Name :.. Form :.. PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN PEPERIKSAAN PERCUBAAN SPM 00 / ADDITIONAL MATHEMATICS Kertas September 00 jam Dua jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. Tulis nama dan tingkatan anda pada ruangan yang disediakan.. Kertas soalan ini adalah dalam dwibahasa.. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam bahasa Melayu.. Calon dibenarkan menjawab keseluruhan atau sebahagian soalan sama ada dalam bahasa Inggeris atau bahasa Melayu.. Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini. Untuk Kegunaan Pemeriksa Soalan Markah Penuh 0 0 Markah Diperolehi TOTAL 0 Kertas soalan ini mengandungi halaman bercetak / [Lihat halaman sebelah

/ 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 / Tolak 0.0 0. 0. 0. 0. 0.000 0.0 0.0 0. 0. 0.0 0. 0. 0. 0.0 0.0 0. 0. 0. 0. 0.0 0. 0.00 0.0 0. 0.0 0. 0.0 0. 0.00 0.0 0.0 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0. 0. 0. 0. 0. 0. 0 0 0 0. 0. 0. 0. 0. 0.0 0. 0.0 0. 0. 0.00 0.0 0. 0.00 0. 0.0 0. 0. 0.0 0. 0. 0. 0. 0.0 0. 0. 0. 0. 0.00 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0. 0.0 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0 0 0 0 0.0.... 0. 0. 0. 0.0 0.00 0. 0. 0. 0.0 0.0 0. 0. 0. 0.0 0.0 0. 0. 0.0 0.0 0.0 0. 0. 0.0 0.00 0.0 0. 0. 0.0 0.0 0.0 0. 0.0 0.0 0.0 0.0 0. 0.0 0.00 0.0 0.00 0.0 0.0 0.00 0.0 0.0 0. 0.0 0.0 0.0 0.0 0 0 0..... 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.00 0.00 0.0 0.0 0.00 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0..0 0.0 0.00 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0... 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.00 0.0 0.00 0.0 0.00 0.0 0.0 0.0 0.000 0.00 0.0 0.0 0.00 0.00 0.0 0.0 0.00 0.0 0.0 0.0 0.00 0.0 0.00 0.0 0.00 0.0 0.0 0.0 0.00 0.0 0.0 0.00 0.00 0 0 0 0 0 0. 0.000 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00..... 0.00 0.00 0.00 0.00 0.00 0.000 0.00 0.00 0.00 0.00 0.00 0.000 0.00 0.000 0.00 0.000 0.00 0.00 0.00 0.00 0.00 0.00 0.000 0.00 0.00 0.00 0.000 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000 0.00 0.000 0.000 0.00 0.00 0.00 0.00 0.00 0.00 0.000 0.00 0.00 0.00 0.00 0 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000 0.000 0.0000 0 f ( z) ep z Q ( z) k f ( z) dz f (z) O Q(z) Eample / Contoh: If X ~ N(0, ), then P(X > k) = Q(k) Jika X ~ N(0, ), maka P(X > k) = Q(k) z / [ Lihat halaman sebelah

/ The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. ALGEBRA b b ac log c b log a b = a log c a a m a n = a m + n a m a n = a m n (a m ) n = a mn log a mn = log a m + log a n m log a n = log a m log a n log a m n = n log a m T n = a ( n ) d 0 n S n = [a ( n ) d] T n = ar n n n a( r ) a( r ) S n = r r a S r, r <, r y = uv, u y, v dy d dy du dy dv du u v d d d dy d v du d u, du d v dv d CALCULUS Area under a curve b = y d or a b = dy a Volume of revolution b = d or a b y = dy a GEOMETRY Distance = Midpoint (, y) = r rˆ y i yj y ) ( y ) ( y y, y A point dividing a segment of a line n m ny my (,y) =, m n m n Area of triangle = ( y y y ) ( y y y ) / [ Lihat halaman sebelah

/ STATISTICS = N = = = f f ( ) N f ( ) f N F m = L C fm Q I 00 Q 0 = = N f f Wi Ii I W n P r n C r i n! ( n r)! n! ( n r)! r! 0 P(A B) = P(A)+P(B) P(A B) P (X = r) = Mean, µ = np npq z = r C p q n r n r, p + q = TRIGONOMETRY Arc length, s = r Area of sector, A = sin A + cos A = r sin (A B) = sina cosb cosa sinb cos (A B) = cosa cosb sina sinb tan A tan B 0 tan (A B) = tan Atan B sec A = + tan A cosec A = + cot A sin A = sina cosa cos A = cos A sin A = cos A = sin A tan A tan A = tan A a b c sin A sin B sin C a = b + c bc cosa Area of triangle = absin C / [ Lihat halaman sebelah

