MATHEMATICS PAPER 121/1 K.C.S.E 1998 QUESTIONS SECTION 1 ( 52 Marks)

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1 f MATHEMATICS PAPER 121/1 K.C.S.E 1998 QUESTIONS CTION 1 ( 52 Maks) Answe all he queions in his cion 1. Evaluae wihou ung mahemaical ables e 2. Facoize a2 b2 Hence find he exac value of The mass of 6 mila books and 4 mila biology books is 7.2 kg. The mass of 2 such a books and 3 such biology books is 3.4 kg. Find he mass of one a book and mass of one biology book. 4. In he figue below, AB is allel o DE, DE bics angle BDG, angle DCF = 6 and angle CFG = 11 Find CDF ABD Give easons fo you answe 5. A salesman ges a cmison of 2.4% on sales up o Kshs 1.. He ges an addiional cmison of 1.5% on sales above his. Calculae he cmison he ges on sales woh Kshs A poin A is diecly below a windo Anohe poin B is 15 m f A and a he same hoizonal level. B angle of elevaion of he op of he bo of he window is 3 and he angle of elevaion of he op of he window is 35. Calculae he veical diance. A o he bo of he window he bo o op of he window 7. A maix A is given by A =x 5 y

2 f a) Deemine A2 deemine he posble i of values of x and y b) If A2 = 1, 1 8. Given ha log y = log (1n ) make n he subjec e 9. A quaniy T is ly conan and ly vaies as he squae oo of S. a) Ung conans a and b, wie down an equaion connecing T and S. b) If S = 16, when T = 24 and S = 36 when T = 32, find he values of he conans a and b, 1. The hid and fifh em of an aihmeic pogeson ae 1 and -1 escively a) Deemine he fi and he cmon diffeence b) The sum of he fi 15 ems 11. A cyndical conaine of adius 15cm has wae in i. When a solid is submeged ino he wae, he wae level is by 1.2 cm. Find, he volume of he wae displaced by he solid leang you answe in ems of If he solid is a cicula cone of heigh 9 cm, calculae he adius of he cone o 2 decimal places. 12. Six wks afe planing he heigh of bean plans wee coec o he neae cenimee. The fequency diibuion able belo Heigh (x) x 4 x 8 8 x x 4 16 equency Cumulaive equency measued is given in he 16 x 2 6 Ene he cumulaive fequency values in he above able Eimae he median heigh of he plans 13. A financial iniuion chages cpound inee on money boowed. A buness wan boowed Kshs. 16, f he financial iniuion. She id back Kshs 25, afe 2 yea. Find he inee ae annum. 14. Solve he equaion cos (3θ + 12) = 3/2 fo θ The adius of cicle is given as 2.8 cm o 2 gnifican figues

3 If C is he cicumfeence of he cicle, deemine he limis bewn which C/ lies By aking o be 3.142, find, o 4 gnifican figues he line bewn which he cicumfeence lies. 16. A and B ae owns 36 km a. An expess bus des fom A a 8 am and mainains an aveage spd of 9 km/h bewn A and B. Anohe bus as f B also a 8 am and moves owads A making fou ops a fou equally sced poins bewn B and A. Each op is of duaion 5 minues and he aveage spd bewn any wo spos is 6 km/h. Calculae diance bewn he wo bus a 1 am. f e 17. Wainaina has wo daiy fams. A and B. Fam A poduces milk wih 3 ½ cen fa and fam B poduces milk wih 4 ¾ cen fa. Deemine The oal mass fa in 5 kg of milk f fam A and 3 kg of milk f fam B The cenage of fa in a mixue of 5 kg of milk f A and 3 kg of milk f B (c) Deemine he ange of values of mass of milk f fam B ha mu be ud in a 5 kg mixue so ha he mixue may have a lea 4 cen fa. 18. The able below shows monhly ince ax aes nhly axable y Rae of ax Kshs K Ove 171 A cil van eans a monhly salay of Kshs 2, and is poded wih a hou a a ninal en of Kshs 7 monh Taxable y is he employ s salay, plus 15% of salay, less ninal en. Calculae he cil van s axable y in K Calculae he oal ax (c) If he employ is eniled o a onal elief of Kshs. Pe monh, wha is he ne ax ) A quadilaeal ABCD has veices A (4, -4), B(2, -4), C(6, -6) and D (4, (c) On he gid poded daw he quadilaeal ABCD. A B C D is he image of ABCD unde poive quae un abou he oigin. On he same gid daw he image A B C D A B C D is he image of A B C D unde he ansfomaion given by he maix 1-2 1

4 f deemine he coodinao of A B C D On he same gid daw he quadilaeal A B C D Deemine a ngle maix ha maps ABCD ono A B C D (d) e 2. The poion of wo owns X and Y ae given o he neae deg as X (45 N, 1W) and Y ( 45 N, 7W) Find The diance bewn he wo owns in Kilee ( ake he adius of he eah as 6371) Nauical miles ( ake I nauical mile o be 1.85 km) (c) The local ime a X when he local ime a Y is 2. pm. 21. A cyndical can has a hemisphee cap. The cylinde and he hemisphee ae of adius 3.5 cm. The cylindical is 2 cm all. Take o be 22/7 calculae he aea of he cicula ba he aea of he cuved cylindical suface (c) he aea of he cuved hemisphee suface (d) The oal suface aea. 22. The figue below shows a gid of equally sced allel lines AB = a and BC = b Expess AC in ems of a and b Ung iangle BEP, expess BP in ems of a and b

