SULIT 347211 Additional Mathematics Kertas 1 Sept. 2008 2 Jam JABATAN PELAJARAN NEGERI JOHOR PEPERIKSAAN PERCUBAAN SPM 2008 ADDITIONAL MATHEMATICS Kertas 1 Dua jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1 Tu1i.r nama dun kelas anda pada ruangan yang disediakan. 2 Kertas soalan ini adalah dalam dw ihahasa 3 Soalan dalam bahasa 1nggeri.r mendahului soalan yang.repadan dalam haha.sa Melayu. I Untuk Kegunaan Pemeriksa 1 Soalan 1 Markah Penuh 2 Markah ~ Diperolehi 4. Calon dibenarkan rnenjawab keseluruhan atau sebahagian soalan sama ada dalam bahasa Inggeris atau bahasa Melayu. 5. Calon dihhendaki membaca maklumat di halarnan belakang kertus soalan ini. 347211 2008 Hak Cpra JPllll [Lihat sebelah SULIT
For examiner ' use only S SULIT Answer all questions 1 Diagram 1 shows the relation between set P and set Q. Rajah 1 menunjukkun hubungan antara set P dan set Q, Set P Set Q State Nyatakan (a) Diagram 1 Rajah 1 the codomain of the relation, kodomain hubungan itu, (b) the type of the relation. jenis hubungan itu. [2 marks] [2 markah] 1 LE 1 - Answer/ Jawapan : (a)... (b)... 2 2! 7 Given the inverse of function k is k-' : x -+-,x t 2. x-2 7 Diben, firngsi songsangan bagi k adalah k-' : x -+-, x # 2. x-2 (a) Calculate the value of k(3). Hitungkan nilai bagi k(3). (b) State the value of x where function k is not defined. Nyatakan nilai bagi x di mana fungsi k tidak tertakrij [ 3 mctrks ] [ 3 markah ] 1 347211 2008 Hnk Cipra JPNJ I Answer/ Jawapan : (a)... (b)... SU LIT
0 SULIT 5 347211 3 Diagram 2 shows the function f that maps set A to set B and the function g that maps set B to set C. For aminer rse only Rojnh 2 rnenunjukkan fungsi f memetakan set A kepada set B dun fungsi g rnemetaknn set B kepada set C. Diagram 2 Rajah 2 Given f (x) = rnx + 1 and d ( x ) = 2 x + n. Find the values of m and n. Diberi f (x) = mx + 1 dun gf(x) = 2 x + n. Carikan nilai bagi rn dun n. [ 3 rnarb ] [ 3 rnarkah ] 3 347211 2008 Hok Cipro JPNJ SULIT
For examiner use only - ULIT 6 1 Form the quadratic equation which has the roots -5 and -. 4 Give your answer in the form d + bx + c = 0, where a, b and c are constants. 1 Bentukkan persamaan kuadratik yang mempunyai punca- punca -5 and -. Berikan 4 jawapan anda dalam bentuk ax2 + bx + c = 0, di mana a, b dun c adalah pemalar. [2 marks] [ 2 markah] 4 Answer / Jawapan:... i Find the range of x for which (x + 3)(x - 4) < - 6. Cari julat x bagi (x + 3)(x - 4) <- 6. [ 3 marks ] [ 3 markah ] Answer/ Jawapan :... 347211 2008 Hak Cipra JPNJ SULIT
SULIT 7 347211 6 Diagram 3 shows the graph y = - 4 - (x - ic)2, where k is a constant. Rqjah 2 menunjukkan graf y = - 4 - (x - k)2, dengan keadaan k adalah pernalar. expminer 's use only y > x 0 (7 1 3 (6,-13) Find C.'arikan Diagram 3 Rajah 3 (a) the value of k, nilai hagi k, (b) the equation of the axis symmetry, persamaan paksi simetri, (c) the coordinates of the maximum point. icoordinat titiic maksimum. [ 3 marks ] [ 3 markah ] El Answer/ Jawapan : (a)... (b)... (c)... 347211 2008 Hak Cipro JPNJ SULIT
For - SULIT 8 examiner's use 7 Given that 32" (9"-') = 1, find the value of x. Diberi 32" (9"-') = 1, carikan nilai x. [ 3 marks ] [ 3 markah] Answer/ Jawapan :... 8 Given that log, x = r and log, y = t, express log, ) ; 7 ; (- in terms of r and t. Diberi log, x = r dun log, y = t, ungkapkan log, (;7i) - dalam sebutan r dun t. [ 4 marks ] [ 4 markah ] fa 0 Answer/ Jawapan :... 347211 2008 Hak Cipta JPNJ SULIT
SULIT 9 347211 9 The first three terms of an arithmetic progression are h, 2h - 2 and 2h + 1. Find the value of h. Tiga sebutan pertama suatu janjang arithmetik adalah h. 2h - 2 und 2h + 1. Carikan nilai bagi h. [ 2 murky ] [ 2 markah] For exorniner use onb 9 Answer/ Jawapan :... 22 10 The sum of the first five terms of a geometric progression is 7- and the common 27 2 ratio is -. Find the first term. 3 22 Hasil tambah lima sebutan pertama suatu janjang geometri ialah 7 - dun nisbah 27 2 sepitnyanya adalah -. Carikan nilai sebutan pertama. 3 [ 3 marks ] [ 3 markah ] Answer/ Jawapan:....,, 347211 2008 Ifak Cipta JPNJ SULIl
