III. (x 2) 2 = (2 x) 2. A. a = 1, b = 3. B. a = 3, b = 1. C. a = 1, b = 3. D. a = 3, b = 1. E. a = 1, b = 3.


 Theodore Edwards
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1 Fom 5 HKEE 1 Mthemtics II 1 If = h 7 1 : 8 1 : 1 : 1 : 1 : = ( ) 1 ( ) ( ) ( + ) 1 ( + ) ( + ), then the tio : h is 5 6 III ( ) = ( ) I onl II onl III onl I nd II onl I nd III onl Given the identit + 1 b + + =, 1 ( 1) ( 1 ) ( 1) find the vlues of the constnts nd b = 1, b = =, b = 1 = 1, b = =, b = 1 = 1, b = If α nd β e the oots of the eqution + + =, find the vlue of α α α + β If 1 + ( ) ( 1) ( ) (1 ) = ( ), then = 7 It cnnot be detemined 1 1 Which of the following is n identit/e identities? I ( + 1)( 1) = + 1, II + 1 =, EMTHS II 1
2 The figue shows n infinite numbe of sques The length of side of the fist sque is 1 The side of the fist sque is equl to hlf of the side of the peceding one Find the sum of the es of the infinite numbe of sques 1 I II III 5 In the figue, is stight line with = = Thee cicles I, II nd III e dwn espectivel on, nd s dimetes es of cicle I : e of cicle II : e of cicle III = 8 Find the el vlue of such tht = k 7, whee k is constnt 1 = k 1 : : 1 : : 1 : : 1 : : 16 1 : 8 : mn dives c t 5 km/h fo hous nd then t 5 km/h fo hous His vege speed fo the whole joune is θ 1 θ 7 km/h 75 km/h 8 km/h 85 km/h km/h The figue shows two sectos with dii nd If these two sectos e equl in e, then θ 1 : θ = 1 R : 1 : 1 : 1 5 : 1 6 : 1 Sphee Right cicul clinede In the figue, if Volume of the sphee = Volume of the ight cicul clinde R, then = EMTHS II
3 1 If the compound inteest on $1 fo two es t % p, p hlfel is $, find 1 1 1(1 + ) 1 5 1(1 + ) 1 1(1 + ) π π π π Which of the following functions m be epesented b the bove gph in the intevl to π? = cos = cos 1 = cos = sin = sin sin θ cos θ = 1 5 1(1 + 1 ) 1 If sin θ cos θ = 1, then (sin θ + cos θ) = 1 1 cos θ sin θ cos θ sin θ cos θ sin θ In the figue, : : = : : 1 : : 1 : : 1 : : 1 EMTHS II
4 18 1 : : The being of lighthouse s obseved fom n ocen line is N7oE, the being of the ocen line s obseved fom the light house is θ In the figue, if the e of the secto is, then c = π π 1 N7 o E N5 o W S7 o E S7 o W S5 o W Which of the following epesents cicle? = + = = = = L =  5 L o 1 1 o In the figue, = = 1 = o nd = 1 o, find cos o 1 o sin o sin cos o sin o In the figue, L 1 nd L e two stight lines pependicul to ech othe nd intesecting t P on the is If the eqution of L 1 is = 5, then the eqution of L is 1 = 5 1 = + 5 = 5 = = P EMTHS II
5 8 o 115 o In the figue,,,, nd E lie on cicle intesects E t K = 1 o nd E = 1 o If E //, then = In the figue, = 8 o 5 o o 6 o o o 5 77 o 8 o 6 o 1 o 115 o F E In the figue,,, E nd EF e ight ngled isosceles tingles If = = 1, how long is F? 5 5 E 1 o 1 o In shooting gme, the pobbilities fo John nd M to hit tget e 5 nd espectivel When both shoot t the 5 tget, wht is the pobbilit tht the both miss Given two goups of numbes + 1, +, + nd b + 1, b +, b +, whee > b m 1 nd m e espectivel the mens of the two goups, nd s 1 nd s e espectivel thei stndd devitions Which of the following is tue? m 1 > m nd s 1 > s m 1 > m nd s 1 = s m 1 = m nd s 1 > s m 1 = m nd s 1 = s m 1 > m nd s 1 < s EMTHS II 5
