FRAMEWORK FOR MAIHEMABBCS PKESCRBPTk8I4 -"a - w-==a=' m-aL ~ = - z a ' ~ - T ~ ~ - - ~ ~ - - ~ - - - - i ..----I_1I -- - --- - - __I___--- Ass~ssme~qi ---__ -.-_____ - -- - - - - - _ _ I - - F F O T 3 ~ - - I [ nwnI 4 I Unit 'I I - Welat~ens a% Funct~uns - -,------ - .- - 1 Unit 1 - Directed Numbers Unit 2 - Rational Numbers Urnit 2 - Products & Factors o 3 taots, one on unik I 2 , one on ur\\!C Unit 3 - Measurement 4 and the other on ursilt 5 The tebk Unit 4 - G~akhernalical Shorthand 'I Unit 3 -- Logar~thrns shoalld be of at least 35 rnln~lter, duration each Untt 4 - 7ngcaraomeluy (wrth PgrtEuagorlis) ca 2 student xssxksheetsl workshsets, Unit 5- Coordinates I Un~i 5 - Properties of Shapes 2 one on unit 3 and hhe other on umhs G !Jail 6 - Social FvPaQhematicsZ 8 r Unit 7 - Statistics 1 Unit 6 - MathemaliceP SB~orthearnd 2 Unit 8 - Properties of Shapes 1 e Gonsts ucti&sw$lDssiqn Un~t 7 - Coord~nabes 2 1 asks rrr 1 errn 3 covet lrlg unrts 8 to 12 Ter~si 3 (Details on these are prov~ded ou-o a Unai 8 - Social Malf~emaliles 2 qepasate sheet) Unit 9 - Translations asad Vecbrs Unit 40 - Rcfiecbis~ns Unat 9 - Stabstrcs 2 -- B ill@ interlea& assscsments will be Unit 11 - Rslaticar-ss worth 50% 06. &he FJG mark. Unit 12 - Enlargement 8 Similarity Unit 10 - Probabal~Py 3 ~ 3 PREAMBLE t.1 The Fiji Junior Cevtificate hJathematics course provides opportunities for sluderlts lo olejrelop further a broad range of sltilis ar~cl ealcurdrayeb; them to be creative and good problem solvers in their daily lives. - - 1.2 1 eachers need to note that the understanding of w~alllerr~atical concepts irluolves more than learning a set of rules or i~sirlg a formula. It involves knowing what method 10 choose, Row to use it and why iE works irr a particular sii.ualioi.r. 1.3 mathevlatical processes include problem solving, togical reasoning, analytical thinking, communication, rnaitirlg co~~neclioris and using mathematical tools. Calculators as tools will feature prcrninenlly irr the new course. These should be developed withirt the context of the iopic::; and emphasised "troughout the course. 1.4 Flriathema"tcs at this level lays the foundation for mathematics learr~ing in Form 5 2.0 AIMS AND OBJECTIVES 2.3 AIMS -- I he FJC Matli~ensatics course aims to develop: (a) in students a sound undefsland~ng of, and the abiliiy lo use ru?;aihemaficdl concepts and processe:> (b) students' mathematical skills and abilities to think and reason logically, and lo cnrnrnanicaie rnaiklemaiicai ideas av?d e:cperier~ce:;, orally and in writing jc) sktadents' knowledge and skills, and the understanding recju~ied for everyday i ~ v ~ n g , atlid for- i-iiilhe~ learning Iri niaihem-ii~cs 3rd oliie; suE3Jects (el sfr.~der~ls' abi!ilies t'u conileef mathematics to everyday siiuaiicins, to sShcer topics within vnattjcanaatics 3rd to otlier' eb!s b $1 -I r$f;*~'"' j ( i') ir: slilcki-~ts favourable aittit'udss ts\\~ards, and continuing int@re:;l in matl.len-rahics (g) iis stlr.rci~:rlts she abiPi'iy f.o recogi'lise and appreciate the mathematics in et~eryday situaiior~s (h) sti~deslts' i:orifidence and ability to do mathenlatics QE,,JEc]'lVES On conipi~iing the i3ji d u r ~ i ~ r Ceri~.[~cate course, pupils seaauld have 2.2."1 develc~psd ihe kna:jwledge and undea-shdding re q t l i ~ ~ d to: ) use wilh increasing cos'lfidence problem-solvirsg approaclles "l investigate and tlrrderstand xnaV~ematEcat cos~ler-lt ! recognise arid 'Tor~.slulate problems fsrarn siiuai~cafss within and outside rnatklemalics jc) develop arid apply a variety of skdtegies &o solve problems wikhil-s and G;~w~s~c"~F: ~ l a i h e ~ ~ a i i c s (..\\I " i :?pisly mathema"lical patterras and re:latiionships to everyday situations (f) make conrtectinns with other Bopics within Mathematics, with otkrer subjects and with tire oukside world (gj zppPy rnlathematics to everyday life 2.2 3 dc~elopad the" values arad attliudes wliic!~ 17eip them 10. (a) appreciate Mathem:=~tics as ark infere~k~ng, enjoyable and cha!lenga~lg subjee:i &I) develop the skills of ~nquiry, investigation, discovery and verificals~n which afe cS:ssei\\$saB lor the Iearrlli~g of I~AaiiB~errii~il~"~ (cj appreclafe Mathematics as a creative, relevarat ar~d i~seful activity in daily iivislg jcZj galn conf~deni:e in their abelrty lo learn and practice self assessm~wt s&w!