LEAVING CERT HIGHER LEVEL · MATHS

2021 — Paper 2

220 marks · fully worked video solutions

📄 View exam paper ☑ Marking scheme

Section A · Concepts & Skills

Q130 marks

Bernoulli Trials

Probability

📚 1 tutorial for this question

Probability 8 — Bernoulli Trials

Q230 marks

Coordinate Geometry of the Line

Coordinate GeometryAlgebra

📚 3 relevant video tutorials

The Line 3 — Dividing a Line into a Specific Ratio The Line 2 — Position of a Point Relative to a Line The Line 5 — Perpendicular Distance From a Point to a Line

Q330 marks

Coordinate Geometry of the Circle

Coordinate GeometryGeometryTrigonometry

📚 1 tutorial for this question

The Circle 5 — Intersecting Circles / Touching Circles (the 🚨 LOAD-BEARING 4-scenario classification: touching externally `|C₁C₂| = R₁ + R₂` / touching internally `|C₁C₂| = |R₁ − R₂|` / intersecting twice / disjoint; plus the elegant 🎯 'set K₁ = K₂' move that produces the common tangent/chord in two lines, then the simultaneous-equation closing to find the point(s) of contact, and the collinearity diagnostic)

Q430 marks

Trigonometry

📚 5 relevant video tutorials

Trigonometry 4.10 — Trig Proof 6: cos 2A = cos²A − sin²A (derived from Proof 5 via B = A)Trigonometry 4.2 — Double Angle Formula Trigonometry 2.2 — Introduction to the Unit Circle (reference angle + ASTC + quadrant rules → all answers in a domain)Trigonometry 2.4 — More Than Two Answers (wider domains → multi-revolution unit-circle walks)Trigonometry 4.0 — Miscellaneous

Q530 marks

Solids of Revolution + Speed/Distance Word Problem

Area & VolumeAlgebra

📚 1 tutorial for this question

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.)

Q630 marks

Formal Geometry Proofs

ProofsGeometry

📚 2 relevant video tutorials

Geometry 1.14 — Proof of Theorem 13 (if two triangles are similar then their sides are proportional, in order — derived via the SAS congruence of a constructed sub-triangle AXY ≅ DEF + corresponding-angles ⇒ XY∥BC + Theorem 12, the LAST 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

Triathlon Course (Non-right-angled Triangle)

Trigonometry

📚 3 relevant video tutorials

AVM 1.4 — Area of a Triangle Using Trigonometry Trigonometry 1.2 — Sin, Cos and Tan Trigonometry 1.6 — Cosine Rule

Q850 marks

Statistics: Normal Distribution + Hypothesis Test + Probability

StatisticsProbability

📚 6 relevant video tutorials

Probability 3 — Independent Events And Conditional Probability 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 19 — Hypothesis Testing Statistics 20 — p-values and Critical Regions

Q950 marks

Aeroplane Navigation + AC Voltage

TrigonometryDifferentiation

📚 7 relevant video tutorials

Differentiation 3 — Trigonometric Functions Trigonometry 1.5 — Sine Rule Trigonometry 2.3 — Radians and the Unit Circle Trigonometry 2.5 — Coefficient In Front Of The Angle Trigonometry 3.2 — Changing the Amplitude Trigonometry 3.3 — Changing the Period Trigonometry 3.6 — Drawing Graphs Accurately

Q1050 marks

Blood Donors + Expected Value

ProbabilityIndices & LogsAlgebra

📚 3 relevant video tutorials

Probability 8 — Bernoulli Trials Probability 9 — Relative Frequency And Expected Value Indices and Logs 5 — Unknown in the Power / The Natural Log