Module 6 Algebric PMR

PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI MATHEMATICS FORM 3 MODULE 6 PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI ALGEBRAIC EXPRESSIONS III & ALGEBRAIC FORMULAE MINISTRY OF EDUCATION MALAYSIA 1

MODULE 1: ALGEBRAIC EXPRESSIONS III & ALGEBRAIC FORMULAE 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 B A C D E 5. Untuk soalan subjektif, jawapan hendaklah ditulis pada kertas berasingan yang disediakan oleh guru. 6. Jawab semua soalan. Modul ini mengandungi 13 halaman bercetak 2

1 The area of a rectangle is given by the product of its length and breadth. x y x What is the area of the rectangle? xy A x+y B x C y x−y D The factors of ( x + y )( x − y ) are ( x + y ) and ( x − y ) . 2 What are the factors of a ( b + c ) ? a and ( b + c ) A (a + b ) and (a − b ) B ab and c C ab and ac D (a − b )2 can be written as (a − b )(a − b ) . 3 Which of the following is equal to ( m − n )2 ? ( m − n )( m − n ) A ( m + n )( m + n ) B m2 − n2 C 2m − 2n D 3

4 The highest common factor of several algebraic terms is the highest factor among all the common factors. The common factors of 2bc and 4ab are 1,2, b and 2b . What is the highest common factor of 2bc and 4ab ? A 1 B 2 C b D 2b x+y x y 6 1 5 If the sum of and is , what is the sum of and ? b b b 9 9 7 A 18 7 B 9 5 C 9 6 D 81 6 What is a variable? A A value that is not fixed. B A value that does not change. A value that is greater than π . C D A value that is the same in all situations. 4

7 Which of the following is a constant? A Total number of tourists who visit Malaysia every month. B Number of books sold in a bookshop every week. C Blood pressure of a football player. D Total number of sides of a triangle. 8 An equation which combines variables with an equal sign is a A value B formula C statement D operations 9 The reverse process of expansion is A subtraction B multiplication C factorization D simplification 10 A single linear variable which is expressed in terms of other variables in a formula is known as the A constant B equation C subject D object 5

11 In which of the following, is E the subject of the formula? L E= A 5E 2E = bh B E = mc 2 C E 2 = u 2 + 2as D ( m + n )2 can be expressed as 12 m + n2 A 2( m + n ) B m2 + n2 C ( m + n )( m + n ) D 13 Which of the following is true? ( a − b) 2 = a2 − b2 A ( a + b ) 2 = a 2 + 2ab + b 2 B ( a − b ) 2 = a 2 − 2ab − b 2 C ( a + b )( a − b ) = a 2 − 2ab + b 2 D 14 Which of the following is a variable? A Total number of days in August. B The number of hours in a day. C Total number of sides of a square. D Number of students in a school bus every day. 6

1 The area, A of trapezium PQRS is given by the formula A = h (a + b ) . 15 2 Q P R S Which of the following is true? h is the length of PS A h is the length of QR B a is the length of PS C b is the length of QR D A rectangle is r cm long, s cm wide and has an area of P cm2. Express P in terms of r 16 and s. P = rs A r P= B s P = 2rs C P = (rs )2 D r (s − 2t ) can be expressed as 17 rs − rt A rs − 2t B rs − 2rt C s − 2t D 7

Which of the following is not true for the expression 4 pq + 4qr . 18 4q ( p + r ) A 4( pq + qr ) B p( 4q + 4r ) C q(4 p + 4r ) D (2 p + 3q )( p − 6q ) = 19 2 p 2 − 12 pq + 3 pq − 18q 2 A 2 p 2 − 12 pq + p − 6q B 2 p + 3q + p − 6q C 2 p + 3 pq − 18q 2 D 2p p = ÷ 20 q2 3q q2 p × A 3q 2p p 2p × B 3q 2 3q 3q 2p × C q2 p p 2p × D q2 3q 8

5e 3 + 20e 2f 21 Simplify 30e 2f 5e + 2 A 3 5e 3 + 2 B 3 e + 4f C 6f e + 20f D 6f 2 3 − = 22 x xy 2y − 3 A xy 2x − 3y B xy 2y − 3 C x 2y 2 xy − 3 D x 2y 3 pq = r , express A in terms of p, q and r. 23 Given A 3 pq A= A r 3 pq 2 A= B r 9 pq A= C r2 9 p 2q 2 A= D r2 9

1 , hence 3 x 2 − 2 xy = Given that x = 5 and y = 24 2 A 25 B 55 C 70 D 85 Simplify (a − 2b )2 + 3ab 25 a 2 − ab + 4b 2 A a 2 + 4b 2 + 3ab B a 2 − 7ab + 4b 2 C a 2 + ab + 4b 2 D All questions from number 26 to number 30 must be answered in words. 26 Explain how to find the common factors for several algebraic terms. Answer: Explain how to expand the expression a( b + c ) . 27 Answer: 10

28 Explain how to simplify an algebraic fraction. Answer: 29 Explain how two algebraic fractions are added. Answer: 30 What is an algebraic formula? Answer: From Question 31 – 35, the teacher reads the questions to the students. Students choose the correct answer. 31 2mp − n A 2mp − np B 2mp − m C 2m − np D 11

32 mn( −n ) A m( n − mn ) B mn(1− n ) C n( m − mn ) D 33 5 A 5m 1 B m 5 C 25m 2 5 D m 12

34 q p r E = pqr A E = p(q + r) B 1 E= pq C 2 1 E= (q + r)p D 2 35 900 A 300 B C 90 D 60 END OF QUESTION PAPER 13

KEMENTERIAN PELAJARAN MALAYSIA KERTAS JAWAPAN OBJEKTIF Ujian Diagnostik Nama Pelajar: Mata Pelajaran: MATEMATIK Tahun/ Tingkatan : 3 Modul: 6 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 1 31 46 B B B C C C D E D E D E 2 32 47 A A A B B B C C C D E D E D E A A A B B B C C C 3 33 48 D E D E D E A A A B B B C C C 4 34 49 D E D E D E A A A 5 B 35 B 50 B C C C D E D E D E A A 6 36 51 B B C C A B D E D E C D E 7 37 52 A A B B C C A B D E D E C D E A A B B C C 8 38 53 A D E D E B C D E A A B B C C 9 39 54 A D E D E B C D E A A 10 40 B 55 B C C A D E D E B C D E A A 41 56 B B C C A 11 B D E D E C D E 42 57 A A B B 12 C C A B D E D E C D E A A B B C C A 43 58 B D E D E C 13 D E A A B B C C A 44 59 B D E D E C 14 D E A A 45 B 60 B C C A 15 B D E D E C D E Konstruk No. Soalan Jumlah Bilangan Soalan Kegunaan Guru A 16 B C D E Soalan Gagal Dijawab 17 A B C D E A B C 18 K1 1-5 5 D E 1 A B C 19 D E 6-10 5 K3 2 A 20 B C D E K5 11-15 5 3 A 21 B C D E K6 16-20 5 22 A 4 B C D E A B C 23 D E K7 21-25 5 5 A B C 24 D E A 25 B C 26-30 5 D E K8 6 K10 31-35 5 7 A 26 B C D E K10 27 A B C D E 8 A B C 28 D E A B C 29 D E 9 A 30 B C D E 10

Module 6 Algebric PMR

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