6 8 f If (1 ) =( z )(5 z ), then which of the following must be tue The figue shows the fequenc cuve of cetin distibution Which of the following cn be the distibution s cummultive fequenc cuve? = z = z = z = z = z + = cf cf ( + ) cf cf 1 The LM of 1 b nd 18b c is 6b 6 b c 6b 6 b c 16 b c (, ) (, ) cf (, ) + = 6 + = EMTHS II 6
7 Let p = + Unde the following constints + 6 wht is the getest vlue of p? If log + log = log z, whee, nd z e positive numbes, which of the following must be tue? I + = z II log + log = log z III = z I onl II onl III onl I nd II onl II nd III onl Let F() = Given tht F() = nd F( ) =, then F() cn be fctoized s ( + ) ( ) ( + 1) ( + ) ( ) ( 1) ( ) ( + ) ( + 1) ( ) ( ) ( + 1) ( ) ( + ) ( 1) 5 If, b nd c e positive numbes, which of the following is possible gphicl epesenttion of = + b + c EMTHS II 7
8 6 If > nd b <, which of the following is/e negtive? I II III 1 1 b b + b b b EFGH is cube of side cm tethedon H is cut w long the plne H The volume of the emining solid is 6 cm cm 15 cm 18 cm 5 cm 7 I onl III onl I nd II onl I nd III onl II nd III onl If < < nd < <, then the nge of vlues of is 1 < < 1 < < 1 < < < < 1 < < The mked pice of n ticle is oiginll P The mked pice is then incesed so tht when discount of 1% is mde on the new mked pice, the selling pice is still P Wht is the new mked pice? P 1 1 P 1 11 P P 1 1 P 8 cm E F H G The totl sufce e of egul tethedon of side cm is cm cm 7 cm cm EMTHS II 8
9 1 cm nnot be detemined 1 Ten lites of mitue contin 6% of lcohol nd % of wte b volume How mn lites of wte should be dded so tht it contins % of lcohol b volume? If,, nd cn finish unning the sme distnce in, nd 5 minutes espectivel, then s speed : s peed : s speed = : : 5 5 : : : 8 : 7 : 15 : 1 5 : 16 : In, =, = nd sin =, then cos = If the five inteio ngles of conve pentgon fom n P with common diffeence of 1 o, then the smllest inteio ngle of the pentgon is 6 5 o 7 o 88 o 8 o 18 o Let p be positive constnt such tht p sin θ = nd p sin θ = 1 Find ll the vlues of θ in the intevl to π In the figue, : = sin : sin cos : cos tn : tn sin : sin cos : cos π π 6 π π, π 7π, 6 7 EMTHS II
10 In the figue, is sque cs nd e dwn with centes nd espectivel, intesecting t c : c = o 8 1 : 1 : 1 : 1 : : E H F G 5 1 o nd e equl chods of the cicle = o nd = 1 o = o 5 o o 5 o o 5 o In the figue, nd EFGH e two sques of side 1 The e plced one upon the othe with thei centes both t to fom st with 16 sides, ech of length Find In the figue, nd e tngents to the cicle If = 5 o, then = o 1 o 85 o 8 o 5 o E 6 EMTHS II 1
11 5 In, P =, Q = 6 nd Q = If PQ =, then P = cicle, cente, touches the secto intenll t, E nd F = 6 o nd = 18 Find the dius of the cicle 6 5 T P R θ Q Thee cicles, centes, nd touch ech othe s shown in the figue The dii of the two cicles with cente nd e both 1 cm nd dius of the cicle with cente is cm Find the e of the shded pt in cm π 6 π π 6 π In the figue, PQ is dimete nd PT is tngent of the cicle QT cuts the cicle t R Let Q = θ nd PQ =, then TR = cosθ sinθ sinθ tnθ sin θ tn θ cos θ tn θ It cnnot be detemined 5 F 6 o E EMTHS II 11
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