SULIT 3472/1 Matematik Tambahan Oktober 2012
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1 SULIT 7/ Matematik Tambahan Oktober 0 Jam Name :... Form :.. BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH DAN SEKOLAH KECEMERLANGAN KEMENTERIAN PELAJARAN MALAYSIA Arahan: PENTAKSIRAN DIAGNOSTIK AKADEMIK SBP 0 PEPERIKSAAN AKHIR TAHUN (TINGKATAN ) MATEMATIK TAMBAHAN Kertas 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. 5. Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini. Soalan Untuk Kegunaan Pemeriksa Markah Penuh JUMLAH 80 Kertas ini mengandungi 8 halaman bercetak Markah Diperolehi 7/ 0 Hak Cipta BPSBPSK SULIT
2 SULIT 7/ The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan. ALGEBRA b b ac m x 6 loga loga m loga n a n a m x a n = a m + n 7 log a m n = n log a m a m a n = a m n ( a m ) n = a m n 5 log mn log m log n a a a 8 log b a log log c c b a CALCULUS y = uv, dy dv du u v dx dx dx dy dx dy du du dx y u v, dy dx du v dx dv u dx v STATISTICS x x x N F 5 m L C N f m fx Q 6 I 00 f Q x x x x 7 N N I Wi I W i i x x fx f f f x 7/ 0 Hak Cipta BPSBPSK SULIT
3 SULIT 7/ GEOMETRY Distance / Jarak = x x y y Midpoint / Titik tengah x x y x, y, y A point dividing a segment of a line Titik yang membahagi suatu tembereng garis nx mx ny my x, y, m n m n Area of triangle / Luas segitiga = x y x y x y x y x y x TRIGONOMETRY Arc length, s = r a = b + c bc cosa Area of sector, a sin A b sin B A c sin C r 5 Area of triangle / Luas segitiga = absin C 7/ 0 Hak Cipta BPSBPSK SULIT
4 SULIT 7/ For Answer all questions. Jawab semua soalan. Diagram shows an arrow diagram for the relation between set P and set Q. Rajah menunjukkan gambar rajah anak panah bagi hubungan antara set P dan set Q. P Q Diagram Rajah State Nyatakan (a) the object of, objek bagi, (b) the type of the relation. jenis hubungan itu. [ marks] [ markah] (a) (b) 7/ 0 Hak Cipta BPSBPSK SULIT
5 SULIT 5 7/ x Given the function g : x, x. x x Diberi fungsi g : x, x. x For Find Cari (a) g (5), (b) g (). [ marks] [ markah] (a) (b) Given the function f : x x, find the values of x such that f( x). Diberi fungsi f : x x, cari nilai-nilai x dengan keadaan f( x). [ marks] [ markah] 7/ 0 Hak Cipta BPSBPSK SULIT
6 For SULIT 6 7/ Given the g : x x and the composite function fg : x x 6. Diberi g : x x dan fungsi gubahan fg : x x 6. Find Cari (a) f( x ), (b) value of x when fg( x) g( x). nilai bagi x apabila fg( x) g( x). [ marks] [ markah] (a) (b) 5 It is given that is one of the roots of the quadratic equation Find the value of q. Diberi bahawa ialah satu daripada punca persamaan kuadratik Cari nilai q. x x q 0. x x q 0. [ marks] [ markah] 5 7/ 0 Hak Cipta BPSBPSK SULIT
7 SULIT 7 7/ 6 Solve the quadratic equation x x( x ). Give your answer correct to four significant figures. Selesaikan persamaan kuadratik x x( x ). Beri jawapan anda betul kepada empat angka bererti. [ marks] [ markah] For 6 7 The roots of the quadratic equation equation which has roots and. Punca-punca persamaan kuadratik kuadratik yang mempunyai punca-punca dan. x x 5x 6 0 are and. Find the quadratic 5x 6 0 adalah dan. Cari persamaan [ marks] [ markah] 7 7/ 0 Hak Cipta BPSBPSK SULIT
8 For SULIT 8 7/ 8 Diagram 8 shows the graph of the function f ( x) ( x h) 5. Rajah 8 menunjukkan graf bagi fungsi f ( x) ( x h) 5. f( x ) f x x h ( ) ( ) 5 O x (, k ) Diagram 8 Rajah 8 The curve has the minimum point (, k ). Lengkung tersebut mempunyai titik minimum (, k ). State Nyatakan (a) the value of h, nilai bagi h, (b) the value of k, nilai bagi k, (c) the equation of the axis of symmetry. persamaan bagi paksi simetri. [ marks] [ markah] (a) 8 (b) (c) 7/ 0 Hak Cipta BPSBPSK SULIT
