Bab 1 Pola dan Jujukan 1 – 8 Patterns and Sequences Bab 2 Pemfaktoran dan Pecahan Algebra 9 – 14 Factorisation and Algebraic Fractions Bab 3 Rumus Algebra 15 – 19 Algebraic Formulae Bab 4 Poligon 20 – 25 Polygon Bab 5 Bulatan 26 – 31 Circles Bab 6 Bentuk Geometri Tiga Dimensi 32 – 37 Three-Dimensional Geometrical Shapes Bab 7 Koordinat 38 – 43 Coordinates Bab 8 Graf Fungsi 44 – 49 Graphs of Functions Bab 9 Laju dan Pecutan 50 – 55 Speed and Acceleration Bab 10 Kecerunan Garis Lurus 56 – 61 Gradient of a Straight Line Bab 11 Transformasi Isometri 62 – 68 Isometric Transformations Bab 12 Sukatan Kecenderungan Memusat 69 – 73 Measures of Central Tendencies Bab 13 Kebarangkalian Mudah 74 – 80 Simple Probability Ujian Akhir Sesi Akademik 81 – 94 Jawapan J1 – J15 Kandungan 0A PT UASA MM Tg2.indd 1 25/01/2024 2:53 PM
1 1 BAB Pola dan Jujukan Patterns and Sequences Bidang Pembelajaran: Nombor dan Operasi Bahagian A / Section A Pola Patterns 1.1 1 Nyatakan pola bagi urutan nombor –16, 8, –4, 2, –1, 0.5, …. State the pattern for the number sequence –16, 8, –4, 2, –1, 0.5, …. A Membahagi nombor sebelumnya dengan –2 Divide the previous number by –2 B Menolak 8 daripada nombor sebelumnya Subtract 8 from the previous number C Mendarab nombor sebelumnya dengan –2 Multiply the previous number by –2 D Menambah 0.5 kepada nombor sebelumnya Add 0.5 to the previous number TP2 BT ms. 4 2 Rajah 1 menunjukkan sebuah Segi Tiga Pascal yang tidak lengkap. Diagram 1 shows an incomplete Pascal’s Triangle. 1 N N 1 1 M 6 1 1 3 3 1 1 2 1 1 1 1 M Rajah 1/Diagram 1 Hitung nilai M + N. Calculate the value of M + N . A 6 C 14 B 8 D 16 TP3 BT ms. 5 3 Rajah 2 menunjukkan urutan Nombor Fibonacci. Diagram 2 shows a Fibonacci Numbers sequence. 1, 1, 2, 3, p, 8, q, … Rajah 2/Diagram 2 Cari nilai q – p. Find the value of q – p. A 5 C 7 B 6 D 8 TP3 BT ms. 6 4 Antara berikut, yang manakah mempunyai pola yang sama seperti urutan nombor 3, 8, 13, 18, …? Which of the following has the same pattern as the number sequence 3, 8, 13, 18, …? A 10, 14, 18, 22, … C 16, 21, 26, 31, … B 2, 10, 50, 250, … D –1, 5, 11, 17, … TP3 BT ms. 4 5 Antara berikut, yang manakah urutan Nombor Fibonacci? Which of the following is a Fibonacci Numbers sequence? A 5, 12, 19, 26, 35, … C 3, 6, 10, 15, 25, … B 1, 4, 6, 15, 24, … D 2, 3, 5, 8, 13, … TP3 BT ms. 6 6 Diberi urutan nombor 11, 16, 21, 26, .... Nyatakan pola bagi urutan nombor ganjil. Given the number sequence 11, 16, 21, 26, .... State the pattern for the odd numbers sequence. A Menambah 4 kepada nombor sebelumnya Add 4 to the previous number B Menambah 5 kepada nombor sebelumnya Add 5 to the previous number C Menambah 10 kepada nombor sebelumnya Add 10 to the previous number D Menambah 11 kepada nombor sebelumnya Add 11 to the previous number TP3 BT ms. 4 7 Rajah 3 menunjukkan susunan segi tiga sama sisi mengikut suatu pola. Diagram 3 shows the arrangement of equilateral triangles according to a pattern. Rajah 3/Diagram 3 Tentukan bilangan segi tiga sama sisi bagi susunan ke-7. Determine the number of equilateral triangles for the 7th arrangement. A 14 C 18 B 16 D 20 TP3 BT ms. 3 01 PT UASA MM Tg2.indd 1 25/01/2024 2:53 PM
