(b) Using the function notation, write a relation between set A and set B.

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1 Paper Percubaan Addmath Kelantan 009 Answer all questions. Jawab semua soalan. For Examiner s Use Diagram shows the relation between set A and set B. Rajah menunjukkan hubungan antara set A dan set B. Set B ( h, 9) (, 9) (, 4) (, 4) (, ) O (, ) Set A Diagram Rajah (a) State Nyatakan (i) the value of h, nilai h, (ii) the range of the relation. julat hubungan itu. (b) Using the function notation, write a relation between set A and set B. Dengan menggunakan tatatanda fungsi, tulis satu hubungan antara set A dan set B. [ marks] [ markah] Answer/Jawapan : (a) (i) h =... (ii)... 47/ [Lihat sebelah SULIT

2 Paper Percubaan Addmath Kelantan 009 Given the functions f : x x+m and find the value of m and of n. 4 (b)..... f : x nx+, where m and n are constants, [ marks] For Examiner s Use Diberi f : x x+m dan f : x nx+, dengan keadaan m dan n ialah pemalar, 4 cari nilai m dan nilai n. [ markah] Answer/Jawapan : m = n = The following information refers to the functions f and g. Maklumat berikut adalah berkaitan dengan fungsi f dan fungsi g. f : x x k, where k is a constant, dengan keadaan k ialah pemalar, x + 4 g : x (a) Given that f(4) = 0, find the value of k. Diberi f(4) = 0, cari nilai k. (b) Find gf(x). Cari gf(x). [4 marks] [4 markah] 47/ [Lihat sebelah SULIT

3 Paper Percubaan Addmath Kelantan 009 Answer/Jawapan : (a) k =... (b). For Examiner s Use 4 Form the quadratic equation which has the roots and. Give the answer in the 4 form ax + bx + c = 0 where a, b and c are constants. [ marks] Bentukkan persamaan kuadratik dimana punca ialah dan. Beri jawapan dalam bentuk 4 ax + bx + c = 0, dengan keadaan a, b dan c ialah pemalar. [ markah] Answer/Jawapan : 47/ [Lihat sebelah SULIT

4 Paper Percubaan Addmath Kelantan 009 For Examiner s Use 5 Diagram 5 shows the graph of a quadratic functions f ( x) = ( x + h) + k, where h and k are constants. Rajah 5 menunjukkan graf kuadratik f ( x) = ( x + h) + k dengan keadaan h dan k ialah pemalar. y 6 y = f(x) x O 5 State Nyatakan (a) the value of h, nilai h, Diagram 5 Rajah 5 (b) the value of k, nilai k, (c) the equation of the axis of symmetry. persamaan garis simetri. [ marks] [ markah] 47/ [Lihat sebelah SULIT

5 Paper Percubaan Addmath Kelantan 009 Answer/Jawapan : (a) h =.. (b) k =.. (c) 6 Find the range of values of x for x (x - 5) 6. [ marks] For Examiner s Use Cari julat nilai x bagi x (x - 5) 6. [ markah] Answer/Jawapan :. 7 Solve the equation : Selesaikan persamaan : 7 x+ = [ marks] 9 x [ markah] Answer/Jawapan :. 8 Solve the equation :. Selesaikan persamaan : 47/ [Lihat sebelah SULIT

6 Paper Percubaan Addmath Kelantan 009 log ( x + ) + = log x. [ marks] [ markah] Answer/Jawapan : 9 The fourth term of an arithmetic progression is 7. The sum of the first six terms is 5. Find the first term and the common difference of the progression. [4 marks] For Examiner s Use Sebutan ke-empat suatu janjang aritmetik ialah 7. Jumlah bagi enam sebutan pertamanya ialah 5. Cari sebutan pertama dan beza sepunya janjang tersebut. [4 markah] Answer/Jawapan : 0 The n th term of a geometric progression is given by of the progression. T n = 4 5 n. Find the sum to infinity [ marks] Sebutan ke-n satu janjang geometri diberi sebagai janjang tersebut. T n = 4 5 n. Cari hasil tambah ketakterhinggaan [ markah] 47/ [Lihat sebelah SULIT

