F4AddMathsFORM FOUR ADDITIONAL MATHEMATICS YEARLY PLAN 200Learning AreaLearning ObjectiveLearning OutcomesJANUARYFEBRUARYMARCHAPRILMAYJUNEJULYAUGUSTSEPTEMBEROCTOBERNOVEMBERDECEMBER123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051521 Functions1 Understand the conceptof relations.Represent relations using:a) arrow diagrams,b) ordered pairs,c) graphsIdentify domain, object,image and range of arelation.Classify a relation shown ona mapped diagram as:one-to-one, many-to-one,one-to-many ormany-to-many relation.2 Understand the conceptof functions.Recognise functions as aspecial relation.Express functions usingfunction notation.Determine domain, object,image and range of afunction.Determine the image of afunction given the objectand vice versa.3 Understand the conceptof composite functions.Determine composition oftwo functions.Determine the image ofcomposite functions giventhe object and vice versa.Determine one of thefunctions in a givencomposite function giventhe other related function.4 Understand the conceptof inverse functions.Find the object by inversemapping given its imageand function.Determine inverse functionsusing algebra.Determine and state thecondition for existence of aninverse function.2 Quadratic Equations1 Understand the conceptof quadratic equations andtheir roots.Recognise a quadraticequation and express it ingeneral form.Determine whether a givenvalue is the root of aquadratic equation by:a) substitution,b) inspection.Determine roots ofquadratic equations by trialand improvement method.2 Understand the conceptof quadratic equations.Determine the roots of aquadratic equation by:a) factorisation,b) completing the square,c) using the formula.Form a quadratic equationfrom given roots.3 Understand and use the conditions for quadratic equations to havea) two different roots;b) two equal roots;c) no roots.Determine types of roots ofquadratic equations fromthe value of b2 4ac .Solve problems involvingb2 4ac in quadraticequations to:a) find an unknown value,b) derive a relation.3 Quadratic Functions1 Understand the conceptof quadratic functions andtheir graphs.Recognise quadraticfunctions.Plot quadratic functiongraphs:a) based on giventabulated values,b) by tabulating valuesbased on givenfunctions.Recognise shapes of graphsof quadratic functions.2 Find the maximum andminimum values ofquadratic functions.Determine the maximum orminimum value of aquadratic function bycompleting the square.3 Sketch graphs ofquadratic functions.Sketch quadratic functiongraphs by determining themaximum or minimumpoint and two other points.4 Understand and use theconcept of quadraticinequalities.Determine the ranges ofvalues of x that satisfiesquadratic inequalities.4 Simultaneous Equations1 Solve simultaneousequations in two unknowns:one linear equation and onenon-linear equation.Solve simultaneousequations using thesubstitution method.Solve simultaneousequations involving real-lifesituations.5 Indices and Logarithms1 Understand and use theconcept of indices and lawsof indices to solveproblems.Find the values of numbersgiven in the form of:a) integer indices,b) fractional indices.the values of numbers inindex form that aremultiplied, divided or raisedto a power.Use laws of indices tosimplify algebraicexpressions.2 Understand and use theconcept of logarithms andlaws of logarithms to solveproblems.Express equation in indexform to logarithm form andvice versa.Find logarithm of a number.Find logarithm of numbersby using laws of logarithms.Simplify logarithmicexpressions to the simplestform.3 Understand and use thechange of base oflogarithms to solveproblems.Find the logarithm of anumber by changing thebase of the logarithm to asuitable base.Solve problems involvingthe change of base and lawsof logarithms.4 Solve equationsinvolving indices andlogarithms.Solve equations involvingindices.Solve equations involvinglogarithms.6 Coordiate Geometry1 Find distance betweentwo points.Find the distance betweentwo points using formula.2 Understand the conceptof division of line segments.Find the midpoint of twogiven points.Find the coordinates of apoint that divides a lineaccording to a given ratiom : n.3 Find areas of polygons.Find the area of a trianglebased on the area of specificgeometrical shapes.Find the area of a triangleby using formula.Find the area of aquadrilateral by usingformula.4 Understand and use theconcept of equation of astraight line.Determine the x-interceptand the y-intercept of a line.Find the gradient of astraight line that passesthrough two points.Find the gradient of astraight line using thex-intercept and y-intercept.Find the equation of astraight line given:a) gradient and one point,b) points,c) x-intercept andy-intercept.Find the gradient and theintercepts of a straight linegiven the equation.Change the equation of astraight line to the generalform.Find the point ofintersection of two lines.5 Understand and use theconcept of parallel andperpendicular lines.Determine whether twostraight lines are parallelwhen the gradients of bothlines are known and viceversa.Find the equation of astraight line that passesthrough a fixed point andparallel to a given line.Determine whether twostraight lines areperpendicular when thegradients of both lines areknown and vice versa.Determine the equation of astraight line that passesthrough a fixed point andperpendicular to a givenline.Solve problems involvingequations of straight lines.6 Understand and use theconcept of equation of locusinvolving distance betweentwo points.Find the equation of locusthat satisfies the