For xaminer 's use onb SULIT 10 347211 11 Given the arithmetic progression 5, 8, 1 1,... find the term that has a value of 13 1. Diberi janjang arithmetic 5, 8, 11,... carikan sebutan ke berapakah nilainya sama dengan 131. [ 2 marks] [ 2 markah ] m Answer/ Jawapan :... 3 3 3 12 Given a geometric progression 3, - - - 5 ' 25' 125'"" 3 3 3 Diheri suatu janjang geometri 3, - - - 5 ' 25' 125'"" Find Cari (a) (b) the common ratio nisbah sepunya the sum to infinity of the progression. hasil lambah ke ~akterhinggaan janjang I ersebut. [ 4 marks ] [ 4 markah ] ii, Answer/ Jawapan : (a)... (b)... 347211 2008 Hak Cipfa JPNJ SULIT
SULIT 347211 I For 13 Given that the variables x and y are related by the equation y = 1 02x-2. Diberi pembolehubah x and y dihubungkan oleh persamaan y = lo2'-*. examiner's me only 0 (O,-q.X Diagram 4 Rajah 4 Find the value of p and q. Hirungkan nilaip dan q. [ 3 marks ] [ 3 markah ] Answer/ Jawapan: p=..........q=............ X Y 14 Find the equation of the straight line which is parallel to -+ - = 1 and passes through 3 4 tlle midpoint of A(-2,3) and B(6,9). X Y Cari persamaan garis Iurus yang selari dengan - + - = 1 dan melalui ritik tengah 3 4 A(-2,3) dan B(6,9) [3 marks] I I 14 347211 20061 Ifak Cipta JPNJ
SULIT 12 For examiner's uye only 15 The point A is (4,-3) and the point B is (1,-2). The point P moves such that PA : PB = 3 : 2. Find the equation of the locus of P. Tirik A ialah (4,-3) dun tirik B ialah (1, -2). Saru titik P bergerak dengan keadaan supaya PA : PB = 3 : 2. Cari persamaan lokus P. [3 marks] [3 markah] 15 LiI Answer/ Jawapan :... 16 Diagram 5 shows vectors and z drawn on a cartesion plane. Rqjuh 5 menunjukkan vekror % and @ pada safah cartesion. Y 3.. P -3-2 -1 ' -1- I ; cx 16 Diagram 5 Rajah 5 t I Ungkapkan dalarn bentuk. (a) Express 5 in the form. (b) (f Find the unit vector in the direction of z. Cari vektor unit dalam arah z. Answer/ Jawupan : (a)... (b)... 347211 2008 Hak Cipm JPNJ SULI?
- SULIT 13 347211 and 17 The points A, B and C are collinear. It is given that?% = [:I, OB = (:) E'o r raminer S only OC = [:).Find the value of k. Titik- titik A, B dun C adalah segaris. Diberi = (')% = ('1 dun z = (:I. C'arikan nilai k. [ 4 marks ] [ 4 markah ] Answer/ Jawapan:... 17 1 18 Solve the equation 8 cos2 x + 2sin x - 5 = 0 for 0' I 6 5 360'. Selesaikanpersamaan 8cos2 x + 2sin x - 5 = 0 bagi 0' I 6 I 360'. [ 4 marks : [ 4 markah ] Answer/ Jawapan:... 3 0 347211 2008 Hak Cipro JPNJ
For examiner's use only SULIT 14 19 Diagram 6 shows a circle with centre 0. Rajah 6 menunjukkan suatu bulatan berpusat 0. Diagram 6 Rajah 6 Given that the length of the minor arc AB is 12.57 cm, find the length, in cm, of the radius. (use ~r = 3.142 ) Diberi panjang lengkok minor AB ialah 12.57 cm, caripanjang, dalam cm, jejari bulatan itu. [ 3 marks ] [ 3 markah] Answer/ Jawapan :... ( 2 ~ 1)' Diberi f (.r) = -, carikan f '(x). x - 1 [3 marks] [ 3 markah] Answer/ Jawapan:... 2008 Hak Cipra JPNJ SULIT
SULIT 15 347211-2 d~ 21 Given that p = 2x - 5 and y = 7, find the value of - when x = 2. P dx -2 d~ Diberi p = 2x - 5 dun y =, carikan nilai - apabila x = 2. P dx [3 marks] [ 3 markah ] ).'or exorniner :s use only 2 1 Answer1 Jawapan :... 3 3 22 Given that ig(x)dx = 5. Find the value of k if I- 2g(x) - b dx = - 18. I 3 3 Diberi ig(x)dx = 5. Carikan nilai k jib I- 2g(x) - b dx = - 18. I I I [4 marks] [ 4 markah ] 22 347211 2008 Hak Cipta JPNJ Answer/ Jawapan : k =... SULIT 0
