1 (=0.5) I3 a 7 I4 a 15 I5 a (=0.5) c 4 N 10 1 (=0.5) N 6 A 52 S 2

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1 Answers: (98-84 HKMO Finl Events) Creted by Mr. Frncis Hung Lst updted: December 05 Individul Events SI 900 I 0 I (=0.5) I 7 I4 5 I5 80 b 7 b b 5 b 6 b 8 b 4 c c 4 c 0 x (=0.5) c 4 N 0 d 9 d 5 d 5 y d x 44 Group Events SG G6 p 0 G7 p 75 G8 M G9 x G0 A b *6 see the remrk q 5 q (=0.5) N 6 A 5 S c 6 r 4 R 8 m 50 n 7 d 7 s 7 m 4 Y P 6 d 5 Smple Individul Event (988 Smple Individul Event) SI. In the given digrm, the sum of the three mrked ngles is. Find. Reference: 987 FSG., 989 FSI. Sum of interior ngles of tringle = 80 ngle sum of three vertices = 60 = 080 = = 900 SI. The sum of the interior ngles of regulr b-sided polygon is. Find b. Reference 989 FSI. = 900 = 80(b ) b = 7 SI. If 8 b = c, find c. 8 7 = c = c c = SI.4 If c = log d 8, find d. = c = log d 8 nd d > 0 d = 8 d = 9 Individul Event I. If 00 = 5 5, find. Reference: 987 FSG., 988 FI. 00 = (5 + 5)(5 5) = 500 = 000 = 0 I. If ( ) = 4b, find b. 9 = 4b 4b = 4 b = I. If b is root of x + cx 5 = 0, find c. Put x = into the eqution: + c 5 = 0 c = 4 I.4 If x + c is fctor of x + x + 4d, find d. x + 4 is fctor Put x = 4 into the polynomil: ( 4) + ( 4) + 4d = 0 d = 5 Pge

2 Answers: (98-84 HKMO Finl Events) Creted by Mr. Frncis Hung Lst updted: December 05 Individul Event I. If, re roots of x 0x + 0 = 0, find, where =. + = 0, = 0 0 = = = = 0 I. If sin = (0 < < 90), nd 0 cos = b, find b. sin = = 0 b = 0 cos 60 = 5 I. The point A(b, c) lies on the line y = x + 5. Find c. Reference: 984 FI. Put x = b = 5, y = c into the line: c = c = 0 I.4 If x cx + 40 (x + k) + d, find d. Reference: 985 FG0., 986 FG7., 987 FSI., 988 FG9. x 0x + 40 (x 5) + 5 k = 5, d = 5 Individul Event I. If is the reminder when x x + x is divided by x +, find. = ( ) ( ) = 7 I. If b cm is the totl surfce re of cube of side (8 + ) cm, find b. Similr Questions: 984 FG9., 985 FSI. 8 + = b = 6 I. One bll is tken t rndom from bg contining b + 4 red blls nd b white blls. If x is the probbility tht the bll is white, find x. There re b + 4 = 0 red blls nd b = 0 white blls x = I.4 If sin = x (90 < < 80) nd tn( 5) = y, find y. sin = = 50 y = tn( 5) = tn 5 = Pge

3 Answers: (98-84 HKMO Finl Events) Creted by Mr. Frncis Hung Lst updted: December 05 Individul Event 4 I4. In figure, DE // BC. If AD 4, DB 6, DE 6 nd BC, find. ADE ~ ABC (equingulr) 0 6 (rtio of sides, ~ s) 4 = 5 B 6 D 4 A 6 E C I4. is n cute ngle such tht cos = 7. If tn =5 b, find b. b = 7 5 b = 8 I4. If c = b, find c. c = 8 = 64 = 4 c = 4 I4.4 The re of n equilterl tringle is c cm. If its perimeter is d cm, find d. Reference: 985 FSI.4, 986 FSG., 987 FG6., 988 FG9. Ech side = d cm 7 5 b d sin 60 c 4 d = Individul Event 5 I5. In Figure, find (80 ) = 60 (sum of ext. of ) = I5. If b = log, find b. 5 b = 6 b = 4 I5. A piece of string, 0 m long, is divided into prts in the rtio of b : b : b +. If N m is the length of the longest portion, find N. b : b : b + = : 4 : 6 = : : N = 0 = 0 I5.4 Ech interior ngle of n N-sided regulr polygon is x. Find x x = = Pge

