- PDF Free Download

Size: px

Start display at page:

Download ""

Sybil Cole
6 years ago
Views:

PEPERIKSAAN BERSAMA SEKOLAH-SEKOLAH MENENGAH NEGERI PAHANG NAMA TINGKATAN PEPERIKSAAN PERCUBAAN 00 / ADDITIONAL MATHEMATICS Kerts September 00 jm Du jm JANGAN BUKA KERTAS SOALAN INI SEHINGGA

1 PEPERIKSAAN BERSAMA SEKOLAH-SEKOLAH MENENGAH NEGERI PAHANG NAMA TINGKATAN PEPERIKSAAN PERCUBAAN 00 / ADDITIONAL MATHEMATICS Kerts September 00 jm Du jm JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. Kerts soln ini dlh dlm dwibhs.. Soln dlm bhs Inggeris mendhului soln yng sepdn dlm bhs Melyu.. Clon dibenrkn menjwb keseluruhn tu sebhgin soln dlm bhs Inggeris tu bhs Melyu.. Clon dikehendki membc mklumt di hlmn belkng kerts soln ini. Untuk Kegunn Pemeriks Kod Pemeriks: Soln Mrkh Mrkh Penuh Diperoleh 0 0 Jumlh 0 Kerts soln ini mengndungi hlmn bercetk.

2 The following formule my be helpful in nswering the questions. The symbols given re the ones commonly used. ALGEBRA b b c x log b log log c c b m x n = m + n T ( n ) d m n = m n 0. S ( n ) d ( m ) n = m n n n Tn n r n n n r r log mn log m log n Sn, r r r m log log m log n S, n r r log m n = n log m CALCULUS KALKULUS y = uv, dy dx u dv dx du v dx Are under curve Lus di bwh lengkung b = y dx or( tu) b x dy du dv v u u dy y, dx dx Volume generted v dx v Isipdu jnn dy dx dy du du dx = b b y dx or ( tu) x dy

3 STATISTICS STATISTIK x x N I Wi I W i i x fx f n P r n! ( n r)! x x x x N N n C r n! ( n r)! r! x x fx f f f x 0 P( A B) P( A) P( B) P( A B) N F m L C f m n r nr P( X r) C p q, p q Men / min, r np I Q 00 Q 0 npq Z x GEOMETRY GEOMETRI Distnce/jrk Are of tringle/ Lus segitig = = x x y y x y x y x y x y x Mid point / Titik tengh x x y y x, y, r x y ~ y x y A point dividing segment of line Titik yng membhgi sutu tembereng gris nx mx ny my, y m n, m n x ^ r ~ x i y j x ~ ~ y

4 TRIGONOMETRY TRIGONOMETRI Arc length, s = r Pnjng lengkok, s= j Are of sector, A r sin A B sin A cos B cos Asin B sin A B sin A kos B kos Asin B cos AB cos A cos B sin Asin B Lus sektor, L = j sin A cos A sin A k A os sec A tn se k A tn A A cosec A cot A kose k A k ot A kos AB k os A k os B sin Asin B 0 tn A B tn A tn B tn A tnb tn A tn A tn A b c sin A sin B sinc sin A = sin A cos A sin A = sin A kos A b c bc cos A b c bc kos A cos A = cos A sin A = cos A = sin A kos A = kos A sin A = kos A = sin A Are of tringle/ Lus segitig = sin b C

5 THE UPPER TAIL PROBABILITY Q(z) FOR THE NORMAL DISTRIBUTION N(0, ) KEBARANGKALIAN HUJUNG ATAS Q(z) BAGI TABURAN NORMAL N(0, ) z 0 Minus / Tolk Exmple / Contoh: f (z) f ( z) exp z If X ~ N(0, ), then Answer ll questions Jik X ~ N(0, ), mk Jwb semu soln Q ( z) f ( z) dz P(X > k) = Q(k). Digrm shows k the mpping of function f followed Q(z) by the function g. P(X >.) = Q(.) = 0.0 O k z

6 Rjh menunjukkn pemetn fungsi f dn diikuti fungsi g. x f x + g x + Find the vlue of Cri nili bgi () f - () (b) gf (0) Digrm Rjh [ mrks] [ mrkh] Answer/Jwpn :( ) ( b )... Given the functions g( x) x n nd g Find the vlue of n nd of k. Diberi fungsi g( x) x n dn g nili n dn nili k. ( x) kx ( x) kx, where n nd k re constnts.,dengn kedn n dn k dlh pemlr, cri [ mrks ] [ mrkh] Answer/Jwpn : n =... k=...

7 . Two functions re defined by f : x px, nd g : x x x Given tht gf ( x) x px q. Find the vlues of p nd of q. Du fungsi ditkrif sebgi f : x px, dn g : x x x Diberi gf ( x) x px q, cri nili p dn nili q. [ mrks] [ mrkh] Answer/Jwpn : p= q=.... Solve the qudrtic eqution x ( x ) ( x)( x ). Give your nswer correct to four significnt figures. Selesikn persmn kudrtik. x ( x ) ( x)( x ) Berikn jwpn nd betul kepd empt ngk bererti. [ mrks] [ mrkh] Answer/Jwpn : x...

