7/ Matematik Tambahan Kertas Sept 00 jam Nama :.... Tingkatan:.. PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA DENGAN KERJASAMA JABATAN PELAJARAN MELAKA PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 00 MATEMATIK TAMBAHAN Kertas Dua Jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. This question paper consists of 5 questions Kertas soalan ini mengandungi 5 soalan.. Answer all questions. Jawab semua soalan.. Give onl one answer for each question Bagi setiap soalan berikan SATU jawapan sahaja.. Write the answers clearl in the space provided in the question paper. Jawapan hendaklah ditulis pada ruang ang disediakan dalam kertas soalan. 5. Show our working. It ma help ou to get marks. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda untuk mendapatkan markah. 6. If ou wish to change our answer, cross out the work that ou have done. Then write down the new answer. Sekirana anda hendak menukar jawapan, batalkan kerja mengira ang telah dibuat. Kemudian tulis jawapan ang baru. 7 The diagram in the questions provided are not drawn to scale unless stated. Rajah ang mengiringi soalan ini tidak dilukiskan mengikut skala kecuali dinatakan. 8. The marks allocated for each question and sub-part of a question are shown in brackets. Markah ang diperuntukkan bagi setiap soalan atau ceraian soalan ditunjukkan dalam kurungan. 9. A list of formulae is provided on page to Satu senarai rumus disediakan di halaman hingga 0. You ma use a non-programmable scientific calculator. Buku sifir matematik empat angka boleh digunakan. This question paper must be handed in at the end of the eamination. Kertas soalan ini hendaklah diserahkan pada akhirpeperiksaan. Kod Pemeriksa Soalan Markah Penuh 5 6 7 8 9 0 5 6 7 8 9 0 5 Jumlah 80 Markah Diperoleh Kertas soalan ini mengandungi 8 halaman bercetak
The following formulae ma be helpful in answering the questions. The smbols given are the ones commonl used. Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan.. Simbol-simbol ang diberi adalah ang biasa digunakan. ALGEBRA b b ac log c b 8 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 nm 5 log a mn = log a m + log a n 6 m log a n = log a m - log a n 7 log a m n = n log a m 9 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 ) = uv, d d dv u d v du d du dv v u u d, d d, v d v d d du d du d CALCULUS( KALKULUS) Area under a curve ( Luas dibawah lengkung) b = d or a b = d a 5 Volume generated ( Isipadu Janaan) b = d or a b = d a GEOMETRY Distance (Jarak) = ( ) ( ) 5 A point dividing a segment of a line Titik ang membahagi suatu tembereng garis Midpoint ( Titik Tengah ) (, ), r rˆ i j n m (, ), m n n m m n 6 Area of triangle ( Luas Segitiga ) = ( ) ( )
= = = N f f ( ) N f ( ) = f = = N F 5 m L C fm Q 6 I 00 Q 0 N STATISTICS _ f f 7 8 9 w I I w n! ( n r)! n! ( n r)! r! n P r n C r 0 P(A B) = P(A)+P(B)- P(A B) P (X = r) = Mean µ = np z = npq n C r p r q n r, p + q = TRIGONOMETRY Arc length, s = r ( Panjang lengkok) s = j Area of sector, A = r ( Luas sektor L = j ) sin A + cos A = sec A = + tan A 5 cosec A = + cot A 6 sin A = sina cosa 7 cos A = cos A sin A = cos A - = - sin A 9 sin (A B) = sina cosb cosa sinb 0 cos (A B) = cosa cosb sina sinb tan (A B) = a b c sin A sin B sinc tan A tan B tan A tan B a = b + c - bc cosa Area of triangle = ab sin C ( Luas Segitiga ) 8 tan tan A tan A A
For eaminer s use onl Answer all questions. Jawab semua soalan The relation between two variables is given b {(, ),(, ),(, ),(0, 6)}. State Hubungan antara dua pemboleh ubah diberi dengan {(, ),(, ),(, ),(0, 6)}. Natakan (a) the object of, objek bagi - (b) the tpe of relation. jenis hubungan [ marks] [ markah] Answer / Jawapan: (a) (b) The functions g and h are defined as ( ) and. ( ) Find Fungsi fungsi g and h ditakrifkan sebagai ( ) and ( ). Cari (a) the value of, g - ( - ) nilai bagi, g - ( - ) (b) hg (). [ marks] [ markah] Answer / Jawapan: (a) (b)