/ Answer all questions. Jawab semua soalan.. The absolute value function f ( ) is defined for the domain 0. Fungsi nilai mutlak f ( ) ditakrifkan untuk domain 0. State Nyatakan (a) the image of. imej bagi. (b) the range of f() corresponding to the given domain. julat f() berdasarkan domain yang diberi. For eaminer s [ marks] [ markah] Answer/Jawapan : (a).. (b).... f n The diagram shows the function Rajah di atas menunjukkan fungsi Find Cari (a) the value of n. nilai n. (b) f ( ) f n : where n is a constant. n f : dengan n ialah satu pemalar. [ marks] [ markah] Answer/ Jawapan : (a)..... (b)... / [ Lihat halaman sebelah

For eaminer s /. Given that function f : and fg :. Diberi fungsi f : dan fg :. Find Cari (a) g (), (b) the value of when gf ( ). nilai apabila gf ( ) [ marks] [ markah] Answer/Jawapan : (a)... (b) =.... One of the roots of the equation k 0 is two times the other root, find the possible value of k. [ marks] Salah satu punca bagi persamaan k 0 adalah dua kali punca yang satu lagi, cari nilai yang mungkin bagi k. [ markah] Answer/Jawapan : k =... / [ Lihat halaman sebelah

/ For eaminer s. The graph of the quadratic function y ( ) has a maimum point ( p, q ) and the y-intercept is h. Graf bagi fungsi kuadratik y ( ) mempunyai titik maksimum (p, q) dan pintasan-y ialah h. Find the value of Cari nilai bagi (a) p, (b) q, (c) h. [ marks] [ markah] Answer /Jawapan: (a) p =... (b) q =... (c) h =.... Find the range of values of for ( ) [ marks] Cari julat bagi nilai-nilai untuk ( ) [ markah] Answer/Jawapan :... / [ Lihat halaman sebelah

For eaminer s /. Solve the equation: Selesaikan persamaan: () ( ). [ marks] [ markah] Answer/Jawapan : =.... The sum of 0 readings of an eperiment was cm and the sum of squares of these readings was cm. However, it was later found that a reading of cm could not be accepted. Find the variance of the remaining readings. [ marks] Hasil tambah 0 bacaan bagi suatu eksperimen adalah cm dan hasil tambah kuasa dua bagi bacaan ini ialah cm. Walaubagaimanapun, didapati satu bacaan yang bernilai cm tidak boleh diterima. Cari variance bagi bacaan yang tertinggal. [ markah] Answer/Jawapan :... / [ Lihat halaman sebelah

/ For eaminer s. Given log p = and log q =, find the value of log pq. [ marks] Diberi log p = and log q =, cari nilai bagi log pq. [ markah] Answer/Jawapan :... 0. The first three terms of an arithmetic progression are, +, +. Tiga sebutan pertama bagi satu janjang aritmetik ialah, +, +. Find Cari (a) the value of, nilai, (b) the sum of the first 0 terms of the progression. hasil tambah 0 sebutan pertama bagi janjang itu. [ marks] [ markah] Answer/Jawapan : (a) =........ 0 (b)... / [ Lihat halaman sebelah

0 / For eaminer s. The second term and the fifth term of a geometric progression are and respectively. Sebutan kedua dan kelima bagi suatu janjang geometri ialah dan. Find the Carikan (a) common ratio, nisbah sepunya, (b) first term. sebutan pertama. [ marks] [ markah] Answer/Jawapan: a)....... b).... Find the sum to infinity of the geometric progression,,,. [ marks] Cari hasil tambah hingga ketakterhinggaan bagi janjang geometri,,,. [ markah] Answer/Jawapan:....... / [ Lihat halaman sebelah

/. A line segment PR is divided by the point Q(,) in the ratio PQ : QR = :. If R is (, ), find the coordinates of P. [ marks ] For eaminer s Garis PR dibahagi oleh titik Q(,) dalam nisbah PQ:QR = :. Jika R ialah (,), cari koordinat P. [ markah] Answer/Jawapan :.... y (,. ) (,.) O Graph above shows the line of best fit obtained by plotting y against for the relation y = q + p. The line of best fit passes through the points (,. ) and (,. ). Find the value of p and of q. Graf di atas menunjukkan garis penyuaian terbaik yang diperolehi dengan memplotkan y p lawan bagi hubungan y = q+. Garisan penyuaian terbaik melalui titik (,.) dan (,.). Cari nilai p dan nilai q. [ marks ] [ markah] Answer/Jawapan : p =.. q =.... / [ Lihat halaman sebelah

For eaminer s /. y B(0, k) A (h,) O The graph above shows points B (0, k) and A (h, ). If value of h and of k. Graf di atas menunjukkan titik B(0, k) dan titik A(h, ). Jika bagi h dan k. BA i j, find the BA i j, cari nilai [ marks] [ markah] Answer/Jawapan : h =... k = h. Given that AB and AC, find the value of h if A, B and C are h collinear. [ marks] h Diberi AB dan AC, cari nilai h jika A, B dan C adalah segaris. h [ markah] Answer/Jawapan : h =... / [ Lihat halaman sebelah