7 Paper Percubaan Addmath Kelantan 009 Answer/Jawapan : The three consecutive terms of a sequence are m 9, m and 4m + 5. Find the value of m such that the sequence is an arithmetic progression. [ marks] Tiga sebutan berturut-turut suatu siri adalah m 9, m dan 4m + 5. Cari nilai m jika siri itu satu janjang aritmetik. [ markah] For Examiner s Use Answer/Jawapan : Diagram shows a straight line graph of xy against x². Rajah menunjukkan graf garis lurus xy melawan x². xy (, 5) (, ) O Diagram Rajah x² 47/ [Lihat sebelah SULIT

8 Paper Percubaan Addmath Kelantan 009 y b Given that a = x, where a and b are constants, find the value of a and of b. [ marks] x Diberi y b a =, dengan keadaan a dan b ialah pemalar, cari nilai a dan nilai b. [ markah] x x Answer/Jawapan : (a) a =.... (b) b = The straight line hy + x = k passes through point (0, ) and is parallel to the straight line joining the points (, ) and (, 5). For Examiner s Use Garis lurus hy + x = k melalui titik (0, ) dan adalah selari dengan garis lurus yang menyambung titik-titik (, ) dan (, 5). Find Cari (a) the value of h, nilai h, (b) the value of k. nilai k. [ marks] [ markah] Answer/Jawapan : (a) h =. (b) k =. 4 Given that the point P ( r, ) divides the line segment A ( 4, t) and B (r, 8) in the ratio AP : PB = : 4, find the value of r and of t. [ marks] Diberi titik P ( r, ) membahagi garis yang menghubung A ( 4, t) dan B (r, 8) dengan nisbah AP : PB = : 4, cari nilai r dan nilai t. 47/ [Lihat sebelah SULIT

9 Paper Percubaan Addmath Kelantan 009 [ markah] Answer/Jawapan : (a) r =.. 5 The following information refers to vector p and vector q. (b) t =.. For Examiner s Use Maklumat berikut merujuk kepada vektor p dan vector q. p = i+ mj, where m is a constants. dengan keadaan m ialah pemalar. q = i 4j Given that p and q are parallel, find the value of m. Diberi bahawa p dan q ialah selari, cari nilai m. [ marks] [ markah] 47/ [Lihat sebelah SULIT

10 Paper Percubaan Addmath Kelantan 009 Answer/Jawapan : m = 6 Diagram 6 shows a triangle ABC. For Examiner s Use Rajah 6 menunjukkan sebuah segitiga ABC. B A S Diagram 6 Rajah 6 C uuur uuur The point S lies on straight line AC. It is given that AC = p, AB = q and AS : SC = :. uuur uuur Titik S berada di atas garis lurus AC. Diberi AC = p, AB = q dan AS : SC = :. Express in terms of p and /or q 47/ [Lihat sebelah SULIT

11 Paper Percubaan Addmath Kelantan 009 Ungkapkan dalam sebutan p dan / atau q (a) (b) uuur AS, uuur BS. [ marks] [ markah] Answer/Jawapan : (a) (b) 7 Solve the equation sin x + cos x = for 0 o x 60 o. [4 marks] For Examiner s Use Selesaikan persamaan sin x + kos x = bagi 0 o x 60 o. [4 markah] Answer/Jawapan :.. 8 Diagram 8 show a semicircle OABC, centre O. Rajah 8 menunjukkan satu semibulatan OABC, berpusat di O. B A θ O Diagram8 C 47/ [Lihat sebelah SULIT

12 Paper Percubaan Addmath Kelantan 009 Given that AC = cm, Diberi AC = cm, (Use / Guna π =.4) (a) θ, in radian, θ, dalam radian, Rajah 8 BOC = 5, find BOC = 5, cari (b) the area, in cm, of sector OAB. luas, dalam cm, sektor OAB. 4 9 Given that gx ( ) = (x ) 4 Diberi gx ( ) = (x ) [ marks] [ markah] Answer/Jawapan : (a) (b).., find g (). [4 marks], cari g (). [4 markah] For Examiner s Use Answer/Jawapan : 47/ [Lihat sebelah SULIT