%s in mb-sfi\\emat~cu (e) show confidence in using tileer own Iciirguage and the larlguage of li~iatRe~18ties to express mellrematicai 3de72s f ) vxerc!se self d~scepllne and be resourcafaal in engaging ila maAemeatical activodss (g) work co-operalively w~Eh others alld padicipade in group d~seusslsr~s (h) appreciate that Matkrematscs is useful to the learning sf other subjects and for job opporaunsi~es. o;a Estirnaking arid approximatiu~g ~r Personnel Q Recognising and using patterns and relationships + a 6 f 3 l l ~ ~ ~ d 1 Organising information b r mathematical analysis o Rc:i1reser-n2atioun and irrterpietatnbr-a / _ Preser~tc~ti~~n __ __ __- - ii$%$MG TQQLS AND 6biANAGBNG RESOURCES Problem soiving plannir~g a 6s'l:ikr~~ent~ 8 Problem soivialg strategies o Calculators Modelling e Corr-ep~iters BlAanagiwg t ~ r r ~ h/las.naging mlsraey o Managiw~GI~er -- resources - -- - - -- - -- - - - - A I . Categorising and interpreting I 6. MAKING CONNf:Glti"iiObJS s VVitPrlin ma"6tlenlatics Recognising and working with patterns e Other eun-ieu6iarn areas ca Reasoning Everyday life inferring o General Proving - -- --.-..----_.__.-____-~~_~~-._-..._I_..- .~ GENERAL PUMS --. -. -,-- -*-"-- "- i\\Aer completing this unit, stkade~rts r;hauid be able to e To revise and extend Ihe use OF 1. (a) ideniify the basic uirits of measurermni used in\\ the rnetric system. rn~irrc units for measurements (b) stale itle values for commonly used metric prefixes. (c) convert frorn one uoil to another with She relevant prefixes o To discuss the accuracy of (d) wrile a gi\\ien number in standard form and \\iice."vessa. measurements 2. (a) estimate comrvlonly used dimension such as length, mass, area, o To Interpret and draw scale \\colurne, and Eiaae dragrams (b) measure objects to the nearest units required (6) write a measurement correct Bca the ~aearesl unit required To measure ci~rect~ons by idsrng (d) slate Ihe smallest and largest possible measurements for ail object compass bearlngs whose recorded measurement is given; Classify tiie dislinr::iion betweer1 (e) wrile an inequality for the aciual measure o.1 al: object wl-ien given a mass and weight. Ci.g. A mass recorded meascnre for it. of 511 kg has a weighi of diO0 N. o To revlse and extend idects of areas and volurne 3. (a) interpret the: scale of a drawing as the ratio of Ieinylh 01 the drawri object to the length of Phe actual ok~ject; (h) calculate lengtlls of objects from a scale dsawirig; (c) draw scale diagramis to a given scale; (d) measure angles of elevation and depression using a ciio~orneher. I. (a) case a magneiic cornpass to give the bearing of an objeci from where the student stands; Irv'uric or1 rsvnljiems deaiing wit!] (b) determine the bearings of points usirrg a map or diagram, and 3 elevation-\\ anrl depressinri are io protractor; be 1%ea9t \\~~,vith as part oi the iilrori; (c) draw sdale diagrenls where the directions or' lines, or the direction frorr~ or1 Trigonometry. one point BC'I another, are given as beauings. 5. (a) apply and manipulate, formulac for tire area of e redangle, square, parallelogram, triangle, rhombus and taapeziusr~. (b) Calccrlale the circosrslerence and area of a circle and relate these b the area and are length sf a sector (c) Calculate approximate ereas for irregular figures by using Irapeziurn; (d) Calanlo'ce the surface area of sirnple cuboids, cylinders ar~d spl-seres. 5. Apply and nlarsi[~uleke, forimuias for the wolurne of prisms, g~yran~ids and sphc!ses. After corr~pleting this urrii, sluderrts should be able lo : I MATHEMATI& 0 'fo introduce stlidenis lo a 1 (a) e;cpiarn the difference between rrumerals and pronumerals, SHORTHAND 4 I nlaihematical language oftell called algebra. (b) narlrie different types of algebraic expressions on the basics or" the number of terms in each - monownial, birroru,ial, trinomial only; (c) difierenliaie between "lilie" and "unlike" terms and then add and subtract polynomials; To practise rnanipulaiii~g (d) multiply and divide rnonon-iials, including those wv~lh powers pronumeral terms, expressior~s and fractions, solving linear equations and inequations, and 2. (a) relate numerical fractions to algebraic fractions using operators. (b) add, subtraci, multiply and divide s~mple algebraic fractions. 3. (a) explain the coileepl of an operator, I (b) know the meaning of the terms "inverse operator'' and "self-inverse operator"; (c) solve problems involviiig operators, their inverses, arid combination o i two operators. 4. solve simple linear equations, such as 2x -4 117; &o($ = 2 ; ,ti2 - x/:3 -. 0 4 5. (a) use set-buiider notation; (b) determine the soli~tion set of an ii?equation, and graph it on an appropriate number line. . ~. . - - - - .~,,,,--,s-~n---3,..LIyA x8-. m. - , I - . m " llllCI_-v-.---- "&" b . m L - .-.>. ,. After cornpietirig this unit, siudr:nis should be zble lo : 1-0 revise and extend the work '1. (a) give rational i~umber coordinates for potrrls on coordinates platted on a number line and vice versa, e To draw graphs of sets of numbers and inequalities in one variable, on a number line (b) graph inequalities on a ilurnber line, using irrlegers or real nurnbers as replacement set: All work era graphs o'i Einc\\iir Ga To draw graphs of lines parallel to the axes on a Cartesian (i) graph ail real numbers greater ihan 5. equaiicjns okkrer than tilose plane. parailel io the x or the y-mi:,, (ii) Graph eq~eaticiils of grrapi~; a ~ t i i )( < 3 6 , x E real number irnecio~aiities associated wit11 line (ii!) Graph all integers where -2s x < 8 graphs is ext:lalded at this skigo. 