2 Jujukan Sequences 1.2 8 Antara berikut, yang manakah merupakan jujukan? Which of the following is a sequence? A 21, 18, 15, 13, 10, … B –9, –4, 1, 5, 10, … C 10, 6, 2, –2, –6, … D –9, 3, –1, 9, –3, … TP3 BT ms. 8 9 Nombor-nombor di bawah disusun mengikut suatu pola. The numbers below are arranged according to a pattern. –27, –23, –19, –15, x, –7, ... Apakah nilai x? What is the value of x? A –11 C –9 B –10 D –8 TP3 BT ms. 8 10 Diberi jujukan nombor 2.3, 2.7, r, 3.5, 3.9, …. Tentukan nilai r. Given the number sequence 2.3, 2.7, r, 3.5, 3.9, …. Determine the value of r. A 2.8 C 3.0 B 2.9 D 3.1 TP3 BT ms. 8 Pola dan Jujukan Patterns and Sequences 1.3 11 Rajah 4 menunjukkan suatu jujukan nombor. Diagram 4 shows a number sequence. 89, 83, 77, 71, ... Rajah 4/Diagram 4 Nyatakan sebutan ke-9 dalam jujukan nombor itu. State the 9th term in the number sequence. A 47 C 36 B 41 D 30 TP3 BT ms. 11 12 Rajah 5 menunjukkan suatu jujukan nombor. Diagram 5 shows a number sequence. 9, 2, –5, –12, –19, … Rajah 5/Diagram 5 Antara berikut, yang manakah benar tentang jujukan nombor ini? Which of the following is true about the number sequence? A Pola bagi jujukan nombor ini ialah menolak 5 daripada nombor sebelumnya The pattern for this number sequence is subtract 5 from the previous number B Sebutan kesepuluh bagi jujukan nombor ini ialah –47 The tenth term of the number sequence is –47 C Beza antara sebutan keempat dengan keenam ialah 14 The difference between the fourth and the sixth terms is 14 D Sebutan kedua bagi jujukan nombor ini ialah –5 The second term of the number sequence is –5 TP3 BT ms. 10 – 11 13 Diberi jujukan nombor 1 2 , 1 4 , 1 8 , 1 16 , ..., cari sebutan ke-8. Given the number sequence 1 2 , 1 4 , 1 8 , 1 16 ..., find the 8th term. A 1 32 C 1 128 B 1 64 D 1 256 TP3 BT ms. 11 14 Cari hasil tambah sebutan kelima dan ketujuh bagi jujukan nombor 34, 42, 50, 58, .... Find the sum of the fifth and seventh terms of the number sequence 34, 42, 50, 58, .... A 132 C 148 B 140 D 156 TP3 BT ms. 11 – 12 15 Tentukan sebutan ke-10 bagi jujukan nombor –5, –1, 3, 7, .... Determine the 10th term of the number sequence –5, –1, 3 , 7, .... A 31 B 27 C 23 D 19 TP3 BT ms. 11 16 Diberi bahawa sebutan ke-n bagi suatu jujukan nombor ialah Tn = n(5n – 7), dengan keadaan n = 1, 2, 3, 4, .... Cari sebutan ke-9 bagi jujukan nombor itu. Given the nth term of a number sequence is Tn = n(5n – 7), where n = 1, 2, 3, 4, .... Find the 9th term of the number sequence. A 350 B 342 C 304 D 279 TP3 BT ms. 11 01 PT UASA MM Tg2.indd 2 25/01/2024 2:53 PM