4 Answers: (98-84 HKMO Finl Events) Creted by Mr. Frncis Hung Lst updted: December 05 Smple Group Event SG. The sum of numbers is 0, their product is 0. If the sum of their reciprocls is, find. Reference: 98 FG6., 985 FSI., 986 FSG. Let the numbers be x nd y. x + y = 0 nd xy = 0 x y = = = x y xy SG. = 0, =, = 4,, b = 57. If b > 0, find b. Reference: 98 FI0., 99 FI. 57 = (6 )(6 + ) = 6 b = 6 Remrk The originl question is: = 0, =, = 4,, b = 57, find b. b = 6 or 6, there re different nswers! SG. If the lines x + y + = 0 nd cx + y + = 0 re perpendiculr, find c. Reference: 98 FG9., 985 FI4., 986 FSG., 987 FG0., 988 FG8. c c = -6 SG.4 The points (, ), (0, ), (c, d) re colliner. Find d. Reference: 984 FG7., 986FG6., 987 FG7.4, 989 HG8 d 6 0 d = 7 Group Event 6 G6. If p =, find p. (Similr questions: 985 FG7.) p = = = 0 G6. If p men cn do job in 6 dys nd 4 men cn do the sme job in q dys, find q. 0 men cn do job in 6 dys. mn cn do job in 60 dys 4 men cn do job in 5 dys q = 5 G6. If the q th dy of Mrch in yer is Wednesdy nd the r th dy of Mrch in the sme yer is Fridy, where 8 < r < 6, find r. (Reference: 985 FG9., 987 FG6.4, 988 FG0.) 5 th Mrch is Wednesdy 7 th Mrch is Fridy 4 th Mrch is Fridy r = 4 G6.4 If *b = b +, nd s = (*4)*, find s. (Reference: 985 FSG.) *4 = 4 + = s = (*4)* = * = + = 7 Pge 4

5 Answers: (98-84 HKMO Finl Events) Creted by Mr. Frncis Hung Lst updted: December 05 Group Event 7 (988 Smple Group Event) G7. The cute ngle between the hnds of clock t :0.m. is p. Find p. Reference: 985 FI. 987 FG7., 989 FI., 990 FG6., 007 HI At :00.m., the ngle between the rms of the clock = 90 From :00.m. to :0.m., the hour-hnd hd moved 60 = 5. The minute hnd hd moved 80. p = = 75 G7. In ABC, B C p. If q sin A, find q. B C 75, A = 0 q = sin 0 = G7. The points (, ), (, 5), (4, 9) re colliner. Find. Reference: 984 FSG.4, 986FG6., 987 FG7.4, 989 HG = 4 4 = G7.4 The verge of 7, 9, x, y, 7 is 0. If m is the verge of x +, x + 5, y +, 8, y +8, find m. 7 9 x y 7 = 0 5 x + y = 7 x x 5 y 8 y 8 m = 5 = x y 6 = 4 5 Group Event 8 In the ddition shown, ech letter represents different digit rnging from zero to nine. It is lredy known tht S = 9, O = zero, E = 5. Find the numbers represented by (i) M, (ii) N, (iii) R, (iv) Y Consider the thousnds digit nd the ten thousnds digits. 0 S, M 9, 9 + M = 0M + 0 or 9 + M + = 0M + 0 M = nd there is no crry digit. Consider the hundreds digit = N N = 6 nd there is crry digit. For the tens digit. 6 + R = R = 9 (sme s S, rejected) or 6 + R + = R = 8 There is crry digit in the unit digit D + 5 = 0 + Y, (D, Y) = (7, ) Y = M =, N = 6, R = 8, Y = S E N D + M O R E M O N E Y Pge 5

6 Answers: (98-84 HKMO Finl Events) Creted by Mr. Frncis Hung Lst updted: December 05 Group Event 9 G9. If x = 4 00, find x in the simplest frctionl form. Reference: 985 FSG., 986 FG x = = G9. The length, width nd height of rectngulr block re, nd 4 respectively. Its totl surfce re is A, find A. Similr Questions: 984 FI., 985 FSI. A = ( ) = 5 G9. The verge of the integers,,,..., 00 is m. Find m. m = = = G9.4 The re of circle inscribed in n equilterl tringle is. If P is the perimeter of this tringle, find P. Reference: 990 FI. Let the rdius be r nd the centre be O. r = r = The length of one side of the equilterl tringle is P = r cot 0 = r = P = 6 P. O r 0 Pge 6

7 Answers: (98-84 HKMO Finl Events) Creted by Mr. Frncis Hung Lst updted: December 05 Group Event 0 G0. If A is the re of squre inscribed in circle of dimeter 0, find A. Reference: 985 FSG.4, 989 FI. Let the squre be BCDE. BC = 0 cos 45 = 5 E 0 D A = 5 = 50 B 45 C G0. If =, nd S =, find S. Reference: 998 HG = = 4 = S = = = ( ) = G0. An n-sided convex polygon hs 4 digonls. Find n. Reference: 985 FG8., 988 FG6., 989 FG6., 99 FI., 00 FI4., 005 FI.4 Number of digonls = C n n n n = n 4 n n 8 = 0 (n 7)(n + 4) = 0 n = 7 G0.4 If d is the distnce between the points (, ) nd (, 7), find d. Reference: 986 FG9.4 d = 7 = 5 Pge 7

Individual Events I3 a 10 I4. d 90 angle 57 d Group Events. d 220 Probability

Individual Events I3 a 10 I4. d 90 angle 57 d Group Events. d 220 Probability 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