8 . Find the rnge of vlues of x for x x. Cri jult nili x bgi x x [ mrks ] [ mrkh]. Answer/Jwpn :.... Digrm shows the grph of f ( x) ( x p) q where, p nd q re constnts The curve y= f(x) hs mximum point t (, -). Rjh menunjukn grf f ( x) ( x p) q dengn kedn, p dn q dlh pemlr.lengkung y = f(x) mempunyi titik mksimum pd (, - ). Ste Nytkn () the rnge of the vlues of, jult nili, (b) the vlue of p, nili p, (c) the vlue of q, nili q, (d). the eqution of the xis of symmetry. persmn pksi simetri. Answer/Jwpn : y O - Digrm Rjh (,-) ).. b) p=... c) q=.... d)... x y = f(x) [ mrks] [ mrkh]

9 . Given tht p log m nd q log m, express log in terms of m nd n. Diberi p log m dn q log m, ungkpkn dlm sebutn m dn n. [ mrks] [ mrkh] Answer/Jwpn :.... Given tht x ( y x y ) = nd ( ) =. Find the vlue of x nd of y. Diberi x ( y x y ) = dn ( ) =.Cri nili x dn nili y. [ mrks] [ mrkh] Answer / Jwpn : x =... y =...

10 0. The sum of the first n terms of n rithmetic progression is given by S n n² n. Diberi hsil tmbh n sebutn pertm bgi sutu jnjng ritmetik ilh S n n² n. Find Cri () the common difference, bez sepuny, (b) the ninth term. sebutn kesembiln. [ mrks] [ mrkh] Answer/Jwpn : ()..,... (b).. 0. The first three terms of sequence re, y,. Find the positive vlue of y such tht the sequence is Tig sebutn pertm sutu jujukn ilh, y,. Cri nili positif y supy jujukn itu merupkn sutu () n rithmetic progression, [ mrks ] jnjng ritmetik [ mrkh ] (b) geometric progression. jnjng geometri 0 Answer/Jwpn : () y =..... (b) y=... 0

11 . Given p = 0. = 0. + h + k +m where,h,k,m form geometric series. Diberi p = 0.. = 0. + h + k +m yng mn h,k,m membentuk stu siri geometri () Find the vlue of h nd of k, Cri nili h dn nili k, (b) Hence, find the vlue of p. [ mrks ]. Seterusny, cri nili p. [ mrkh] Answer/Jwpn : () h =. k=. (b) p =... Given tht the coordintes of point A is (,) nd point B is (,). A point P(x,y) moves such tht AP = PB. Find the eqution of the locus of P. Diberi bhw koordint titik A dlh (,) dn titik B dlh (,).Stu titik P(x,y) bergerk dengn kedn AP = PB.Cri persmn lokus P. [ mrks ] [ mrkh] Answer/Jwpn....

12 . Digrm shows stright line grph of y x ginst x. Rjh menunjukkn grf gris lurus y x melwn x. A(,) x B(,-) Digrm Rjh Given tht y = h + kx, where k nd h re constnts. Clculte the vlue of h nd of k. Diberi y = h + k, yng mn k dn h dlh pemlr. Cri nili h dn nili k. [ mrks] [ mrkh] Answer/Jwpn : h=. k=..

13 x y. The eqution of stright line PQ is Find the eqution of the stright line tht is prllel to PQ nd psses through the point (-,) x y Diberi persmn gris lurus PQ ilh. Cri persmn gris lurus yng selri dengn PQ dn mellui titik (-,). [ mrks] [ mrkh] Answer/Jwpn :.... Given tht = -i + j, = i + j nd = -i + j, find the vlue of h nd of k such tht Diberi = -i + j, = i + j dn = -i + j, cri nili h dn nili k supy [ mrks] [ mrkh] Aswer/Jwpn : h =... k =...

14 . In Digrm,OPQR is prllelogrm. T nd U re the midpoints of RQ nd OT respectively. Given OP = nd OR = b, express OU in terms of nd b. Dlm Rjh, OPQR ilh segiempt selri.titik T dn U dlh titik tengh bgi RQ dn OT msing-msing. Diberi bhw OP = dn OR = b.ungkpknou dlm sebutn nd b [ mrks] [ mrkh] P Q O U R T Digrm Rjh Answer/Jwpn :. Solve the eqution cos x + cos x + = 0, for 0 x 0 Selesikn persmn bgi kos x + kos x + = 0, bgi 0 x 0 [ mrks] [ mrkh] Answer/Jwpn :

15 . Digrm (i) shows semicircle ABC where AC is the dimeter. Digrm (ii) shows sector POQ with centre O. Rjh (i) menunjukkn semibultn ABC yng mn AC dlh dimeterny. Rjh (ii) menunjukkn sektor POQ berpust O. Given tht both the semicircle ABC nd the sector POQ hve the sme perimeter, AC = cm nd POQ =. rdins. Find the rdius of sector OPQ. [ mrks] Diberi kedu-du semibultn ABC dn sektor POQ mempunyi perimeter yng sm, AC = cm dn POQ =. rdins. Cri jejri sektor OPQ. (Use =.) [ mrkh] (Gunkn =.) Answer/Jwpn :.. Given tht V= t ( - t ), clculte the mximum vlue of V. Diberi V= t ( - t ), Cri nili mksimum bgi V. [ mrks] [ mrkh] Answer/Jwpn:.