5 Given function g: - and function hg() = - 5. Find the function of h Diberi fungsi g: - dan hg() = - 5. Cari fungsi bagi h [ marks ] [ markah ] For eaminer s use onl Answer/ Jawapan: Solve the following quadratic equation, Selesaikan persamaan kuadratik berikut, Give our answer correct to significant figures. Berikan jawapan anda betul kepada angka bererti. [ marks ] [ markah ] Answer/Jawapan: (a)
6 For eaminer s use onl 5 The quadratic equation ( ) has no real roots. Find the range of values of k. Persamaan kuadratik ( ) tidak mempunai punca nata Cari julat bagi k [ marks ] [ markah ] 5 Answer/Jawapan: 6 Diagram 6 shows the graph of function ( ) where q is a constant Rajah 6 menunjukkan graf fungsi dengan keadaan q ialah pemalar 5 Diagram 6 Rajah 6 Find Cari (a) the value of q nilai bagi q (b) equation of the ais of smmetr persamaan bagi paksi simetri (c) the coordinate of minimum point koorninat bagi titik minimum 0 [ marks] [markah] 6 Answer/Jawapan:(a) p = (b) q = (c)
7 Solve the equation ( ) Selesaikan persamaan ( ) 7 [ marks ] [ markah] For eaminer s use onl 7 Answer /Jawapan: = 8 Given that log P - = log 9 R. Epress R in terms of P Diberi bahawa log P - = log 9 R. Ungkapkan R dalam sebutan P. [ marks ] [ markah ] 8 Answer /Jawapan : = 9 Epress ( ) in the simplest form. Ungkapkan ( ) dalam bentuk ang termudah. [ marks] [ markah] Answer/ Jawapan : 9
For eaminer s use onl 0 0 The first three term of an arithmetic progression are q 5, q + 5, and q +. Find Tiga sebutan pertama bagi suatu janjang aritmetik adalah q 5, q + 5, dan q +. Cari (a) the value of q nilai bagi q (b) the sum of the first 6 terms hasiltambah 6 sebutan pertama 8 [ marks] [ markah ] Answer/Jawapan: (a) (b) The sum of the first n term of a geometric progression,,, 8, is 0. Find Hasil tambah n sebutan pertama janjang geometri,,, 8, adalah 0. Cari (a) the common ratio of the progression nisbah sepuna bagi janjang itu (b) the value of n nilai n [ marks ] [ markah ] Answer/Jawapan: (a) (b) Given the first and the fourth term of a geometric progression are 6 and respectivel. Diberi ungkapan pertama dan keempat suatu janjang geometri adalah 6 dan Find the sum to infinit of the progression. Cari jumlah hingga tak terhingga janjang itu. masing-masing [ marks] [ markah] Answer:
9 Diagram shows the graph of the straight line that is related b the equation = p q where p and q are constants. Rajah menunjukkan graf garis lurus ang dihubungkan oleh persamaan = p q di mana p dan q adalah pemalar. log For eaminer s use onl (,0) log (0,-) Diagram Rajah Find, Cari (a) the values of p and q, nilai-nilai p dan q (b) the value of when = 5. nilai apabila = 5 [ marks] [ markah] Answer/Jawapan: (a) p = q = (b)
For eaminer s use onl 0 A point P (8, s ) divides the line joining G (, ) and H ( r, 7 ) such that GP = PH. Find the value of Titik P (8,s) membahagi garis ang menghubungkan G (,) dan H(r,7) dalam keadaan GP=PH. Carikan nilai (a) r (b) s [ marks] [ markah] Answer : (a) (b)
5 Diagram 5 shows a parallelogram PQRS with QTS as a straight line. Rajah 5 menunjukkan segiempat selari PQRS dengan QTS merupakan garis lurus For eaminer s use onl S T P R Given that, and ST = TQ. Epress in terms of and. Diberi,, dan ST = TQ. Ungkapkan dalam sebutan dan. (a) Diagram 5 Rajah 5 Q (b) [ marks] [ markah ] 5 Answer / Jawapan: (a) (b)
For eaminer s use onl 6 Diagram 6 shows triangle OPQ. Rajah 6 menunjukkan segi tiga OPQ O Q P Diagram 6 Rajah 6 Given that and. Find Diberi bahawa dan. Cari a) b) unit vector in the direction of. vektor unit dalam arah [ marks] [ markah] 6 Answer /Jawapan: ( a) ( b)
