# SS 1 Further Mathematics (1st Term) ## STATISTICS | MEASURES OF CENTRAL TENDENCY

STATISTICS: MEASURES OF CENTRAL TENDENCY See also SURDS BINARY OPERATIONS OPERATION OF SET AND VENN DIAGRAMS BASIC CONCEPT OF SET LOGARITHM ## BINARY OPERATIONS: IDENTITY AND INVERSE ELEMENTS

BINARY OPERATIONS: IDENTITY AND INVERSE ELEMENTS Identity element and Inverse element CONTENT: Identity Element: Given a non- empty set S which is closed under a binary operation * and if there exists an element e € S such that a*e = e*a = a for all a € S, then e is called the IDENTITY or NEUTRAL element. The element is unique. Example: The operation * on the set R of real numbers is defined by a*b = 2a-1 ┼ b 2 for all a, b € R. Determine the identity element. Solution: a*e= e*a = a a*b= 2a-1 ┼ b 2 a*e = 2a-1 ┼ e = a 2 2a-1+ 2e = 2a 2e = 2a-2a +1 e   = ½.   Evaluation Find the identity element of the binary operation a*b = a +b+ab Inverse Element; If x € S and an element x-1 € S such that x*x-1… Read More »BINARY OPERATIONS: IDENTITY AND INVERSE ELEMENTS ## BINARY OPERATIONS: BASIC CONCEPT OF BINARY OPEATIONS

BINARY OPERATIONS: BASIC CONCEPT OF BINARY OPEATIONS CONTENT Concept of binary operations, Closure property Commutative property Associative property and Distributive property. Definition Binary operation is any rule of combination of any two elements of a given non empty set. The rule of combination of two elements of a set may give rise to another element which may or not belong to the set under consideration. It is usually denoted by symbols such as, *, Ө e.t.c.   Properties: Closure property:  A non- empty set z is closed under a binary operation * if for all a, b € Z. Example; A binary operation * is defined on the set S= {0, 1, 2, 3, 4} by X*Y = x + y –xy. Find (a) 2 * 4 (b) 3* 1 (c) 0* 3.  Is the set S closed under the operation *? Solution 2 * 4, i.e, x= 2,y=4 2+… Read More »BINARY OPERATIONS: BASIC CONCEPT OF BINARY OPEATIONS ## OPERATION OF SET AND VENN DIAGRAMS

OPERATION OF SET AND VENN DIAGRAMS See also BASIC CONCEPT OF SET LOGARITHM INDICIAL AND EXPONENTIAL EQUATIONS INDICES Trigonometric Identities and graphs ## BASIC CONCEPT OF SET

BASIC CONCEPT OF SET See also LOGARITHM INDICIAL AND EXPONENTIAL EQUATIONS INDICES Trigonometric Identities and graphs Graphs of Trigonometric Function ## LOGARITHM

LOGARITHM – SOLVING PROBLEMS BASED ON LAWS OF LOGARITHM See also INDICIAL AND EXPONENTIAL EQUATIONS INDICES Trigonometric Identities and graphs Graphs of Trigonometric Function Logical reasoning ## INDICIAL AND EXPONENTIAL EQUATIONS

INDICIAL AND EXPONENTIAL EQUATIONS See also Trigonometric Identities and graphs Graphs of Trigonometric Function Logical reasoning Cubic equations and their factorization Factorization of polynomial

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