LEAVING CERT HIGHER LEVEL · MATHS
2019 — Paper 2
300 marks · fully worked video solutions
Section A · Concepts & Skills
Q125 marks
Probability
📚 2 relevant video tutorials
Q325 marks
Coordinate GeometryAlgebra
📚 2 relevant video tutorials
The Circle 3 — Proving a point lies ON / INSIDE / OUTSIDE a circle (two diagnostic methods: SUB-THE-POINT for on-circle, DISTANCE-TO-CENTRE for inside/outside; plus the 🚨 LOAD-BEARING 'divide by leading coefficient' rule when x² and y² have coefficients other than 1)The Circle 6 — Circles With The Axes As A Tangent
Q425 marks
Trigonometry
📚 3 relevant video tutorials
Q525 marks
Geometry
📚 2 relevant video tutorials
Geometry 1.5 — Construction 22: Orthocentre (the §10 Synthetic Geometry view — same video as The Line 9; altitudes-intersection construction + coordinate-geometry treatment)Geometry 1.11 — Questions on Theorem 19 (Circle Questions) (🎯 the FIRST worked-examples tutorial in the strand: 5 exam-style problems applying Theorem 19 + Corollaries 2/3/4/5 + Theorem 20. 🚨 LOAD-BEARING — the canonical exam-question patterns: (1) inscribed-X configuration → identify two angles on same arc via Corollary 2 → triangle angle sum to get the unknown; (2) cyclic quadrilateral with diameter → angle-in-semicircle (Corollary 3) gives 90° → cyclic-quadrilateral opposite-angles-sum-180° (Corollary 5) closes; (3) multiple radii from centre → isosceles triangles (radii are equal) → base angles equal → subtract to find unknown; (4) tangent-tangent from external point → symmetric kite with two right angles (Theorem 20: tangent ⊥ radius) → central angle → halve via Theorem 19 to get inscribed angle; (5) algebraic angles → set up equation via Theorem 19 + Corollary 5 → solve for x. All 5 examples involve the same toolbox: arc-identification, angle-equality on same arc, isosceles-triangle base angles, cyclic-quad opposite-180°, central-vs-inscribed halving)
Q625 marks
ProbabilityAlgebra
📚 1 tutorial for this question
Section B · Contexts & Applications
Q750 marks
TrigonometryArea & VolumeGeometry
📚 6 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 TheoremTrigonometry 1.2 — Sin, Cos and TanTrigonometry 1.7 — Area of a Non-Right-Angled Triangle (`A = ½ ab sin C` on page 16; the third of the three non-right-angled-triangle formulae; the 🚨 LOAD-BEARING two-sides-plus-the-angle-between-them setup; the 🎯 sine-rule-or-cosine-rule-as-a-setup-step pattern when the question doesn't give those three pieces directly)Trigonometry 1.8 — Sector of a Circle
Q845 marks
Statistics
📚 5 relevant video tutorials
Statistics 15 — z-scores 7Statistics 13 — z-scores 5 (The standardising formula z = (x − μ)/σ; practical-applications pivot for the entire arc)Statistics 14 — z-scores 6 (Standardising sample means; z = (x̄ − μ)/(σ/√n); Central Limit Theorem in practice)Statistics 17 — Confidence IntervalsStatistics 20 — p-values and Critical Regions
Q955 marks
TrigonometryGeometryCoordinate Geometry