1 (c) descnbe sets sl pomrs graphed on d wunlber fine 4- -+. e 9 (1) <&k%-~~+~4i$=~~~~~ e l e n l i t ~ i ~ ~ b t i - 2 0 2 4 -$* (ii) + ('11tegeis less 1lt:rii 3 ) 01 k 57, x all 1nti:gel - r 0 P 2 2. (a) give integer coordinates for points plotled on a Cartesian plane and vi;:e versa; (b) Determine ilie coordinates OF points and graph the lines of the ~faliovvin~g types of equations : e.g. x = 2 , B/ =: 5 ' 7 y == x = .I4 (c) m~ie down ihe equation of a givers line that is parallel Ica one oi iCle axes After completing this unit, sludents sbio~~ld be able 10: 1-0 revise and exierad students' 1. peiform simple money (;alculaiions for domestic pilrcklases; SOClAL M A T H E M A W / knowledge and use of money 01 t''fo ohle(:tsl j- calculations and percentages, 2. (a) write a ratio to coi~qpare tiis corres~or!aincj ~ i ~ a ~ l J ~ e (b) deiermine the larger (or ~irialitr) o l iwo objecis cornpared in a rail0 w To inlroduce stadenls to the and if the measure of one o i the objects is given, calc;ulate ihe concepts of ratio, proportion and measure of tile other object; rate and apply these in (c) identi@ ratios that are eqvivaleni; everyday situations. (d) simplify ratios; (el apply ratios to incita.;lng or decreasing u i quarrliiies, and lo tiivlsion into parts; I 3. ( 8 ) identify when two variable qi~aiitiias are proportinrial, and lo explali~ why they are proportional; (b) perform sirlapie calculations involving two variables ?hat are proportional; 4. (a) calculate a rate or ail average sale; (b) perform simple calculaiions in\\~olving rakes or average sates; 5. (a) convert a traction or decimal irilo a percentage, arid vice versa; The use of calculraiors to \\h1oldf d, i! on percentages \\ ~ l \\ i greatly 1 (b) express one quantity as a percentage o i another; reduce h e tiroe ieyirire:! io 1 solve problems. 1 I (c) calcuiaie the percentage of a cluairliiy; il 1 1 I i (d) increase or decrease a quantity by a given percentage; i ii (8) pe&rm sirnple calcl;laiions iil\\/oIvis;lcj percentages, inc:l~.idincj ~ ~ r o t l i 2ild loss calculations , - * . - ' - a . --___ _ ------ m . ~ . ~ ~ - o , , = . ~ m s ~ ~ A , - ru.-o--,ss, ---= - a - . - _ Y _ _ a i i ------ ~-~ "-.-~'." m~ --.-*--.=" -,--" u-~.u--..4.--b~a,.~~--~.-- .-,.a-,.s.-e ~ .-,.- ----~~------w.c.,u...~ %-<*-.A.-Ls<-. ~ =>.<.-.-d.c-sv.~, ~~ . * . % A **.." -..- .*-, -.. - : , ~4.d--w*. ..-ad-*.,%.-*. , UP%!% TD"E 1 ---- - .,-*.--*--.= .-..------- - - - - * m - . a - G e = - GENERAL AIMS SDAECBF'If.; OBJECTIVES ~ ~, I ,-~ - - , . ~ . - ~ A ~ ~ ~ ~ ~ ~ ~ - V ~ - , - - V ~ ~ ~ < - ~ ~ "-. ~ - , - ~ -I- c;opjjpiflr!;bj~ s 1 ~ --,-.~~-u"&- ,. &.<.-,-." ----------.-.-. " &-au. - 1 I I- I Y i *- At the end o i this unit, skwde!>Ps shoi~ld be able io : In this unit, siuder~ls will loo/( at 1. (a) draw charts lo represerii tables of slalisticai data usirig pie charts, piciograms, bar-graphs and line gr-aplis represeriling statistical data in graphical or chart form; (b) comment on the irverall Isends illinsirated in a graph of staiistii:al data and also read vaiues from it: computing R e mean, median, mode and range for a given (c) decide when, and how, a chart coi~ld be used l o critically analyse sample coriclusions drawn from statistical data; C"..jc / . . f , a l u ii 01 work on siaiislicai 2. firndions is r~oi necessary ;,i tliis 0 organising data from a sample caiciilale the range, mode, median arrd mean for a given set of nurneric~;I into a frequency distribution and data. si3ge. representing this by a frequency line graph or 3. (a) organise numerical data irrto a frequency table, where equal width hislogmm. class intervals are given, and draw a frequency line graph.or a (:aicul;-aiioris of the rnear) \\rtil! riiii histogram lo illustrate ii; in\\!oive using grouped ciala as ir.1 a Giequency table. (b) when given nul-uerical data i i ~ the lonn ol a freqirerscy table or a frequency lirle graisii or a histogram, delermirre the i-anye, Ihe mode or khe rnodal class, and the median; (c) read off a freques~cy lirle graph or a histagraurr, record the data in a irequency labie, and answei questions related ko the graph and ",he table. After completing this unit, students shocild be able to: TBIS unit has been pill %o:~,cV~~cr with units on transl'orrnatioils to a 10 exterid students' knouiledge of the angie and symmetry enable siadents lo relaie move properties of krangles, 1. (a) classify iriangies as equilateral, isosceles or scalene, and as obiuse- easily io puoperlies .it figures quadrilaterals, polygons and angled