13 Paper Percubaan Addmath Kelantan Two variables r and s are related by the equation r = s+. Given that r increase at a s constant rate of 5 units per second, find the rate of change of s when s =. [ marks] Dua pembolehubah r dan s dihubungkan oleh persamaan r = s+. Diberi r bertambah s pada kadar malar sebanyak 5 unit persaat, cari kadar perubahan s apabila s =. [ markah] Answer/Jawapan :.. For Examiner s Use Given that gxdx= ( ) 0, find the value of m if [ gx ( ) mxdx ] = 6m. [ marks] Diberi gxdx= ( ) 0, cari nilai m jika [ gx ( ) mxdx ] = 6m [ markah] Answer/Jawapan : m = The mean of 5 numbers is h. The sum of the square of the numbers is 605 and the variance is k. Express h in terms of k. [ marks] Min bagi 5 nombor ialah h. Hasil tambah kuasa dua nombor-nombor itu ialah 605 dan 47/ [Lihat sebelah SULIT

14 Paper Percubaan Addmath Kelantan 009 variansnya ialah k. Ungkapkan h dalam sebutan k. [ markah] Answer/Jawapan : A team of 6 students is to be chosen from 8 boys and 4 girls. Find the number of different ways the team can be formed if the team consists of For Examiner s Use Sekumpulan 6 orang pelajar akan dipilih daripada 8 orang pelajar lelaki dan 4 orang pelajar perempuan. Cari bilangan cara pasukan itu dapat dibentuk jika pasukan itu terdiri daripada (a) only boys, hanya pelajar lelaki,, (b) the number of boys and girls are equal. bilangan pelajar lelaki dan perempuan adalah sama. [4 marks] [4 markah] 47/ [Lihat sebelah SULIT

15 Paper Percubaan Addmath Kelantan 009 Answer/Jawapan : (a). (b) 4 Diagram 4 shows the graph of bonimial distribution for discrete variable X. For Examiner s Use Rajah 4 menunjukkan graf taburan binomial bagi pembolehubah diskrit X. P(X = x) 0.4 m x 0 Diagram 4 47/ [Lihat sebelah SULIT

16 Paper Percubaan Addmath Kelantan 009 Rajah 4 Find Cari (a) the value of m, nilai m, (b) P(x ). [4 marks] [4 markah] Answer/Jawapan : (a) m = (b) 5 X is a continuous random variable of a normal distribution with a mean of 40 and a For Examiner s Use standard deviation of. X ialah pembolehubah rawak selanjar bagi suatu taburan normal dengan min 40 dan sisihan piawai. Find Cari (a) the z-score when X = 405, skor-z apabila X = 405, (b) the value of k when P(z > k) = nilai k apabila P(z > k) = [4 marks] [4 markah] 47/ [Lihat sebelah SULIT

17 Paper Percubaan Addmath Kelantan 009 Answer/Jawapan : (a)... (b)... END OF QUESTION PAPER KERTAS SOALAN TAMAT 47/ [Lihat sebelah SULIT

18 Percubaan Addmath Kelantan 009 Paper Section A Bahagian A [40 marks] [40 markah] Answer all questions. Jawab semua soalan. Solve the simultaneous equations n m + = 0 and m 9 = n. Give your answers correct to three decimal places. Selesaikan persamaan serentak n m + = 0 dan m 9 = n. Beri jawapan anda betul kepada tiga tempat perpuluhan. [5 marks] [5 markah] 8 A curve with gradient function x has a turning point at (k, 6). x 8 Suatu lengkung dengan fungsi kecerunan x mempunyai titik pusingan di (k, 6). x (a) Find the value of k. Cari nilai k. [ marks] [ markah] (b) Determine whether the turning point is a maximum or minimum point. [ marks] Tentukan sama ada titik pusingan ini adalah titik maksimum atau titik minimum. [ markah] (c) Find the equation of the curve. Cari persamaan lengkung itu. [ marks] [ markah]

