LEAVING CERT HIGHER LEVEL · MATHS
2015 — Paper 1
300 marks · fully worked video solutions
Section A · Concepts & Skills
Q125 marks
Sequences & SeriesProofs
📚 2 relevant video tutorials
Q325 marks
Area & VolumeIntegration
📚 4 relevant video tutorials
AVM 1.3 — Area, Volume & Measurement Trapezoidal Rule (the page-12 log-tables formula `A = (h/2)[y₁ + yₙ + 2(y₂ + y₃ + … + yₙ₋₁)]` for estimating areas of irregular shapes, Paul's key insight that 'we're pretending each strip is a rectangle' as the load-bearing approximation, and the canonical exam pattern of pairing the trapezoidal estimate with an exact integration check to compare estimate vs actual)Functions and Graphs 9 — Drawing GraphsIntegration 1 — AlgebraIntegration 7 — Integration with Limits
Q425 marks
Complex NumbersSequences & Series
📚 2 relevant video tutorials
Q525 marks
AlgebraDifferentiation
Q625 marks
Financial Maths
Section B · Contexts & Applications
Q750 marks
DifferentiationAlgebraCoordinate Geometry
Q850 marks
Differentiation
📚 3 relevant video tutorials
Differentiation 20 — Rate ProblemsAVM 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.)Functions and Graphs 9 — Drawing Graphs
Q950 marks
TrigonometryDifferentiationIntegration