Algorithms

The knowledge of thedifferent algorithms and how different algorithms affect the value of numbers,when symbols are missing or not used is on the syllabus for PCS1/SY1 and ASY and it could feature as a minor part of a higher level question on a PCS2/SY2 paper.Algorithms are a way of sorting numbers,finding the necessary information through manipulation of algebra ,number and other forms of math-complex algorithms can even be conveyed as several instructions to a computer.There are two main types of Algorithm that you will need to know and understand:

Expansion Algorithms:Increases the value of a number-Common Examples are the Algebraic Algorithm and Reaction Algorithm.The Algebraic Algorithm times together values and is most commonly used in Algebra.The Reaction Algorithm adds together values and is most commonly used in Number.The use of the Algebraic Algorithm in Number,is always a lateral solution,unless there are more than 2 terms and the use of the Reaction Algorithm in Algebra is always a lateral solution,unless there are more than 2 terms.Reaction Algorithms,in number, can create lateral solutions if minus numbers are involved for example -16=-10+6=-4 or -(10+6)=-16,with -4 being the lateral solution.All lateral solutions can be removed, through the use of SNF.

Algebraic Algorithm:2x=2*x

Reaction Algorithm:24=20+4

Contraction Algorithms:Decreases the value of a number-Common Examples are the Reduction Algorithm,which takes away values and the Pressuriser Algorithm,which divides values.These Algorithms are in a completley different universe of maths,to Expansion Algorithms,which are by the far the most commonly used Algorithms.

A common error is to assume that sums like 5*0.5 are Contraction Algorithms because the number 5 is decreased but the number 0.5 is increased,this number being the focus of the Expansion Algorithm and the opposite for the division.Some algorithm calucuations don't include a focus point because they don't obey the direct function but they still contact as the algorithm used to create the answer eg. 50.1=5/0.1=50 but it is still a contraction algorithm.

Lateral Solutions are created,when we form a solution through uncommon means for that form of expression eg.10 being a solution to 25.Be careful though because in Algebra 25x=25*x isn't a Lateral solution even though,it includes the Reaction Algorithm and these equations get very complex because 25x can be equal to 250*x,250+x,100*x or 100+x,the Reaction Algorithm only works for digits between 0 and 9 in Algebra.A lateral equation is one,whghere only lateral solutions exist,a common example is 5x=5x+14,try finding non-lateral solutions.

Non-Lateral Solutions are solutions formed through the common use of terms,these can be most easily found and a non-lateral equation,contains no lateral solutions like 5(x).

You will also need to know about Algorithms that affect number base,all numbers are usually set to the Denary Algorithm,which means it includes 10 digits.To convert between different number systems,from the denary algorithm,you look at howmany of the different powers of that number fit it,with the highest powers starting first eg.5 in binary is 1 lot of 4 and 0 lots of 2 and 1 lots of 1-101-binary is the 2 digit numeral system.

Applications
Algebraic algorithms are used in complex scenarios to find out if a value is timesed by itself and other values and equals a value,what the original value must equal.Reaction Algorithms are used in basic addition and to work out the products of a chemical reaction,in which reactants are combined into one product.Reduction Algorithms are used to calculate the amount left of a displaced substance in a reduction/displacement reaction.Pressuring Algorithms are used to calculate the decrease in volumer of a gas after it has been compressed into a liquid or very dense gas.