INSTRUCTION: This section consists of FOUR (4) structured questions. Answer THREE (3) questions only.
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1 SECTION A: 75 MARKS BAHAGIAN A: 75 MARKAH INSTRUCTION: This section consists o FOUR (4) structured questions. Answer THREE (3) questions only. ARAHAN : Bahagian ini mengandungi EMPAT (4) soalan berstruktur. Jawab TIGA (3) soalan sahaja. QUESTION 1 SOALAN 1 a. List down two graphical methods in presenting data. C1 Senaraikan dua kedah graik untuk mempersembahkan data. [ marks] [ markah] CLO C b. The table shows the number o readers o our types o newspapers. 180 readers were asked about the types o newspapers read by them. Construct a pie chart to show based on the given data. Data yang diberikan memberikan bilangan pembaca empat jenis surat khabar harian di Malaysia. Seramai 180 pembaca ditanyakan jenis akhbar yang dilangganinya setiap hari. Bina carta pai bagi data tersebut. Newspaper Utusan Malaysia New Straits Times Berita Harian Malay Mail Number o Readers [5 marks] [5 markah] SULIT
2 CLO c. Draw the relative less than ogive below by using 1 30 as a irst class. Then determine the 7 th decile rom the given data. Plotkan gra ogi relati kurang daripada bagi data di bawah dengan menggunakan 1 30 sebagai sela kelas pertama. Kemudian tentukan nilai Desil ke [10 marks] [10 markah] CLO d. In a sample o 50 people, 1 had type O blood, had type A blood, 5 had type B blood and had type AB blood. Find the ollowing probabilities : Dalam satu sampel yang terdiri daripada 50 orang, 1 daripadanya mempunyai darah jenis O, orang mempunya darah jenis A, 5 orang mempunyai darah jenis B dan orang mempunyai darah jenis AB. Cari kebarangkalian yang berikut: i. A person who has type O blood. Seorang yang mempunyai darah jenis O. ii. A person who has type A or type B blood. Seorang yang mempunyai darah jenis A atau B. iii. A person who has netiher type A nor type O blood. Seorang yang bukan darah jenis A atau B. iv. A person who does not have type AB blood. Seorang yang tidak mempunyai darah jenis AB. [8 marks] [8 markah] 3 SULIT
3 QUESTION SOALAN C1 a. Identiy the mode rom the given data: Cari mod dari data berikut : 668, 89, 714, 97, 1000, 668, 989, 777, 989 [ marks] [ markah] CLO C b. The thickness o 00 samples o steel plate are measured and the results (in milimetres) are as ollow : Ketebalan 00 sampel plat keluli diukur dan keputusan (dalam millimeter) adalah seperti berikut : Thickness (mm) Frequency From the data above, construct a histogram and ind the mode. Dari data di atas, bina histogram dan cari mod. [7 marks] [7 markah] 4 SULIT
4 CLO c. The height o the pivot blocks were measured : Ketinggian blok pangsi diukur seperti berikut : Height (mm) Frequency Calculate : Kirakan : i. The mean height. Purata ketinggian. ii. The standard deviation. Sisihan piawai. [9 marks] [9 markah] CLO d. A bo contains 100 copper plugs where 7 are oversized while 16 are undersized and the rest are acceptable. A plug is taken, tested but not replaced: a second plug is treated similarly. Determine the probability that: Sebuah kotak mengandungi 100 palam tembaga di mana 7 daripadanya terlalu besar,16 terlalu kecil dan yang selebihnya adalah boleh diterima. Satu palam tembaga diambil dan diuji tetapi tidak diletakkan kembali. Begitu juga dengan palam tembaga kedua. Tentukan kebarangkalian bahawa i. both plugs are acceptable. Kedua-dua palam yang diambil boleh diterima. ii. the irst is oversized and the second is undersized. yang pertama adalah terlalu besar dan yang kedua adalah terlalu kecil. [7 marks] [7 markah] 5 SULIT
