Form 5 HKCEE 1990 Mathematics II (a 2n ) 3 = A. f(1) B. f(n) A. a 6n B. a 8n C. D. E. 2 D. 1 E. n. 1 in. If 2 = 10 p, 3 = 10 q, express log 6
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1 Form HK 9 Mthemtics II.. ( n ) =. 6n. 8n. n 6n 8n f(). f(n). n n If = 0 p, = 0 q, epress log 6 in terms of p nd q.. p q. pq. p q pq p + q Let > b > 0. If nd b re respectivel the st nd nd terms of geometric progression, the sum to infinit of the progression is. b If =, then b = b b b b b b b + 8 =. If f(n) = n(n ), then f(n + ) f(n) =. ( )( + + ) --MTHS II
2 ( )( + + ) ( + )( + ) ( + )( + ) ( + )( + ) If p nd q re the roots of the eqution + = 0, then ( p )( q ) = If : b = : nd b : c = :, then : c =.. In the figure, the circulr clinder nd the circulr cone hve the sme height. The rdius of the bse of the clinder is twice tht of the cone. If the volume of the cone is 0 cm, wht is the volume of the clinder?. 0 cm. 80 cm. 0 cm 0 cm 00 cm The length, width nd height of cuboid re in the rtios : :. If the totl surfce re of the cuboid is 88 cm, find its volume.. : 0. 9 :. 9 : 00 6 : 6 : cm. 8 cm. 8 cm 96 cm 8 cm 0. If U.S. dollr is equivlent to 7.8 H.K. dollrs nd 000 Jpnese en re equivlent to. H.K. dollrs, how mn Jpnese en re equivlent to 0 U.S. dollrs? In the figure, there re nine circles, ech of rdius. Find the shded re MTHS II
3 If tn = nd lies in the second qudrnt, then sin cos =. Find the mount (correct to the nerest dollr) of $0 000 t % p.., compounded monthl, for ers If flt is sold for $70 000, the gin is 0%. Find the percentge loss if the flt is sold for $ %. 6 %. 0% % 9 % 9. V H The figure shows right prmid with squre bse. V, V, V nd V re equilterl tringles. Find sin VH sin(80 o + ) + sin( o ) =. sin + cos. sin cos. cos sin cos sin sin If 0 o < 60 o, which of the following equtions hs onl one root?.... sin = 0. sin =. sin = cos = 0 cos = --MTHS II
4 0. T 8 o P Q. F G In the figure, TQ is the tngent to the tngent to the circle t. If rc = rc nd PQ = 8 o, then Q =. o. 8 o. 66 o 7 o 8 o. In the figure, //, FG // nd : F : F = : :. If = 0, find FG o M R Q F P In the figure, is the centre of the circle. If R // PQ nd RQ = o, find RMQ.. o. o. 6 o 8 o 6 o. In the figure, is regulr pentgon. Find F. 0 o. o. 0 o 08 o 00 o If the men of the numbers,,,,,,,, 6, is lso, which of the following is/re true? I. Men = Medin II. Mode = Rnge III. Medin = Mode. I nd II onl --MTHS II
5 .. I nd III onl. II nd III onl None of them ll of them Ten ers go, the men ge of bnd of musicins ws 0. ne of them is now leving the bnd t the ge of 0. Wht is the present men ge of the remining 0 musicin? b. b. b b b l l l l There re 7 bgs, of which re empt nd the remining ech contins bll. n dditionl bll is now put into one of the bgs t rndom. fter tht bg is rndoml selected. Find the probbilit of selecting n empt bg is line segment. : : = : :. If = (, ), = (0, ), find.. (, 6). (6, 7). (7, 8) (8, 9) (9, 0) 0. In the figure, the slopes of the stright lines l, l, l, nd l re m, m, m, m respectivel. Which of the following is true?. m > m > m > m. m > m > m > m. m > m > m > m m > m > m > m m > m > m > m (, ) 8. If the line = m + b nd perpendiculr, find m. = re b --MTHS II
6 In the figure, circle cuts the -is t tow points 6 units prt. If the circle hs centre (, ), then its eqution is., correct to deciml plces.7, correct to deciml plces. ( ) + ( ) =. ( ) + ( ) =. ( ) + ( ) = ( + ) + ( + ) = ( + ) + ( + ) =. + = The grph of = + b + c is given s shown. Which of the following is/re true? I. < 0 II. b < 0 III. c < 0. I onl. I nd II onl. I nd III onl II nd III onl I, II nd III onl.. Let f() = + k. If f() is divisible b k, find the reminder when f() is divided b + k.. k. k. 0 k k Let m be constnt. Find the vlue of m such tht 6 m. Sign of f() From the tble, root of the eqution f() = 0 must be..0, correct to deciml plces.., correct to deciml plces.., correct to deciml plces If < b < 0, which of the following must be true?. < b. < b. < b 0 < 0 b --MTHS II 6
7 7. < b The H..F. nd L..M. of three epressions re z nd z respectivel. If two of the epressions re z nd z, find the third epression. 0.. z. z. z z z In the figure, n equilterl tringle is inscribed in circle of rdius. The circumference of the circle is greter thn the perimeter of the tringle b 8. Let,,, b nd,,,, b be two rithmetic progressions Three equl circles of rdii touch ech other s shown in the figure. 6. M.. In the figure, M = M = M = nd = 6. The re of tringle = If is 0% greter thn nd is 0% less thn, then. is 9% less thn --MTHS II 7
8 . is 9% less thn. = is 9% greter thn is 9% greter thn. Which of the following grphs shows tht is prtl constnt nd prtl vries inversel s?.. If sin nd cos re the roots of the eqution + k = 0, then k = P The figure shows the grph of = sin. The point P is.. (, ) (, ). (, ) (, ) (, ) --MTHS II 8
9 6. 60 o 8. 0 o 7. In the figure, is prllelogrm. = H NRTH In the figure, is dimeter nd = 0 o. If the re of is, then the rdius of the circle is o In the figure,, nd re three points on the sme horizontl plne. is due north of, is due est of nd H is point verticll bove. Which of the following ngles is/re o? I. H II. III. H. I onl. II onl. I nd II onl I nd III onl I, II nd III 0 o In the figure, =, = 0 o nd = 0 o.... = --MTHS II 9
10 0. In the figure, if = F, = nd =, then = P 8 o In the figure, P nd P re tngents to the circle. If P = 8 o, then =.. 0 o. 6 o. 0 o o 60 o. 8 o. 96 o. 06 o o o. In the figure, nd re three tngents touching the circle t, nd F respectivel. If =, = 8 nd = o, find the rdius of the circle. F In the figure, T nd T re tngents to the circle. If T T nd, find. 0 o. 0 o. o 0 o 60 o S Q R. U T F P In the figure, PTQ, SQR nd RUT re equilterl tringles. Which of the following is/re true? --MTHS II 0
11 I. UPT RQT II. PU = QS III. PQSU is prllelogrm. ll of them. None of them. I nd II onl I nd III onl II nd III onl --MTHS II
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