SULIT For - I 16 examiner '3 use only 23 Given six digits 1, 3,4, 5, 6 and 8. A digit number is to be formed using four of these digits. Find Diberi enam digif 1, 3, 4, 5, 6 dun 8. Suafu nombor empaf digit hendak dibenfuk dengan mengpinakan empaf daripada digit tersebut.curi 347211 (a) the number of different four -digit numbers that can be formed, bilungun nombor empar digit yang berlainan yang dapat dibentuk (b) the number of different four-digit odd numbers which are greater than 6000. bilungun nornbor empat digir yang ganjil dun berlainan yung melebihi 6000. [ 4 marks ] [ 4 markah ] Answer / Jawapan: (a)... (b)... 24 Given two bags P and Q, each contains blue and red marbles. Bag P contains 3 blue marbles and 4 red marbles. Bag Q contains 3 blue marbles and 5 red marbles. A bag is chosen at random and a marble is picked from it. Find the probability that Diberi dua beg, musing- musing mengandungi guli berwcrrna biru dun merah. Beg P mengandzingi 3 biji guli biru dun 4 biji guli merah. Bag Q mengandungi 3 biji guli biru dun 5 biji gull merah. Sebuah beg dipilih secara rawak dun sebiji guli akan dikeluurkan dari beg tersebut. Carikan kebarangkalian bahawa (a) (b) a red marble from bag Q is chosen. sebiji guli merah dari beg Q dipilih. the marble is blue. [ 3 marks ] [ 3 markah ] Answer/Jawapan : (a)... (b)... 347211 2008 Hak Cipra JPNJ SULIT
SULIT 25 Diagram 7 shows a standard normal distribution graph. Rajah 7 menunjukkan graf taburan normal piawai. 347211 For examiner 's use only Given the probability represented by the area of the shaded region is 0.7019. Diheri keharangkalian yang diwakili oleh luas kawasan berlorek ialah 0.7019. (a) Find the value of k. Carikan nilai k. (b) Xis a random variable of a normal distribution with a mean of 45 and a variance of 25. Find the value ofx when the Z-score is k. X ialah pemboleh ubah rawak suatu taburan normal dengan min 45 dun varians 25. Cari nilai X jika skor-z ialah k. END OF QUESTION PAPER 347211 2008 Hak Cipfa JPNJ SULIT
SlJLIT INFORMATION FOR CANDIDATES MAKL UMA T UNTUK CALON 1. This question paper consists of 25 questions. Kertas.voalan ini mengandungi 25 soalun. 2. Answer all questions. JUWLI~ semua soalan. 3. Give only one answer for each question. Bugi seliup soal~~n berikan satu jawapan sahaja.. 4. Write your answers clearly in the spaces provided in the question paper. Jawupan hendaklah ditulis dengan jelas dalam ruang yang disediakan dalam kertas soalcrn. 5. Show your working. It may help you to get marks. Tzinjukkcrn langkah-langkah penting dalam kerja mengira andu. Ini boleh membantu undu unruk mendapatkan markah. 6. If you wish to change your answer, cross out the work that you have done. Then write down the new answer. Sekircrnya anda hendak menukar jawapan, batalkan kerja mengira ylrng teluh dibuat. Kemudi~ln tulis jawupan yang baru. 7. The diagrams in the questions provided are not drawn to scale unless stated. Rojah yang rnengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan. 8. Thc marks allocated for each question are shown in brackets. Alurkah yang diperuntukkan hagi set@ soalan ditunjukkan dalarn kurungan. 9. A list of formulae is provided on pages 2 to 3. Sutu senarai rlrmus disediakan di halaman 2 hingga 3. 10. You may use a non - programmable scientific calculator..4nj~r dihenarkan rnenggunakan kalkulator saintlfik yang tidak holeh diprogram. 1 1. Hand in this question paper to the invigilator at the end of the examination. k'err~lsoulun ini hendaklah diserahkan di akhir peperiksaan. 347211 2008 IIuk Cipra JPNJ SlJLIT
347211 Additional Mathematics Kertas 1 Sept. 2008 2 Jam JABATAN PELAJARAN NEGERI JOHOR KEMENTERIAN PELAJARAN MALAYSIA PEPEPUKSAAN PERCUBAAN SPM 2008 ADDITIONAL MATHEMATICS I I Kertas 1 SKEMA PEMARKAHAN Skema pemarkahan ini mengandungi 7 halaman bercetak 347211 Hak Cipta JPNJ 2008
MARKING SCHEME PEPERllKSAAN PERCUBAAN SPM 2008 MATEMATIK TAMBAHAN, KERTAS 1 Num Solution and mark scheme Sub Full marks marks 7 I (4 { 2,4,6,8, 10 I (b) many to many (b) x = 0 -- 5-2<~<3 (x-3)(x+2) +=++ <O B2 : factorize and try to solve 3 B2 3 6 (a) k = 3 (b) x = 3 (c) ( 3, - 4
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