LEAVING CERT HIGHER LEVEL · MATHS

2019 — Paper 1

300 marks · fully worked video solutions

📄 View exam paper ☑ Marking scheme

Section A · Concepts & Skills

Q125 marks

Algebra

📚 1 tutorial for this question

Algebra 4 — Revision Of Junior Cert Fractions

Q225 marks

Functions & GraphsInduction

📚 2 relevant video tutorials

Functions and Graphs 9 — Drawing Graphs Induction 2 — Inequalities

Q325 marks

AlgebraIndices & LogsNumber TheoryDifferentiation

📚 4 relevant video tutorials

Algebra 1 — Revision Of Junior Cert Factorising Differentiation 6 — Product Rule Differentiation 9 — Logs Indices and Logs 2 — Rules of Logs Part 1

Q425 marks

IntegrationAlgebra

📚 3 relevant video tutorials

Algebra 11 — Solving Cubic Equations Integration 1 — Algebra Integration 8 — Finding f(x) When Given the Slope

Q525 marks

Complex Numbers

📚 3 relevant video tutorials

Complex Numbers 10 — Introduction to Polar Form Complex Numbers 14 — Using De Moivre's theorem to find more than one answer Complex Numbers 8 — Quadratic Equations with Complex Roots (conjugate-pair theorem, sum-and-product, non-real coefficients)

Q625 marks

AlgebraStatisticsNumber TheoryProofs

📚 3 relevant video tutorials

Number Theory 3 — Proof by Contradiction: √2 is Irrational Indices and Logs 1 — Junior Cert Revision (Powers and Surds)Statistics 3 — Mean, Mode, Median, Range, IQR, Standard Deviation, Percentiles (LOAD-BEARING summary statistics video; page 33 SD formula; 50:31 longest in Statistics strand)

Section B · Contexts & Applications

Q745 marks

Sequences & SeriesFunctions & Graphs

📚 2 relevant video tutorials

Sequences and Series 5 — Geometric Sequences 1 Sequences and Series 8 — Geometric Sequences 4

Q850 marks

Differentiation

📚 4 relevant video tutorials

Differentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)Differentiation 16 — Increasing / Decreasing Curves Differentiation 3 — Trigonometric Functions Trigonometry 2.3 — Radians and the Unit Circle

Q955 marks

AlgebraCoordinate GeometryDifferentiation

📚 5 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 14 — Manipulation of Formula Differentiation 1 — Introduction Differentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)Functions and Graphs 9 — Drawing Graphs