3 17 Puan Suriati perlu makan ubat tiga kali sehari. Dia makan ubat yang pertama pada pukul 7:30 a.m. Pada pukul berapakah dia akan makan ubat untuk kali ketiga? Puan Suriati needs to take medicine three times a day. She took the first medicine at 7:30 a.m. At what time will she take the medicine for the third time? A 8:30 p.m. C 10:30 p.m. B 9:30 p.m. D 11:30 p.m. TP4 BT ms. 12 KBAT Menganalisis 18 Maklumat berikut merujuk suatu pola bagi satu jujukan nombor. The information below refers to a pattern for a number sequence. • Bermula dengan nonbor 7. Starts with number 7. • Pola menolak 3 daripada nombor sebelumnya. Patterns of subtracting 3 from the previous number. Berdasarkan maklumat yang diberi, nyatakan pola bagi jujukan nombor itu. Based on the given information, state the pattern of the number sequence. A 7n – 3, n = 1, 2, 3, .... B 7 – 3n, n = 1, 2, 3, .... C 10n – 7, n = 1, 2, 3, ... D 10 – 3n, n = 1, 2, 3, ... TP3 BT ms. 10 19 Sebuah tangki mengandungi 500 ℓ air. 13 ℓ air akan ditambah ke dalam tangki itu pada setiap hari berikutnya. Pada hari ke berapa isi padu air akan menjadi 760 ℓ? A tank contains 500 ℓ of water. 13 ℓ of water will be added to the tank on each subsequent day. On what day will the volume of water be 760 ℓ? A 20 B 21 C 22 D 23 TP4 BT ms. 12 Bahagian B / Section B 20 (a) Lengkapkan jujukan nombor pada ruang jawapan dengan nombor yang betul. TP3 BT ms. 8 Complete the number sequence in the answer space with the correct numbers. –35 –40 –17 –25 [2 markah/marks] Jawapan/Answer: –53, –44, , –26, , –8, ... (b) Tandakan (✓) bagi urutan nombor yang merupakan jujukan. TP3 BT ms. 8 Tick (✓) for the set of numbers that is a sequence. [2 markah/marks] Jawapan/Answer: (i) 2, 6, 18, 54, 162, … (ii) 1, 4, 7, 10, 13, … (iii) –1, 0, 2, 3, 5, … (iv) –4, 0, 4, 16, 20, … 01 PT UASA MM Tg2.indd 3 25/01/2024 2:53 PM
4 21 Padankan jujukan nombor dengan pola yang betul. TP3 BT ms. 10 Match the number sequences with the correct patterns. [4 markah/marks] Jawapan/Answer: 3, 5, 7, 9, 11, … n − 1, n = 1, 2, 3, … 5n − 1, n = 1, 2, 3, … –3, 9, –27, 81, … 2(n – 1), n = 1, 2, 3, ... 0, 2, 4, 6, 8, … n + 2, n = 1, 2, 3, ... 4, 9, 14, 19, 24, … (–3)n, n = 1, 2, 3, ... 1 + 2n, n = 1, 2, 3, ... 22 Bulatkan jawapan yang betul bagi pola setiap jujukan nombor berikut. TP3 BT ms. 4 Circle the correct answers for the pattern for each of the following number sequences. [4 markah/marks] Jawapan/Answer: (a) 9,14,19,24, … Menambah Add Menolak Subtract 4 5 kepada nombor sebelumnya. to the previous number. (b) 1.3, −2.6, 5.2, −10.4,... Mendarab Multiply Membahagi Divide –2 2 nombor sebelumnya dengan the previous number by . 01 PT UASA MM Tg2.indd 4 25/01/2024 2:53 PM
5 Bahagian C / Section C 23 (a) Nyatakan pola bagi jujukan nombor berikut dalam perkataan. TP3 BT ms. 4 State the pattern for the following number sequences in words. (i) 2, 9, 16, 23, … (ii) 57, 47, 37, 27, … [2 markah/marks] Jawapan/Answer: (i) (ii) (b) Lengkapkan jujukan nombor berikut. TP3 BT ms. 8 Complete the following number sequences. (i) −23, −16, −9, , 5, , 19, ... (ii) 78, , 54, 42, , 18, .... [4 markah/marks] Jawapan/Answer: (i) (ii) (c) Rajah 6 menunjukkan