Rules for Algebra
Rule 1 Addition of two Numbers with the same sign The result is the sum of the numbers with the given sign ( the sign of the two numbers ) . When we add two plus numbers we get a plus number When we add two minus numbers we get a minus number . Example 5 + 6 + 8 = 19 . Example -5 + – 8 + – 6= Ex : 3+6=9.
Ex : -5 + – 6 = – 11
– 19 .
Rule 2 : Addition of two numbers with different signs the result is the difference between the numbers with the sign of the” bigger number ” . Ex 6 + – 9 = – 3 : Ex 19 + -5 = 14 . Ex Note Ex : 14 12 -15 + 13 = – 2 .
– 9 is the same as 14 + – 9 = 5 . and – 7 – 5 is really -7 + – 5 = 9 7 + 3+ 6 – 8 = – 6 – 7 – 8 + 9 + 3 + 6 = – 21 +
Example simplify – 6 + 18 = – 3 .
Note we add the minus numbers ,we add the plus numbers then tidy it up . Rule 3 : Multiplication and signs : The basic rules for multiplication and signs are as follows (Minus ) x ( Minus ) = Plus . ) = Plus . ( Minus ) x ( Plus ) = Minus , (Plus ) x (Plus
This can be expressed as follows that (a) when we multiply two numbers with the same sign we get plus ( b) when we multiply two numbers with difference signs we get a minus . Example : – 7 x – 5 = + 35 , = 84 . -7 x 5 = -35 . Example – 7. x – 4 x 3 = 28 x 3
Example : – 5 x – 6 x – 2 = 30 . x. – 2 = – 60 . Note if we are asked to multiply three or more numbers remember you can only multiply two numbers at a time . Example – 4 x -3 x 5 x -2 = 12 x 5 x – 2 = 60 . x – 2 = – 120 .
The Coursework on White Squares Number Pattern Formula
Borders Coursework 1) Investigate the different patterns of development Order of squares going dow 13 New additions. In each case 2 has been added. 1 + 3 +5 7 + 5 + 3 + 1 = 25 Like the previous pattern there are Additions with 2 being added on. For the next pattern I predict that the total number of squares will be 41, using the following pattern 41 I am now going to check to test my prediction. ...
Rule 4 : Letters
Letters are often used in place of numbers , letters are often referred to as variables or unknowns . Rules 1,2,3 above apply to all calculations with letters , we have to remember one further rule which applies to letters that is we can only add things
together that are the same ie we can only add x’s to x’s and y’s to y’s etc . Note also 5a means 5 times a . Example 5a – 7a = – 2a , Example – 3x + 7x = 4x, Example 5a + 6b – 4a – 11b ,= 5a 4a + 6b – 11b = a – 5b . Multiplying letters by letters : Rule 5 : Brackets :
(a) A number immediatly outside a bracket means that everything inside the bracket gets multiplied by that number Ex Ex (b)Minus sign outside a bracket will change all the signs inside the brackets when the brackets are removed : ex (c)Minus number outside a bracket does two things (i) everything inside the bracket gets multiplied by the number and (ii) all the signs change ]
Brackets by brackets : Multiply everything in the second bracket by everything in the first bracket and tidy it up . Mathematical Words : The following words appear frequently in Mathematics Exam Papers . (1) Expression : This is a collection of letters and numbers : eg (4x + 3y)(5x-7y) : 7×2+4xy-6 . Words associated with expressions. Simplify : Means get rid of the brackets and tidy it up : ex Simplify Factors : The factors of of an expression are two or more things which when multiplied together give that expression
.Example the factors of 14 are 7 and 2 because 7 x 2 =14 Factorise : means find the factors of : Example factorise (2) Equation : This is an expression which contains an equals sign : All equations contain an equals sign . 7x- 5y = 10 : 4×2-6x+5 = 0, 3x+2y = 4 4x- 5y = 10. Word associated with equations Solve : Means find the value(s) of the letter that makes the equation true . Example Solve Types of equation (1) Linear equation one variable Example 3x-4=10
(2)Linear equations 2 variables equations
these are called simultaneous are called quadratic
The Term Paper on Cover Letter. What is it?
It is generally accepted practice to include a cover (or covering) letter, together with your resume and any other documentation that you forward to the employer as part of a job application. Your covering letter essentially provides an explanation of why you are communicating with the employer. Imagine a prospective employer’s confusion if they received your resume without a covering letter ...
(3)Quadratic equations : Equations of the form equations:
the solutions of a quadratic equation are called the roots of the equation , all quadratic equations have two roots! is a quadratic equation Inequality : This is an expression which contains one of the following symbols Word associated with Inequalities Solve; Example Solve Verify : this means show that the information you are given is true
Verify if
Calculate means work out ( using maths) the value of : Example Calculate
Evaluate : (normally applies to a given expression) we are asked to simplify and find the value of .
Example Evaluate Words associated with fractions : Numerator : the top half of the fraction, Denominator :the bottom half of the fraction. common denominator : this is the smallest number that the bottom halves of two or more fractions will divide.
Example the common denominator of can be divided by 2,3, and 5 .
is 30 as it is the smallest number that
Lowest common multiple (LCM) is another name for the smallest number that a given set of numbers will divide . Highest common factor (HCF) : this is the biggest factor a set of numbers have in
common
example the highest common factor of 15,25 and 30 is 5 : the HCF of 8,12,and 28 is 4 .
Words Associated with graphs :
Plot this means place on a coordinate plane some given points . Estimate (from your graph ) read answers from your graph .
Types of Numbers and their Symbols
(1) Natural Numbers Symbol N This is the set of positive whole numbers . N =(0,1,2,3,4,…..) On the numbers line we use” dots ” to indicate Natural numbers
(2) Integers Symbol Z This is the Set of positive and negative whole numbers Z={-3,2,-10,1,2,3}
on the number line we show the integers as “dots” (3)Rational Numbers Symbol Q : This is the set of numbers that can be written as a fraction Most numbers can be written as a fraction eg
The Coursework on Number Of Squar Equation Sequence Pattern
Plan of Investigation In this experiment I am going to require the following: A calculator A pencil A pen Variety of sources of information Paper Ruler In this investigation I have been asked to find out how many squares would be needed to make up a certain pattern according to its sequence. The pattern is shown on the front page. In this investigation I hope to find a formula which could be used ...
In general you will not be asked to put rational numbers on the number line . (4)Irrational Numbers Symbol Ir : Numbers that cannot be written as a fraction : The only numbers that cannot be written as a fraction are numbers such as repeating non terminating decimal) or surds such as (5)Real numbers Symbol R : This is the set which includes all of the above types of numbers On the number line we use a thick line to show real numbers (6)Complex numbers : These are numbers of the form x+yi where x and y are Real numbers and ( i ) = complex numbers are plotted on an Argand diagram. Inequality symbols In general read all information from left to right >” is greater than “, “is less than or equal to” equal to” x is greater than y .