/ For eaminer s. Solve the equation sin( ) for 0 0. Selesaikan persamaan sin( ) bagi 0 0. [ marks ] [ markah] Answer/Jawapan:......... B P Q cm rad. O cm A The diagram above shows two sectors OAB and OPQ which are equal in area. Given that OA = cm, OQ= cm, AOB = radian and POQ = radian, find the value of. [ marks] Rajah di atas menunjukkan dua sector OAB dan OPQ yang mempunyai luas yang sama. Diberi OA = cm, OQ= cm, AOB = radian dan POQ = radian, cari nilai. [ markah] Answer/Jawapan: =. / [ Lihat halaman sebelah

For eaminer s /. y S Q y T P The diagram above shows two perpendicular lines PQ and ST. S is the point (0, ) and T is on the -ais. Given the equation of PQ is y, find Rajah di atas menunjukkan dua garis lurus berserenjang PQ dan ST. S ialah titik (0, ) dan T terletak pada paksi-. Diberi persamaan PQ ialah y=, cari (a) the equation of ST, persamaan bagi ST, (b) the coordinates of point T. koordinat titik T. [ marks ] [ markah] Answer/Jawapan: (a) (b)... ' 0. Find the value of f (0) if f ( ) ( )( ). ' Cari nilai f (0) jika f ( ) ( )( ). [ marks] [ markah] 0 Answer/Jawapan:........ / [Lihat halaman sebelah

/. A curve with gradient function the equation of the curve. dy d Satu lengkung dengan fungsi kecerunan persamaan bagi lengkung tersebut. passes through the point (, ). Find dy d [ marks ] melalui titik (, ). Cari [ markah] For eaminer s Answer/Jawapan:... Given that y, find, in terms of p, the approimate change in y when increases from to + p. [ marks ] Diberi y, cari dalam sebutan p, perubahan kecil bagi y apabila bertambah dari ke + p. [ markah] Answer/Jawapan:. / [ Lihat halaman sebelah

For eaminer s /. The probability that an egg picked at random is rotten is 0.. If a sample of 0 eggs is chosen at random, find the probability that eggs of the sample chosen are rotten. [ marks] Kebarangkalian sebiji telur dipilih secara rawak adalah rosak ialah 0.. Jika satu sampel yang terdiri daripada 0 biji telur dipilih secara rawak, cari kebarangkalian bahawa tiga biji telur dari sampel yang dipilih adalah rosak. [ markah] Answer/Jawapan:... Three letters will be selected from the word PHYSICS. Find the number of possible selections if Tiga huruf dipilih daripada perkataan PHYSICS. Cari bilangan pilihan yang mungkin jika a) no condition is imposed, tiada syarat dikenakan, b) all the three letters selected must be different. ketiga-tiga huruf yang dipilih mesti berbeza. [ marks] [ markah] Answer/Jawapan: (a) (b) / [ Lihat halaman sebelah

/. A random variable X is normally distributed with mean and standard deviation. Find the value of Satu pembolehubah rawak X bertaburan normal dengan min dan sisihan piawai. Cari nilai bagi (a) the z-score if X 00. skor z jika X = 00. (b) P ( X ). [ marks] [ markah] Answer/Jawapan: (a) (b). END OF QUESTION PAPER KERTAS SOALAN TAMAT / [ Lihat halaman sebelah

Nama Pelajar : / Additional Mathematics Paper September 00 Tingkatan :. PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN PEPERIKSAAN PERCUBAAN SPM 00 ADDITIONAL MATHEMATICS MARKING SCHEME Paper.

/ SPM Trial Eamination 00 Kedah Darul Aman Marking Scheme Additional Mathematics Paper Question Solution/ Marking Scheme Answer Marks (a) n (a) (a) B: (a) B: g ( ) (b) 0 f ( ) (b) (a) ( ) (b) B: (b) B: k B : or k (a) (b) (c) - B: - B: ( )( ) B: ( ) B : () or = / Additional Mathematics Paper

/ Question Solution/ Marking Scheme Answer Marks B: B: or B: B: log log p p p log log or or q q q or log p log q 0 B: log pq log p log q (a) - 0 (b) B: S 0 [( ) ()] (b) B: a and d (a) B: r B: ar or ar (a) (b) B: B: S ( r ) y B : and (, 0) y B : or B : p. or q. B :.. p or. q. or. q.() p = -. q =. B: h= or k= B: BA hi ( k ) j h= k= / Additional Mathematics Paper

/ Question Solution/ Marking Scheme Answer Marks B: h h h B: k or AB // AC h B : 0 or 0 0 B : 0 or 0 0 0 0, 0 B : () ( ) (). rad B: () () or () (a) B: m (b) B: 0 (a) y (b) (, 0) 0 B: (0 )( 0) ( 0) B: ( )( )( ) ( ) B: ( )( )( ) or () B : B: () or c ( ) y / Additional Mathematics Paper

/ Question Solution/ Marking Scheme Answer Mark B : y () p -p B : dy d or p 0 B: C (0.) (0.) 0. (a) (b) B: C C or C C (b) 0 (a) B : 00 (a). (b) B : (b)0. END OF MARKING SCHEME / Additional Mathematics Paper