Additional Mathematics Form 5 Chapter 1 (Progression) PROGRESSION (JANJANG) Paper 1
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1 PROGRESSION (JANJANG) Paper 1 1) Given that the seventh, eighth and ninth term of arithmetic progression is, and respectively. Find the first term of the progression. Diberi sebutan ketujuh, kelapan dan kesembilan suatu janjang aritmetik masing-masing ialah,, dan. Cari sebutan pertama bagi janjang itu. 2) The sum of first terms in a geometric progression, 1, 3,... is 364. Hasil tambah bagi sebutan pertama bagi janjang geometri, 1, 3,... ialah 364. a) Find the common ratio of the progression. Nyatakan nisbah sepunya janjang ini. b) Find the value of. Cari nilai. [4 marks] [4 markah] 1
2 3) The 8th and 53th term of an arithmetic progression is 118 and -62 respectively. Find Sebutan ke-8 dan sebutan ke-53 suatu janjang aritmetik masing-masing ialah 118 dan -62. Cari a) the common difference. beza sepunya. b) the first term sebutan pertama. 4) Find the number of terms in an arithmetic progression -20, -17, -14,..., 223. Cari bilangan sebutan bagi janjang aritmetik -20, -17, -14,...,
3 5) The first three terms in a progression is 3,, 12. Find the positive value of is this progression is Tiga sebutan pertama bagi suatu janjang ialah 3,, 12. Cari nilai positif bagi jika janjang ini adalah a) arithmetic progression. janjang aritmetik. b) geometric progression. janjang geometri. [4 marks] [4 markah] 6) Express as a fraction in simplest form. Ungkapkan sebagai pecahan dalam bentuk paling ringkas. [4 marks] [4 markah] 3
4 7) 3rd term of a geometric progression is 16. The sum of 3rd term and 4th term is 18. Find Sebutan ke-3 bagi suatu janjang geometri ialah 16. Hasil tambah sebutan ke-3 dan sebutan ke-4 ialah 18. Cari a) the first term and common ratio. sebutan pertama dan nisbah sepunya. b) the sum to infinity. hasil tambah hingga ketakterhinggaan. [4 marks] [4 markah] 8) Find the sum of multiples of 12 between 100 and 400. Cari hasil tambah semua gandaan 12 antara 100 dan
5 9) 9th term of arithmetic progression is and the sum of first four terms is, where is constant. Given that the common difference of the progression is 5, find the value of. Sebutan ke-9 suatu janjang aritmetik ialah dan hasil tambah empat sebutan pertama ialah, dengan ialah pemalar. Diberi beza sepunya janjang ini ialah 5, cari nilai. 10) First and fourth term of a geometric progression is 81 and 24 respectively. Find Sebutan pertama dan sebutan keempat suatu janjang geometri masing-masing ialah 81 dan 24. Cari a) the common ratio. nisbah sepunya. b) the sum to infinity. Hasil tambah hingga ketakterhinggaan. 5
6 11) The sum of first terms in a progression is. Find Hasil tambah sebutan pertama bagi suatu janjang aritmetik ialah. Cari a) the second term. sebutan kedua. b) common difference. Beza sepunya. 12) Given that is a geometric progression, express in terms of. Diberi merupakan suatu janjang geometri, ungkapkan dalam sebutan. [2 marks] [2 markah] 6
7 13) Three first terms in an arithmetic progression is 46, 43, and 40. The th term of the progression is negative. Find the smallest value of. Tiga sebutan pertama bagi suatu janjang aritmetik ialah 46, 43, dan 40. Sebutan kejanjang ini adalah negatif. Cari nilai terkecil bagi. 14) Given that the first term and the common ratio of a geometric progression is 4 and. Find the sum from seventh term to eleventh term. Diberi sebutan pertama dan nisbah sepunya bagi suatu janjang geometri ialah 4 dan. Cari hasil tambah dari sebutan ketujuh hingga sebutan kesebelas. 7
8 15) 1, 4, 7,... is an arithmetic progression. Find the four consecutive terms in the progression that sums up to , 4, 7,... merupakan suatu janjang aritmetik. Cari empat sebutan berturutan dalam janjang ini yang mempunyai hasil tambah