19 Percubaan Addmath Kelantan 009 Paper Diagram shows a series of circles. The total circumference of first five circles are 60π cm. The lengths of diameter of circles is cm more than the previous circle. Rajah menunjukkan satu siri bulatan. Jumlah panjang perimeter bagi lima bulatan yang pertama ialah 60π cm. Panjang diameter bulatan-bulatan itu adalah cm lebih berbanding bulatan sebelumnya. Diagram Rajah (a) Find the diameter of the smallest circle. [ marks] Cari diameter bagi bulatan yang terkecil. [ markah] (b) Calculate the number of circular rings that can be made by using a piece of wire with length of 60π cm. Hitung bilangan bulatan yang boleh dibentuk dengan menggunakan seutas dawai yang panjangnya 60 π cm. [4 marks] [4 markah] 4 (a) Sketch the graph of y = sin x + for 0 x л. Lakarkan graf bagi y = sin x + untuk 0 x л. (b) Hence, by drawing a suitable straight line on the same axis, find the number of solutions satisfying the equation л sin x = x for 0 x л. Seterusnya, dengan melakar satu garis lurus yang sesuai pada paksi yang sama, Cari bilangan penyelesaian bagi persamaan л sin x = x untuk 0 x л. [7 marks] [7 markah]

20 Percubaan Addmath Kelantan 009 Paper 5 Diagram 5 is a histogram which represent the distribution of the times taken by a group of 45 students to travel to school. Rajah 5 ialah histogram yang mewakili taburan masa yang diambil oleh sekumpulan 45 orang pelajar untuk pergi ke sekolah. Number of Students Bilangan Pelajar k Calculate Hitung (a) the value of k, nilai k, (b) the range of the times taken, julat bagi masa diambil, Diagram 5 Rajah 5 [ mark] [ markah] [ mark] [ markah] (c) the standard deviation of the distribution. [4 marks] sisihan piawai bagi taburan itu. Time taken (minutes) Masa diambil (minit) [4 markah]

21 Percubaan Addmath Kelantan 009 Paper 6 Diagram 6 shows triangle OPQ. The point S lies on OQ and PR. The straight line PR intersects the straight line OQ at the point S. Rajah 6 menunjukkan segitiga OPQ. Titik S terletak pada OQ dan PR.Garis lurus PR bersilang dengan garis lurus OQ di titik S. R 6 x Q S 5 y (a) Express in terms of x and y : O Diagram 6 Rajah 6 Ungkapkan dalam sebutan x dan y : x P (i) (ii) RP OQ [ marks] [ markah] (b) Using OS = h OQ and PS = k PR, where h and k are constants, find the value of h and of k. Menggunakan OS = h OQ dan PS = k PR, dengan keadaan h dan k ialah pemalar, cari nilai h dan nilai k. [5 marks] [5 markah]

22 Percubaan Addmath Kelantan 009 Paper Section B Bahagian B [40 marks] [40 markah] Answer any four questions from this section. Jawab mana-mana empat soalan daripada bahagian ini. 7 Diagram 7 shows part of the curve y = 4 x. The line y = x cuts the curve at Q(0,-) and P(x, y). Rajah 7 menunjukkan sebahagian dari lengkung y = 4 x. Garislurus y = x memotong lengkung pada titik Q(0, -) dan P(x, y). y y² = 4 x P y = x O 4 x Q Diagram 7 Rajah 7 Find Cari (a) the coordinates of P, koordinat P, [ marks] [ markah] (b) the area of the shaded region, [4 marks] luas kawasan berlorek, [4 markah] (c) the volume generated, in term of when the shaded region bounded by the curve y² = 4 x and the line y = x is revolved 60 o about the y axis. [4 marks] isipadu yang dijanakan dalam sebutan apabila rantau berlorek yang dibatasi oleh lengkung y² = 4 x dan garis lurus y = x diputarkan melalui 60 o pada paksi y. [4 markah]

23 Percubaan Addmath Kelantan 009 Paper 8 Use graph paper to answer this question. Gunakan kertas graf untuk menjawab soalan ini. Table 8 shows the values of two variables, x and y, obtained from an experiment. Variables x and y are related by the equation y = p x+ q, where p and q are constants. Jadual 8 menunjukkan nilai-nilai bagi dua pembolehubah, x dan y, yang diperoleh daripada satu eksperimen. Pembolehubah x dan y dihubungkan oleh persamaan y = p x+ q, dengan keadaan p dan q ialah pemalar. x y Table 8 Jadual 8 (a) Plot y against x, using a scale of cm to unit on the x-axis and cm to 0 units on the y-axis. Hence, draw the line of best fit. [5 marks] Plot y melawan x, dengan menggunakan skala cm kepada unit pada paksi x dan cm kepada 0 unit pada paksi-y. Seterusnya, lukis garis lurus penyuaian terbaik. [5 markah] (b) Use your graph in 8(a) to find the value of Gunakan graf di 8(a) untuk mencari nilai (i) p, (ii) q, (iii) x when y = 7.0. x apabila y = 7.0. [5 marks] [5 markah]

