FURTHER MATHEMATICS SSS2 FIRST TERMWEEK 1SOLUTION TO QUADRATIC EQUATIONContentsFINDING QUADRATIC EQUATION GIVEN SUM AND PRODUCT OF ROOTS CONDITION FOR EQUAL ROOTS, REAL ROOTS AND NO ROOTWe recall that if ax2 + bx + c = 0, where a, a and c are constants such that a ≠ 0, then,x =-b+b2-4ac2a or x = -b-b2-4ac2a

WEEK 2TANGENTS AND NORMAL TO CURVESContentsFor any curve, dydx is the gradient function. At any point on the curve, dydx at that point gives the gradient of the tangent at the point. The derivation of y with respect to x at x = x1 is denoted.

FURTHER MATHEMATICS SSS2 FIRST TERMWEEK 3POLYNOMIALSContentsConsider the expressions formed from the sum of integral non-negative powers of a variable x taken together with some numerical constants. Such expressions are called Polynomials.The general polynomial takes the form anXn + an1Xn1 + … a2X2 + a1X + a0 where a11 an-1…a0(a0 ≠0) are numerical constants.The numerical constants an’ an1…. a2, a1 are called coefficients of Xn, Xn1, … X2, X respectively while a0 is called the constant term of the polynomial.

FURTHER MATHEMATICS SSS2 FIRST TERMWEEK 4POLYNOMIAL (CONTINUED)ContentFactorization of polynomialShow that x - 1 is a factor off(x) = 2x3 + 3x2 – 5x – 6Solutionf(-1) = 2(-1)3 + 3(-1)2 – 5(-1) – 6 = -2 + 3 + 5 – 6Hence x + 1 is a factor of f(x)

FURTHER MATHEMATICS SSS2 FIRST TERMWEEK 5CUBIC EQUATIONS AND THEIR FACTORIZATION, GRAPH OF CUBIC EQUATIONSContentsPolynomials of degree three have the general form y = ax3 + bx2 + cx + d(a ≠ 0). The curve is usually called a cubical parabola.A cubical parabola has two shapes depending on whether a > 0 or a < 0.

FURTHER MATHEMATICS SSS2 FIRST TERMWEEK 6REVIEWContentsWEEK 1 FINDING QUADRATIC EQUATIONS WITH GIVEN SUM AND PRODUCT OF ROOTSWEEK 2 TANGENT AND NORMAL TO CURVESWEEK 3 POLYNOMIALWEEK 4 POLYNOMIAL ( CONTINUED)WEEK 5 CUBIC EQUATIONS

FURTHER MATHEMATICS SSS2 FIRST TERMWEEK 7LOGICAL REASONINGContentsStatementsA statement in a logical context is a declaration, verbal or written that is either true or false but not both.A true statement is said to have a truth value, T, while a false statement is said to have a truth value F.

FURTHER MATHEMATICS SSS2 FIRST TERMWEEK 8TRIGONOMETRIC FUNCTIONSContentsThe basic trigonometric ratios can be defined in two ways:(i)traditional definition;(ii) modern definition.Traditional DefinitionThe basic trigonometric ratios can be defined in terms of the sides of a right–angled triangle.

FURTHER MATHEMATICS SSS2 FIRST TERMWEEK 9GRAPHS OF TRIGONOMETRIC FUNCTIONContentsThe graph of the followings will be considered(a) y = sinѳ, 0◦ ≤ ѳ ≤ 360◦(b) y = cosѳ, 0◦ ≤ ѳ ≤ 360◦(c) y = tanѳ, 0◦ ≤ ѳ ≤ 360◦The graph of y = sinѳ, ѳ◦ ≤ ѳ ≤ 360◦On the graph sheet, draw a long horizontal axis in the middle. Mark a point 0’, 3cm to the left of the origin 0. With centre 0’ draw a circle of radius 2cm. Draw a vertical axis through 0. Call the horizontal axis ѳ – axis and the vertical axis y–axis.

FURTHER MATHEMATICS SSS2 FIRST TERMWEEK 10TRIGONOMETRIC IDENTITIES AND GRAPHS OF INVERSE TRIGONOMETRIC RATIOS PYTHAGORAS THEOREM