5 QUESTION 3 SOALAN 3 CLO C1 a. Write the inequality or the ollowing statements: Tuliskan ketaksamaan bagi kenyataan-kenyataan berikut: i. The number o participants ( χ ) in a competition is more than 50. Bilangan peserta ( χ ) dalam suatu pertandingan lebih dari 50. [1 mark] [1 markah] ii. The area (A) o the shaded region is at least 150cm. Luas (A) kawasan berlorek sekurang-kurangnya 150cm. [1 mark] [1 markah] iii. The speed limit (s) o a motorcycle is not eceeding 100km/h. Had laju (s) motosikal tidak melebihi 100km/j. [1 mark] [1 markah] CLO C b. A painter plans to mi as many gallons as possible unit o color A that requires 4 units o yellow dye and 1 unit o green dye. He also wants to mi y unit o color B that requires 1 unit o yellow dye and 6 units o green dye. He has eactly 3 units o yellow dye and 54 units o green dye. Write THREE (3) inequalities that satisy the conditions above. Seorang tukang cat bercadang untuk membuat sebanyak mungkin unit campuran warna A yang memerlukan 4 unit pewarna kuning dan 1 unit pewarna hijau. Dia juga ingin membuat y unit campuran warna B yang memerlukan 1 unit pewarna kuning dan 4 unit pewarna hijau. Dia mempunyai 3 unit pewarna kuning dan 54 unit pewarna hijau. Tuliskan TIGA (3) ketaksamaan yang memenuhi syarat-syarat di atas. [5 marks] [5 markah] 6 SULIT
6 CLO c. X and Y represent Mechanical and Electrical engineering students respectively. The number o Mechanical engineering students eceeds the number o Electrical engineering by 00. The number o Mechanical engineering students must be at least 3 4 o the number o Electrical engineering students. The total number o both students rom the two departments does not eceed 500. Diberi dan y masing-masing mewakili pelajar kejuruteraan mekanikal dan pelajar kejuruteraan elektrik. Bilangan pelajar kejuruteraan mekaninal melebihi daripada bilangan pelajar kejuruteraan elektrik paling banyak 00. Bilangan pelajar kejuruteraan mekanikal mesti sekurang-kurangnya 3 4 daripada bilangan pelajar kejuruteraan elektrik.jumlah keseluruhan pelajar dari kedua-dua bidang adalah tidak lebih dari 500 orang. i. Write THREE inequalities that ulill the given conditions. Tuliskan tiga ketaksamaan yang memenuhi syarat-syarat yang diberikan. [3 marks] [3 markah] ii. Using scale o cm to 100 students or both -ais and y-ais, draw and shade the easible region which ulill the given condition. Menggunakan skala cm mewakili 100 pelajar pada kedua-dua paksi dan paksi y, lukiskan dan lorek rantau yang dibatasi yang memenuhi syarat-syarat yang diberikan. [7 marks] [7 markah] 7 SULIT
7 QUESTION 4 SOALAN 4 iii. Based on the graph, draw the isoline i the monthly ee o Mechanical and Electrical engineering student is RM50 and RM40 respectively, hence ind the maimum monthly collection o ees by the college. Berdasarkan gra, lukiskan isoline jika yuran bulanan bagi pelajar kejuruteraan mekanikal dan elektrik masing-masing adalah RM50 dan RM40, seterusnya dapatkan jumlah maksimum yuran bulanan yang terkumpul bagi kolej. [7 marks] [7 markah] A boutique wants to sell 00 shirts and 100 pairs o pants. They have decided to make two packages A dan B. Package A consist o one shirt and a pair o pants and B consists o 3 shirts and a pants. The proit o package A is RM30 while package B is RM50. They want to sell at least 0 o package A and at least 10 o package B. Satu butik hendak menjual 00 helai tshirt dan 100 pasang seluar. Mereka bercadang