24 Percubaan Addmath Kelantan 009 Paper 9 Diagram 9 shows a sector OMN of a circle, centre O and radius 0 cm. The point P lies on OM and PN is perpendicular to OM. It is given that OP = PM. Rajah 9 menunjukkan sektor OMN bagi suatu bulatan pusat O dengan jejari 0 cm. Titik P berada di atas OM dan garis PN adalah berserenjang kepada garis OM. Diberi bahawa OP = PM. (Use / Guna π =.4) Diagram 9 Rajah 9 Calculate Hitung (a) the length, in cm, of OP, panjang, dalam cm, OP, (b) the angle, θ, in radian, sudut, θ, dalam radian, (c) the perimeter, in cm, of the shaded region, perimeter, dalam cm, kawasan berlorek, (d) the area, in cm, of shaded region. luas, dalam cm, kawasan berlorek. [ mark] [ markah] [ marks] [ markah] [4 marks] [4 markah] [ marks] [ markah]

25 Percubaan Addmath Kelantan 009 Paper 0 Solution by scale drawing is not accepted. Penyelesaian secara lukisan berskala tidak diterima. Diagram 0 shows a triangle PQR. Point S lies on PQ. Rajah 0 menunjukkan segitiga PQR. Titik S terletak pada garis PQ. f(x) P (5, k) S(, ) Q O R(4,0) x Diagram 0 Rajah 0 (a) A point M moves such that its distance from point S is always 5 units. Find the equation of the locus of M. Suatu titik M bergerak dengan keadaan jaraknya dari titik S adalah sentiasa 5 unit. Cari persamaan lokus M. (b) It is given that point P and Q lie on the locus of M. Diberi bahawa titik P dan titik Q terletak pada lokus M. Calculate Hitung (i) the value of k, nilai k, (ii) the coordinates of Q. koordinat Q. (c) Hence, find the area, in unit, of triangle PQR. Seterusnya, cari luas, dalam unit, bagi segitiga PQR. [ marks] [ markah] [5 marks] [5 markah] [ marks] [ markah]

26 Percubaan Addmath Kelantan 009 Paper (a) A student is considered pass the test whenever six of ten questions are being answered correctly. If 8 students are chosen at random, calculate the probability that Seorang pelajar dianggap berjaya dalam ujian jika dapat menjawab enam dari sepuluh soalan yang diberi. Jika 8 orang pelajar dipilih secara rawak, hitung kebarangkalian (i) exactly students pass, tepat orang pelajar berjaya, (ii) more than student pass the test. lebih daripada seorang berjaya dalam ujian tersebut. [5 marks] [5 markah] (b) The heights of students in School A are normally distributed with a mean of 50 cm and a standard deviation of 0 cm. Ketinggian pelajar di Sekolah A adalah bertaburan secara normal dengan minnya 50 cm dan sisihan piawai 0 cm. (i) Height exceeds 70 cm are classified as tall. It is found that 57 students are tall. Find the total enrolment of the school. Ketinggian melebihi 70 cm dikatakan tinggi di sekolah itu. Didapati 57 pelajar adalah tinggi. Cari enrolmen sekolah itu. (ii) If 0% of the students are categorized as short. What is the height which is still short? Jika 0% daripada pelajar itu dikategorikan rendah. Berapakah ukuran ketinggian yang masih dikatakan rendah? [5 marks] [5 markah]