7 Solve the equation for 0 o θ 60 o. For eaminer s use onl Selesaikan persamaan bagi 0 o θ 60 o [ marks ] [ markah ] 8 Diagram 8 shows a circle with centre O Rajah 8 menunjukkan sebuah bulatan berpusat O. P Answer/ Jawapan:.. 7 O Q Diagram 8 Rajah 8 Given the radius of the circle is 8 cm and the angle of minor sector is 0.76 rad. Using =., find the perimeter of major sector PQR. Diberi jejari bulatan ialah 8 cm dan sudut sektor minor ialah 0.76 rad. Dengan menggunakan =., carikan perimeter major POQ. [ marks] [ markah ] 8 Answer/Jawapan:
For eaminer s use onl 9 Find the values of for = Carikan nilai-nilai bagi = 7 d when d 7 apabila 0 d 0 d. [ marks] [ markah ] 9 Answer/Jawapan: 0 A curve = p² + has an equation of normal + 5 = 6 at =. Find the value of p Suatu lengkung = p² + mempunai persamaan normal + 5 = 6 pada =. Cari nilai bagi p. [ marks] [ markah] 0 Answer/Jawapan:
5 Given that ( ), find the value of t if [ ( )] Diberi bahawa ( ), cari nilai bagi t jika [ ( )] For eaminer s use onl [ marks] [ markah ] Answer/Jawapan : The mean of the set of data 5, p -, 8, 5 and ( p ) is 0. Min bagi set data 5, p -, 8, 5 and ( p ) adalah 0. (a) Find the possible values of p. Cari nilai ang mungkin bagi p. (b) Hence, find the mode and the median of the set of the data based on the positive value of p. Seterusna, cari nilai mod dan median bagi data tersebut berdasarkan nilai positif p [ marks] [ markah ]. Answer / Jawapan: a) p= b) mode = median =
For eaminer s use onl 6 The probabilit that Ihsan being chosen as a school prefect is while the probabilit of 5 Akram being chosen is. 9 Kebarangkalian Ihsan dipilih sebagai pengawas sekolah ialah manakala kebarangkalian 5 Akram dipilih ialah. 9 Find the probabilit that Cari kebarangkalian bahawa (a) neither of them is chosen as a school prefect, kedua-duana tidak dipilih sebagai pengawas sekolah, (b) onl one of them is chosen as a school prefect. hana seorang daripada mereka dipilih sebagai pengawas sekolah. [ marks] [ markah] Answer/ Jawapan : (a) (b)
7 6 students are chosen to take part in a leadership course. These 6 students are chosen from monitors, assistant monitors and 5 prefects. 6 orang pelajar dipilih untuk mengikuti kursus kepimpinan. 6 orang pelajar itu dipilih daripada ketua darjah, penolong ketua darjah dan 5 pengawas. For eaminer s use onl Calculate the number of different was the team can be formed if Hitung bilangan cara ang berlainan pasukan itu boleh dibentuk jika (a) there is no restriction, tiada sarat dikenakan, (b) the team contains onl monitor and eactl prefects. pasukan itu mengandungi hana ketua darjah dan tepat pengawas. [ marks] [ markah] Answer/ Jawapan : (a) (b) 5 X is a random variable of a normal distribution with mean of. and a variance of..find X adalah pembolehubah rawak bagi suatu taburan normal dengan min. dan varians.. Cari (a) the z-score if X=6. nilai skor - z apabila X = 6. (b) P. 5.6 [ marks] [ markah] Answer/ Jawapan:(a) (b) 5 END OF THE QUESTION PAPER KERTAS SOALAN TAMAT
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SULIT 7/ 7/ Matematik Tambahan Kertas Sept 00 ½ jam PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA DENGAN KERJASAMA JABATAN PELAJARAN MELAKA PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 00 MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. This question paper consists of three sections : Section A, Section B and Section C Kertas soalan ini mengandungi tiga bahagian : Bahagian A, Bahagian B dan Bahagian C.. Answer all questions in Section A, four questions from Section B and two questions from Section C. Jawab semua soalan dalam Bahagian A, empat soalan daripada Bahagian B, dan dua soalan daripada Bahagian C.. Give onl one answer/solution to each question. Bagi setiap soalan, berikan satu jawapan / penelesaian sahaja.. Show our working. It ma help ou to get marks. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda untuk mendapatkan markah. 5. The diagrams in the questions provided are not drawn to scale unless stated. Rajah ang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinatakan, 6. The marks allocated for each question and sub-part of a question are shown in brackets Markah ang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan dalam kurungan. 7. A list of formulae is provided on pages and. Satu senarai rumus disediakan di halaman dan. 8. A booklet of four-figure mathematical tables is provided. Buku sifir matematik empat angka boleh digunakan. 9. You ma use a non-programmable scientific calculator. Anda dibenarkan menggunakan kalkulator saintifik ang tidak boleh diprogram. Kertas soalan ini mengandungi 6 halaman bercetak [ Lihat sebelah 7/ SULIT
