Proofs Higher Level Leaving Certificate Maths

Paper 1

Prove that Root 2 is not rational (Proof by Contradiction)

Must be able to Construct Root 2 and Root 3

Derive the Formula for a Mortgage Repayment (Amortisation Formula)

Derive the Formula for the Sum to Infinity of Geometric Series (Using Limits)

Derive the Formula for the Sum of a Finite Geometric Series (Proof by Induction)

Prove De Moivre’s Theorem (Proof By Induction)

Others that you might be asked to ‘prove’ but because they can be asked in different ways you can’t learn them off specifically.

Apply De Moivre to Prove certain Trigonometric Identities (more than 1 type)

Differentiation by 1st Principles (more than 1 type)

Paper 2

Geometric Theorems 11, 12, 13 (4, 6, 9, 14 and 19 learned for JC)

Trigonometric Theorems 1 – 7 and 9

Constructions 16 – 22 (1 – 15 learned for the JC)

Definitions for a theorem, proof, axiom, corollary, converse, is equivalent to, if and only if, proof by contradiction

Likewise there is a host of definitions in Statistics and Probability that should be learned such as the type of sample, conditions for Bernoulli etc but they are not specifically outlined in the syllabus.

Bernoulli Trials