y h Find the coordinates of fl c Fi nd the coordinates of the minimum point x

Y h find the coordinates of fl c fi nd the

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y (h) Find the coordinates of fl. (c) Fi nd the coordinates of the minimum point. x Answ er (a) c - { I J (b) (_ , _ _) l 2 J (c) ( ~ ' - ) f2 1 ,. ,, , /~\ ' 1J m l11 t'f' 0 .'.l {h1
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1 ·,"jr 11 and Han· s ub~c1s pflhc universal set€. The number of clements in c;ich ~uh~cl" as s hown in the Venn Diagram. Given that n(A) 2.r. n(B) ~ 5x - 7 and n(A n B) ~ n{A v B} ', fi nd t he value of' (:i) ( h) n(A 'r. B). (c) n{e ). Ans w er (a) (b) (c) JO Shade t he required regions in t he Venn Diagrams. (a) A' r. IJ'. (b) (A'r.B)' ~,) (An B ). (~!\ - - "\ ~ , _) [ 1 J l 2] [ I J r I I { 1 l ,. ,,..,,.,,, , .
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Fo·· :x: m1 ;:;., ,.'s (,:f;' 11 10 ll1e scores of a basketball team in a series of matches are given below. 63 63 75 67 69 52 70 52 50 63 56 51 (a) Find the mean, median and mode of the scores. (h) Find lhe probability thal the t ea m scored more than 60 puinls. Answ er (") Mean= Median ~ Mocle= (IJ) ( I J ( I I I I l ( I J /'fll /,\(J mmn { /, ,.
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lllUh'I' ' .) 12 f' t .T '!.¥ atr.:rrt' r"'i I.At' Th e lirsl term of a seque nce of numbers is 56. The follo win g l e1 ms arc g iven hy subtracting five from the previ ous 1enn. (a) Write: down the next two terms in 1hc sc 4uen cc. (b) Write down an ell:pression , 1n 1em1s of 11, for the 11 1 h tenn . 12 ' l11c: diagram show~ the siue view of a wheel s1op. Find ( a) the angle x, (b) the value ofy, 1l1c hei ght of the wh ee l stop . 4 y 7 l)imensions are n o\ 10 scale. fo fjQnUf1C ' I' $ U?J ' o.'
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TKSS 201 l Sec 2 Mathematics Marking S ch eme Paper I End of Y ea r Ex ominations Qns ~ ! Details An swers la) 66 = 2x3x I I 126 = 2 x 3 2 x 7 lb) I HCF ~ 2 x 3 x a x b x c = 6abc LCM ~ 2 x ) 2 x 7 x 11 x a2 x b x c 2 = 1386a 2 bc 1 n 2 (n+ l) - 3(n+ I) (n 2 - 3)(n+I) 2b) x 1 - (F - 2f [x - (y - 2 Jix~ · (y - 2)j , [x y+2][x +y - 2] ' '3ai - ! -- 1W "' 2; ,+J- 3v - J I I ;~~~~~:~~?: 1 + 1 ) 3b) 4 a) 3vw-2v = w + l v(3w- 2) = w+ I w+I v= - - 3w - 2 I + l v = - 4- 3 - 2 4 v = -1 z x <x-2) x- 2 - - ~ ' C on c lu sion: l 5 3 3 ~ -- -'-= (x -=- -2 ) = 3z 2 8 6 3 3 11 9 3 - ·~ I -1 i I I I I =~ -=1
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TKSS 20 I I S ec 2 Ma1hematics l\fa rk ing Sc heme Paper I End ol'Ycar E xam inations ! 5.1) l- 5b )_ _ .. 1 sc) 3.5 x 2 = 7 m I 6a) 7a) - --- - l Area of study room on map = 12 -- 12.? c...: l .... : c ::. n :.:_ 1 _ _ ____ _ Li near scale lcm : 2m Area Scale I cni2: 4m 2 Actu al area ofstudv room = 48 - 50.84 m 2 · -'-'- -- · I 3x - 5 y - 6 = o -------·-···- ( l) I ' 2x 3y 5 = 0 ---··---·- -- -(2) ( l)x2: 6x - 10y- 12 =0---------- (la) (2)x3: 6x - 9y - l 5 = 0-----··---·-(2a) ( l a)-(2a): - IOy - 12 + 9y - ~ 15 =0 - y+3 =- 0 y = 3 subt. y = 3 into (I) : 6x - 10(3) - l2 = 0 x = ? :__ ___ _ ____ ______ _ _ 2x+ 3y = 5 2 5 Y "' - 3 x+ :i . 2 . · 5 gradie nt = - 3 , y-m terccpt = 3 7~ 2 5 Subst (q, q + 6) into y =- - x+ - 7c) c1+6 = - Zq + ~ 3 3 2q 5 q+ - ~ + - - 6 3 3 13 l/ = - 5 Any va l ue cxccp1 5 3 3 ~ - - 8b) 1 2x 1 - 4x = 0 1 x(x - 2) = 0 x =O or x = 2 B (2, ()) 8c) Equation of line of symmetry: x = I Subt. x = I into y= 2x 2 - 4x y =- 2 9a) n( AnB) ~ n(AvB)' 2x = 8 X=4 2
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TKSS 20 11 Sec2 Mathcm a 11 c~ Marking Scheme Paper I I : nd of Y car E.\amin.itiuus -- -r i %) I n(A'nB)-3x - 7 I n(A'n8)=3(4} 7 I n (A 'n B) = 5 9c) i n(s ) -= 5.x - 7 +8 '11(1;)=21 IO a) I Ob) - 11 a) 63+63 + 75+6 7+ 69 • )2 I 70 t 52 +5 0+6 3+ 5 6• 51 niean- - - -- 12 mean - 60.9 (3 s.f.) 50,51,52,52,56,63,63, 61 , 67,69, 70 , 75 median - 63, m()dc = 63 I lb) 7 P(rnorc than 60 points) = - 12 12a) Next 2 tcnns - 51 , 46 12b) T 1 = 56 Ti - 56 - 5 I 3a} Ti - 56 - 5 - 5 T. - 56 - 5(11 - I) T,, = 56 - 511 + 5 T. = 61 - 511 ~ 3 cosx-=- 7 y 3
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TKSS 2011 St.><: 2 :-.1athcn1a1ic.-; Mai king S~hcmc Pap.:1 End of Year E xa111111ati ons 1 .-" - M . 6(1 d.p) 4
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Class R c9 Number Candio:itc N ame c -r J TANJONG KATONG SEC ONDARY SC HOOL End of Year Examination MA TH EMA TIC S PAPER2 Seco nd ary Two - 0750 - 0905 Thui·sday 6 October 2011 - I ho ur 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in.
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