SULIT 7/ The following formulae ma be helpful in answering the questions. The smbols given are the ones commonl used. Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan.. Simbol-simbol ang diberi adalah ang biasa digunakan. b b ac a ALGEBRA 8 log a b = log log c c b a a m a n = a m + n a m a n = a m - n (a m ) n = a nm 5 log a mn = log a m + log a n 6 m log a n = log a m - log a n 7 log a m n = n log a m 9 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 ) = uv, d d dv u d v du d du dv v u u d, d d, v d v d d d du du d CALCULUS ( Kalkulus) Area under a curve ( Luas dibawah lengkung ) b = d or (atau ) a b = d a 5 Volume generated ( Isipadu janaan ) b = d or a b = d a Distance (Jarak ) = ( ) ( ) GEOM ETRY 5. A point dividing segment of a line (Titik ang membahagi suatu tembereng garis) Midpoint (Titik tengah ) (, ) =, r n m (,) =, m n 6. Area of triangle (Luas segitiga ) = n m m n ( ) ( ) i j r [ Lihat sebelah 7/ SULIT
SULIT STATISTICS ( STATISTIK ) = = = N f f ( ) N = N _ 7 8 9 w I I w n n! P r ( n r)! n n! C r ( n r)! r! 0 P(A B)=P(A)+P(B)-P(A B) = f ( ) f = f f P(X=r) = Mean, µ = np r C p q n r n r, p + q = N F 5 m = L C fm Q I 00 Q 6 0 npq z = TRIGONOMETRY Arc length, s = r (Panjang lengkok, s = j ) Area of sector, A = r ( Luas sektor, L = j ) sin A + cos A = sek A = + tan A 5 cosec A = + cot A 6 sina = sinacosa 7 cos A = cos A sin A = cos A- = - sin A tan A 8 tana = tan A 9 sin (A B) = sinacosb cosasinb (sin (A B) = sinakosb kosasinb) 0 cos (A B) = cos AcosB sinasinb (kos (A B) = kos AkosB sinasinb ) tan A tan B tan (A B) = tan Atan B a sin A b sin B c sinc a = b +c - bc cosa ( a = b +c - bckosa ) Area of triangle (Luas segitiga) = absin C 7/ Lihat sebelah SULIT
SULIT Section A Bahagian A [0 marks] / [0 markah] Answer all questions in this section Jawab semua soalan dalam bahagian ini. Solve the following simultaneous equations: [5 marks] Selesaikan persamaan serentak berikut: [ 5 markah ] 0 0 Solutions b scale drawing will not be accepted. Penelesaian secara lukisan berskala tidak diterima. In Diagram, LMN is a straight line. Dalam Rajah, LMN ialah satu garis lurus. L (, ) M (0, ) O N (p, ) Diagram Rajah (a) Find Cari (i) the value of p. nilai p. (ii) the equation of the straight line passing through L and perpendicular to LMN. persamaan garis lurus ang melalui titik L dan berserenjang dengan LMN. [ 5 marks ] [ 5 markah ] (b) Given that LM : MN = : q, find the value of q. [ marks ] Diberi LM : MN = : q, cari nilai q. [ markah ] 7/ SULIT
SULIT 5 (a) Sketch the graph of sin for 0 < < π. [ marks ] Lakar graf bagi sin untuk 0 < < π. [ markah ] (b) Hence, using the same aes, sketch a suitable straight line to find the number of solutions for the equation sin for 0 < < π. State the number of solutions. [ marks ] Seterusna, dengan menggunakan paksi ang sama, lakar satu garis lurus ang sesuai untuk mencari bilangan penelesaian bagi persamaan sin untuk 0 < < π. Natakan bilangan penelesaian itu. [ markah ] One of the turning points of a curve with gradient function k is (, ). Satu daripada titik pusingan suatu lengkung dengan fungsi kecerunan k ialah (, ). Find Cari (a) the value of k. [ marks ] nilai k. [ markah ] (b) the equation of the curve. [ marks ] Cari persamaan lengkung itu. [ markah ] (c) the other turning point on the curve and determine whether this turning point is a