LEAVING CERT HIGHER LEVEL · MATHS

2015 — Paper 2

300 marks · fully worked video solutions

📄 View exam paper ☑ Marking scheme

Section A · Concepts & Skills

Q125 marks

Probability

📚 3 relevant video tutorials

Probability 1 — JC Revision Probability 3 — Independent Events And Conditional Probability Probability 8 — Bernoulli Trials

Q225 marks

Statistics

📚 3 relevant video tutorials

Statistics 17 — Confidence Intervals Statistics 19 — Hypothesis Testing Statistics 20 — p-values and Critical Regions

Q325 marks

Coordinate Geometry

📚 2 relevant video tutorials

The Line 5 — Perpendicular Distance From a Point to a Line The Line 1 — JC Revision

Q425 marks

Coordinate Geometry

📚 3 relevant video tutorials

The Circle 1 — Introduction 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)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)

Q525 marks

Trigonometry

📚 3 relevant video tutorials

Trigonometry 4.12 — Trig Proof 8: tan(A+B) = (tan A + tan B) / (1 − tan A · tan B) — closes out the eight proofs Trigonometry 2.4 — More Than Two Answers (wider domains → multi-revolution unit-circle walks)Trigonometry 2.5 — Coefficient In Front Of The Angle

Q625 marks

GeometryProofs

📚 2 relevant video tutorials

Geometry 1.4 — Construction 21: Centroid (the §10 Synthetic Geometry view — same video as The Line 8; medians-intersection construction with the 2:1 division property + coordinate-geometry treatment)Paper 2 Proof 14 — Proof of Theorem 11 (Three parallel lines cut equal segments on any transversal)

Section B · Contexts & Applications

Q740 marks

Coordinate GeometryTrigonometry

📚 2 relevant video tutorials

Trigonometry 1.1 — Pythagoras Theorem Trigonometry 1.2 — Sin, Cos and Tan

Q865 marks

ProbabilitySequences & Series

📚 3 relevant video tutorials

Probability 3 — Independent Events And Conditional Probability Sequences and Series 5 — Geometric Sequences 1 Probability 8 — Bernoulli Trials

Q945 marks

TrigonometryAlgebra

📚 3 relevant video tutorials

Trigonometry 1.2 — Sin, Cos and Tan Trigonometry 1.1 — Pythagoras Theorem Trigonometry 1.6 — Cosine Rule