27 Percubaan Addmath Kelantan 009 Paper Section C Bahagian C [0 marks] [0 markah] Answer any two questions from this section. Jawab mana-mana dua soalan daripada bahagian ini. A particle moves along a straight line and passes through a fixed point O. Its velocity, v m s -, is given by v = t 7t +, where t is the time in seconds after leaving points O. Satu zarah bergerak di sepanjang suatu garis lurus dan melalui satu titik tetap O. Halajunya, v m s -, diberi oleh v = t 7t +, dengan t ialah masa dalam saat selepas melalui titik O. Find Cari (a) (i) the time interval during which the particle moves towards the left, (ii) (iii) julat masa apabila zarah itu bergerak arah ke kiri, the acceleration of the particle when t = seconds, pecutan zarah itu apabila t = saat, the time when the velocity is constant. masa apabila halajunya malar. (b) Sketch the velocity-time graph of the motion of the particle for O t. Lakarkan graf halaju-masa bagi pergerakan zarah itu untuk O t. [5 marks] [5 markah] [ marks] [ markah] (c) Calculate the total distance, in m, traveled during the first seconds after leaving point O. Hitung jumlah jarak, dalam m, yang dilalui dalam saat yang pertama selepas melalui titik O. [ marks] [ markah]

28 Percubaan Addmath Kelantan 009 Paper Table shows the prices, the price indices and percentage of usage of four items A, B, C and D, which are the main ingredients in the manufacturing of a types of biscuits. Jadual menunjukkan harga, indeks harga dan peratus penggunaan empat barangan A, B, C dan D, yang merupakan bahan utama dalam penghasilan sejenis biskut. Price per unit (RM) Harga per unit (RM) Item Item Price index for the year 007 based on the year 005 Indeks harga pada tahun 007 berasas tahun 005 Percentage of usage (%) Peratus penggunaan (%) A p m B 55 q 0 8m C D r 9m Table Jadual (a) Find the value of p, of q and of r. Cari nilai p, nilai q dan nilai r. (b) State the value of m. Hence, calculate the composite index for the cost of manufacturing the biscuits in the year 007 based on the year 005. Nyatakan nilai m. Seterusnya, hitung nombor indeks gubahan bagi kos penghasilan biskut itu pada tahun 007 berasaskan tahun 005. [ marks] [ markah] [ marks] [ markah] (c) Calculate the price of a box of biscuits in the year 005 if the corresponding price in the year 007 is RM 5.70 [ marks] Hitung harga sekotak biskut yang sepadan pada tahun 005 jika harganya pada tahun 007 ialah RM 5.70 [ markah] (d) The coast of manufacturing the biscuits is expected to increase by 0% from the year 007 to the year 009. Find the expected composite index for the year 009 based on the year 005. [ marks] Kos penghasilan biskut ini dijangka meningkat sebanyak 0% dari tahun 007 ke tahun 009. Cari nombor indeks gubahan yang dijangkakan pada tahun 009 berasaskan tahun 005. [ markah]

29 Percubaan Addmath Kelantan 009 Paper 4 Diagram 4 shows two triangle ABC and ACD. ABC is obtuse and sin ABC = 5. Given that AB = 7 cm, BC = 5 cm and CD = 9 cm. Rajah 4 menunjukkan dua segitiga ABC dan ACD. ABC adalah cakah dan sin ABC = Diberi bahawa AB = 7 cm, BC = 5 cm and CD = 9 cm. B. 5 A 40 o C D Diagram 4 Rajah 4 Calculate Hitung (a) the length, in cm, of AC, [4 marks] panjang, dalam cm, bagi AC, [4 markah] (b) ADC, [ marks] [ markah] (c) the area, in cm, of the ABCD. [4 marks] luas, dalam cm, ABCD. [4 markah] 5 Use graph paper to answer this question.

30 Percubaan Addmath Kelantan 009 Paper Gunakan kertas graf untuk menjawab soalan ini. The English Language society sells x packets of snack A and y packets of snack B at a school funfair. Persatuan Bahasa Inggeris menjual x bungkus snek A dan y bungkus snek B pada hari pasaria sekolah. The number of packets of snacks is based on the following constraints : Bilangan bungkus snek berdasarkan pada kekangan berikut : I : The number of packets of snack A is at least 50. Bilangan bungkus snek A sekurang-kurangnya 50. II : The number of packets of snack B is at least 50. Bilangan bungkus snek B sekurang-kurangnya 50. III : The total number of snacks A and B is at least 500 but not more than 800. Jumlah bilangan snek A dan B sekurang-kurangnya 500 tetapi tidak lebih dari 800. (a) Write three inequalities, other than x 0 and y 0, which satisfy all the above constraints [ marks] Tulis tiga ketaksamaan selain dari x 0 and y 0, yang memenuhi semua kekangan di atas. (b) By using a scale of 4 cm to 00 packets of a snacks on both axes, construct and shade the region R which satisfies all the above constraints. Dengan menggunakan skala 4 cm kepada 00 bungkus snek pada kedua-dua paksi, bina dan lorek rantau R yang memenuhi semua kekangan di atas. [ markah] [ marks] [ markah] (c) The profit of a packet of snack A is RM0.5 and the profit of snack B is RM0.40 by using the graph from (b), find Keuntungan bagi sebungkus snek A ialah RM0.5 dan keuntungan bagi snek B ialah RM0.40, dengan menggunakan graf dari (b), cari (i) the maximum profit from the sale of snacks A and B, keuntungan maksimum jualan snek A dan B, (ii) the minimum profit from the sale of snacks A keuntungan minimum jualan snek A dan B and B. [4 marks] [4 markah] END OF QUESTION PAPER KERTAS SOALAN TAMAT