conditionif:a) the distance of amoving point from afixed point is constant,b) the ratio of the distancesof a moving point fromtwo fixed points isconstant.Solve problems involvingloci.7 Statistics1 Understand and use theconcept of measures ofcentral tendency to solveproblems.Calculate the mean ofungrouped data.Determine the mode ofungrouped data.Determine the median ofungrouped data.Determine the modal classof grouped data fromfrequency distributiontables.Find the mode fromhistograms.Calculate the mean ofgrouped data.Calculate the median ofgrouped data fromcumulative frequencydistribution tables.Estimate the median ofgrouped data from an ogive.Determine the effects onmode, median and mean fora set of data when:a) each data is changeduniformly,b) extreme values exist,c) certain data is added orremoved.Determine the most suitablemeasure of central tendencyfor given data.2 Understand and use theconcept of measures ofdispersion to solveProblemsFind the range of ungroupeddata.Find the interquartile rangeof ungrouped data.Find the range of groupeddata.Find the interquartile rangeof grouped data from thecumulative frequency table.Determine the interquartilerange of grouped data froman ogive.Determine the variance of:a) ungrouped data,b) grouped data.Determine the standarddeviation of:a) ungrouped data,b) grouped data.Determine the effects onrange, interquartile range,variance and standarddeviation for a set of datawhen:a) each data is changeduniformly,b) extreme values exist,c) certain data is added orremoved.Compare measures ofcentral tendency anddispersion between two setsof data.8 Circular Measure1 Understand the conceptof radian.Convert measurements inradians to degrees and viceversa.2 Understand and use theconcept of length of arc of acircle to solve problems.Determine:a) length of arc,b) radius,c) angle subtended at thecentre of a circlebased on given information.Find perimeter of segmentsof circles.Solve problems involvinglengths of arcs.3 Understand and use theconcept of area of sector ofa circle to solve problems.Determine the:a) area of sector,b) radius,c) angle subtended at thecentre of a circlebased on given information.Find the area of segments ofcircles.Solve problems involvingareas of sectors.9 Differentiation1 Understand and use theconcept of gradients ofcurve and differentiation.Determine the value of afunction when its variableapproaches a certain value.Find the gradient of a chordjoining two points on acurve.Find the first derivative of afunction y = f (x), as thegradient of tangent to itsgraph.Find the first derivative ofpolynomials using the firstprinciple.Deduce the formula for firstderivative of the functiony = f (x) by induction.2 Understand and use theconcept of first derivative ofpolynomial functions tosolve problems.Determine the firstderivative of the functiony = axn using formula.Determine value of the firstderivative of the functiony = axn for a given value ofx.Determine first derivative ofa function involving:a) addition, orb) subtractionof algebraic terms.Determine the firstderivative of a product oftwo polynomials.Determine the firstderivative of a quotient oftwo polynomials.Determine the firstderivative of compositefunction using chain rule.Determine the gradient oftangent at a point on acurve.Determine the equation oftangent at a point on acurve.Determine the equation ofnormal at a point on acurve.3 Understand and use theconcept of maximum andminimum values to solveproblems.Determine coordinates ofturning points of a curve.Determine whether aturning point is a maximumor a minimum point.Solve problems involvingmaximum or minimumvalues.4 Understand and use theconcept of rates of changeto solve problems.Determine rates of changefor related quantities.5 Understand and use theconcept of small changesand approximations to solveproblems.Determine small changes inquantities.Determine approximatevalues using differentiation.6 Understand and use theconcept of secondderivative to solveproblems.Determine the secondderivative of y = f (x).Determine whether aturning point is maximumor minimum point of acurve using the secondderivative.10 Solution of Triangles1 Understand and use theconcept of sine rule to solveproblems.Verify sine rule.Use sine rule to findunknown sides or angles ofa triangle.Find the unknown sides andangles of a triangleinvolving ambiguous case.Solve problems involvingthe sine rule.2 Understand and use theconcept of cosine rule tosolve problems.Verify cosine rule.Use cosine rule to findunknown sides or angles ofa triangle.Solve problems involvingcosine rule.Solve problems involvingsine and cosine rules.3 Understand and use theformula for areas oftriangles to solve problems.Find the areas of trianglesusing the formula() ab sin C or its equivalent.Solve problems involvingthree-dimensional objects.11 Index Number1 Understand and use theconcept of index number tosolve problems.Calculate index number.Calculate price index.Find Q0 or Q1 givenrelevant information.2 Understand and use theconcept of composite indexto solve problems.Calculate composite index.Find index number orweightage given relevantinformation.Solve problems involvingindex number andcomposite index.Project Work1 Carry out project work.Define the problem/situation to bestudied.State relevant conjectures.Use problem-solving strategies tosolve problems.Interpret and discuss results.Draw conclusions and/orgeneralisations based on criticalevaluation of results.Present systematic andcomprehensive written reports.Revision1 Practice techniques answering questions.

