LEAVING CERT HIGHER LEVEL · MATHS

2016 — Paper 2

300 marks · fully worked video solutions

📄 View exam paper ☑ Marking scheme

Section A · Concepts & Skills

Q125 marks

Coordinate GeometryAlgebra

📚 2 relevant video tutorials

The Line 1 — JC Revision The Line 9 — Construction 22: Orthocentre

Q225 marks

Coordinate Geometry

📚 2 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 Revision

Q325 marks

Trigonometry

📚 2 relevant video tutorials

Trigonometry 4.2 — Double Angle Formula Trigonometry 4.3 — Products to Sums/Differences and Sums/Differences to Products (the eight factor + product formulae on page 15: four sum-to-product directions — `cos A + cos B`, `cos A − cos B`, `sin A + sin B`, `sin A − sin B`; four product-to-sum directions — `2 cos A cos B`, `2 sin A sin B`, `2 sin A cos B`, `2 cos A sin B`; 🚨 LOAD-BEARING the formula's coefficient is **2** on the left and **1** on the right, so when the question's coefficient isn't 2, scale the right-hand side by the ratio (e.g. `6 cos 15x cos 3x = 3(cos 18x + cos 12x)` because the question's coefficient `6` is `3×` the formula's `2`); not examined as a proof but appears in exam-style integration setup)

Q425 marks

GeometryProofs

📚 1 tutorial for this question

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)

Q525 marks

Probability

📚 3 relevant video tutorials

Probability 3 — Independent Events And Conditional Probability Probability 1 — JC Revision Probability 2 — Mutually Exclusive And Not-Mutually Exclusive Events

Q625 marks

Probability

📚 2 relevant video tutorials

Probability 9 — Relative Frequency And Expected Value Probability 1 — JC Revision

Section B · Contexts & Applications

Q755 marks

Trigonometry

📚 4 relevant video tutorials

Trigonometry 1.1 — Pythagoras Theorem Trigonometry 1.2 — Sin, Cos and Tan AVM 1.4 — Area of a Triangle Using Trigonometry Trigonometry 1.6 — Cosine Rule

Q845 marks

TrigonometryDifferentiation

📚 6 relevant video tutorials

Trigonometry 3.4 — Changing The Midline Differentiation 3 — Trigonometric Functions Trigonometry 3.1 — Shapes of Trigonometric Graphs Trigonometry 3.2 — Changing the Amplitude Trigonometry 3.3 — Changing the Period Trigonometry 3.6 — Drawing Graphs Accurately

Q950 marks

Statistics

📚 6 relevant video tutorials

Statistics 13 — z-scores 5 (The standardising formula z = (x − μ)/σ; practical-applications pivot for the entire arc)Statistics 15 — z-scores 7 Statistics 16 — Margin of Error Statistics 17 — Confidence Intervals Statistics 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)Statistics 19 — Hypothesis Testing