LEAVING CERT HIGHER LEVEL · MATHS

2020 — Paper 2

300 marks · fully worked video solutions

📄 View exam paper ☑ Marking scheme

Section A · Concepts & Skills

Q125 marks

Coordinate Geometry

📚 2 relevant video tutorials

The Line 5 — Perpendicular Distance From a Point to a Line The Line 6 — Angle Between Two Lines

Q225 marks

Coordinate GeometryTrigonometryAlgebra

📚 2 relevant video tutorials

The Circle 1 — Introduction The Circle 8 — Equation of the Tangent(s) to a Circle FROM an External Point (the two-step routine: write a generic line through the external point in slope form, then enforce perpendicular-distance-from-centre-equals-radius to solve for the slope)

Q325 marks

TrigonometryCoordinate Geometry

📚 2 relevant video tutorials

Trigonometry 1.2 — Sin, Cos and Tan Trigonometry 1.5 — Sine Rule

Q425 marks

Trigonometry

📚 4 relevant video tutorials

AVM 1.4 — Area of a Triangle Using Trigonometry Trigonometry 1.8 — Sector of a Circle Trigonometry 2.3 — Radians and the Unit Circle Trigonometry 2.5 — Coefficient In Front Of The Angle

Q525 marks

Probability

📚 2 relevant video tutorials

Probability 3 — Independent Events And Conditional Probability Probability 1 — JC Revision

Q625 marks

ProbabilityAlgebra

📚 2 relevant video tutorials

Probability 8 — Bernoulli Trials Probability 1 — JC Revision

Section B · Contexts & Applications

Q755 marks

Biodegradable Paper Cups

TrigonometryArea & VolumeGeometryDifferentiationAlgebra

📚 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.)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 Trigonometry 1.8 — Sector of a Circle

Q870 marks

Statistics Workout (Normal Distribution + CI + Hypothesis Testing + Descriptive Stats)

StatisticsAlgebra

📚 8 relevant video tutorials

Statistics 12 — z-scores 4 Statistics 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 15 — z-scores 7 Statistics 16 — Margin of Error Statistics 17 — Confidence Intervals Statistics 19 — Hypothesis Testing 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)

Q925 marks

Two Ships at Sea (Min Distance)

TrigonometryCoordinate GeometryDifferentiation

📚 2 relevant video tutorials

Trigonometry 1.1 — Pythagoras Theorem Differentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)