or acute-angled: airld ihe iransic~mmaiiorrs ?hey clrcies undergo. o To explore the angles i o ~ ~ r ~ e by d (b) stale and use in simple problems, the property of the sum of llie a transversal on tho parallel knterior angles of a triangle, and the property or' the exterior angle of a i~nes tri~anglr?; a To construct, examine and draw two-drmens~onal pictures of (c) draw the lines of symmetry For eyt;ilai'eual, isosceles and scalene some solrd objecis triangles and state ihe order of rotational symmetry for them; To shaw the applrcafion of properties of shapes in real-l~le (d) use the symmetry of a triangle to make deductions about the sizes of s ~ t ~ ~ a l ~ o n s its sides and angles; je) decide whether a triangle can be drawn from the inforrnaliori given about its sides and angles; (f) make an accurate drawing of a given triangle. 2. (a) g!ve correct names oC polygons with 3 lo 10 sides e.g. Ir~angEe, quadrilaleral, penlagon, i~exagon etc. (b) calculate, and use irr sirnple problems, the sum of the lriter~or angles of a polygon. (c) know, and use the properly of the sum o i the exlerlor angles or' a polygon (d) skate the number of axes of symmetry and !he order of rotational symmetry of a regular polygon, and show these on diagram of the iegiliar polygon; SPECIFIC OBJEGP'YVES -- .-*.- a~.-~a,'%-*".a%-L"-w--,m--.,---a~-- .s-Ax-Ls=-.-%-- a~z~.&~~~.~..--s."~ 3. (a) name from a diagram pails of alternate, allied, corresponding, vertically opposite, adjacent, cowrplenaenl'ar'y and supplerrlentary angles; (b) give the cornplernenl, and supplement of a given angle; (e) use in si~mple numerical problems, the properties of verCcalEy opposite angles, the :ium of tile angles OPI straight line, and the sum of Ike angles around a point. (d) stale, and use, Ilhe properties of alternate, allieti, and correspondirng angles, when lines are parallel; je) stale a definition of parallel lines; (f) identify parallel lines arrd non-parallel lines ( g ) draw a line parallel to another, and th~ough a given point, by ~rsing a st& square and straigllt edge. 4. (a) identify avrd name trapeziums, parallelograi~~s, rectangles, rhombus, squares, kites and arrowheads (b) for the quadrilaterals in (a), indicate Vieir syrnrneir'ies arid use !lien.\\ to deduce lengths and arigierj of given cquadriialerals; (c) state, and use, ihe basic side, angle and diagonal preperhes of the quadrilaterals in (a) above 5. (a) state tlrnat a circle is syn~metsical about any ciiaaneler; (b) use the properly that the mediator of a chord is a diarneler of the circle (c) construct toe centre ol the circle by using a straight edge and a compass jd) define a cyclic qldk3diifat@r~u/; (e) racogr~ise when a quadrilateral is cyclic; (9 recognise, and use, the follu~diiing angie properties: (g) identify the axes of syrnmeivy in diayrarr~s showing ohe or two langeruis %o circle; (hj use symmekvy to deduce the sizes sf angles and line segmerrl;, n d~agrarns showing one or two tangents ?o c~ucle, 6 . (a) slate the difierence between pyramids and prisms; (b) idenliiy prisms and pyramids frovu\\ a colledon of solids; (c) name prisms and pyuaulids, e.g. triaiigular prism, cuboid, square pyramid. (d) ident~fy atlci coiiiil edges, faces, and vertices when given a prism:, square, pyramid etc; (e) recognise possible r~els for cubes and cuboids, (f) draw nets fgr simple solids sucil as cubes, cuboids, triangular prism, square pyramids elc. r h! / (g) consirlrci a solid objsci given its net: (h) draw p:c%uues d cubes, cubo~ds, l~yiirzs bdsed on cubo~ds, and rectangular pyrarnrds After completing this topic, students should be able to. To introduce simple translation properties and 2-component 7 . (a) identify lrasrslalions used in patterns where some basic shape is The General A1111 has been vectors to students. repeated, in one or. two dimensions ~rodiiieid. Po show the application of (b) desigrr their own patterns by banslating some basic sihape; translation and (c) stale the basic translation properties; vectors to everyday (d) use the notation A - -* A" P13Q -+ AB; situations. 2. (a) descnbc a trscssiabon by giving us vector lu? the Eoxrn (b) pe~.forrn a translalio~a when given the image of orie point, or when givesa the translation veclor; (c) draw an arrow vector for the G ~ ~ L B W I W vector 3. (a) combine trailslations by pedorming one lmnslatisn afler arlolher ($) add two vectors algebraically, and draw their addition rdiagsal~?; (c) wile down the inverse of a translation vector, and give the prhapefiies of a vector and its inverse; jci) givs the position vector for one ol~ject relative lo anotl-rar. 4. (a) pedc~rn-, transiztions when ail operator symbol is 1ar;ed. (b) perform the translation i",B where and B are operator syalrbois for transiations. a To revise and extend s i ~ l p l e After ~ o r n ~ l e l i n g this topic, students shoaloi be all1e to: Unit -lO reflection properties. 