**Material to be Learned Off:**

Some samples have been attached.

**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.