induction + Arithmetic Sequence

InductionSequences & SeriesNumber Theory

📚 2 relevant video tutorials

Sequences and Series 1 — Arithmetic Sequences 1 Induction 4 — Divisibility

Q530 marks

Differentiation

DifferentiationFunctions & GraphsAlgebra

📚 5 relevant video tutorials

Algebra 6 — Inequalities Differentiation 1 — Introduction Differentiation 14 — Slopes Differentiation 3 — Trigonometric Functions Functions and Graphs 3 — Vertex form / Completing the square (algebraic technique)

Q630 marks

Derivative-from-Graph + Max Slope + Anti-derivative

AlgebraFunctions & GraphsDifferentiationIntegration

📚 2 relevant video tutorials

Differentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)Integration 8 — Finding f(x) When Given the Slope

Section B · Contexts & Applications — answer any 2

Q750 marks

Pendulum / Geometric Series

Sequences & SeriesIndices & LogsAlgebraTrigonometry

📚 3 relevant video tutorials

Sequences and Series 5 — Geometric Sequences 1 Sequences and Series 8 — Geometric Sequences 4 Trigonometry 1.8 — Sector of a Circle

Q850 marks

Rollercoaster Cubic

AlgebraFunctions & GraphsDifferentiationIntegration

📚 5 relevant video tutorials

Differentiation 1 — Introduction Differentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)Differentiation 17 — Points of Inflection Functions and Graphs 9 — Drawing Graphs Integration 11 — Average Value

Q950 marks

Coffee Cooling (Exponential Model + Related Rates)

DifferentiationIndices & Logs

📚 3 relevant video tutorials

Differentiation 20 — Rate Problems Differentiation 5 — Exponentials Indices and Logs 5 — Unknown in the Power / The Natural Log

Q1050 marks

Water Tank + Tree Growth

AlgebraDifferentiation

📚 3 relevant video tutorials

Differentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)Algebra 2 — Factorising Quadratic Equations Differentiation 18 — Rates of Change (Distance/Displacement → Speed/Velocity → Acceleration; physics-flavoured first-and-second-derivative application)