31 Percubaan Addmath Kelantan 009 Paper

32 Marking Scheme Paper Trial SPM 009 Additional Mathematics Number (a) (i) Solution and mark Scheme Sub marks Full marks (b) (ii) {0,, 4, 9} f ( x) = x Note : accept any letters m = 4 and n = B : m = 4 or n = B : f ( x) = x m (a) B : (4) k = 0 (b) B : x (x ) x + x = 0 or x + x = B : x ( + ) x+ ( )(4) = 0 or (x + )(4x )=0 4 or ( x+ )( x ) = (a)

33 (b) 6 (c) x = 6 4 x 9 B : ( x + 4)( x 9) 0 or -4 9 B : x 5x B : B : = ( x+ ) ( x ) = ( ) 8 4 or. or B : log8(x ) = logx or equivalent 9 : log 8 or x x log or log x x B a = 6 and d = B : a = 6 or d = B : (7 d) + 5d = 7 or equivalent 4 4 B: a + d = 7 or 6 5 = [ a+ (6 ) d]

34 0 5 or B: 4 5 B: a = or 4 r = 5 4 B : m ( m 9) = 4m+ 5 m B : a = 4 and B : xy = a x +b (a) 4 B : (b) 5 h = 4 r = and t = or 0.5 B : r = or t = or 0.5

35 B : 4(4) + r() = r + 4 or t (4) + 8() = m = 6 B : k = B : k = or 4k = m 6 (a) p % (b) p q uuur uuur uuur B : BS = AS AB 7 o o o 0, 90, 50 B : ( sin x )(sin x ) = 0 B : sin x + ( sin x) = 8 (a) (b) B : (6) (.5) 9 B : 4( 4)[() ] -5 () B : 4( 4)(x ) () -4-5 B : 4( )(x ) () 0 B : ds 5 = dt 4 4 4

36 dr B : 5 dt = or dr = + ( ) s ds B : B : x (0) m = 6m g( x) dx mxdx = 6m k h = 4 B : k 605 = ( ) h 5 B : x = h or Σ x = 605 or (a) 8 B : 8 C 6 σ = k (b) 4 B : C C (a) B : m + m = or equivalent B : m + m (b) (a).5 B : (b) P(z > k) = 0.9 B :

37

38 ADDITIONAL MATHEMATICS PEPERIKSAAN PERCUBAAN SPM 009(KELANTAN) MARKING SCHEME PAPER No Solution Marks Total n = n = m = n + P m 9 = ( m m 9 = m (n + ) 9 = n m m 7 = 0 4n + 6n 5 = 0 5 ( ) ( ) 4()( 7) m = () ± n = (4) 6 (6) 4(4)( 5) m =.9,.9 n = 0.596,.096 n = 0.597,.097 m =.9,.9 (both) (both) (a), k = (b) (c) When x =, d y 6 ( dx = + = >0) so, the turning point (,6) is a minimum point 8 y = x dx x x 8 y = + + c x 7 Therefore,

39 (a) Let x is diameter of smallest circle first term a = x and common difference d = [( x) + 4( )] = 60 P x = 8 (b) a = 8 d = 4.5 n [ (8 π ) + ( n )π] = 60π n + 7n 60 = 0 (n + 0)(n ) = 0 n = P 7 4(a) y = sin x + x (b) sin x = π x sin x = π y = sin x + x = + π The number of solution is 4 0 y = sin x y = sin x y = sin x + л л л л P P P P (Graph) 7