5 1b/9-8a/3 f (c) PR poduced ms BA poduced a X and P = By wiing PX as kpr and BX as hba and ung he iangle BPX deemine he aio PR: RX 23. U a ule and a i of css only fo all conucions in his queion. On he line BC given below, conuc iangle ABC such ha ABC = 3 and BA = 12 cm Conuc a ndicula f A o m BC poduced a D. Measue (c) Conuc iangle A B C such ha he aea of iangle A B C is he h quae of he aea of iangle ABC and on he same de of BC as iangle ABC. (d) Descibe he lucus of A e CD 24. In a liveock each aions a new dug fo a ceain fowl dia is being ied. A sample of 36 fowls wee diagnod o have he dia. Tweny (2) fowls wee eaed wih he dug and he e wee no. Calculae he pobabiliy ha a fowl picked a and is eaed wih he dug No eaed wih he dug 25. If a fowl is eaed, pobabiliy of dying is 1/1 while if no eaed he pobabiliy is 7/1 calculae he pobabiliy ha, a fowl picked a and f he 36 fowl is (iii) eaed wih he dug and will die No eaed wih he dug and will die No eaed wih he dug and will no die

6 f MATHEMATICS PAPER 121/2 K.C.S.E QUESTIONS CTION 1 ( 52 MARKS) Answe he enie queion in his cion 1/5 1. U logaihms o evaluae 55.9 (2621 x.1177) e 2. Simplify he expeson x 1-2x + 1 x 3x Hence solve he equaion x- 1-2x + 1 = 2 x 3x 3 3. Simplify as fa as posble, leang you answe in he fom of sud 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 AC BC 5. A plo of land was valued a Kshs 5, a he a of I appeciaed by 2% duing Theeafe, evey yea, i appeciaed by 1% of is peous yea value. a. The value of he land a he a f 1995

7 b. The value of he land a he end f 1997 f 6. Duing a ceain iod, he exchange ae wee follows 1 eling pound = Kshs eling pound = Kshs. U.S dolla 1 U.S dolla = Kshs 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 The ade s buying pice e A school managemen inended o impo exbooks 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 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 The ndicula bico of AB A poin P on line xy 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

8 f 1. Given ha P = 3 y expess he equaion 3 2y x 3y-1= 1 ems of AP Hence o ohewi find he value of y in he equaion 3 2y x 3y-1= A balloon, in he fom 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 12. Find x if -3 log 5 + log x2 = log e 13. Wie down he mple exnon ( 1 + x) 6 U he exnon up o he fouh em o find he value of ( 1.3) 6 o he neae one housandh. 14. A science club is made up of boys and gils. The club has 3 officials. Ung a diagam o ohewi find he pobabiliy ha: The club official ae all boys Two of he officials ae gils 15. A ive is flowing a unifom spd of 6km/ h. A canoei who can ddle a 1 km/h hough ill wae wishes o go aigh acoss he ive. Find he diecion, elaive o he bank in which he should. 16. The iangula pism shown below has des AB= DC = EF = 12 cm. The ends ae equilaeal iangle of des 1cm. The poin N is he midpoin FC. Find he lengh of BN EN Find he angle bewn he line EB and he plane CDEF CTION II (48 maks) Answe any x queions f his cion

9 A cylindical wae ank is a diamee 7 mee and heigh 2.8 mee Find he caciy of he wae ank in lies f 17. x 18. Six membe of a family u 15 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. Cplee he able below fo he value of y = 2 n x + cos x e n x Co sx y Ung he gid poded daw he gaph of y= 2 n x + cos x fo. Take 1 cm epen 3 on he x- axis and 2 cm o epen 1 uni on he axis. (c) U he gaph o find he ange of x ha saisfy he inequaliies 2 n x cos x > In he figue below, QOT is a diamee. = 37 QTR = 48, TQR = 76 and SRT Calculae RST SUT (c) Obu (d) 2. axis RUT PST Find he value of x a which he cuve y= x- 2x2 3 coss he x-

10 s(x2 2x 3)dx f (c) Find he aea bounded by he cuve y = x 2 2x 3, he axis and he lines x= 2 and x = 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 eximen involng he wo vaiables R and V. V R e Cplee he able of log V and R given below, by ging he value o 2 decimal places. Log V Log R On he gid poded daw a suiable aigh line gaph o epen he elaion R= kvn (c) he gadien of he line 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. Ung a scale of 1 cm o epens 1km, make a scale dawing o show he poion of he aeoplane afe 4 minues. U he scale dawing o find he diance bewn he wo aeoplane afe 4 minues. (c) Deemine he beaing P f Q Q f P 23. The figue below epens a ecangle PQRS inscibed in a cicle cene and adius 17cm. PQ = 16cm. Calculae (d) The lengh PS of he ecangle

11 (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 x be he numbe of y A shis and y be he numbe of ys B shis. On he gid poded, daw he inequaliies and shade he unwaned egions Ty A: Kshs 6 shi e Wie down in ems of x and y all he linea inequaliies epening he infomaion above. Ty B: Kshs 4 shi U he gaph o deemine he numbe of shis of each y ha should be made o maximize he pofi. Calculae he maximum posble pofi.

MATHEMATICS PAPER 121/2 K.C.S.E QUESTIONS SECTION 1 ( 52 MARKS) 3. Simplify as far as possible, leaving your answer in the form of surd

MATHEMATICS PAPER 121/2 K.C.S.E QUESTIONS SECTION 1 ( 52 MARKS) 3. Simplify as far as possible, leaving your answer in the form of surd 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 +