untuk menyediakan pakej A dan B. Pakej A mengandungi sepasang tshirt dan sepasang seluar dan pakej B mengandungi 3 pasang tshirt dan sepasang seluar. Keuntungan untuk pakej A ialah RM30 sementara keuntungan untuk pakej B ialah RM50. Mereka hendak menjual sekurang-kurangnya 0 pakej A dan sekurang-kurangnya 10 pakej B CLO C1 CLO C a. State the important inormation or the statement above in the simplest table Nyatakan maklumat penting untuk kenyataan di atas dalam bentuk jadual yang mudah diahami [3 Marks] [3 Markah] b. State the constraints or the problem statement above Nyatakan kekangan-kekangan untuk pernyataan masalah di atas [4 Marks] [4 Markah] 8 SULIT
8 CLO c. Based on the statement above, calculate how many packages o each do they have to sell to maimize the proit by using Simple Method. Berdasarkan kenyataan di atas, gunakan kaedah simple untuk menetukan berapakah bilangan untuk setiap pakej yang perlu dijual bagi memaksimumkan keuntungan. [18 Marks] [18 Markah] SECTION B : 5 MARKS BAHAGIAN B : 5 MARKAH INSTRUCTION: This section consists o TWO () structured questions. Answer ONE (1) question only. ARAHAN : Bahagian ini mengandungi DUA() soalan struktur. Jawab SATU (1) soalan sahaja. QUESTION 5 SOALAN 5 C1 a. Write the equation o 4e = 1 in term o as the subject o ormula Tuliskan persamaan untuk 4e = 1 dalam bentuk sebagai perkara rumus [ Marks] [ Markah] C b. Obtain the root or equation 4e = 1 by using simple iteration method. Give answer in 4 decimal point. Assume X 0 = 1 Dapatkan punca persamaan 4e = 1 dengan menggunakan kaedah lelaran mudah. Berikan jawapan kepada 4 titik perpuluhan. Ambil X 0 = 1 [5 Marks] [5 Markah] 9 SULIT
9 c. Solve the simultaneous equation below by using Doolittle Method Selesaikan persamaan serentak di bawah dengan kaedah Doolittle. 5y + z = 1 4 y z = y + z = 16 [18 Marks] [18 Markah] QUESTION 6 SOALAN 6 a. Form a dierential equation or each o the ollowing unctions: Bentukkan persamaan pembezaan bagi setiap ungsi yang berikut: C i. y B [4 marks] [4 markah] ii. y Bsin C cos [4 marks] [4 markah] b. Solve the ollowing dierential equations: Selesaikan persamaan pembezaan berikut: C1 dy i d [3 marks] [3 markah] ii. dy y d 3 y 1 [4 marks] 10 SULIT
10 c. Solve the ollowing second order dierential equations: Selesaikan persamaan pembezaan peringkat kedua berikut: [4 markah] d y dy i. 3y 0 d d [4 marks] [4 markah] d y dy ii y 0 d d [6 marks] [6 markah] SOALAN TAMAT 11 SULIT
11 1 SULIT FORMULA Descriptive Statistics Number o class k = log n Mean n ) ( Median Median = C F N L m Mode Mode = C d d d L Mo 1 1 First Quartile C F N L Q m 4 1 Third Quartile C F N L Q m Decil C F N k L D DK k 10 Percentile C F N k L P PK K 100 Mean Deviation n E E
12 Variance s s n s = s n il i n n Standard Deviation s var iance Numerical Method Crout Method l A l l l l l 33 0 u u13 u3 1 Doolittle Method 1 A l l l 3 0 u u u 1 0 u u u Newton Raphson 1 1 y1 0 Method y y y 1 n1 n ( ) '( ) Probability E() = P(s)X(s) sεs P(A B) = P(A) + P(B) P(A B) P(B A) = P(B A) P(A) P(A B) = P(A). P(B) P(A B) = P(A). P(B A) 13 SULIT
13 SOLUTION FOR 1 st ORDER DIFFERENTIAL EQUATION Linear Factors (Integrating Factors) Homogeneous y IF Q IF d Equation P d Where IF e y v and dy dy Logarithmic v ln a a e d d ln a a e a a d c ln a GENERAL SOLUTION FOR nd ORDER DIFFERENTIAL EQUATION d y dy Equation o the orm a b cy 0 d d m1 1. Real & dierent roots: Ae Be m y. Real & equal roots: m y e ( A B) 3. Comple roots: y e ( Acos Bsin ) 14 SULIT
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