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Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
Module 9 linear equations PMR
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Module 9 linear equations PMR

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  • 1. PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI MATHEMATICS FORM 3 MODULE 9 PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI LINEAR EQUATIONS II MINISTRY OF EDUCATION MALAYSIA 1
  • 2. MODULE 9: LINEAR EQUATIONS II Arahan: 1. Modul ini mengandungi tiga puluh lima soalan. Semua soalan adalah dalam bahasa Inggeris. 2. Modul merangkumi tujuh konstruk yang diuji K1 - Memahami soalan dalam bahasa Inggeris K3 - Memahami istilah matematik dalam bahasa Inggeris K5 - Menguasai konstruk pengetahuan K6 - Menguasai konstruk kefahaman K7 - Menguasai konstruk kemahiran K8 - Mengungkapkan idea/informasi dalam bahasa Inggeris K10 - Memahami pengajaran dan pembelajaran dalam bahasa Inggeris 3. Murid hendaklah menulis maklumat diri dalam kertas jawapan objektif disediakan. Murid juga perlu memastikan maklumat konstruk, nombor soalan dan jumlah soalan seperti yang dibaca oleh guru di dalam ruangan disediakan dalam kertas jawapan objektif sebelum ujian. 4. Bagi soalan objektif, anda perlu menandakan jawapan dengan menghitamkan pilihan jawapan pada pilihan jawapan A , B , C atau D pada kertas jawapan objektif. Contoh: Antara berikut, yang manakah haiwan? A. Pokok B. Kambing C. Kereta D. Pen A B C D E 5. Untuk soalan subjektif, jawapan hendaklah ditulis pada kertas berasingan yang disediakan oleh guru. 6. Jawab semua soalan. Modul ini mengandungi 15 halaman bercetak 2
  • 3. 1 A linear equation in two variables is an equation involving two variables raised to the power of 1. Which of the following is not a linear equation in two variables? 7h + k = 9 A x + y2 = 0 B 2x = y + 5 C 5 x + 3 = 6y D The value of y in the equation y = 3 x + 1 can be calculated by substituting a 2 given value of x in the equation. Example: When x = 2 y = 3(2) + 1 Which of following is true when x = 4 ? y = 3 (4 + 1) A y = 3 (4 ) + 1 B y = 4 (3 + 1) C y = 3 (2 ) + 1 D 3
  • 4. 3 Simultaneous linear equations in two variables contain the same set of variables. The variables are raised to the power of 1. Which of the following is a pair of simultaneous linear equations in two variables? x+y =5 A y = 2 − 3x 3 m − 2n = 2 B 3m − mn = 5 p2 − q = 0 C 3 p + 2q = 2 r + 3s = 5 D 3r − t = 6 In the linear equation 2 x + 3 y = 7, x and y are known as variables. 4 What are the variables in equation 4 p + 3q = 11 ? x and y A x and p B p and q C p and y D 5 When writing a linear equation in two variables, we represent the two unknowns with two suitable letters. Which of the following is a linear equation in two variables? 2 p = 11 A 4m − n = 2 B 3x + 5 = x C 4p − q = r D 4
  • 5. 6 An equation involving variables raised to the power of 1 which are connected by “+” or “─” is known as a A cubic equation B linear equation C quadratic equation D simultaneous equation 7 a − 3b = 4 3a + b = 8 The pair of equations shown are known as A linear equations B quadratic equations C simultaneous equations D simultaneous linear equations 8 Quantities which do not have a fixed value are known as A coefficents B constants C equations D variables 5
  • 6. 9 a – b = 3 ---------- 1 2a – 4b = 4 ------- 2 From , a = 3 + b ------- 3 1 2(3 + b) – 4b = 4 6 + 2b – 4b = 4 6 – 2b = 4 b=1 Then from ,a=3+1 3 a=4 The method of solving a pair of simultaneous linear equations shown above is known as A elimation method B substitution method C factorisation method D trial and improvement method 10 A value that satisfies a linear equation is known as a A coefficient B variables C solution D factor 6
  • 7. 11 Which of the following is a linear equation in two variables? xy = 15 A x +5 =8 B x + y = 12 C xy + 2 = 18 D 12 Which of the following pairs of equations are simultaneous linear equations? x + 2y = 6 A 3 x + 2 = −2 2a + b = 8 B 2c + d = 12 y = xy C x+y =6 x+y =6 D 3 x + z = 15 13 Which of the following pairs of simultaneous linear equations is best solved using the substitution method? 6a = 14 − 7b A 3a + 5b = 14 x = 8 − 2y B 6 x + 5 y = 15 3 x + 2y = 8 C 3 x + 5 y = 15 4a − 5b = 17 D 6a + 3b = 4 7