1. (a) show that the n~irror line is tkie mediator of Ihe line segnient joining a RE&L.EC%IBNS e TO show the application of point and its image; reflections to everyday situations. (b) const~uct the image given 2n object (point, line, line segment, etc.) and the mirror line!, jc) construct the mirror lirre, and lo state [hat this is an axis of symmetry; given an object and its image, All ;niasic on l~jore I h a ~i ~ o combined ir;dnsformal,ion::; i:. (d) shovv Cial an object and its Image are congiuent and therefore length, angle and area measures are ~ n v a r ! a ~ ~ t , / (el show that sense or olionhiion is changed in reflectiol~, jf) identify puirels arld lines that are invariant in a reflection 2, (a) carry out s~~ccessive reflections in two yawilc4 mirror lines, and specify the equivalent translation; ($1 carry oui successive refiecliorls in two inteiseciiilg mirrors and speciiy the equivaierrl rotation; i! is expected that graph paper 3. use operator symbols for refeelions rand cornhinations of refiedons; and lo a lesser exteill, coordinatcs will bz ust?d. 4. carry out giver) cornb~nakiorls of reflecilorls and translations _ -_______-Y_."-w-X _-svxe.-" -.-T,w-<.s%--m>%. ~ & a , . "v- V-CY-^.I-"~I~---- _sj_i___-v-, SPEciFjC OB J$CTIVE% -*--., ~ . . - , L - , A * - n , m s * a - --.a,--mAa .m*-#*,-.*7 *.-.-- - - u - w . - A . S >----*a .a ,fter completing inis iopic, students should be able 20: -ro revise and extend simple . (a) use the c~nventiow oB positive rotation (anti- cBodtwise) and negative rotation properties rotation (clock-vjise) to cor~strucl the image given an object (point, line, line segment, etc.), centre arid angle of roklian, 8 To show the application of rotations to everyday /b) find the cenlie of roldtion and skate the angle of rotation given an okajech situations. and its image; To show the me of rotation in (6) slate that an object and its irnaye under rotation are gwc.@fij and obtaining 'ine properties of therefore length, angle and area measures are invariant; some common shapes. (d) identify the point that is invariant in a ro'cateon and stale that it. is Itle cerltre of roeation. I. (a) identify figures which )lave rutalinruai syi~rmeiry and give tlie ovdeu of rotational symmetr)?; (bj identify figures ifi~hich have point syrnn3eki.y 3. use operator syvrrbols far ~o&aii~ou;s and combinahesns of rotalaoul5, 4. (a) iderrl.ify khe "Iransformskios; used; choosrng froin [tra~~sBalion, retlection, \\Miirk on hnoee llaan l!*vis rotatbnj. when given an ok1jea:t and its image, transf(irnlrlriicjns are ex~;8mded. (h) carry out given cornbination ot rslations, refections and transiaiions, and to describe the single Iransfe~r.rnat9op-r choosing from {transltrtion, reflection, and rslakion] that wokrid sr~ip the object to its fsnai image. (cp elst? o~~erators 10 carry successive Isansiormations of Grapaslalihans, reflections arld rotations. - m*-z---w---t-r-- _- _ _ m-m=. ___s,l__i _" " _ l ~ _ l i I ~ " - . i ' ~ i i l i X - . i i e - ~ j_____jIj.-Ta. -- -- -.- -- /AaY/-A I _ I Y I L A L - i l l - 2 % SPk-elFB(; OBJEbGTlVE S --- ---" - - % - - = __-mLY I" <*-- _I L M A + -M" o To introduce students to the After complehng Erlrs unit, shwdene should be able ro transformation of ENLAWGEMEM AKD enlargement, and to the idea 1 (a) identify blrllei-~ oile objecl is related to auaoihei by an enParge!nenl, SIMILARITY - of similar figures jb) make sirrsple er:iargemenls of figures drawn un gap11 paper, giveiz ikte centre of the enlargernewt and %he scale factor, {or posib!ve scele factors, (c) ident~fy the centre and the scale factor, whei3 given an c~aldrgcmeiit of figures drawn on paper, (d) use the scale fa~kor when calcuialing lengths on correspoird~ng 31des 117 an enlargemeiit, (e) use a symbol as an eniasgemer~t operator, jf) give the a i m scale Factors when rile ierrqIl\\ scale factor of dn \\jiIork oil more 1P!a1i t\\tiln enlargemerri is given, and use these in elenlentary problems, consecutive rdr'js3ornlaiions aie ni?l 2 (a9 carry 0148 com$iwatioi-r$ of tha transforrnat~ons of refltacitoils, rotations studied. i ~ n d translations with enlargement, thus obtaining s~rn~lar figures, (b) identify pass~ble Irranslormai~orns used in Pnapplng from one figure to a similar figuee, (c) ~denuty corresponding verbces, angles and line stlgrnewls given kviw ssrniiar figures (d) calculate the length scale factor and use t l ~ ~ s lo calculate orhee lengths of given sin-soilar figures (el rdea-atdy pars @a figures as sim~lai or nor 3. @-se~!ct a pantograph, given ihe ~nskructiou-i; Ass6 g ~ g li, to enlarge simple pictizres ------sa- 7- ,?---->-A ---=--A b- -.a-"-m .