F5AddMathsFORM FIVE ADDITIONAL MATHEMATICS YEARLY PLAN 2009Learning AreaLearning ObjectiveLearning OutcomesJANUARYFEBRUARYMARCHAPRILMAYJUNEJULYAUGUSTSEPTEMBEROCTOBERNOVEMBERDECEMBER123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051521 Progressions1 Understand and usethe concept of arithmeticprogression.Identify characteristics ofarithmetic progressions.Determine whether a givensequence is an arithmeticprogression.Determine by using formula:a) specific terms in arithmeticprogressions,b) the number of terms inarithmetic progressions.Find:a) the sum of the first n terms ofarithmetic progressions,b) the sum of a specific numberof consecutive terms ofarithmetic progressions,c) the value of n, given the sumof the first n terms ofarithmetic progressions.Solve problems involvingarithmetic progressions.2 Understand and use theconcept of geometricprogression.Identify characteristics ofgeometric progressions.Determine whether a givensequence is a geometricprogression.Determine by using formula:a) specific terms ingeometric progressions,b) the number of terms ingeometric progressions.Find:a) the sum of the first n termsof geometric progressions,b) the sum of a specific numberof consecutive terms ofgeometric progressions,c) the value of n, given the sumof the first n terms ofgeometric progressionsFind:a) the sum to infinity ofgeometric progressions,b) the first term or commonratio, given the sum to infinityof geometric progressions.Solve problems involvinggeometric progressions.2 Linear Law1 Understand and use theconcept of lines of best fit.Draw lines of best fit byinspection of given data.Write equations for lines of bestfit.Determine values of variablesfrom:a) lines of best fit,b) equations of lines of best fit.2 Apply linear law to nonlinearrelations.Reduce non-linear relations tolinear form.Determine values of constantsof non-linear relations given:a) lines of best fit,b) data.Obtain information from:a) lines of best fit,b) equations of lines of best fit.3 Integration1 Understand and use theconcept of indefiniteintegral.Determine integrals by reversingdifferentiation.Determine integrals of axn, wherea is a constant and n is an integer,n 1.Determine integrals of algebraicexpressions.Find constants of integration, c, inindefinite integrals.Determine equations of curvesfrom functions of gradients.Determine by substitution theintegrals of expressions of theform (ax + b)n, where a and b areconstants, n is an integer andn 1.2 Understand and use theconcept of definite integral.Find definite integrals ofalgebraic expressions.Find areas under curves as thelimit of a sum of areas.Determine areas under curvesusing formula.Find volumes of revolutions whenregion bounded by a curve isrotated completely about thea) x-axis,b) y-axisas the limit of a sum of volumes.Determine volumes of revolutionsusing formula.4 Vector1 Understand and use theconcept of vector.Differentiate between vector andscalar quantities.Draw and label directed linesegments to represent vectors.Determine the magnitude anddirection of vectors representedby directed line segments.Determine whether two vectorsare equal.Multiply vectors by scalars.Determine whether two vectorsare parallel.2 Understand and use theconcept of addition andsubtraction of vectors.Determine the resultant vector oftwo parallel vectors.Determine the resultant vector oftwo non-parallel vectors using:a) triangle law,b) parallelogram law.Determine the resultant vector ofthree or more vectors using thepolygon law.Subtract two vectors which are:a) Parallel,b) non-parallel.Represent a vector as acombination of other vectors.Solve problems involvingaddition and subtraction ofvectors.3 Understand and usevectors in the Cartesianplane.Express vectors in the form:a) xi + yjb)Determine magnitudes of vectors.Determine unit vectors in givendirections.Add two or more vectors.Subtract two vectors.Multiply vectors by scalars.Perform combined operations onvectors.Solve problems involving vectors.5 Trigonometric Functions1 Understand the conceptof positive and negativeangles measured in degreesand radians.Represent in a Cartesian plane,angles greater than 360o or 2radians for:a) positive angles,b) negative angles.2 Understand and use thesix trigonometric functionsof any angle.Define sine, cosine and tangent ofany angle in a Cartesian plane.Define cotangent, secant andcosecant of any angle in aCartesian plane.Find values of the sixtrigonometric functions of anyangle.Solve trigonometric equations.3 Understand and usegraphs of sine, cosine andtangent functions.Draw and sketch graphs oftrigonometric functions:a) y = c + a sin bx,b) y = c + a cos bx,c) y = c + a tan bxwhere a, b and c are constantsand b > 0.Determine the number ofsolutions to a trigonometricequation