maimum or a minimum point. [ marks ] titik pusingan ang satu lagi dan seterusna tentukan sama ada titik pusingan ini adalah titik maksimum atau titik minimum. [ markah] 5 Table 5 shows the frequenc distribution of the masses of a group of pupils in a class. Jadual 5 menunjukkan taburan jisim sekumpulan murid dalam suatu kelas. Mass (kg) Jisim (kg) Number of pupils Bilangan murid 0 9 0 9 50 59 60 69 70 79 80 89 7 9 k 6 Table5 Jadual 5 (a) Given that the median mass of the distribution is 5.5, calculate the value of k. [ marks] Diberi bahawa jisim median taburan ini ialah 5.5, cari nilai k. [ markah] (b) Use the graph paper to answer this question. Using a scale of cm to 0 kg on the horizontal ais and cm to pupil on the vertical ais, draw a histogram to represent the frequenc distribution of the masses. Hence, find the mode mass. [ marks] Dengan menggunakan skala cm kepada 0 kg pada paksi mengufuk dan cm kepada orang murid pada paksi mencancang, lukis sebuah histogram untuk mewakili taburan frekuensi bagi jisim itu. Seterusna, cari jisim mod. [ markah] 5
SULIT 6 6 Two cars start together in the same direction at the same place. The first goes with uniform speed of 50 km h, the second goes at the speed of 0 km h in the first hour and increases the speed b 5 km h - each succeeding hour. Dua kereta bermula serentak pada tempat ang sama mengikut arah ang sama. Kereta pertama bergerak dengan halaju seragam 50 km j -, kereta kedua bergerak dengan halaju 0 km j - pada jam pertama dan meningkatkan kelajuanna 5 km j - pada setiap jam berikutna. (a) Calculate the speed of the second car at the fifth hour. Hitungkan halaju kereta kedua pada jam ang kelima. (a) After how man hours will the second car over take the first car? Selepas berapa jam, kereta kedua memintas kereta pertama? [ marks] [ markah] [ marks] [ markah] (b) Find the total distance travelled b the second car while over take the first car. [ marks] Cari jumlah jarak ang dilalui oleh kereta kedua semasa memintas kereta pertama. [ markah] 6
SULIT 7 Section B Bahagian B [0 marks] [0 markah] Answer four questions from this section. Jawab empat soalan daripada bahagian ini. 7 Use graph paper to answer this question. Gunakan kertas graf ang disediakan untuk menjawab soalan ini. Table 7 shows the values of two variables, and, obtained from an eperiment. Variables and are related b the equation k, where h and k are constants. h Jadual 7 menunjukkan nilai-nilai bagi dua pembolehubah, dan, ang diperoleh daripada satu eksperimen. Pembolehubah dan dihubungkan oleh persamaan k dengan h keadaan h dan k adalah pemalar. 0.5.0.5.0.5.0.8.59..7..9 Table 7 Jadual 7 (a) Based on table 7, construct a table for the values of and. [ marks ] Berdasarkan Jadual 7, bina satu jadual bagi nilai nilai dan. [ markah] (b) Plot against, using a scale of cm to unit on both aes. Hence, draw the line of best fit. [ marks ] Plotkan melawan, dengan menggunakan skala cm kepada unit pada kedua-dua paksi. Seterusna, lukiskan garis lurus penuaian terbaik. [ markah] (c) Use our graph in 7 (b) to find the value of Gunakan graf anda dari 7(b) untuk mencari nilai ( i ) k ( ii ) h [ 5 marks ] [5 markah] 7
SULIT 8 8 Diagram 8 shows triangles AOD and BOC. The straight line AD intersects the straight line BC at E. Rajah 8 menunjukkan segitiga AOD dan BOC. Garis lurus AD bersilang dengan garis lurus BC di titik E. B D E O C Diagram 8 Rajah 8 It is given that OA, OB 5, OC : CA = :, OD : DB = :, BE k BC,, where h and k are constants. Diberi bahawa OA, OB 5, OC : CA = :, OD : DB = :, BE k BC, dengan keadaan h dan k adalah pemalar. A AE h AD and AE h AD dan (a) Epress Ungkapkan (i) in terms of h, and, dalam sebutan h, dan, (ii) in terms of k, and. dalam sebutan k, dan. (b) Find the value of h and of k. Cari nilai h dan nilai k. [5 marks] [5 markah] [ marks] [ markah] (c) Given that = units, = units and ADO = 90, find AE. [ marks] Diberi = unit, = unit dan ADO = 90, carikan AE. [ markah] 8
