Secondary Express Math Mindmaps

-dary 2ExpressNotes - TESTCOMMONFACTOR(HCF) definitionarefactorisation ①Lookfor commonfactors. ②Ta kethenumberwiththe ⑪. RA TIONALNumBERS * smallestpower mersthat canbe expressedas S LOWESTCommonMUL TIPLE(LCM) fractions - i. e. 2 = 2, 0. 5 = 5, 0. =I ①Lookforcommonfactors . &IRRATIONALNUMBERS & Ta kethe numberwiththe - best power . - numbersthatcannotbeexpressed ③Multiplythemtogetherwiththe as fractions al otheruncommonnumbers . i. e. 12, I , . . . . E. g. FindHCFandLCMof36and64· ③ NUMBERS 36= 22x32 - numbersthatcanbedividedonly byitselfand1 . b SIGNIFICANT 64 = 26 i. 2. 2, 3, 5, 7.... -- FIGURES Thus, HCF = 2 2 = 4 ④INTEGERS * zeroesin betweennon-zerodigitsare significant LCM = 20x 32 = 576 - i. e. 5. 003 = 4significantfigures - wholenumbers * zeroesin frontofdecimalsarenotsignificant i. e. .-1 , 0, 2, . . . . i. e. 0. 00305=3significantfigures * zeroesbehinddecimalpointis significant . i.e.. 4. 000 = 4significantfigures - * zeroesbehindin wholenumbersmayor maynotbe significant . i. e. 200 = 1/2/3significantfigures .

W mustbe inthesameunits · PAPROPORTION⊥ cannotbeinfractionnordecimals If yisdirectlyproportionaltos, then properties N SCALE * y = kx bothunitsare incm) map scales ↑ SE PROPORTION AREASCALE If yis in proportional toce, thee Fin -- L E. g. (a)Giventhat2cmrepresents5km, i. e. Giventhatyis directlyproportionaltoC findthescaleintheform1 : m. andy = 12when = 2, findanequation M: A connectingyandx . -- 2cm : 5 km Step1 : Formequation = > y = kx2 :. k= 3 1 cm : 250000cm 1cm : 2. 5km M Step2 : Findconstantvalue, k. = 12= k(24 Step3: substituteKintoequation. = y = 3x* #1 : 250000# (b)If theareaonthemapis 5cm, find theactualarea, in km2 · distance= speedx time AA · speed= distance - 1cm: 2. 5km (mapscale) time distance· time=-(1cm)2 : (2. 5km speed 1cm2 : 6. 25km2Careascale) · AVERAGESPEED 5cm2: 31. 25kmA =total distancetaken - totaltime taken.

E. g. GiventhatSGD$1=Us$1. 30, PROFIT - findhowmuchAaronwillget, · monigetes PROF omLosS - gainmoneyfromthedeal if hewantstoexchangeUS$100· sellingprice - costprice us $1. 30-> SGD$1 Loss US$10U-> SGD$(b) -losemoneyfromthedeal. Es Iatt price - sellingprice = $76. 92# S - DME TAX * FAXATION- C TERESTBSIN - Income - whereP= principalCamtof$$Iloan/invest)I ble=AnnualGross totriesi ⊥↑ RE PURCHASEStrate 100 - E . g . T= time(unitsmustbeinyears) Alanearns$36, 000 in a year . Hegetswiferelief E. G . -- of $1000, childreliefof$500eachandNSreliefof$200. Danboughta TVset on hirepurchase . TheTVcosts$3500 . Hepaida downpayment Hehasthreechildren. Calculatetheamountof taxhe RVICE of10%andpaidthe balanceover a period CHARGE of2yearsat a rateof 2%perannum. hasto pay , - Calculatehismonthlyinstalment . Income * GSTisalwayscalculated -SOLUTION afterservicecharge Balance = 90%of$3500= $3150 - ⊥Freeincome , pari is addedto the bill. - 100 First$20000 0 ⑧ - Interest = $2X2 = $126- ~M Totalhehasto pay = $3150+$126 LOOK09 350 = $3276 ⑧ = $33300 : monthlyinstalments=$t * ChargeableIncome = $36, 000 - ($1000 + $1500 + $200) First$300U Ta xtoPaY=$2,8of$3e Tota tax = $200 + $115 . 50 = $315 . 50

Truntantterat In eIn⑧ -e firstterm constantIndifference Egt . Findthenthterm of Al 3, 9, 15, 21, . . . . V ~v + 6+ 6+ 6 : Tn = 3+ (n - 1)(6) = 3+ 6n- 6 => 64- 3# Eathenthtermof 12, 9, 6, 3, 0, .... -33 : Tn = 12 + (n - 1) - 37 = 12-3n+3 = 15-34#

"IOW"METHOD &ab= axb - ②1 = a =bA①a(bId) = ab1 ad b A · Stone ③& = dxd②(attetd Esansion : d = dxdx... .. xd - = actadtbc+ad n times - ④Ab = &I⑪out commonfactors FACTORISATION ⑤ab = qxbor axd Factorise2xy+by2. · EgsolutionI simplify, , z2xy + by 2 = 2y(x + 3y)# t * alwayscheckwhetherthereareany②grouping expressionsthatcanbefactorised . Factorise(a) xdtyctictyd . Ifyes, factorisefirst . - I (b)2xtax-2y-9y -Gete Findcommondenominator . solution (a)(xd + x) + (yc+yd)* groupingcommontermstogether . 2 c - x(d+c) + y(c+d)* takingout commonfactorsfromeachgroup ①(atb)= a +2ab+b2 (b)(2x + ax) - (2y+ay) - - = (dtc)(x+y)# ②(a - b) * = a - 2ab+b = 4(x+27 + 3(x - 13 =x(2 + a) - y[z + a) ③a2 - = (a- b)(a + b) (x - 1)(x - 2)L I =(2 + a)(x - y) = 4x+8 + 3x - 3 OBycross-factorisationimplicationframe - 3 - (x - 1)(x - 2)- Factorise(2-5x+6 = 7x=- altion (x - 1)(x - 2)* STAYRSATION +RAME : ee e