FURTHER MATHEMATICS SSS2 THIRD TERMWEEK 2PROJECTILES: MOTION UNDER GRAVITY IN TWO DIMENSION, DERIVATION AND APPLICATION OF EQUATION INVOLVING GREATEST HEIGHT, TIME OF FLIGHT AND RANGEContentMotion Under Gravity in Two Dimensions:If a particle is projected with an initial velocity u at angle θ to the horizontal, the particle will be resolved into vertical and horizontal components of the velocity.

FURTHER MATHEMATICS SSS2 THIRD TERMWEEK 3BINOMIAL EXPANSION: PASCAL TRIANGLE, BINOMIAL THEOREM OF NEGATIVE, POSITIVE AND FRACTIONAL POWERContentPASCAL’S TRIANGLEConsider the expressions of each of the following:(x + y)0; (x + y )1; (x + y)2; (x + y)3; (x + y)4(x + y)0 = 1(x + y)1 = 1x + 1y

FURTHER MATHEMATICS SSS2 THIRD TERMWEEK 4MECHANICS (VECTOR GEOMETRY)ContentSCALAR OR DOT PRODUCT OF TWO VECTORSThe scalar or dot product of two vectors a and b is written as a.b and pronounced as (a dot b). Therefore, a.b =|a| |b| cosƟ dot is defined as a.b = a b cos Ɵ where Ɵ is the angle between vectors a and bIf a = a1 I + a2j and b = b1 I b2jThus a .b = (a)1bi ii + ab2j I 1 + 2 bi I h +a2 b2 j

FURTHER MATHEMATICS SSS2 THIRD TERMWEEK 5MECHANICS: VECTORS OR CROSS PRODUCT ON TWO OR THREE DIMENSION, CROSS PRODUCT OF TWO VECTORS AND APPLICATION OF CROSS PRODUCTContentVector Product of two vectorsGiven two vectors a andb whose directions are inclined at an angleθ, their vector product is defined as a vector r whose magnitude isabsinθand whose directions is perpendicular to both aandb and also being positive relative to a rotation from them vector a and b also being positive relative to a rotation from the vector a to the rectorb. The vector product of a and b is designated

FURTHER MATHEMATICS SSS2 THIRD TERMWEEK 7INTEGRATIONContentIntegration: This is defined as anti-differentiation. Suppose, y = x3 + 2x, the first derivative is 3x2 + 2. (dy/dx = 3x2 + 2)then the antiderivative of 3x2 + 2 = x3 + 2x Thus, integration is the reverse process of differentiation and is denoted by the symbol ∫.If dy/dx = xn , then ∫ dy/dx = xn+1 + Cn + 1 (n ≠ -1)where c is the arbitrary constant.

FURTHER MATHEMATICS SSS2 THIRD TERMWEEK 8INTEGRATION (INDEFINITE INTEGRAL, DEFINITE INTEGRAL AND AREA UNDER CURVEContentThe process of reversing differentiation is called Integration. If dy/dx = 3x2, then y could be x3, as the derivative of x3 is 3x2.We say that x3 is an integral of 3x2 with respect to x. The symbol for integration sign is given by ∫ . The expression to be integrated is put between the ∫ sign and dx.∫ 3x2 dx could be x3Since differentiating any constant gives zero, the following also have derivation 3x2.

FURTHER MATHEMATICS SSS2 THIRD TERMWEEK 9APPLICATION OF INTEGRATION II: SOLID REVOLUTION AND TRAPEZOIDAL RULEContentA solid which b has a central axis of symmetry is a solid of revolution. For example, a cone, a cylinder, a vase etc.

FURTHER MATHEMATICS SSS2 THIRD TERMWEEK 10REGRESSION LINE AND CORRELATION COEFFICIENT SCATTER DIAGRAMContentDefinition: a scatter diagram is a graphic display of bivariate data. A bivariate data involves two variablesTYPES OF SCATTER DIAGRAM:Linear positive correlation.A positive correlation between two variables x and y means that in general, an increase in x is accompanied by an increase in y. The regression line has a positive slope.