Mathematician's Brain Differs
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Playing this simple game boosts the mathematical ability of five-year-olds
MATHEMATICS ABILITY BOOST
QUADRATIC EQUATION
GO TO QUADRATIC EQUATION QUADRATIC EQUATION A polynomial of degree two is called quadratic polynomial General form of quadratic polynomial is ax 2 +bx+c, a,b,c are real numbers and a≠0. If for x= α, α ϵ R, the value of quadratic polynomial becomes zero, then α is called zero of the quadratic polynomial. The equation ax 2 +bx+c=0, a≠0 is called quadratic equation. If α and β are two zeros of ax 2 +bx+c=0, then we say that α and β are roots of the quadratic equation.
LINEAR EQUATIONS
GO TO LINEAR EQUATIONS LINEAR EQUATION A statement of equality which involves literals / variables is called equation. An equation in which the highest degree of the variable is one is called linear equation . LINEAR EQUATION IN ONE VARIABLE If only one variable is involved, then it is called linear equation in one variable. An equation of the form ax+b=c, where a,b,c are numbers, a≠0 and ‘x’ is a variable LINEAR EQUATION IN TWO VARIABLES A linear equation with two variables is called linear equation in two variable say x and y but the highest degree of each variable is one. Linear equation of the form ax+by+c=0 is called linear equation in two variables.
POLYNOMIALS
GO TO POLYNOMIALS POLYNOMIALS A polynomial is an algebraic expression consisting of sum of terms with each term containing a variable or variables raised to a power and multiplied by a coefficient. In polynomial, variables have non-negative integral exponents. A polynomial that contains only one variable, say x, is known as polynomial in one variable x. Highest exponent of polynomial is called degree of the polynomial .
ALGEBRAIC EXPRESSION
GO TO ALGEBRAIC EXPRESSIONS ALGEBRAIC EXPRESSIONS The letters which are used to represent numbers are often given the name literal numbers or literals An algebraic expression is a combination of numbers, literals and arithmetical operations. Monomials: An algebraic expression consisting of only one term e.g. 23, 3y, xyz etc. Binomials : An algebraic expression consisting of two terms e.g. 3x-y, 2x+1 etc.
SEQUENCE AND SERIES
GO TO SEQUENCE AND SERIES SEQUENCE AND SERIES SEQUENCE – An arrangement of numbers in a definite order according to some rules. TERM – various numbers occurring in a sequence are called its terms. We denote a sequence as : a 1 , a 2 , a 3 , …, a n It is a sequence having n terms. a 1 is the first term and a n is the n th term. n th term is also called the general term of a sequence. Sequence having finite number of terms is called finite sequence and sequence having infinite number of terms is called infinite sequence. 1. Arithmetic Progression (A.P) A sequence a 1 , a 2 , a 3 , …, a n is called arithmetic progression if a n+1 = a n + d, n ϵ N 2. Geometric Progression (G.P.) A sequence a 1 ,a 2 ,a 3 ,…,a n is called geometric progression if each term is non-zero and, a k+1 / a k =r (const...
LOGARITHMS
GO TO LOGARITHMS LOGARITHMS John Napier, a Scotish Mathematician invented logarithms in 1614. Logarithm is derived from word ‘logos’ meaning ratio and ‘arithmos’ meaning number. Henry Briggs introduced common logarithms in 1624. Definition – For each positive real number a, a≠1, the unique real number ‘m’ is called the logarithm of ‘b’ to the base ‘a’. Mathematically, log a b = m, iff a m = b. e.g. 9 3 = 729 where a = 9, m = 3 and b = 729, then log 9 729 = 3 NATURAL LOGARITHM AND COMMON LOGARITHM Natural Logarithm – log to the base ‘e’ (e = 2.71828 approx.) Common Logarithm – log to the base 10
SETS
GO TO SETS Theory of Set was developed by German mathematician Georg Cantor. Set is a well-defined collection of objects so that we can definitely decide whether a given object belongs to a given collection or not. e.g. Vowels in English language, Solution of a quadratic equation Set is usually denoted by capital alphabets. Elements are denoted by small alphabets.Sets can be written in two ways : 1. Roster form – e.g. {a,e,i,o,u}, {1,2,3,4} 2. Set builder form – e.g. {x : x is a vowel}
PERCENTAGE AND ITS APPLICATIONS
GO TO PERCENTAGE AND APPLICATIONS PERCENTAGE AND ITS APPLICATIONS A fraction with denominator 100 is called a percent. Latin word “per centum” means ‘per hundred’. APPLICATIONS OF PERCENTAGE Profit and Loss Profit – The margin (extra money) earned after selling a product at a higher price than its cost is called profit. Loss – The money lost on selling a product at a price lower than its cost. Simple Interest Principal (P) – the amount of money borrowed or deposited Rate (R) – a percentage of the principal is added to the principal, making money grow in a given period of time. Time (T) – time for which the money is borrowed or deposited. Interest (I) – the additional or extra money returned or obtained on borrowing or depositing a money for a given period of time at a given rate of interest. ...
RATIO AND PROPORTION
GO TO RATIO AND PROPORTION RATIO AND PROPORTION 1. RATIO – When we compare two quantities of the same kind (with respect to their magnitudes) by division, we say that we have formed a ratio. Points to remember – 1. A ratio has no units in itself i.e. a ratio is purely a number, it has no unit attached to it. 2. The numbers a and b in a ratio a:b are called terms of a ratio. 2. PROPORTION – Equality of two ratios is called proportion. We write proportion as a:b :: c:d or a/b = c/d.
NUMBER SYSTEM
GO TO NUMBER SYSTEM NUMBER SYSTEMS 1. Natural Numbers 2. Whole Numbers 3. Integers 4. Rational Numbers Irrational Numbers Natural Numbers (Or counting numbers) {1,2,3,4…} e.g. a. Numbers of Days in a week. b. Number of pages in a book. c. Number of schools in a city. Whole Numbers {0,1,2,3, 4…} Integer Numbers – Number system consisting of natural numbers, their negatives and number 0 is called integer number. {…-3, -2, -1,0,1,2, 3…} Rational Numbers – A rational number is of the form p/q where p and q are integers and q≠0. e.g. 6/5, 5/6, -8/9 etc. Irrati...