Surds - Rationalising the Denominator What does it mean to rationalise a denominator? Rationalising a denominator changes a fraction with surds in its denominator, into an equivalent fraction where...
Manipulating Surds What are surds? If n is a positive integer and is not a square number, then √n (or any multiple of √n ) is a surd Surds are examples of irrational numbers What do I need to know ...
Laws of Indices What do I need to know about laws of indices? Laws of indices (or index laws – 'index' is the singular, 'indices' is the plural) allow you to simplify and manipulate expressions inv...
Proof by Contradiction What is proof by contradiction? A proof by contradiction assumes the opposite result is true Then, through a series of logical steps, shows that this cannot be so How do I do...
Disproof by Counter Example What is disproof by counter-example? Disproof by counter-examples involves finding a value that does not work for the given statement That value is called a counter-exam...
Proof by Exhaustion What is proof by exhaustion? Proof by exhaustion is a way to show that the desired result works for every allowed value How do I prove a result by exhaustion? Using proof by exh...
Proof by Deduction What is proof by deduction? Proof by deduction is when a mathematical and logical argument is used to shows whether or not a result is true How to do proof by deduction Y...
Language of Proof What is proof? Proof is a series of logical steps which show whether a result is true or not for a set of specified numbers e.g. All intigers, all even numbers etc Notation in pro...
Moments - Ladder Problems How do I model ladder problems? We can model the ladder as a rod There will be two (likely different) reaction forces a vertical reaction force Rf between the bottom of th...