using sketched graphs.Solve trigonometric equationsusing drawn graphs.4 Understand and usebasic identities.Prove basic identities:a) sin2A + cos2A = 1,b) 1 + tan2A = sec2A,c) 1 + cot2A = cosec2A.Prove trigonometric identitiesusing basic identities.Solve trigonometric equationsusing basic identities.5 Understand and useaddition formulae anddouble-angle formulae.Prove trigonometric identitiesusing addition formulae forsin (A B), cos (A B) andtan (A B).Derive double-angle formulae forsin 2A, cos 2A and tan 2A.Prove trigonometric identitiesusing addition formulae and/ordouble-angle formulae.Solve trigonometric equations.6 Permutations and Combinations1 Understand and use theconcept of permutation.Determine the total number ofways to perform successiveevents using multiplication rule.Determine the number ofpermutations of n differentobjects.Determine the number ofpermutations of n different objectstaken r at a time.Determine the number ofpermutations of n different objectsfor given conditions.Determine the number ofpermutations of n different objectstaken r at a time for givenconditions.2 Understand and use theconcept of combination.Determine the number ofcombinations of r objects chosenfrom n different objects.Determine the number ofcombinations r objects chosenfrom n different objects for givenconditions.7 Probability1 Understand and use theconcept of probability.Describe the sample space of anexperiment.Determine the number ofoutcomes of an event.Determine the probability of anevent.Determine the probability of twoevents:a) A or B occurring,b) A and B occurring.2 Understand and use theconcept of probability ofmutually exclusive events.Determine whether two events aremutually exclusive.Determine the probability of twoor more events that are mutuallyexclusive.3 Understand and use theconcept of probability ofindependent events.Determine whether two events areindependent.Determine the probability of twoindependent events.Determine the probability of threeindependent events.8 Probability Distributions1 Understand and use theconcept of binomialdistribution.List all possible values of adiscrete random variable.Determine the probability of anevent in a binomial distribution.Plot binomial distribution graphs.Determine mean, variance andstandard deviation of a binomialdistribution.Solve problems involvingbinomial distributions.2 Understand and use theconcept of normaldistribution.Describe continuous randomvariables using set notations.Find probability of z-values forstandard normal distribution.Convert random variable ofnormal distributions, X, tostandardised variable, Z.Represent probability of anevent using set notation.Determine probability of an event.Solve problems involvingnormal distributions.9 Motion Along A Straight Line1 Understand and usethe concept ofdisplacement.Identify direction of displacementof a particle from a fixed point.Determine displacement of aparticle from a fixed point.Determine the total distancetravelled by a particle over a timeinterval using graphical method.2 Understand and use theconcept of velocity.Determine velocity function of aparticle by differentiation.Determine instantaneous velocityof a particle.Determine displacement of aparticle from velocity function byintegration.3 Understand and use theconcept of acceleration.Determine acceleration functionof a particle by differentiation.Determine instantaneousacceleration of a particle.Determine instantaneous velocityof a particle from accelerationfunction by integration.Determine displacement of aparticle from accelerationfunction by integration.Solve problems involving motionalong a straight line10 Linear Programming1 Understand and use theconcept of graphs of linearinequalities.Identify and shade the region onthe graph that satisfies a linearinequality.Find the linear inequality thatdefines a shaded region.Shade region on the graph thatsatisfies several linearinequalities.Find linear inequalities that definea shaded region.2 Understand and use theconcept of linearprogramming.Solve problems related to linearprogramming by:a) writing linear inequalities andequations describing asituation,b) shading the region of feasiblesolutions,c) determining and drawing theobjective function ax + by = kwhere a, b and k areconstants,d) determining graphically theoptimum value of theobjective function.Project Work1 Carry out project work.Define the problem/situation to bestudied.State relevant conjectures.Use problem-solving strategies tosolve problems.Interpret and discuss results.Draw conclusions and/orgeneralisations based on criticalevaluation of results.Present systematic andcomprehensive written reports.Revision1 Practice techniques answering questions.

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