S.4 Mathematics Book 4 Caltec S.4

UCE M a t h e m a t i c s 4 (For S.4) BY Chepa Y. M Department of Mathematics, Kibuli Secondary School. Telephone: +256 772 481628 Email: y mussy @yahoo.co m 3 Contents Chapter Page 1 Gradients and rates of change ................................ ............. 5 The gradient of a straight line ................................ ...................... 5 The equation of a straight line ................................ ...................... 6 The graph of a straight line ................................ ....................... 13 The gradients of parallel lines ................................ .................... 14 The gradients of perpendicular lines ................................ ............ 16 Rates of change ................................ ................................ ..... 18 2 Equation s ................................ ................................ ........... 31 Simultaneous equations ................................ ........................... 31 Problem solving involving simultaneous equations ......................... 35 Quadratic equations ................................ ................................ 37 Solving quadratic equations by factors method .............................. 38 Solutions of quadratic equations by formula ................................ .. 41 Solutions of quadratic equations by formula ................................ .. 41 Problems solved by quadratic equations ................................ ...... 43 Graphs of quadratic functions ................................ .................... 46 Graphical solution of equations ................................ .................. 50 Simultaneous eq uations – one linear and one quadratic ................... 57 3. Circles ................................ ................................ ................ 59 Area of a sector ................................ ................................ ...... 59 Chord of a circle ................................ ................................ ..... 61 Angle properties of a circle ................................ ........................ 62 4 4. Linear programming ................................ ............................ 78 Forming linear inequalities ................................ ........................ 78 Forming and solving inequalities ................................ ................ 80 Optimization ................................ ................................ .......... 83 The objective function ................................ .............................. 85 5. Constructions and Loci ................................ .................. 94 Perpendicular bis ector of a line joining two points ........................... 94 Constructing parallel lines ................................ ......................... 95 Bisecting an angle ................................ ................................ .. 96 Constructing angles ................................ ................................ 97 Circumscribed circle ................................ ................................ 99 Inscribed circle ................................ ................................ ..... 101 The Locus of a point ................................ .............................. 102 Intersecting loci ................................ ................................ …