GEOMETRY
Proofs, Theorems & Constructions
Project Maths Site- Junior Cert - Project Maths Site
Project Maths Site- Leaving Cert - Project Maths Site
Proof of Theorem 13 - Alison.com
SERIES
Derive the formula for the sum to infinity of geometric series by considering the limit of a sequence of partial sums - Project Maths Site
Proof of the Sum of Geometric Series by Induction - Project Maths Site
ARITHMETIC
Optional: Deriving the formula for a mortgage repayment Watch Alison. com derive it
CALCULUS
differentiate linear and quadratic functions from first principles youtube video
TRIGONOMETRY
derive the trigonometric formulae 1, 2, 3, 4, 5, 6, 7, 9
1. cos2A + sin2A = 1 Proving Trigonometric Identity – (Sin squared + cos squared = 1) - Alison.com
2. sine formula: a/Sin A=b /Sin B=c /Sin C Proving the Sine Rule - Alison.com
3. cosine formula: a2 = b2 + c2 – 2 bc cos A Proving the Cosine Rule - Alison.com
4. cos (A–B) = cos A cos B + sin A sin B Proof from Youtube KeysToMaths1
5. cos (A+B) = cos A cos B – sin A sin B Proof from Youtube KeysToMaths1
6. cos 2A = cos2 A – sin2 A Proof from Youtube KeysToMaths1
7. sin (A+B) = sin A cos B + cos A sin B Proof from Youtube KeysToMaths1
9. tan (A+B) = tan A + tan B / 1 – tan A tan B Proof from Youtube KeysToMaths1
PROOF BY INDUCTION
The sum of the first n natural numbers – Proof by induction - Alison.com
Sum of the first n Natural Numbers Method 1 - Project Maths Site
Sum of the first n Natural Numbers Method 2 - Project Maths Site
Proof by induction applied to a geometric series - Alison.com
Proof of the Sum of Geometric Series - Project Maths Site
Further proof by induction – Multiples of 3 - Alison.com
Factorisation results such as 3 is a factor of 4n–1 Proj Maths Site 1 Proj Maths SIte 2
Further proof by induction – Factorials and powers - Alison.com
(1+ x)n ≥ 1+nx (x > –1) - Project Maths Site
NUMBER
geometrically construct √2 and √3
Root 2 - Project Maths Site
Root 3 - Project Maths Site
Root 2 is Irrational – Proof by contradiction - Alison.com
Proof of De Moivre’s Theorem - Alison.com
OTHER
Completing the Square - Alison.com
General Completing the Square - Alison.com