SULIT 9 9 Diagram 9 shows a semicircle PSR, centre Q and radius 7 cm inscribed in a quadrant PRT of a circle, centre R. The straight lines, QT intersect the semicircle at S. Rajah 9 menunjukkan sebuah semibulatan PSR berpusat Q dan berjejari 7 cm terterap dalam sukuan PRT bagi sebuah bulatan berpusat R. Garis lurus QT bersilang dengan semibulatan di S. [Use/Guna π =.] Calculate Hitung (a) RQS, in radians, RQS, dalam radian, Diagram 9 Rajah 9 [ marks] [ markah] (b) the perimeter, in cm, of the sector PQS, panjang, dalam cm, bagi sektor PQS, (b) the area, in cm, of the coloured region. luas, dalam cm, bagi kawasan berwarna. [ marks] [ markah] [ marks] [ markah] 9
SULIT 0 0 Diagram 0 shows part of the curve which intersect the straight line k at (8,), where k is a constant. Rajah 0 menunjukkan sebahagian daripada lengkung ang bersilang dengan garis lurus k pada (8,) keadaan k adalah pemalar. Find Cari Diagram 0 Rajah 0 (a) the value of k. nilai k. (b) the area of the shaded region, luas rantau berlorek, [ marks] [ markah] [5 marks] [5 markah] (c) the volume generated, in terms of π, when the region which is bounded b the curve, the straight = and the -ais, is revolved through 60 about the -ais. [7 marks] isipadu ang djanakan, dalam sebutan π, apabila rantau ang dibatasi oleh lengkung itu,garis lurus = dan paksi-, dikisarkan melalui 60 pada paksi-. [7 markah] 0
SULIT (a) In a surve carried out in a district, it is found that 75% of 50 families own a computer. Dalam satu tinjauan ang dijalankan ke atas 50 keluarga di sebuah daerah, didapati 75% daripada mereka memiliki sebuah komputer. (i) Find the mean of the surve. Cari min dalam tinjauan ini. (ii) If 8 families from that district are chosen at random, calculate the probabilit that all of them own a computer. Jika 8 keluarga daripada daerah itu dipilih secara rawak, hitung kebarangkalian bahawa kesemuana memiliki sebuah komputer. [ marks] [ markah] (b) The ages of the residents of a cit are normall distributed with a mean of 0 ears and a variance of 6 ears. Umur penduduk daripada sebuah bandar adalah mengikut satu taburan normal dengan min 0 tahun dan varians 6 tahun. (i) Find the probabilit that the age of a resident selected randoml is between 7 ears and ears. Cari kebarangkalian bahawa umur penduduk ang dipilih secara rawak antara 7 tahun dan tahun. (ii) It is found that the number of residents are between 7 ears and ears is 5 000. Find the total number of residents in that cit. Didapati bilangan penduduk berumur antara 7 tahun and tahun ialah 5 000. Cari jumlah penduduk di bandar itu. [6 marks] [6 markah]
SULIT Section C Bahagian C [0 marks] [0 markah] Answer two questions from this section. Jawab dua soalan daripada bahagian ini. A particle moves along a straight line and passes through a fied point O. Its velocit, v m s, is given b v pt qt 5, where p and q are constants, and t is the time, in seconds, after passing through O. When t = s, the acceleration of the particle is zero and its velocit is - 9 m s. Suatu zarah bergerak di sepanjang suatu garis lurus dan melalui satu titik tetap 0. Halajuna, v m s, diberi oleh v pt qt 5, dengan keadaan p dan q adalah pemalar, dan t ialah masa, dalam saat, selepas melalui O. Pada ketika t = s,zarah bergerak dengan pecutan sifar dan halajuna ialah 6 m s. [Assume motion to the right is positive.] [Anggapkan gerakan ke arah kanan sebagai positif] Find Cari (a) the value of p and of q. [5 marks] nilai p dan nilai q. [5 markah] (b) the time when the particle reverse its direction, masa ketika zarah itu bertukar arah gerakan. (c) the total distance, in m, travelled b the particle in the first seconds. jumlah jarak, dalam m, ang dilalui oleh zarah itu dalam saat pertama. [ marks] [ markah] [ marks] [ markah]