---*- -- - -- - s - - - - ~ - - ~ ~ = = = - " - - UWlT TITLE 1 GENERAL AIMS SF3EGIFilC OE$&IECTIVES _ __UY---- --I--=~---I----- -I--I--1-~---~------ -----L-=~-Y-I---.-~%=- a a ~ 9 1 ~ After comp!eZ~ny this umt, sludcriils should bc able to RELATlONS AND -- or Po lormalrse tile csneepk o?f FUNCTIONS a relat~on as gainng of 1. (a) draw a graph o.l a rdaiion giver) in vmrd ic~rm-pl EIY given 241; a set elements of one set, or of of ordered pairs of elements. Suitable types of graphs are elements of one set \\mf!th given belavv. elements of another. - I:; - .(J o i o introduce furec"njons as -"- special types of relations. ..__ - -=.- (b) !ist the ordered pairs sf a relation given as a gra~,A% or as a rule, with domain; (e) geb~erate ordered pairs of a relation given in the form -+3x or ((rc, 3 ~ ) ) or y = 3x, each wit11 its donaaiird; Id) listhe dornaila and rarlge ~ i / a s-ela1:sous; (e) dsavw the graph (I$ tkse inverse of the relation, given its graph; jt) list the ordered pairs of the inverse relation, given a relation as a set o.! olderecj pairs of elernenis. 2. (a) recsgnise 'al~:.st for a furletion, aaclh clerrsent 6m tile domain or" the relation is w~apped 'eo orsly silt? element of the range; (b> differentiate betbveen a function arsd a rron-.Function (a;) calculate the values of a fsrraclio~ using ns%ations such as: if "f : x -+ 2x, evaluate f 7 ; and ,if r - 2 3, find the value (;of npJ. - .,.~-*,r-=ser-,,-.-~~~*A--~,#> , u-L.- ' ,L--.u.=,a" ==.-asE b . L - * & ~ n s ~ ~ d . . . - - ~ . ~ ~ - ~ ! -->=. - . . . - . % . , ---- '""."" T-i-l-="--..--"" - " - a -w-mv------=--" - L - - * l [ UCIB ;:TL.i: p r ' <I r akRiU2AL AIMS i AAer corn[dleting ihis topic, students shreould be able tow: To apply khe distributive prspedy to the PWODLICTS ANQ - product of two polynomial expressions 1. express a given movlomial expression in kenns of fiad.ors and FACTORS and the corresponding factorasation vice versa, Example: 3 a $ - = 3 x a b = 3 a : i b = 3 x a x $ I 0 To introduce $Re use of factors ID salv~ng polynomial equations and in simpBif\\flng I ratsonal algebraic expressrrans 2 . use the distributive law Do write producls of iactoors as sums of terms 4. sirr~piify rational algebraic expressions such as: by usirng common factors Afes compleling this iogsic, steadca~ls should be able io: To begin the steady of logarithms, espedaE1y those using base 2 and base 10. 1. (a) write najrnbers iia base-index form and vice-.versa (b) simplify index expressiesrrs for positive, zero, and negative indices, 2 (a) use the expouuential grdphs y ;: 2"arld y:lO~> xr R, to write wiimbers as powers of 2 or "10, and vice versa; (b) use ihe graphs of y=2x and y:-'!Was appropiatr? to express rgiurnbers ;as ps~vers; (c) express the base-index forrrr of a slt~rntper in Bogaiiilarn fweal and vice-versa eg. giver] 32 = z5, the12 log232 = 5 and given R0g,~49 = "1.98, then 4.9 = 101 98 3 (a) use ca1cuIators tc~ iliir~d Iogarifhm~s 0% r ~ i ~ ~ n b e ; ~ ~ (b) case ca8ea1lats%rs Is fend a number, gwcn its logar~~ilrn - - - - i I --"."-C> I - L Y S I U _ a % - c r J -1 - X L E &CI , - - a C Y " _ GENEIqhL AIMS SPECIFBC OB$ECTBVE,S ' _ ,,*_l_l_ YI_UVIY__a.a.-7-,ma-ssa&% - w , - - , ~ ~ ~ - ~ ~ , ~ ~ ~ - - ~ - - " ~ - - - . ~ - - - - = LY- J.m.LP_ . l a _ , . - - - ~ . - ~ Y U ~ ~ U ~ ~ . s m . m ~ ~ . * 3 * = " - , - - - . Tx'{er oon.ipisti.~g f:i>is l~ p i c , sttide~;k sk:auid be able lo: I i 1 . Use calc~a$al~:~rr, to find squares and srguare rdds d [\\umbers I correct "r~ either one or %WJO decir~lal places. v on B 3-0 use calculabrs tra firid squares a i d 2. (a) state the f~rmula for the Pytklagoras' Theorem far any given square roots. ' C ~ ~ O Y G " ~ is part ui' lkie re'gtlt-angled triangle; 'I'rigos?oanelry I$) calc~slate the length of a side sf a riglit-angled triangle when To introduce and apply the theorem of ii Ine lengths of the other Bifiso sides are giver) as natural Pythagoras. numbers; and the square n'r side to be eaicetialed is not I 1 greater thaur 100; I Q To introduce the basic sine, cosine and (c) sfats whether a triangle is right-angled or not, by using the 1 tangent functions. concept of pythagorean lriatis (restricted to natural speciiic, obeciiw? 5, t">? 1 numbers). B pupil does not Irave io b;r e I! ; ident~ky the lengths of tile sides of fight-angled tria~syie in ferrlas able lo solve the hypoiesriisn " length lisiilg tl-~c-: 1 of r CosO rsirtd r Sin0 given the hypdenuse (r) and angle O i Brigsnomciric fur'ictioris. j/ 4. Identify the side whose Eeng'rh is :c tar! 8, for nilvnerical vr;lues 0.i b x and 63; given a side x (which is not the hypotenttse) arid an / angle 0 sf a righi- angled triangle, "ihs use rii calcuiaio!~ will I ease 1 \\ , i . v 1 r&U, ii 081 1 5. For a given right angled iriangle, select the appropriate f~liwction irigonurfielry iur'lcticuls. 