Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 I 800 I Individul Events I 0 I4 no. of routes 6 I5 + + b b 0 b b c *8 missing c 0 c c See the remrk 600 d d 90 ngle 57 d 000 Group Events G6 R G7 sum 60 G8 AC 5 m G9 5 4 G0 A 578 b 80 S AC 5 cm 60 step N 0 c 8 c 6 OA 56 d 6 8 9 d 0 Probbility 44 4 Individul Event I.. In the following figure, the sum of the mrked ngles is, find. Angle sum of tringle = 80, ngles sum of tringles = 60 Angle t point = 60, ngles sum t 6 vertices = 660 = 60 = 60 60 = 800 I.. The sum of the interior ngles of regulr b-sided polygon is. Find b. 80(b ) = 800 b = I. Find c, if b = c 4 nd c > 0 = ( ) 4 = 8 4 c = 8 Remrk Originl question: Find c, if b = c 4. c = 8 I.4 Find d, if c b = k nd c : d = k : 00. k = = 8 X 46 8 : d = : 00 8 : d = : 00 00 600 d = 8 = http://www.hkedcity.net/ihouse/fh7878/ Pge
Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 Individul Event I. If =.8 5.0865 + 0.0865.8, find. =.8 (5 + 0.0865) + 0.0865.8 = 9 + = 0 I. In the digrm shown, OH = OK = units nd OAC is rectngle. AC = b units. Wht is b? b = O = OH = = 0 A H I. In the epression shown, wht is c when it is epnded to the term with (b ) s the numertor? b = 0 = 8 T() =, T() = 6, T() = 0, this is n rithmetic sequence with first term =, common difference = 4. T(8) = + (8 )4 = 0 I.4 As shown rbbit spends c minutes in trvelling from A to long hlf circle. With the sme speed, it spends d minutes in trvelling from A D long hlf circles. Wht is d? Rdius of the smller circle = Rdius of the lrger circle = Circumference of the smller semi-circle A = Circumference of the lrger semi-circle D = Speed = = d = c = 90 c d O K 0 6 0 4 b c O (0,0) C A(,0) D (,0) http://www.hkedcity.net/ihouse/fh7878/ Pge
Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 Individul Event 4 I4. The figure shows bord consisting of nine squres. A counter originlly on squre X cn be moved either upwrds or to the right one squre t time. y how mny different routes my the counter be moved from X to Y? Reference: 998 HG6, 000 HI4, 007 HG5 y dding numbers on the right s shown (Pscl tringle), the number of different routes = 6 I4. Given b tn. Find b. b b = p q I4. Given tht p * q = p, find c if c = ( + b) * (b ). Y X 6 4 8 c = (6 )*( 6) = 4*( 8) = = 4 I4.4 A wire of c cm is bent to form sector of rdius cm. Wht is the ngle of the sector in degrees (correct to the nerest degree)? Let the ngle t centre be rdins. + = 80 = rdin = 57. = 57 (correct to the nerest degree) Individul Event 5 I5. If ( + ) = + + +, find in terms of. ( + ) = ( + ) = ( + ) = + + I5. If = 0, then the vlue of is 0 or b, wht is b? = = ( + ) + = 0 = 0 or b = I5. If pc 4 =, pc = b nd c is positive, wht is the vlue of c? pc 4 = () pc = ( ) = 4 () ()(): c = 8 c = I5.4 P is n opertion such tht P(A) = P(A) + P(). P(A) = y mens A = 0 y. If d = A, P(A) = nd P() = c, find d. P(A) = A = 0 = 0 P() = c = 0 = 00 d = A = 000 = 000 cm O cm C http://www.hkedcity.net/ihouse/fh7878/ Pge
Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 Group Event 6 G6. The tble shows the results of the opertion * on P, Q, R, S tken two t time. Let be the inverse of P. Find. P*S = P = S*P, Q*S = Q = S*Q, R*S = R = S*R, S*S = S The identity element is S. P*R = S = R*P, the inverse of P is R. G6. The verge of nd is 05, the verge of, nd is b. Find b. Reference: 99 FG6. ( + ) = 05 + = 0 () 80 + = (dj. s on st. line, et. of ) = + 80 () Sub. () into (): = 0 80 = 0 b = (0 + 0) = 80 * P Q R S P Q R S P Q R S P Q R S P Q R S P Q R S G6. The sum of two numbers is 0, their product is 0. The sum of their reciprocl is c. Wht is c? Reference 984 FSG., 985 FSGI., 986 FSG. Let the two numbers be, y. + y = 0 () y = 0 () y 0 c = = = = y y 0 G6.4 It is given tht 90 = 9.49, to deciml plces. If d < 7 0. 9 < d +, where d is n integer, wht is d? 7 0. 9 = 0.7 90 = 0.79.49 (correct to deciml plces) = 6.64 d = 6 http://www.hkedcity.net/ihouse/fh7878/ Pge 4
Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 Group Event 7 G7. Find + 6 + 9 + + 45. The bove is n rithmetic series with first term =, common difference =, no. of terms =5. 5 S5 = 45= 60 G7. In the figure shown, ACDE is squre nd AC = C, AC = 90. Find the re of AC if the re of ACDE is A E 0 cm. AC CED ECA (S.A.S.) The re of AC = re of ACDE = 5 cm G7. Given tht. Evlute. Reference: 996 FI., 998 FG5., 00 FI. = 9 = 7 = = (7 ) = 8 n G7.4 Given tht. y n Find 0 y 0 y y y y. (Epress your nswer in frction.) Reference: 99 FSG. 0 0 = y y y y 8 9 8 = = 9 9 C D http://www.hkedcity.net/ihouse/fh7878/ Pge 5
Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 Group Event 8 G8. Peter is stnding t A nd John is t C. The distnce between nd D is m. Wht is the shortest distnce between John nd Peter? Reference: 99 HG9, 99 HI, 996 HG9 A 7m m D m C AC = 7 m = 5 m G8. The following figure shows prt of the grph y = sin. Wht is the -coordinte of P? sin = 0 = 80 = 60 G8. If f () =, then epress f () f ( ) in terms of. f () f ( ) = ( ) = G8.4 If mnp, nmp, mmp nd nnp re numbers in bse 0 composed of the digits m, n nd p, such tht: mnp nmp = 80 nd mmp nnp = d. Find d. 00m + 0n + p (00n + 0m + p) = 80 00(m n) 0(m n) = 80 m n = d = mmp nnp = 00m + 0m + p (00n + 0n + p) = 0(m n) = 0 http://www.hkedcity.net/ihouse/fh7878/ Pge 6
Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 Group Event 9 G9. If sin =, = tn, find. 5 cos = sin 9 6 = = 5 5 tn 9 sin 5 9 = = 6 = cos 5 6 9 5 = tn = = 6 4 G9. Emine the following proof crefully: To prove. 8 4 Steps > Multiply both sides by log, then log > log log > log 4 > 8 4 Which step is incorrect? Step is incorrect becuse log < 0. Multiply both sides by log, then log < log. G9. If the lines y + + = 0 nd y + c + = 0 re perpendiculr, find the vlue of c. Reference: 984 FSG., 985 FI4., 986 FSG., 987 FG0., 988 FG8. Product of slopes = c c = 6 G9.4 There re 4 red blls nd blck blls in bo. If blls re chosen one by one with replcement, wht is the probbility of choosing red blls nd blck bll? 4 44 P( red, blck) = = 7 7 4 http://www.hkedcity.net/ihouse/fh7878/ Pge 7
Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 Group Event 0 G0. = 0 = = 4 4 = 5 A = 577 579 If A > 0, find A. Reference: 984 FSG.., 99 FI. A = (578 ) (578 + ) A = 578 G0. The sides of n N-sided regulr polygon re produced to form str. If the ngle t ech point of tht str is 08, find N. (For emple, the str of si-sided polygon is given s shown in the digrm.) Consider n isosceles tringle formed by ech point. The verticl ngle is 08. 80 08 Ech of the bse ngle = = 6 6-sided regulr polygon. 6N = 60 (sum of et. s of polygon) N = 0 G0. A, P, re three points on circle with centre O. If AP = 46, find OA. P Add point Q s shown in the digrm. 46 AQ = 80 46 = 4 (opp. s cyclic qud.) AO = 4 = 68 ( t centre twice t ce ) A O OA = O = rdii OA = OA (bse s isos. ) 80 68 = = 56 (s sum of ) G0.4 A number X consists of digits whose product is 4. y reversing the digits, the new number formed is 8 greter thn the originl one. Wht is X? (Reference: 99 FG6.-) Let the tens digit of X be nd the units digit be b. X = 0 + b, reversed number = 0b + b = 4 b = 4 () 0b + (0 + b) = 8 b = () 4 Sub. () into (): = 4 = + 4 = 0 ( 4)( + 6) = 0 = 4 or 6 (rejected) b = 6 X = 46 http://www.hkedcity.net/ihouse/fh7878/ Pge 8