16 0. The totl surfce re of closed cylinder is given by A = r +0 r, where r is the rdius of the cylinder. Find the smll chnge in the totl surfce re of the cylinder when its rdius chnges from cm to.0 cm. Give your nswer in terms of. Jumlh lus permukn bgi sebuh silinder tertutup dlh A = r +0 r, dimn r merupkn jejri silinder tersebut. Cri tokokn kecil lus permukn silinder itu pbil jejriny berubh dripd cm ke.0 cm. Berikn jwpn nd dlm sebutn. [ mrks] [ mrkh] 0 Answer/Jwpn : d x. () Given tht ( ) f ( x) dx x, find the vlue of x 0 [ f ( x)] dx d x Diberi ( ) f ( x) dx x, cri nili bgi [ x f ( x)] dx 0 (b) Find the vlue of [ mrks ] Cri nili bgi [ mrkh] Answer/Jwpn : () (b)

17 A set of dt contins 0 numbers. The men of these numbers is nd the vrince is.. Stu Set dt mengndungi 0 nombor. Min bgi 0 nombor ini dlh dn vrins dlh. () Find the sum of their squres for these 0 numbers. Cri hsiltmbh kusdu 0 nombor ini. (b) If number is dded to this set of dt, such tht the men does not chnge, find the vrince of this new set of numbers. [ mrks] Jik stu nombor ditmbh ke nombor set dt ini, dn nili min ny tidk berubh, cri vrins bgi nombor set dt yng bru. [ mrkh] Answer/Jwpn ().... (b). Digrm shows five crds of different letters. Rjh menunjukn lim keping kd huruf yng berlinn. B A G U S Digrm Rjh () Find the number of possible rrngements, in row, of ll the crds. Crikn bilngn cr susunn yng mungkin, dlm stu bris, semu kd itu. (b) Find the number of these rrngements in which the letters U nd A re not side by side. Crikn bilngn cr susunn itu dengn kedn huruf U dn huruf A dlh tidk bersebelhn. [ mrks ] [ mrkh] Answer/ Jwpn:() (b)

18 . A box contins x blue mrbles nd red mrbles. Two mrbles re chosen t rndom from the box. Find the vlue of x if the probbility of getting both mrbles red is. [ mrks] Sebuh kotk mengndungi x biji guli biru dn biji guli merh. Du biji guli dipilih secr rwk dri kotk itu. Crikn nili x jik kebrngklin kedu-du guli berwrn merh ilh. [ mrkh] Answer/Jwpn : x=.... X is rndom vrible of norml distribution with men of 0 nd vrince of. Find the vlue of r such tht P ( X r) 0.. X dlh sutu tburn norml dengn min 0 dn sisihn piwi. Cri nili r dengn kedn P ( X r) 0.. [ mrks] [ mrkh] Answer/Jwpn :: r = END OF QUESTION PAPER KERTAS SOALAN TAMAT

19 JAWAPAN SPM TRIAL 00 PAHANG SECONDARY SCHOOLS FORM ADDITIONAL MATHEMATICS PAPER MARKING SCHEME No Soln Answers/Jwpn Mrks - B k = or, n = B k = nd n = gf(x) = (px-) +(px-)+ p = or q = - p =±, q = - B B B x =. or x = -0. x =. nd x = -0. (x-)(x-)= 0 B B B < x <

20 () < 0 (b) p = - (c) q = - (d) x = ( chnging to bse m) B or equivlent B x + y = or x + y = solve simultneous liner equtions x=, y = - () d = (b) S S = B B 0 () y = (b) y = () h = 0.0 k= 0.00 (b) p = B

21 ( x ) ( y ) or ( x ) ( y ) [x²- x + + y ²- y + ] = x² - x + + y² -y + x +y -y+=0 B B = hx² + k h = or k= - h = nd k = - m = y = ( x+) or = (-)+C B B B B y = x - or equivlent -i + i = h(i j ) + k(i + j) - = h + k or = - h + k h = - or k = h = - nd k = RT = ½ or B B B B OT = b + + ½ B ( cos²x ) + cos x + = 0 (cos x + )(cos x ) = 0 X = 0 0 or, 0. seen 0., 0 0,. B B B

22 + =.*.*= r + r (.) *follow through. t- t t( -t) =0 Mx V, V= () - () r or r = 0.0 [0 + ()] (0.0). cm² () or B B B B B B B B - (b) or () (b) * follow through B B 0. )! or 0 ()!! or (b) B B

23 or B (x+)(x-)=0 B B. =. B B r =.

SULIT /1 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. ALGEBRA. log.

SULIT /1 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. ALGEBRA. log. Use SULIT 7/ The following formule my be helpful in nswering the questions. The symbols given re the ones commonly used. ALGEBRA b b c 8 log b log log c c b m n = m + n 9 Tn = + (n -)d m n = m n 0 S n