10 If 3, a, b, c, 23 are in A.S., then a + b + c = 15 Find the perimeter of the sector in the figure. A. 1:3. A. 2.25cm B. 3cm
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1 HK MTHS Pper II P. If f ( x ) = 0 x, then f ( y ) = 6 0 y 0 + y 0 y 0 8 y 0 y If s = ind the gretest vlue of x + y if ( x, y ) is point lying in the region O (including the boundry). n [ + (n )d ], then d = (s n ) n(n ) (s n ) n s n (n ) s n(n ) (s n ) n(n ) ( )( 7 ) 8 O x x +, x + x +, x x x 0, x + x x + x + 0,, b + b 8 b b+ =, b = =, b = =, b = =, b = =, b = If log( p + q ) = log p + log q, then p = q = b + b b p= p = q + q +b b q q p= q q + p = q q If x + x (bx )( x ), then x. + b b b x + bx = cx + d re + The digrm shows the grphs of y = x + bx x + b x + y = 0 Simplify y nd y = cx + d. The solutions of the eqution Simplify x x + x + x + HK MTHS Pper II The expression x x + k is divisible by ( x + ). ind the reminder when it is divided by ( x + ). 6 8
2 HK MTHS Pper II P. 0 If,, b, c, re in S., then + b + c = 6 6 ind the H.. nd L.M. of b c H.. bc bc L.M. b c b c b b c bc b c bc c nd bc If α nd β re the roots of the qudrtic eqution x x = 0, find the vlue of +. α β y = x If the simultneous equtions y = x hve only one solution, find k. k The price of cylindricl cke of rdius r nd height h vries directly s the volume. If r =cm nd h = cm, the price is $0. ind the price when r = cm nd h =6cm. $ r $8.80 $.0 h $6 $ ind the perimeter of the sector in the figure..cm cm π + cm 60.cm 6cm 6 In the figure, the bse of the conicl vessel is inscribed in the bottom of the cubicl box. If the box nd the conicl vessel hve the sme cpcity, find h : r. : π : 6 : π : π 8 : π 7 The figure shows solid consisting of cylinder of height h nd hemisphere of rdius r. The re of the curved surfce of the cylinder is twice tht of the hemisphere. ind the rtio volume of cylinder:volume of hemisphere. : : : : h rd h r r.cm
3 HK MTHS Pper II P. : 8 merchnt mrks his goods % bove the cost. He llows 0% discount on the mrked price for csh sle. ind the percentge profit the merchnt mkes for csh sle.% % %.% 7.% cosθ cos θ = sin θ sinθ sin θ cos θ sinθ tn θ 0 cos θ sin θ + sin θ = 0 cosθ cos θ ( ) ( sin θ ) ( cos θ sin θ ) In the figure, 7 8 cos =. ind. The lrgest vlue of sin θ + cos θ is 8 In the figure, =, P=P nd P P. ind tn θ. In the figure, points,, nd re concyclic. ind x. 0º.º º 7.º 0º In the figure, // nd = ind θ. º º 70º 7º 76º 6 In the figure, is dimeter. ind 00º 0º 0º º 0º x+ x 0 θ P 7 8 θq 0 x
4 HK MTHS Pper II P. 7 If the point (, ), (, ) nd (7, k) re on the sme stright line, then k = (0, 0), (, 0) nd (, 6) re the vertices of tringle. P(, ), Q(6, 6) nd R(, ) re three points. Which of the following tringles hs/hve re(s) greter thn the re of? I. P II. Q III. R I only II only I nd II only III only II nd III only circle of rdius touches both the positive x-xis nd the positive y-xis. Which of the following is/re true? I. Its center is in the first qudrnt. II. Its center lies on the line x y = 0. III. Its center lies on the line x + y =. I only II only I nd II only III only I nd III only 0 Wht is the re of the circle x + y 0x + 6y = 0? π π π Two fir dice re thrown. Wht is the probbility of getting totl of or 0? 6 6 group of n numbers hs men m. If the numbers, nd 6 re removed from the 7 6 group, the men of the remining n numbers remins unchnged. ind m. 6 n The figure shows the frequency polygons of two symmetric distributions nd with the sme men. Which of the following is/re true? I. Interqurtile rnge of <Interqurtile rnge of II. Stndrd devition of >Stndrd devition of III. Mode of > Mode of I only II only I nd III only III only II nd III only x+ If = 6 x, then =