40 5(a) (b) 4 P P (c) Times x f fx fx taken Σfx = 765 Σfx =545 σ = =.464 6(a)(i) uuur uuur uuur RP= RQ+ QP = 6x + 5 y (ii) uuur uuur uuur OQ = OP + PQ = x 5y (b) OS = h OQ = h ( x 5 y ) = hx 5hy P 7 PS = k PR = k ( 6x 5 y ) = 6kx 5ky P OS = OP + PS = x 6kx 5ky = ( 6k)x 5ky hx 5hy = ( 6k)x 5ky h = 6k or 5h = 5k

41 7(a) when h = k h = 6h h = ¼ and k = ¼ y² = 4 (y + ) (y + )(y ) = 0 (b) y =, y = when y =, x = + ; P(, ) Area = = = = ] = unit 0 (c) Volume = = = = = 9(a) OP = 6 cm P (b) (c) cos = 0.6 = PN = 8 cm MN = 0 x = 9.74 Perimeter = =.74 cm P 0 (d) The area = (0.974) - x 6 x 8 =.7 cm

42 0(a) (b)(i) = 0 = 7 k > 0, k = 7 (ii) Midpoint of PQ = (, ) 0 or = Therefore, Q (-,-) (c) Area PQR = 7 unit (a)(i) (ii) (b)(i) p = 0.6 q = 0.4 p(x = ) = 8 6 C (0.6) (0.4) = p(x > ) = p(x = 0) p(x= ) = 8 C (0.6) (0.4) 8 C (0.6) (0.4) 7 = P(X > 70) = P(Z > ) 0 = P(Z > ) = 0.08 P

43 = 500 (ii) P(Z < P(X < k) = 0. k 50 ) = 0. 0 k 50 = k = cm (a)(i) (ii) (iii) (b) t 7t + < O (t )(t ) < O < t < dv a = dt = 4t 7 = 4() 7 = m s - 4t 7 = O t = 7 4 when t = O, v = when v = O, t 7t + = O (t )(t ) = O when t = 7 4, t = or v = ( 7 4 ) -7( 7 4 ) + = 8

44 v (m s - ) [any points t(s) include ( 7 4, 8 )] 8 (c) s = ( 7 + ) t t dt 7 = t t + t+c When t = O, s = O, c = O 7 = t t + t+c When t =, s = 7 ( ) ( ) + ( ) = 7 4 When t =, s = 7 () () + () = 4 t = t = t = O 4 O 7 4 Total distance traveled = = 5 m

45 (a) 45 q 5 = 00 or 0 = 00 or p r = p = 6 q = 66 r = 94 N,, 0 (b) 7m + 8m m = 00 m = 5() + 0(4) + 05(8) + 94(7) I = 00 P = 09.8 (c) = 09.8 P005 P = RM (d) P = P = OR I = (a) 0.84 I = =.79 =.79 sin ABC = /5 = 6 o 5 // 6.87 o ABC = 80 o - 6 o 5 = 4 o 8 AC = x 7 x 5 cos 4 o 8 =.40 cm P P (b) SinADC.40 = Sin40 9 sin ADC = 0.84 ADC = 54 o 0 // 54.5 o 0 (c) ABC = ½ x 7 x 5 x Sin 4 o 8 = cm ACD = 80 o 40 o 54 o 0 = 85 o 0 A ADC = ½ x 9 x.40 x Sin 85 o 0 = 5.4 cm Area of ABCD = = 6.64 cm P

46 No. 8 y x y (a) ~ Correct axes, uniform scale and one point plotted correctly ~ All 6 points plotted correctly ~ Line of best fit Correct at least decimal places y = p x + p q P 90 (b) (i) gradient, p 64 = =.5 p = 4.67 (ii) y-intercept, p q = 0 X 80 q = (iii) y = 7, y = 49 x =.8 X 60 X 50 X 40 X 0 X x

47 No.5 a) i)x 50 ii)y 50 iii) 500 x + y 800 c) max, Profit =0.5(50) + 0.4(650) = RM8.50 min, Profit =0.5(50) + 0.4(50) = RM7.50 R

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