LEAVING CERT HIGHER LEVEL · MATHS
2017 — Paper 2
300 marks · fully worked video solutions
Section A · Concepts & Skills
Q125 marks
ProbabilityIndices & Logs
Q225 marks
StatisticsDifferentiationProbability
📚 1 tutorial for this question
Q325 marks
Coordinate Geometry
Q425 marks
Coordinate GeometryTrigonometry
📚 1 tutorial for this question
Q525 marks
GeometryArea & Volume
📚 2 relevant video tutorials
Geometry 1.16 — Similar Triangles (applications: the 'write out three fractions, then eliminate the irrelevant one' workflow, the colour-coded opposite-angle technique for matching corresponding sides, and the semicircle 'bridge through a third triangle' pattern that's the most common exam setup)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.)
Q625 marks
GeometryTrigonometry
📚 2 relevant video tutorials
Section B · Contexts & Applications
Q740 marks
Cones in a Cylinder vs. Sphere
TrigonometryCoordinate GeometryGeometry
📚 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.)Geometry 1.16 — Similar Triangles (applications: the 'write out three fractions, then eliminate the irrelevant one' workflow, the colour-coded opposite-angle technique for matching corresponding sides, and the semicircle 'bridge through a third triangle' pattern that's the most common exam setup)Trigonometry 1.1 — Pythagoras Theorem
Q860 marks
Normal Distribution + Galway Rain Tree
StatisticsProbability
Q950 marks
Tree Across the River
TrigonometryAlgebraProbability
📚 3 relevant video tutorials