SULIT Table shows price indices of four items, A, B, C and D in the ear 009 based on the ear 005. Jadual menunjukkan indeks harga bagi empat item, A, B, C dan D pada tahun 009 berasaskan tahun 005. Item Item Price Inde Indeks harga Weightage Pemberat A 5 B 0 8 C 0 D 8 5 (a) Find the value of and of if the composite inde for the ear 009 based on the ear 005 is 0.8 and the total weightage is 0. [5 marks] Cari nilai dan nilai jika indeks gubahan pada tahun 009 berasaskan tahun 005 ialah 0.8 dan jumlah pemberat ialah 0. [5 markah] (b) Given that the total paments for the four items is RM 600 in the ear 005, calculate the total pament in the ear 009. [ marks] Diberi bahawa jumlah baaran bagi keempat empat item itu ialah RM 600 pada tahun 005, hitungkan jumlah baaran pada tahun 009 [ markah] (c) The price of item C increases b 5% from the ear 005 to the ear 007. Calculate the price inde for item C in the ear 009 based on the ear 007. [ marks] Harga item C meningkat 5% dari tahun 005 ke tahun 007. Hitung indeks harga bagi item C pada tahun 009 berasaskan tahun 007. [ markah]
SULIT Use graph paper to answer this question. Gunakan kertas graf untuk menjawab soalan ini. A school intends to send pupils to attend two tpes of motivation courses, A and B. The number of participants for course A is and for course B is. The fees for attending course A and course B are RM 50 and RM 0 respectivel. Sebuah sekolah ingin menghantar murid murid untuk menertai dua jenis kursus motivasi, A dan B. Bilangan peserta untuk kursus A ialah dan untuk kursus B ialah. Yuran penertaan kursus A dan kursus B adalah RM 50 dan RM 0 masing-masing. The selection of the participants is based on the following constraints: Pemilihan peserta adalah berdasarkan kekangan berikut: I : The total number of participants is at least 0. Jumlah peserta adalah sekurang kurangna 0. II : The number of participants for course B is not more than three times the number of students for course A Bilangan peserta kursus B tidak melebihi tiga kali bilangan peserta kursus A. III : The maimum allocation for the courses is RM 000. Peruntukan maksimum bagi kedua-dua kursus adalah RM 000. (a) Write three inequalities, other than 0 and O, which satisf all the above constraints. [ marks] Tulis tiga ketaksamaan, selain 0 dan O,ang memenuhi semua kekangan di atas. [ markah] (b) Using a scale of cm to 0 participants on both aes, construct and shade the region R which satisfies all of the above constraints. [ marks] Menggunakan skala cm kepada 0 peserta pada kedua-dua paksi, bina dan lorek rantau R ang memenuhi semua kekangan di atas. [ markah] (c) Use our graph in (b), to find Gunakan graf anda di (b), untuk mencari (i) the maimum number of participants of course A if the number of participants of course B is 55. bilangan maksimum peserta kursus A jika bilangan peserta kursus B ialah 55 (ii) the minimum fees for the courses. Yuran minimum untuk menertai kedua-dua kursus. [ marks] [ markah]
SULIT 5 5 Diagram 5 shows a pentagon ABCDE. AEC and BED are straight lines. AB is parallel to DC and AB = DC. Rajah 5 menunjukkan satu pentagon ABCDE. AEC dan BED ialah garis lurus. AB adalah selari dengan DC dan AB = DC. C D 7.5 cm E 9. cm B Calculate Hitung (a) CDE, A Diagram 5 Rajah 5 [ marks] [ markah] (b) the length, in cm, of BC, panjang, dalam cm, bagi BC, (c) Calculate the area, in cm, of triangle ABC. Hitung luas, dalam cm, bagi segitiga ABC. [ marks] [ markah] [ marks] [ markah] END OF QUESTION PAPER KERTAS SOALAN TAMAT 5
SULIT 6 6
SULIT 7/ Additional Mathematics Paper Sept 00 PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA DENGAN KERJASAMA JABATAN PELAJARAN MELAKA PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 00 ADDITIONAL MATHEMATICS Paper MARKING SCHEME This marking scheme consists of 5 printed pages