  • 8. 14 A pair of simultaneous linear equations is shown below: 2x + 3y = 1 5 x − 3 y = 13 To eliminate y, A add the two equations B multiply the two equations C divide the second equation by the first equation D subtract the first equation from the second equation 15 Which of the following is not a linear equation? 2x + 3 = 8 A x+y =7 B 2 xy + 4 = 12 C 2x + 3 = y D Sharifah spent RM 55.00 to buy x kg of ciku and y kg of papaya. The ciku costs 16 RM 5.00 per kg and the papaya costs RM 3.00 per kg. Write a linear equation in two variables for the situation above. x + y = 55 A 3 x + 5 y = 55 B 5 x + 3 y = 55 C 8( x + y ) = 55 D 8
  • 9. Given that 2h − k = 10 , and h = 8 , then 17 k = 2(8 ) − 10 A k = 10 − 2(8 ) B k = 10 + 2(8 ) C k = −10 − 2(8 ) D 3 x + 2 y = 7 and y = 3 − 2 x are a pair of simultaneous linear equations. 18 Which of the following is true? 3 x + (3 − 2 x ) = 7 A 3 x + (3 + 2 x ) = 7 B 3 x + 2(3 + 2x) = 7 C 3 x + 2(3 − 2 x ) = 7 D 19 During the Chinese New Year season, Mr. Choo bought x boxes of L-sized oranges at RM 30 per box and y boxes of M-sized oranges at RM 25 per box for RM 120.00. If he bought a total of 5 boxes of oranges, write a pair of simultaneous equations for the situation above. x+y =5 A 25 x + 30 y = 120 x+y =5 B 30 x + 25 y = 120 x + y = 120 C 30 x + 25 y = 5 x + y = 120 D 25 x + 30 y = 5 9
  • 10. 20 Equations and are simultaneous linear equations 2 1 2x + y = 4 -------------- 1 4x – y = 16 ------------- 2 Which of the following is an incorrect step in solving the equations? Subtract equation from equation A 1 2 B Add equation to equation 2 1 C Multiply equation by two 1 D Divide equation by two 2 Given that 2 x − y = 2 , find the value of x when y = 12 21 A 12 B 7 C -5 D - 10 Part of the solution of the simultaneous linear equations 5m + n = −6 and 22 3m + 2n = 2 is as follows: 10m + 2n = -12 3m + 2n = 2 7m = What is the number in the box? A -14 B -10 C 10 D 14 10
  • 11. 23 An equilateral triangle PQR is shown below. P 4x + y 3y R Q 48 Calculate the value of x. A 8 B 16 C 32 D 64 Given y = 5 − 3 x and y = 2 x − 10 , find the value of y . 24 A -4 B -1 C 1 D 3 Given 3f − m = 21 and 6f + m = 24 , find the value of f − m . 25 A -11 B -6 C 5 D 11 11
  • 12. All questions from number 26 to number 30 must be answered in words. Why is the equation 3 pr − 8 = 7r not a linear equation? 26 Answer: 27 State two characteristics of linear equations in two variables. Answer: 28 Give two characteristics of simultaneous linear equations. Answer: Explain how to use the elimination method to eliminate x from the given pair of 29 simultaneous linear equations. x + 3 y = 7 ---------- 1 2 x + y = 19 ---------- 2 Answer: 12
  • 13. 30 Explain the meaning of “solution” of a pair of simultaneous linear equations. Answer: From Question 31 – 35, the teacher reads the questions to the students. Students choose the correct answer. 31 5 x + 4y = 6 A 3 x + 2y = 4 5 xy + 4 = 6 B 3 x + 2y = 4 5 x + 4z = 6 C 3x + y = 4 5 x + 4y = 6 D 3 xy = 4 32 A 3 B 5 C 10 D 15 13
  • 14. 33 x – 3y = 1 ------------ 1 2x – y = -1 ----------- 2 x = 1+ 3 y A x − 6x − 3 = 1 B 2(1 + 3 y) − y = −1 C 2( −3 y + 1) − y = −1 D 34 A 8 _ B 8 C 47 _ D 47 35 A 1 B 2 C 4 D unlimited END OF QUESTION PAPER 14
  • 15. KEMENTERIAN PELAJARAN MALAYSIA KERTAS JAWAPAN OBJEKTIF Ujian Diagnostik Nama Pelajar: Tahun/ Tingkatan : 3 Mata Pelajaran: MATEMATIK Modul: 9 Nama Sekolah: GUNAKAN PENSIL 2B ATAU BB SAHAJA. TENTUKAN TIAP-TIAP TANDA ITU HITAM DAN MEMENUHI KESELURUHAN RUANG. PADAMKAN HINGGA HABIS MANA-MANA TANDA YANG ANDA UBAH SILA HITAMKAN JAWAPAN DI BAWAH MENGIKUT HURUF JAWAPAN YANG ANDA PILIH A A A B C D E B C D E B C D E 1 31 46 A A A 2 32 47 B C D E B C D E B C D E A A A B C D E B C D E B C D E 3 33 48 A A A B C D E B C D E B C D E 4 34 49 A A A B C D E B C D E B C D E 5 35 50 A A B C D E B C D E 6 36 51 A B C D E A A 7 37 52 B C D E B C D E A B C D E A A B C D E B C D E A 8 38 53 B C D E A A B C D E B C D E A 9 39 54 B C D E A A B C D E B C D E 10 40 55 A B C D E A A B C D E B C D E 41 56 A B C D E 11 A A 42 57 B C D E B C D E A 12 B C D E A A B C D E B C D E A 43 58 B C D E 13 A A B C D E B C D E A 44 59 B C D E 14 A A B C D E B C D E 45 60 A B C D E 15 Jumlah Bilangan Soalan Konstruk No. Soalan Kegunaan Guru A B C D E 16 Soalan Gagal Dijawab A 17 B C D E A K1 1-5 5 B C D E 1 18 A B C D E 19 K3 6-10 5 2 A B C D E 20 K5 11-15 5 3 A B C D E 21 K6 16-20 5 4 A 22 B C D E A B C D E 23 K7 21-25 5 5 A B C D E 24 A B C D E 25 26-30 5 K8 6 31-35 5 K10 7 A B C D E 26 A 27 B C D E 8 A B C D E 28 A B C D E 9 29 A B C D E 30 10

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