11 (sine, cosine or tangent) and use it k3 solve the size of the r i; required angle or side 1 i 6. Use calculators to delermlr~e !he sine, cosine and iariyenl values fog3: given angles 7 . Skelch the graphs of sine, cosine and tangent fo:or, arlgles from 0" to 360" 8. Identify the sine, cosine and tangent graphs for arlgles irowi 0" lo 360" frorm a selection of graphs 9. Use a clinometei' lo uzeastdrc? arrgies of elewation and deprc;ssion and make subsequent calculaiica~?~ for heights. After completing this topic, students sho~sld be able b: ~3 2 study couipass and ruler 1. (a) construct, Zfae bisectclr sf an angle, mid.-point 04' a PROPERTIES QF constructions, simple loci, centres of a Bine seygmenl, the rr~edialor of a line segnsent and SHAPES 2 ---- tuianyle, and intersecting ckb~rds of a avlgles of 90°, 6OU, 45", 30" at a point on a gi~~en circle. line, usirlg ruler and compass. (a) %:onstruct the centroid, srlhoceniue, circ;u~~ceraQre asxd circuml-,irt;Re, ineenfie and incircle of a triarpigie and rdentiiy these i:~ given diagrams; 2. crsnstnsck, or iderslify on a given diagram, sets of points based sn the follw~ing loci: Ihs locus of psivats equidestant from a .fixed point, or ~ W C B .filled poiills; 13 ; she l~scus uf points equidistan.! from a given line, or froren tWo given lines; 3 state and usc it1 problems, the prcjpeny of the anple subteraded at the cenlrtt (of a circle being "awice thc sire of tl~e areqle subtended al the csrcas~nfcresoce by &he same asc, 4 slak end use in sample wumernf:a! calculaiions, the propedy QI chords inte~eciing itnissde or suBsde a elrcle, and the special case of the tauagents _ --- -.-- -- Y Z _ , Y Y _ _ _ ~ ~ _ _ ^ _ _ l _ , ~ - s = - ~ - I k - I I X I Y . I M I - L , -",. L--IY - * L_i - - - - - - B UNIT TI"FLE F GENERAL AIMS SPECIFIC OBJECTiVES F- __-- -- _-- ------ - ---- *w----x^.--;a_uru-=r;u;r- -==--*-=--i '" - -=*--=*-- -= -&- -* ! illis $pic has to be giv;:ii 1 ffi l o practise manEp~n9akion of algebraic After csmple~ng tlr~,is "rppi, S~IEC!B;~I$S S ~ P O U ! ~ be able to: expressjonr; and formulae, and solve greater em[~hasis becaiise cf ;I algebraic equations. 1. (a) substilute values inlo algebraic expressisns; tile nee! ii reinlorcn s i ~ s i n b i ' 1 (kz) add and s~rbtrac'r polynomials aiglsbnic sltiiis -- a prsi~lem c examples: encoiirllewd by sitrdeniv in lini: 1 latier school years. li. i:i aniicipaied i;ilai 1 iifiar, iniiod~ced at Forri; 7 i e ~ d wili 1 b(+ ic,',*r,? *..,(j ,' .;->I nr;)Kt . I ~ Q $ K I ~ I ~ ~~S ~ r S i (1 h solving rc;al pro\\,lsm% !I 1 (6) pe,'~f~$rm the bur basic erperations (-b-,..p:;,-f-) v~ijt!u arithmetic and zigebraic; fractions, necessitates t17j0&, ijb'i f~~rrji':{j 1 examples : cqwfons arid liiidirig soiutioiii; I io eqtn:dions so !omed. i 2. I-ind solutions sB 8&1c: follomflfing types 0 8 equatia~is: - gi) 2~ -2- 1 5~ - - fj (ii) E . J - ~ 2 3 (EiA) x' ~ 4 " ()(1.9)2=9, jx',: 3) z (i%$> (x-4) (~-2.2) ($4) 2 0 3. (a) substit~lle valeres into a giver) iormuia and give the answer it-] the sirnp9esl form; (b) ckafige the stjbjesk. of a given lownul;t. estampls: Make v 1he scrb,jec:t o'i ihe fornr~~la d=x~~Iv; (c) se~!ve problevns by translating flrOin verbal sf wrhtters slater~ent into nrathematical eqgatior~s or forrflula AAer comralcting this kogric, students should be able li?: o 1-0 dra\\czr glaphs of simple linear equations and inequaticarls in t ~ 8 1. (a) slate the intercepts on Bhe axes and Ike yradierrd vauiables on a ca~esian plane, and or slope of a giver1 liree sais tb~e cadesian plane, sr introduce the ideas of iw"hrcepls and of a line brrl-sose equation is given. slopes. 2. drawl grap81s ow a e;,ari.k:sian plane Po sb~aw pairits tisat saiisfy given inequatio~ts such as:. y - KI]X + k: .Aficr c~rnpleting this topic, sludenis sbesuld be able to. 1. (a) verify enb'ies made in savings bank accoua-lls; SOCIAL e 1 TJ look a! Sdvirlgs Bank Accounts, i+re Purchase or Credit Accourats, and Tax Ccsracepis iir this topic are aiso MATHEMATICS ---- 2 Returns as examples of scrcsal uses ra8 (b) calculat~ the tolal amouni as be paid, and ihe s~i~v~ngs 641 Bosses elementaq mathematrcs. ancurred, when goods are bought on hfre-gsirrcha"ic:, credit Beoms, Economics n! Papbuy (c) ccamplek a tdx return, gwcn !Re aelevdnl ~nfomfat~on, - i o apply pei-centages in problems sisck 2 (a) increase or decrease quantities by a given b~cucentage; as ir1teres.i earned on lending and in?resting money, and compou12d groba~tarth (b) calculaie the ancaunt afiii\\ieresi receivable and payable annually, of a town's populajion given the principal and the rake of interest; when money is loaned, interested or borrovved at simpie inferesl (c) slate She differe~ace $elween sianple and cniinpourrd Enteresi; (d) calculate the amoa.sb-~f: and the interest earned, or' paid when the phncipal, rate and period of time is given when money is