9 SULIT 9 7/ 9 Given that quadratic equation x( x k) x has no roots. Find the range of values of k. Diberi persamaan kuadratik x( x k) x tidak mempunyai punca. Cari julat nilai k. [ marks] [ markah] For 9 0 The minimum value of the quadratic function constant. Nilai minimum untuk fungsi kuadratik keadaan p adalah pemalar. Find Cari is 0, where p is a f ( x) x 0x p adalah 0, dengan f ( x) x 0x p (a) the value of x at which the function f is minimum, nilai x di mana fungsi f adalah minimum, (b) the value of p. nilai p. [ marks] [ markah] (a) (b) 0 7/ 0 Hak Cipta BPSBPSK SULIT
10 For SULIT 0 7/ Solve the equation Selesaikan persamaan x 7. x x 7. x [ marks] [ markah] Solve the equation : Selesaikan persamaan : x 6 x [ marks] [ markah] 7/ 0 Hak Cipta BPSBPSK SULIT
11 SULIT 7/ Solve the equation log 5(x) log 5( x ). Selesaikan persamaan log 5(x) log 5( x ). [ marks] [ markah] For Given points P( h, k ), Q(,8) and M (,) lie on the straight line PQ where M is the midpoint. Find the value of h and of k. Diberi titik P ( h, k), Q (,8 ) dan M (,) terletak di atas garis lurus PQ dengan keadaan M adalah titik tengah. Cari nilai h dan nilai k.. [ marks] [ markah] 7/ 0 Hak Cipta BPSBPSK SULIT
12 For SULIT 7/ 5 The straight line x py q passes through the point (,) and is perpendicular to the line xy7 0. Find the value of p and of q. Garis lurus x py q melalui titik (,) dan berserenjang dengan garis xy7 0. Cari nilai p dan nilai q. [ marks] [ markah] 5 6 The point A is (,) and the point B is (,5). The point P moves such that AP : PB :. Find the equation at the locus of P. Titik A ialah (,) dan B ialah (,5). Titik P bergerak dengan keadaan AP : PB :. Cari persamaan lokus bagi P. [ marks] [ markah] 6 7/ 0 Hak Cipta BPSBPSK SULIT
13 SULIT 7/ 7 The mean of a set of numbers, x,x 5,x, x 7 and x Min bagi satu set nombor, x,x 5,x, x 7 dan x is 8. ialah 8. For Find Cari (a) the value of x. nilai x. (b) the standard deviation of the set of numbers. sisihan piawai bagi set nombor itu. [ marks] [ markah] (a) (b) 7 8 A set of positive integers consists of,5and m. The variance of this set of integers is. Find the value of m. Satu set integer positif terdiri daripada,5dan m. Varians bagi set integer ini ialah. Cari nilai m. [ marks] [ markah] 8 7/ 0 Hak Cipta BPSBPSK SULIT
14 For SULIT 7/ 9 A set of six numbers has a mean of 0.5. Satu set yang terdiri daripada enam nombor mempunyai min 0.5. (a) Find x. Cari x. (b) When a number p is added to this set, the new mean is 0. Find the value of p. Apabila satu nombor p ditambah kepada set ini, min baru ialah 0. Cari nilai p. [ marks] [ markah] (a) 9 (b) 0 Diagram 0 shows two sectors, MOL and NOK of a circle with centre O. Rajah 0 menunjukkan dua buah sektor, MOL dan NOK bagi sebuah bulatan yang berpusat O. Diagram 0 Diagram 0 Rajah 0 0 Calculate the perimeter of the shaded region. Hitung perimeter kawasan berlorek. [ marks] [ markah] 7/ 0 Hak Cipta BPSBPSK SULIT
15 SULIT 5 7/ Diagram shows a sector OPRQ of a circle with centre O. Rajah menunjukkan sektor OPRQ bagi sebuah bulatan berpusat O. For Given that the length of the chord PQ = 9 cm and the radius, r 5. cm, find the area of the segment PRQ. Give your answer correct to two decimal places. Diberi panjang perentas PQ = 9 cm, cari luas tembereng PRQ. Beri jawapan anda betul kepada dua tempat perpuluhan. Diagram Rajah [ marks] [ markah] A wire with the length 80 cm is used to form a sector of a circle with a radius r and angle θ subtended at the centre O. Find the area of the sector in terms of r only. Seutas dawai yang mempunyai panjang 80 cm digunakan untuk membentuk sebuah sektor bulatan berjejari r dan sudut tercangkum θ di pusat bulatan O. Cari luas sektor tersebut dalam sebutan r sahaja. [ marks] [ markah] 7/ 0 Hak Cipta BPSBPSK SULIT
