ADVANCED MATHEMATICS FORM 5 & 6

LOGIC LOGIC (II) SENTENCE HAVING A GIVEN TRUTH TABLE Example.1 Find a sentence which has the following truth table P Q – T T T T F T F T T F F F Step: 1. Mark lines which are T in last column 2. Basic conjunction of P and Q 3. Required sentence is … Read more

TRIGONOMETRY(II) iii) Consider = But = = = Alternative: Using = Dividing by cos3θ numerator and denominator Applications of the double and triple formulae A. Proving Identities Examples: Prove the following identities (i) + (ii) = (iii) Solution(i) I. Proof Dealing with L.H.S = =cos2A+cos2A-sin2A =2cos2A-sin2A – =2 – = R.H.S II. Solution(ii) Dealing with … Read more

TRIGONOMETRY Trigonometry is the study of angle measurement and functions that depends on angle. The fundamental trigonometric ratios are Sine (sin) Cosine (Cos) Tangent (Tan) Others are cosecant (cosec) Secant (sec) Cotangent (cot ) Let θ be the angle in a right angled triangle; then we say Sin θ COS θ Tan θ And = … Read more

LOGIC Logic concerns with the study of analysis of methods of reasoning which lead to certain conclusion or statement. Example If it rains today we shall play football. It rained we did not play football Simple and compound sentence Consider the following sentence i) The medians of a triangle meet at a point ii) The … Read more

LINEAR PROGRAMING Is a branch of mathematics which enables one to solve problems which either the greatest or minimum/least value of a certain quantity is required under some given limitations or constraints. Example In a big – organization, decision about distribution in order to realize maximum profit or reduce costs of production are done by … Read more

ALGEBRA Indices (law of exponents) Three basic rules including the Indices are: i) am x an = am + n ii) am ÷ an = am – n iii) (am) n = am Negative indices Consider a5 ÷ a2 = a5 – 2 = a3 = a2 ÷ a5 = a2 – 5 = a … Read more

TOPIC 4: COORDINATE GEOMETRY I ~ ADV MATHEMATICS FORM 5 TOPIC 4: COORDINATE GEOMETRY I ~ ADV MATHEMATICS FORM 5 COORDINATE GEOMETRY -Is the conic section whose eccentricity is equal to zero. -Coordinate geometry is the study of representation of geometry figure either on two or three dimension under the one of the following steps. … Read more

DIFFERENTIATION DERIVATIVES Slope of a curve A curve has different slopes at each point. Let A, B, and C be different points of a curve f (x) Where ðx is the small increase in x ðy is the small increase in y The slope of chord AC = If C moves right up to A … Read more

INTEGRATION Integration :Is the reverse process of differentiation, i.e. the process of finding the expression for y in terms of x when given the gradient function. The symbol for integration is  , denote the integrate of a function with respect to x If  This is the general power of integration it works for all values of n … Read more