f MATHEMATICS PAPER 2/2 K.C.S.E. 998 QUESTIONS CTION ( 52 MARKS) Answe he enie queion in his cion /5. U logaihms o evaluae 55.9 (262.77) e F 2. Simplify he epeson - 2 + 3 Hence solve he equaion - - 2 + = 2 3 3 3. Simplify as fa as posble, leang you answe in he f of sud 4 2 3 4 + 2 3 4. In he figue below ABC = 3, ACB = 9, AD = 4 3 and DC = 4cm 8 + I if A is lo 3 3 Calculae he lengh of (a) AC (b) BC 5. A plo of land was valued a Kshs 5, a he a of 994. I appeciaed by 2% duing 994. Theeafe, evey yea, i appeciaed by % of is peous yea value. a. The value of he land a he a f 995
b. The value of he land a he end f 997 f 6. Duing a ceain iod, he echange ae wee follows eling pound = Kshs. 2. eling pound = Kshs. U.S dolla U.S dolla = Kshs. 6.6 7. A manufacue lls bole of fui juice o a ade a a pofi of 4%. The ade lls i fo Kshs 84 a a pofi of 2%. Find (a) The ade s buying pice e F A school managemen inended o impo ebooks woh Kshs 5, f U.K. I changed he money o eling pounds. Lae he managemen found ou ha books wee chea in U.S.A. Hence i changed he eling pounds o dolla. Unfounaely, a financial cis ao and he money had o be econveed o Kenya shillings. Calculae he oal amoun of money he managemen ended up wih (b) The co of manufacue of one bole 8. In he figue below a line XY and h poins. A,B and C ae given. On he figue conuc (a) The ndicula bico of AB (b) A poin P on line y such ha APB = ACB 9. In he figue, KLMN is a azium in which KL is allel o NM and KL = 3 NM Given ha KN = w, NM = u and ML = v Show ha 2 u = v= w
f. Given ha P = 3 y epess he equaion 3 2y + 2 3y-= ems of AP Hence o ohewi find he value of y in he equaion 3 2y + 2 3y-=. A balloon, in he f of a sphee of adius 2 cm, is blown up so ha he volume incea by 237.5%. Deemine he new volume of balloon in ems of 2. Find if -3 log 5 + log 2 = log 25 e F 3. (a) Wie down he mple enon ( + ) 6 (b) U he enon up o he fouh em o find he value of (.3) 6 o he neae one housandh. 4. A science club is made up of boys and gils. The club has 3 officials. Ung a diagam o ohewi find he pobabiliy ha: (a) The club official ae all boys (b) Two of he officials ae gils 5. A ive is flowing a unif d of 6km/ h. A canoei who can ddle a km/h hough ill wae wishes o go aigh acoss he ive. Find he diecion, elaive o he bank in which he should. 6. The iangula pism shown below has des AB= DC = EF = 2 cm. The ends ae equilaeal iangle of des cm. The poin N is he midpoin FC. (a) Find he lengh of (i) BN (ii) EN (b) Find he angle bewn he line EB and he plane CDEF CTION II (48 maks) Answe any queions f his cion
A cylindical wae ank is a diamee 7 mee and heigh 2.8 mee (a) Find he caciy of he wae ank in lies f 7. 8. (b) Si membe of a family u 5 lies day. Each day 8 lies ae ud fo cooking and washing and a fuhe 6 lies ae waed. Find he numbe of cplee days a full ank of wae would la he family. (a) Cplee he able below fo he value of y = 2 n + cos. 3 45 6 9 2 35 5 8 225 27 35 36 e F 2.4.7 2.7.4-2 -.4 n Co.7.5 -.5 -.7 -.9 -.7 s y 2. 2.2 2.2.7. - -2 -.7 (b) Ung he gid poded daw he gaph of y= 2 n + cos fo. Take cm epen 3 on he - ais and 2 cm o epen uni on he ais. (c) U he gaph o find he ange of ha saisfy he inequaliies 2 n cos >.5 9. In he figue below, QOT is a diamee. = 37 QTR = 48, TQR = 76 and SRT Calculae (a) RST (b) SUT (c) Obu (d) 2. ais RUT PST (a) Find he value of a which he cuve y= - 22 3 coss he -
s(2 2 3)d (b) f (c) Find he aea bounded by he cuve y = 2 2 3, he ais and he lines = 2 and = 4 2. Two vaiables R and V ae known o saisfy a elaion R = kv n, whee k and n ae conans. The able below shows daa colleced f an eimen involng he wo vaiables R and V. V 3 4 5 6 7 8 R 27 48 75 8 47 92 e F (a) Cplee he able of log V and R given below, by ging he value o 2 decimal places. Log V.48.6.7.78.85.9 Log R.43.88 2.3.8 2.28 (b) On he gid poded daw a suiable aigh line gaph o epen he elaion R= kvn (c) (i) he gadien of he line (ii) a elaionship connecing R and V. 22. Two aeoplane P and Q leaves an aipo a he same ime. P lies on a beaing of 24 a 9 km/ h while Q flies due ea a 75 km/ h. (a) Ung a scale of cm o epens km, make a scale dawing o show he poion of he aeoplane afe 4 minues. (b) U he scale dawing o find he diance bewn he wo aeoplane afe 4 minues. (c) Deemine he beaing (i) P f Q (ii) Q f P 23. The figue below epens a ecangle PQRS inscibed in a cicle cene and adius 7cm. PQ = 6cm. Calculae (d) The lengh PS of he ecangle
(e) The angle POS f (f) The aea of he shaded egion 24. A da is equied o supply wo ys of shis A and y B. The oal numbe of shis mu no be moe han 4. He has o supply moe y A han of y B howeve he numbe of ys A shis mu be moe han 3 and he numbe of y B shis no be less han 8. Le be he numbe of y A shis and y be he numbe of ys B shis. (b) On he gid poded, daw he inequaliies and shade he unwaned egions Ty A: Kshs 6 shi e F (a) Wie down in ems of and y all he linea inequaliies epening he infaion above. Ty B: Kshs 4 shi (i) U he gaph o deemine he numbe of shis of each y ha should be made o maimize he pofi. (ii) Calculae he maimum posble pofi.