LEAVING CERT HIGHER LEVEL · MATHS

2017 — Paper 1

300 marks · fully worked video solutions

📄 View exam paper ☑ Marking scheme

Section A · Concepts & Skills

Q125 marks

Functions & GraphsAlgebra

📚 2 relevant video tutorials

Functions and Graphs 3 — Vertex form / Completing the square (algebraic technique)Algebra 9 — Nature of Quadratic Graphs

Q225 marks

Complex Numbers

📚 3 relevant video tutorials

Complex Numbers 10 — Introduction to Polar Form Complex Numbers 11 — Rules for Polar Form Complex Numbers 13 — Converting to polar form and applying De Moivre's theorem

Q325 marks

DifferentiationFunctions & Graphs

📚 2 relevant video tutorials

Differentiation 2 — First Principles Differentiation 9 — Logs

Q425 marks

Sequences & SeriesIndices & Logs

📚 2 relevant video tutorials

Sequences and Series 5 — Geometric Sequences 1 Sequences and Series 8 — Geometric Sequences 4

Q525 marks

AlgebraDifferentiationFunctions & Graphs

📚 3 relevant video tutorials

Algebra 11 — Solving Cubic Equations Algebra 12 — Nature of Cubic Roots Differentiation 15 — Turning Points / Maximum and Minimum points (the second-derivative test for max/min discrimination)

Q625 marks

DifferentiationFunctions & GraphsIntegration

📚 3 relevant video tutorials

Functions and Graphs 9 — Drawing Graphs Integration 12 — Area between a curve and the x-axis Integration 3 — Exponentials

Section B · Contexts & Applications

Q755 marks

Sapphire City and Avalon Populations

DifferentiationIndices & LogsIntegration

📚 4 relevant video tutorials

Indices and Logs 5 — Unknown in the Power / The Natural Log Differentiation 5 — Exponentials Indices and Logs 8 — Log Problems Integration 11 — Average Value

Q855 marks

Loan Repayment, Credit Card, Credit Union

Financial MathsSequences & SeriesIndices & Logs

📚 3 relevant video tutorials

Financial Maths 4 — Converting Interest Rates from Monthly to Yearly etc.Financial Maths 6 — Annuities (Paying Money Back)Financial Maths 7 — Proof of the Amortization Formula (the only proof in FM strand; geometric-series + algebra)

Q940 marks

Tide Model

Trigonometry

📚 8 relevant video tutorials

Trigonometry 3.5 — Identifying Functions From Their Graph Trigonometry 2.3 — Radians and the Unit Circle Trigonometry 2.5 — Coefficient In Front Of The Angle Trigonometry 2.9 — Use The Calculator To Find The Reference Angle Trigonometry 3.2 — Changing the Amplitude Trigonometry 3.3 — Changing the Period Trigonometry 3.4 — Changing The Midline Trigonometry 3.6 — Drawing Graphs Accurately