9 Paper 2 1) Alpha Company and Beta Company starts selling motorcycles at the same time. Syarikat Alpha dan Syarikat Beta mula menjual motosikal pada masa yang sama. a) Alpha Company starts selling units of motorcycles in first month and the sale increases constantly by units at the following month. The sale at 8th month is 240 units and the total sales throughout first 10 months are 1900 units. Find the value of and. Syarikat Alpha mula menjual unit motosikal pada bulan pertama dan jualannya bertambah secara malar sebanyak unit pada bulan berikutnya. Jualannya pada bulan ke-8 ialah 240 unit dan jumlah jualannya bagi 10 bulan pertama ialah 1900 unit. Cari nilai dan. [5 marks] [5 markah] b) Beta Company sells 80 units of motorcycles in first month and the sale increases by 22 units every month. If the number of motorcycles sold by the two companies is equal in th month, find the value of. Syarikat Beta menjual 80 unit motosikal pada bulan pertama dan jualannya bertambah secara malar sebanyak 22 unit setiap bulan berikutnya. Jika bilangan motosikal yang dijual oleh kedua-dua syarikat itu adalah sama pada bulan ke-, cari nilai. [2 marks] [2 markah] 2) Syuhada starts working in Permata Company in 1 January 2003 with RM as initial yearly salary. Every January, the company raises her salary by 5% from her last yearly salary. Find Syuhada mula bekerja di Syarikat Permata pada 1 Januari 2003 dengan permulaan gaji tahunan sebanyak RM Setiap bulan Januari, syarikat itu menaikkan gajinya sebanyak 5% daripada gaji tahunan sebelumnya. Cari a) the yearly salary, to the nearest RM, for year gaji tahunannya, kepada RM terdekat, untuk tahun b) minimum value of, such that her yearly salary in th year exceeds RM nilai minimum, supaya gaji tahunannya pada tahun ke- melebihi RM [2 marks] [2 markah] c) total salary, to the nearest RM, which have been paid to Syuhada by the company, from year 2003 to year jumlah gaji, kepada RM terdekat, yang telah dibayar kepada Syuhada oleh syarikat itu, dari tahun 2003 hingga tahun [2 marks] [2 markah] 9
10 3) Bakri releases a ball from a height of cm from the ground. After the first bounce, the ball reaches a height of cm where. After second bounce, the ball reaches a height of cm, where. The ball keeps bouncing until it stops. Given that, find Bakri melepaskan sebiji bola dari suatu ketinggian cm dari tanah. Selepas lantunan pertama, bola itu mencapai suatu ketinggian cm dengan keadaan. Selepas lantunan kedua, bola itu mencapai suatu ketinggian cm dengan keadaan. Bola itu seterusnya melantun sehingga ia berhenti. Diberi, cari a) the number of bounce when the maximum height of the ball from the ground is less than 15 cm for the first time. bilangan lantunan apabila ketinggian maksimum bola itu dari tanah adalah kurang daripada 15 cm untuk kali pertama. [4 marks] [4 markah] b) total distance, in cm, the ball moves until it stops. [2 marks] jumlah jarak, dalam cm, yang dilalui oleh bola itu sehingga ia berhenti. [2 markah] 4) Hashim and Salleh is given a thread respectively to be cut into several parts. The length of first part must be cm and the length of the following thread is being shortened by cm respectively. Hashim s thread of 5 0 cm is divided into 0 parts while Salleh s thread of 1090 cm is divided into 20 parts. Find Hashim dan Salleh masing-masing diberikan seutas benang untuk digunting kepada beberapa bahagian. Panjang bahagian pertama mesti cm dan panjang bahagian berikutnya masing-masing dipendekkan sebanyak cm. Benang Hashim sepanjang 530 cm dibahagikan kepada 10 bahagian manakala benang Salleh sepanjang 1090 cm dibahagi kepada 20 bahagian. Cari a) the value of and. [4 marks] nilai dan. [4 markah] b) the difference between lengths of the last part of both threads. [2 marks] beza antara panjang bahagian terakhir bagi kedua-dua benang tersebut. [2 markah] 10
11 5) Figure below shows a part of several rectangles. The height of each rectangle is 4 cm. The length of the first rectangle is 75 cm and the length of the following rectangles is 3 cm less than the preceding rectangle. Rajah di bawah menunjukkan sebahagian daripada beberapa segi empat tepat. Tinggi setiap segi empat tepat itu ialah 4 cm. Panjang segi empat tepat yang pertama ialah 75 cm dan panjang segi empat tepat yang berikutnya kurang daripada 3 cm daripada segi empat tepat sebelumnya. a) Calculate the area of tenth rectangle. Hitung luas segi empat tepat yang kesepuluh. b) Find the number of rectangles that can be formed. Cari bilangan segi empat tepat yang dapat dibentuk. c) Calculate the number of rectangles required so that the total area is 2064 cm. Hitung bilangan segi empat tepat yang diperlukan supaya jumlah luas ialah [4 marks] [4 markah] 11
12 ANSWERS Paper 1 1) -15 2) a) 3 b) 7 3) a) -4 b) 146 4) 82 5) a) 5 b) 6 6) 7) a) b) 0 8) ) 8 10) a) b) ) a) 4 b) 6 12) 0 13) 17 14) 5 15) 58, 61, 64, 67 Paper 2 1) a) 00 0 b) 11 2) a) RM b) 16 c) RM ) a) 5 b) 600 cm 4) a) b) 3 cm 5) a) 192 cm. b) 25 c) 8 12
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