PAPER QUESTION NUMBERS a) - b) one to one WORKING MARKS FULL MARKS (a) - ( ) @ + 5 = - (b) ( ) h() = + h() = (+) 5 B h(-) = - 5 B.609, -.09 @.608, -.08 ( ) ( ) ( )( ) ( ) or.609 @ -.09 B - 5-8 = 0 B -7 < k < 5 5-7 5 or (k+7)(k-5) < 0 or -7 and 5 ( seen) B B (+k) ()(9) < 0 (a) q = - 6 (b) = (c) (, -) = 6 7 + 9 = + ( (+) ) - ( ) (+) B B
QUESTION NUMBERS R = ( ) or R = WORKING MARKS FULL MARKS 8 Log ( ) = log R or log P log = log B log P = B ( ) ( ) 9 ( ) ( ) ( ) B B 0 (a) p = (b) 0 S 6 = [(9)+(6-)0] or a=9 and d = 0 seen @ 9+9+9+9+9+59 B B (a) r = (b) n= 0 S n = ( ( ) B 9 B B p = 0 - @ p= 0.0 and q = 0.5 q = 0.5 @ log p = - B log = log p + q loq B = 0. (a) r =, ( ) ( ) B (a) s= 7 5 ( ) ( ) B
QUESTION NUMBERS 5 (a) -5 + WORKING MARKS FULL MARKS (b) + (-5+) * + 5 * answer from part a B 6 (a) ( ) +. B (b) ( ) @ ( ) B ( ) ( ) 7 5, 8 5 @., 8.59 cos θ = 0.75 (cosθ -)(cosθ+)=0 Change cosθ = cos θ - 8 6.08 6 + 8(л 0.76 ) B B B B л 0.76 B 9 = B B 0 ( ) ( ) B B * + ( ) B B
QUESTION NUMBERS (a) p = 5, p = -7 WORKING MARKS FULL MARKS ( ( ) ( ) ) B (b) Mod = 5 Med = 8 (a) (b) 9 5 ( ) ( ) B (a) 9 (b) 60 B 5 (a).77 (b) 0.986 @ 0.985 (cal) P( Z ) or B
SULIT 7/ Additional Mathematics Paper Sept 00 PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA DENGAN KERJASAMA JABATAN PELAJARAN MELAKA PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 00 ADDITIONAL MATHEMATICS Paper MARKING SCHEME This marking scheme consists of printed pages
MARKING SCHEME FOR ADDITIONAL MATHEMATICS TRIAL SPM 00 PAPER NO. Solution Mark Scheme or or 7 0 ) 7)( ( 0 ) ( ) ( OR or 7 or 0 ) )( ( 0 ) ( [5] (a) (b) (i) 6 0 ) ( p p (ii) 7 )] ( [ m () ) ( q q q OR 0 ) ( (6) q q q [7]
NO. (a) Graph sinus Amplitude.5 units Two ccles in 0 π 0 Solution Mark Scheme sin or Straight line drawn 5 solutions [6] (a) (b) (c) k k 0 () 9 9 (0,8) d () c 8 d 8 d d 0,, d c 9 a maimum point [8]
NO. 5 (a) L 9.5, F 6, f 9.5 k 0 (8 m k k) 6 (0) 5.5 k Solution Mark Scheme 6(a) (b) (c) Uniform scales + height of an bar correct Use boundaries or midpoints All heights of 6 bars correct Mode = 50.5 T5 0 (5 )(5) 50 t [(0) ( t )(5)] t [(0) ( t )(5)] 50t t 9 hours 9 [(0) 50 km (9 )(5)] or 50 (9) [7] [7]
NO. 7(a) (b) Solution 0.5.0.5.0 6.5 9.0 0.6.59. 5. 8.5.79 Uniform scale + one of the points plotted correctl 6 Points plotted correctl Line of best fit Mark Scheme (9,.79) 0 9 8 (6.5,8.5) 7 6 5 (,5.) (.5,.) (c) (0.5,0.6) (,.59) (i) 5 6 7 8 9 k hk (ii).8 k k = 0.78 0. hk h = 8.55 [0]
NO. 8(a) AD AO OD AD BC 5 OR Solution BC BO OC Mark Scheme OE k (5 5k) OE ( h) h (b) 5 5k ( k h or 5 5k h ) and ( k or h 5 5 h ) 5 h 9 k (c) AD 9 8.06 9(a) (b) (c) AE 5 (8.06).665 tan RQS 7 RQS.07rad. RQS..07.05 S 7(.05) Perimeter 7(.05) 7 7 8.5 (7 )(.05) or. ( )( ) or (7 )(.07) (7)(). ( )( ) (7 )(.05) (7)( ) + (7 )(.07) 8. [0] [0]
NO. Solution Mark Scheme 0(a) (b) (c) ) ( k, ) (()) k k Limit integral, 8 8 )() ( ) ( )() ( ) ( )() ( ) 8 ( 8 units 9 (6)() or ) ( d 5 5 5 units 5 () 5 () 5 5 [0]
NO. Solution Mark Scheme (a) (b) (i) mean = (50)(0.75) 75 (ii) 0.00 (0.5) (0.75) 8) ( 0 8 8 C8 X P (i) 0.89 0.5) ( 0.5) ( 6 0 6 0 7 6 z P z P z P (ii) 69 or 68 5000 0.89 n n [0] (a) (b) (c) 8 and subt. 6 5 () () 8 or 0 () q p p q q p p q q p q pt a 5 s 0 5 t t t m S t t t dt t t S 0 5 5) ( 0 0 [0]
NO. Solution Mark Scheme (a) (b) (c) 0.8 0 ) 8(5 ) 0( ) 0(8 ) 5( 0 ) (5 ) ( ) (8 RM8.80 0.8 00 600 09 09 P P 5 is seen.7 00 5 0, [0]
NO. (a) (b) 0 50 0 000 00 Solution or equivalent or equivalent or equivalent Mark Scheme 90 80 70 60 50 0 0 0 0 0 0 0 0 50 60 70 80 90 Uniform Scale + one of the straight lines drawn correctl Three straight lines drawn correctl Shade region R eactl (c) (i) 6 (ii) (0,0) 50(0) + 0(0) or subt. an point in Region R into 50+0 700 [0]
NO. 5(a) (b) sin D sin 9. 7.5 D 0.5 or 0' BE =.5 cm or AE =.8 cm BEC = 7.5 or 7 or 7 Solution BC = 9. +.5 (9.)(.5)cos7.5 BC =. cm Mark Scheme (c) BEA = 07.6 or 07 7 or 07 8 A = Area BEC = (9.)(.5)sin 7.5 or A = Area BEA = (.8)(.5) sin07.6 Total area = A + A =. cm [0]