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1 function characterssummaryexamplesa.domain and rangeb.odd and even functionsc.composite and inverse functionsexercises2 function transformationssummaryexamplesa.dilation, reflection and translationb.graphs of1f(x),fx and|fx|exercises3 exponents and logarithmssummaryexamplesa.exponents and exponential equationsb.logarithms and logarithmic equationsexercises4 basic functionssummaryexamplesa.linear and quadratic functionsb.polynomial and rational functionsc.exponential and logarithmic functionsexercises5 trigonometric identitiessummaryexamplesa.definitions of trigonometric ratiosb.pythagorean identitiesc.compound angle identitiesd.double and half angle formulasexercises6 trigonometric functionssummaryexamplesa.graph of trigonometric functionsb.trigonometric equationsc.inverse trigonometric functionsexercises7 lengths and areas in circles and trianglessummaryexamplesa.lengths (arc length, radius and perimeter)b.areas (area of a sector, area of a triangle and area of a segment)c.the sine rule and its ambiguous cased.the cosine ruleexercises8 vectors and their operationssummaryexamplesa.using vectors to find area of a triangleb.parallel and perpendicular vectorsexercises9 complex numberssummaryexamplesa.operations of complex numbersb.modulus and argument of a complex numberc.cartesian form, modulus-argument form and euler¡¯s formd.conjugate of a complex numbere.de moivre¡¯s theoremf.th roots of a complex numberexercises10 lines and planessummaryexamplesa.linesb.planesexercises11 sequences and seriessummaryexamplesa.arithmetic sequences and seriesb.geometric sequences and seriesc.compound interests and populationexercises12 differentiationsummaryexamplesa.limit, convergence and continuityb.first principlesc.simple rules of differentiationd.chain rule, product rule and quotient rulee.& implicit differentiationf.the equations of tangents and normalsg.the second and higher derivativesexercises13 integrationsummaryexamplesa.simple rules of integrationb.integral ofc.integral of trigonometric functionsd.integral by substitutione.integral by partsexercises14 applications of calculussummaryexamplesa.rate of change and related rate of changeb.graphical behaviors of a functionc.optimisationd.areas and volumese.kinematicsexercises15 statisticssummaryexamplesa.measurement of the center and spread of a data setb.frequency distribution tablec.histogramd.cumulative frequency table and graphe.boxplotf.& the relationship between variance and meang.t correlation and linear regressionexercises16 counting principlessummaryexamplesa.sum and product principlesb.permutation and combinationexercises17 probability calculationsummaryexamplesa.tree diagram and venn diagramb.2-dimensional table or 2-dimensional gridsc.independent events and mutually exclusive eventsd.conditional probabilityexercises18 binomial expansionsummaryexamplesa.pascal triangle and binomial coefficients (binomial theorem)b.coefficients and terms in the binomial expansionc.coefficients and terms in the product of binomial expansionsexercises19 probability distributionssummaryexamplesa.discrete distributionb.continuous distributionc.binomial distributiond.poisson distributione.normal distributionexercises20 mathematical inductionsummaryexamplesa.divisibilityb.sequences and seriesc.differentiationexercisesanswers to exercises