5 HK MTHS Pper II P. 6 If : b = : nd b : c = :, then + b + c = b + c 7 8 In the figure, the rectngle hs perimeter 6cm nd re cm. ind the length of its digonl cm cm y 7cm 6 cm x 6 x Sign of f ( x) rom the tble, root of the eqution f ( x) = 0 is.7(correct to sig.fig.)..7(correct to sig.fig.)..77(correct to sig.fig.)..7(correct to sig.fig.)..8(correct to sig.fig.). cm In fctorizing the expression we find tht ( b ) ( b ) ( b b ) ( b + b ) is fctor. + is fctor. is fctor. is fctor. + b b, + it cnnot be fctorized. 0 If the solution of the inequlity x x is c x, then =, c = =, c = 7 Given tht the positive numbers p, q, r, s re in G.S., which of the following must be true? I. kp, kq, kr, ks re in G.S., where k is non-zero constnt. II. p q r s,,, re in G.S., where is positive constnt. III. log p, log q, log r, log s re in S. I only II only =, c = =, c = =, c = In the figure, is squre nd is n re of equilterl tringle. = re of 8
6 HK MTHS Pper II P.6 In the figure, the rdii of the sectors OPQ nd ORS re cm nd cm respectively, re of shded region = re of sector OPQ 6 Q Which of the following gives the compound interest on $0000 t 6% p.. for one yer, S O R P Solve tn θ + tn θ = 0 for 0 θ < 60. º, º only º, º only º, 60º, º, 0º º, 0º, º, 00º º, º, º, º 6 The figure shows the grph of the function compounded monthly? 0.06 $ 0000 $0000(.06 ) 0.06 $ $ $ Originlly of the students in clss filed in y = sin ( 0 x) y = sin( x + 0 ) y = sin( x 0 ) y = cos( x + 0 ) y = cos( x 0 ) 7 In the figure, is n equilterl tringle nd the rdii of the three circles re ech equl to. ind the perimeter of the tringle. n exmintion. fter tking re-exmintion, 0% of the filed students pssed. ind the totl pss percentge of the clss. ( + tn 0 ) 6 ( + tn 0 )
7 HK MTHS Pper II P.7 + tn tn 0 8 In the figure, GH is cuboid. The digonl H mkes n ngle θ with the bse ind 78 In the figure, if tn θ rc : rc : rc = : : G H, which of the In the figure, O is the center of the circle. touches the circle t N. Which of the following is/re correct? I. M, N, K, O re concyclic. II. HN ~ NK III. ON = NO I only H II only O III only M K I nd II only I, II nd III N following is/re true? In the figure, nd GH re two squres I. : : = : : II. : b : c = : : nd H is n equilterl tringle. ind :. III. sin : sin : sin = : : I only b II only III only I nd II only I, II nd III only c : : : : : H G 0 In the figure, TP nd TQ re tngents to the circle t P nd Q respectively. If M is point on the minor rc PQ nd PMQ= θ, then PTQ = P
8 HK MTHS Pper II P.8 N O PPR In the figure, rectngulr piece of pper is folded long so tht nd coincide. If = cm, = 6. cm, find.cm.cm 8cm cm.cm In the figure, the three circles touch one nother. XY is their common tngent. The two lrger circles re equl. If the rdius of the smller circle is cm, find the rdii of the lrger circles. 8cm 0cm cm X Y
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
Form HK 9 Mthemtics II.. ( n ) =. 6n. 8n. n 6n 8n... +. 6.. 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
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