loaned, invest,ed or borrowed at compn~ne~ interest (el snse tables Chat give ssmsple and cspi~gaa~~lnd sntercs!. on $'I for grvem ~ntebesk rales and numbes crf years, (0 apply tire compound g1~3wBh vnodel io ot81er praci~cal examples S F I C ~ as pspula8oias, and deprec;~aticlan of values In this unit of work students wvil1 Book 1. (a) calculat6: the anlhrnebc i;neai% Posn a kaequency table, by elsi1168 further at cornpeeting sb;atisties such as She rnsd-laalkses 691 !he class intervals (wb\\ere necessay) mean, median, upper and lower qua~iles and infer--:-quaflplile range. (b) solve bimpYe prc~bleans related to !Re mean value -. VV&gs..k on frcxgtsar~cy potygows and ct~~rrruialiu~e frcif~uenn;y is exa;lud~:ii. 2 determsne the med~an, the upper and Bower quahlles, and tire ~rste;iu- qr~arfile range for a last of scores, and for sa:o#es in 8 frequer~c~y table (without class rnten!als) 3 apply the statistical correepk learnt in this topic Po real-lik situations. PRORABlhiSY -- 1 1, (a) perform simple s%atir;tical experim-rrerits, and trorn tRc?sc I TO ~ntroda~ce elementary ideas of B 1 1 probability determine the relative R'equeixy of a particular orrkcomo examples : tossing a coin, rolli~g a dice, di-aw~iny a card; (b) (i) recognise Ilaa'i as the number- of times Ihe e~iperiment pedocrrrned increases, the relative fsecquencies approach a particular value (limit) jii) estinrra8@ this paiqicular value (limit); and jiii) use this limit as a probability, eg in tossing a coin. 2. (a) explaii? the meaning ok Il-re terms s i ~ h as "rarjdon event", "equally like outccornes", '"fair", "biased" jb) (leterrnine the probability of each outcome of an experinser~t, where the oulcomes are eqeiaily likely io occur, or where Ihc outcomes can be easily related to eqli?ally likely oukcomes, eg. in ilra~jiing colonred balls f w m a box; (c) explain why the sum (1% the probabilities of an experimerrt I:; orre, and that the probability of an event is-betweeurn zero and one, ineiusive; (e!) calculate the probability of an evcl-it; 3. determine ,the expeclc;d svurnber ol occesi-rences of an event giver1 ih pprobabilihi, and i . 8 ~ nutpabes of trials io he carried out.. / apply the probability ccsncepks ~,eal-i~t:: !;ikuatinns FORM 3 UNITS - -. -- - -- -- - --- . - - . -- TASK , % r ~ j ~ ~ l , t F ~ ~ R I ~ ~ - I O ~ ~ Y. a , , 3 1 1 I _ - - Iisrw units i and 3 - _ - / (Vlieei: 7 of 'I eri-ai 1) - - - - - _ - - - - - - -_ -- - - - - -- - -- 1 I 2 35 msnutes k:nd of Unit n Paper avad pen 8ssl ~~\\lei-rng objcct~~es -- - 4 I 1 (lingeek l 4 of -lerm "1) flsrn u n l l 4 - _ - - -- - - - - I ._ - _ _- _ - -_ _. - - - - - -- - - -- - - 3 35 mineii tes End sf \\$(sit 5 Papel and Pen &ash coverir~g skalec:tivt:l; I be l~rovided co Illat students could c.oiTrgrfip1 - - - - 11 I I frelri7 ilxg~ii 5 - I . - _ -- - - _ - - - _- - - - lei: ! par! of the tasks aPer scllool ur during weekc~ds. - - - -- - - No more hlsan 3 pei.isds End of Unit ? I F<cfc:r Po %11e sample (Wet;lk 9 sf 1 err! I - - - - - .- -- -- - - - - - E r ~ d of Unii 3 $?,I8 sthaden& swill be rec11nirc.d to follow CI (Weel; 9 of "I errn I) task sln~ilar lo lhf: .;a~nplc provided. Studeii~ls wil! klave to subn~i"ekie csrripleted !ask sl~eet The: wsarksng crilersa sl~ould be cliscussed with the students in adjsanee, 9) ('Te3c;her.s are rerrsjdczij n c ~ t to use tlie same task year after year) . -. - _ . Activity 1 : 2 per~ods Activity I r\\Mk 4 of 'l"ern1 "l"hese activities will Cie desigraed %cs ,4etivity 2: 2 -3 3 a ~ 5 ,,, ohjd~cfi~~es COVC:T~I.II~ sjnits 8 to 'I 2. , L > , 4 c e " weeks Activities 2 8[ r.3: \\ A h "10 Refer to the ~:?i.ampde:;~ proltiided. Acliviv 3: "periods 'Tern 3 w2 rO- ,=- < B 2% cn 4 3 0 5 a- $2 * r,* 3, Q 4 g ;< - a-d : j el: w Y: a s ~ 6aL d E" Q" 0 "-a 5' "it;d P. ,% ? . . J s .* 1 . 4 9 4 0 $2. 4 8 (pa "a <Q :2 * w+> , c n I '% L2 $2 t-, 0 8 v 2 s . 4 P &*- 0 g - . ~ , W", 4 1 . .-.y C3 ,-. ~ :,5 , -5. : : i a ". L c.: *,"' J C. ,- . . ." ., * C J i 4; c i i r* " .," pi . 3 Gi v- ,. PD I a ,.I cs f.?,.. ,- " ":, - c2 ,. 6 b u v. ,- h ,~ + k, s D r:z> t7C i f D 0 t '.<> ,- ?.-,< * . ~ $z$ C Y r : p. ., ~ ,- .> i i.. b.* , l li a{> . '.Cb !U ,- 2 * 3 :ti Eg3e$eaa of 9im;. Both pra&cni wEhp;d w&t;"r'", work o:? f;KK average worker T@s 39~-++1 ( C ~ K ~ ~ F S S adc&!~sjde) 1. 'The 'fst'a3a.t of r &je exalminati~n paper for FJG s&ri;Ai remaiiil as it is, '['&re I1,J&; k4a%l1err1a&#esc paper vwil! be !-ja:;ed an Fofm?j; 4 units O S P B ~ . 2. fak3ie 65:8uw sasmmarises the weightibag of the uni,%s in1 the e x a r n i n a t paper 3. \\[iA1-8ie the er:ariiiiii.-tatiu2r1 will have a few knowledge type questions, the errlpk~asls vvill be on wand pra;~blersas arid ~ : ~ r n i ~ ~ i a t ~ t : ~ i r ~ 2nd a p p l i c : .type c~l;,.ecstltsras.
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