Class notes COMPLETE MATHEMATICS23108

About the book Education is a key for a countries development, but it becomes a hindrance when it is unequally distributed. This big problem of disparity in Education system can be solved through technology. Hence it’s high time we embrace technology in Education sooner than later. Teachers will therefore use the book in their laptops to teach and even give students notes to read online after revision. The book is divided into three parts: Part one – paper one Part two – paper two 3 WWW.TEACHER.CO.KE Acknowledgment We would like to acknowledge K.L.B for using some of their examples and illustration. We would also like to acknowledge K.N.E.C for using their past papers or revision questions. 4 WWW.TEACHER.CO.KE Table of Contents Format for mathematics paper one-------------------------------------------------------10 Natural Numbers --------------------------------------------------------------------------11 Factors -------------------------------------------------------------------------------------18 Divisibility test ----------------------------------------------------------------------------23 G.C.D ---------------------------------------------------------------------------------------26 L.C.M ---------------------------------------------------------------------------------------29 Integers------------------------------------------------------------------------------------32 Fractions ----------------------------------------------------------------------------------38 Decimals -----------------------------------------------------------------------------------53 Square and square roots ------------------------------------------------------------------63 Algebra and algebraic expressions -------------------------------------------------------69 Rates, Ratio, proportion and percentages--------------------------------------------------79 Length --------------------------------------------------------------------------------------90 Area ---------- ------------------------------------------------------------------------------98 Volume and capacity ----------------------------------------------------------------------113 Mass, weight and density-----------------------------------------------------------------119 Time ---------------------------------------------------------------------------------------124 Linear inequalities ------------------------------------------------------------------------129 Commercial arithmetic -------------------------------------------------------------------140 Co-ordinates and graphs -----------------------------------------------------------------150 Angles and Plane Figures------------------------------------------------------------------155 Geometric construction-------------------------------------------------------------------167 Scale drawing -----------------------------------------------------------------------------180 Common solids ----------------------------------------------------------------------------195 Cubes and cube roots --------------------------------------------------------------------209 Reciprocal ---------------------------------------------------------------------------------212 Indices and logarithms------------------------------------------------------------------- 216 Gradient and Equation of a straight line------------------------------------------------ 227 Reflection and congruence----------------------------------------------------------------235 Rotation------------------------------------------------------------------------------------241 Similarity and Enlargement ------------------------------------------------------------- 245 The Pythagoras theorem ---------------------------------------------------------------- 256 Trigonometric ratios ---------------------------------------------------------------------259 Area of a triangle ----------------------------------------------------------- 267 Area of quadrilateral -------------------------------------------------------- 270 Area part of a circle --------------------------------------------------------- 277 Surface area of solids --------------------------------------------------------288 Volume of solids ---------------------------------------------------------------302 Quadratic equations and expressions --------------------------------------- 315 Linear inequality --------------------------------------------------------------322 5 WWW.TEACHER.CO.KE Linear motion ------------------------------------------------------------------333 Statistics 1 -------------------------------------------------------------------342 Angle properties of a circle---------------------------------------------------354 Vectors ------------------------------------------------------------------------364 Format for paper two ---------------------------------------------------------376 Quadratic expressions and equations --------------------------------------- 377 Approximation and error------------------------------------------------------ 392 Trigometry --------------------------------------------------------------------- 401 Surds ----------------------------------------------------------------------------420 Further logarithms------------------------------------------------------------- 427 Commercial arithmetic II ------------------------------------------------------439 Circles ,chords and Tangents--------------------------------------------------- 460 Matrices ------------------------------------------------------------------------ 489 Binomial expansion---------------------------------------------------------------528 Graphical methods--------------------------------------------------------------546 Probability ----------------------------------------------------------------------567 Vectors --------------------------------------------------------------------------583 Statistics II-------------------------------------------------------------------- 623 Three dimensional Geometry--------------------------------------------------- 642 Longitudes and latitudes --------------------------------------------------------665 Linear programming--------------------------------------------------------------682 Locus -----------------------------------------------------------------------------694 Calculus: Differentiation, integration and area approximation ---------------707 6 WWW.TEACHER.CO.KE MATHEMATICS (121) PAPER ONE ALTERNATIVE A INTRODUCTION Questions in this paper will mainly test topics from Form 1 and 2. The time allocated for this paper is 2 ½ hours The paper consist of a total of 100 marks The paper shall consist of two section: : Section 1 and II Section I This section will have 50 marks and sixteen (16) compulsory short- answer questions Section II This section will have 50 marks and a choice of eight (8) open ended question, for candidates to answer any five (5).The students should note that any attempted questions in this section will be marked if they are not cancelled