16 For SULIT 6 7/ Given that Diberi g x g x ( ) ( x), evaluate g(). ( ) ( x), nilaikan g(). [ marks] [ markah] Given that y x x, Diberi bahawa y x x, dy (a) find the value of, dx dy cari nilai, dx when x, apabila x, (b) express, in terms of k, the approximate change in y, when x changes from to k, where k is a small value. ungkapkan dalam sebutan k, perubahan kecil bagi y, apabila x berubah daripada kepada k, dengan keadaan k ialah satu nilai kecil. [ marks] [ markah] (a) (b) 7/ 0 Hak Cipta BPSBPSK SULIT
17 SULIT 7 7/ 5 A cubic ice block with sides of x cm, melts at a rate of 0.8 cm per second. Find the rate of change in x at the instant when x =. Seketul ais berbentuk kubus dengan panjang tepinya x cm, mencair pada kadar 0.8 cm sesaat. Cari kadar perubahan x pada ketika x =. [ marks] [ markah] For 5 END OF QUESTION PAPER KERTAS SOALAN TAMAT 7/ 0 Hak Cipta BPSBPSK SULIT
18 SULIT 7/ INFORMATION FOR CANDIDATES MAKLUMAT UNTUK CALON. This question paper consists of 5 questions. Kertas soalan ini mengandungi 5 soalan.. Answer all questions. Jawab semua soalan.. Write your answers in the spaces provided in the question paper. Tulis jawapan anda dalam ruang yang disediakan dalam kertas soalan.. Show your working. It may help you to get marks. Tunjukkan langkah langkah penting dalam kerja mengira anda. Ini boleh membantu anda untuk mendapatkan markah. 5. If you wish to change your answer, cross out the answer that you have done. Then write down the new answer. Sekiranya anda hendak menukar jawapan, batalkan jawapan yang telah dibuat. Kemudian tulis jawapan yang baru. 6. The diagrams in the questions provided are not drawn to scale unless stated. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan. 7. The marks allocated for each question are shown in brackets. Markah yang diperuntukkan bagi setip soalan ditunjukkan dalam kurungan. 8. A list of formulae is provided on pages to. Satu senarai rumus disediakan di halaman hingga. 9. You may use a scientific calculator. Anda dibenarkan menggunakan kalkulator saintifik. 0. Hand in this question paper to the invigilator at the end of the examination. Serahkan kertas soalan ini kepada pengawas peperiksaan di akhir peperiksaan. 7/ 0 Hak Cipta BPSBPSK SULIT
19 SULIT 7/(PP) BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH DAN SEKOLAH KECEMERLNGAN KEMENTERIAN PELAJARAN MALAYSIA PENTAKSIRAN DIAGNOSTIK AKADEMIK SBP 0 PEPERIKSAAN AKHIR TAHUN (TINGKATAN ) ADDITIONAL MATHEMATICS Paper MARKING SCHEME 7/(PP) Kertas ini mengandungi 6 halaman bercetak SULIT
20 SULIT 7/(PP) MARKING SCHEME Question Answers Mark (a) -, (b) Many- to- one (a) 5/ (b) x x or g ( x) x x -5 and -5 or (a) x x y g ( x) or x (b) x6 (x ) 0 5 ( ) ( ) q 0 6 x and x.78 x () ()( ) x x 0 B x 0x 0 7 SOR (5) 0 or POR ( ) (6) SOR 5 or POR 6 B 7/(PP) SULIT
21 SULIT 7/(PP) (a) 8 (b) 5 (c) x k 8 9 ( k )( k8) 0 or 8 B ( k ) ()() 0 (a) x 5 f ( x) ( x 5) 5 p 0 (b) p 5 5 p 0 x x 6 x B ( ) x 5 x x 5 x or 6 x x x 6 B B 7/(PP) SULIT
22 SULIT 7/(PP) x x x 5 x or log5 log55 x B x log5 x h k 0 and h or k 0 B h ( ) or k 8 5 p and q 5 p or q 5 p x q y p p or y x 7 x y 6x 6y 0 B B ( x ) ( y ) ( x ) ( y 5) B 6 ( x ) ( ) y or AP PB ( x ) ( y 5) or 7/(PP) SULIT
23 SULIT 5 7/(PP) 7 a) x = ( x ) (x 5) (x ) ( x 7) ( x ) 5 b) standard deviation = m = or 8 (m + ) (m ) = 0 m m88 0 B B 5 m a) x 6 5 m 9 0 7/(PP) b) p = 7 x p 0 7 Perimeter = 0.6 S KN + S LM + MN (8.5 x.) + (0.5 x.) + () (8.5 (0.5 x.) Area of segment =. cm (5.) (0.6) 5. sin(.7) Area of sector OPQ = (5.) (0.6) or Area of triangle POS = 5. sin(.7) B B SULIT
24 SULIT 6 7/(PP) Area of sector = 0r r 80 r r r 80 r r B B r r r ( ()) ()( x )( ) a) 5 dy x dx b) 7k y ( () ) k cms - dx ( dt () dv x dx 0.8) ` B B 7/(PP) SULIT
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