LEAVING CERT HIGHER LEVEL · MATHS
2018 — Paper 2
300 marks · fully worked video solutions
Section A · Concepts & Skills
Q125 marks
Expected Value with a Competition Twist
Probability
📚 1 tutorial for this question
Q225 marks
The Normal Distribution
Statistics
Q325 marks
Counting + Factorial Algebra
Probability
📚 3 relevant video tutorials
Q425 marks
Trig: Equation with Coefficient + Double-Angle Identity
Trigonometry
Q525 marks
Coordinate Geometry: Parallel Lines + a Touching-Circles Twist
Coordinate Geometry
📚 3 relevant video tutorials
The Circle 7 — Equation of a Tangent to a Circle at a Point, or Parallel to a Given Line (the two tangent techniques: perpendicular-to-radius for a point on the circle; perpendicular-distance-equals-radius for tangents parallel to a known line)The Line 1 — JC RevisionThe Line 2 — Position of a Point Relative to a Line
Q625 marks
Geometry: Theorem 12 Proof + Similar Triangles
ProofsGeometryTrigonometry
📚 2 relevant video tutorials
Geometry 1.13 — Proof of Theorem 12 (line parallel to one side of a triangle cuts the other two sides in the same ratio s:t — derived from Theorem 11 via the 'divide AX into s equal parts and XB into t equal parts' construction, and the second of the three LC-required proofs)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)
Section B · Contexts & Applications
Q750 marks
The Garden Railing
Sequences & SeriesTrigonometry
📚 4 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.)Sequences and Series 1 — Arithmetic Sequences 1Sequences and Series 5 — Geometric Sequences 1Trigonometry 1.1 — Pythagoras Theorem
Q860 marks
Acme Confectionery (Statistics + Pension Annuity)
StatisticsDifferentiationFunctions & GraphsFinancial Maths
📚 7 relevant video tutorials
Statistics 17 — Confidence IntervalsDifferentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)Financial Maths 6 — Annuities (Paying Money Back)Financial Maths 8 — PensionsStatistics 14 — z-scores 6 (Standardising sample means; z = (x̄ − μ)/(σ/√n); Central Limit Theorem in practice)Statistics 16 — Margin of ErrorStatistics 18 — Central Limit Theorem (sample means of any population converge to normal at n ≥ 30; population size doesn't matter; p̂(1−p̂) maximised at p̂=0.5)
Q940 marks
Crank-and-Slider Mechanism
Trigonometry