susunan butang mengikut suatu pola. TP4 BT ms. 12 KBAT Mengaplikasi Diagram 6 shows the arrangements of buttons according to a pattern. Corak 1 Corak 2 Corak 3 Pattern 1 Pattern 2 Pattern 3 Rajah 6/Diagram 6 (i) Lukis susunan butang bagi corak ke-4. Draw the arrangement of buttons for the 4th pattern. (ii) Berapakah bilangan butang bagi corak ke-7? How many buttons are there in the 7th pattern? (iii) Pada corak ke berapa bilangan butang ialah 35? In which pattern will there be 35 buttons? [4 markah/marks] 01 PT UASA MM Tg2.indd 5 25/01/2024 2:53 PM
6 Jawapan/Answer: (i) (ii) (iii) 24 (a) Lengkapkan Nombor Fibonacci berikut. TP3 BT ms. 6 Complete the following Fibonacci Numbers. (i) 1, 1, 2, 3, 5, 8, , 21, 34, … (ii) 2, 2, 4, , 10, 16, … (iii) 1, 3, 4, 7, , 18, 29, 47, … (iv) 11, 14, 25, 39, , 103, 167, … [4 markah/marks] Jawapan/Answer: (i) (ii) (iii) (iv) (b) Rajah 7 menunjukkan susunan jubin yang terdiri daripada segi empat sama berwarna putih dan hitam. Diagram 7 shows the arrangement of tiles which consists of white and black squares. Corak 1 Corak 2 Corak 3 Corak 4 Pattern 1 Pattern 2 Pattern 3 Pattern 4 Rajah 7/Diagram 7 01 PT UASA MM Tg2.indd 6 25/01/2024 2:53 PM
7 Cari beza antara bilangan jubin berwana putih dengan jubin berwarna hitam bagi corak ke-32. Find the difference between the number of white tiles and black tiles for the 32nd pattern. TP4 BT ms. 12 KBAT Menilai [2 markah/marks] Jawapan/Answer: (c) Rajah 8 menunjukkan lakaran bagi susunan meja dan kerusi murid-murid di sebuah dewan untuk satu aktiviti berkumpulan. TP4 BT ms. 12 Diagram 8 shows a sketch of the table and chair arrangements for students in a hall for a group activity. Meja Table Kerusi Chair Petunjuk: Key: Rajah 8/Diagram 8 (i) Ungkapkan bilangan meja bagi corak ke-n dalam ungkapan algebra. Express the number of tables for the nth pattern in algebraic expression. (ii) Bilangan kerusi bagi corak ke-n boleh ditentukan dengan menggunakan rumus Tn = 8n. Tentukan nilai n jika bilangan kerusi dan meja adalah sama banyak. KBAT Menganalisis The number of chairs for the nth pattern can be determined by using the formula Tn = 8n. Determine the value of n if the number of chairs and tables are the same. [4 markah/marks] Jawapan/Answer: (i) (ii) 01 PT UASA MM Tg2.indd 7 25/01/2024 2:53 PM
8 25 (a) Diberi jujukan nombor 5, 9, 13, 17, …, hitung sebutan ketujuh dan kesepuluh. TP3 BT ms. 11 Given the number sequence 5, 9,13, 17, …, calculate the seventh and tenth terms. [2 markah/marks] Jawapan/Answer: (b) Aiza menyusun beberapa keping logam seperti ditunjukkan dalam Rajah 9. TP4 BT ms. 12 Aiza arranges some pieces of metal in stacks as shown in Diagram 9. Rajah 9/Diagram 9 (i) Lengkapkan jadual pada ruang jawapan dengan bilangan keping logam yang digunakan untuk membentuk setiap susunan dalam Rajah 9. Complete the table in the answer space with the number of metal pieces used to form each stack in Diagram 9. (ii) Susunan logam itu diteruskan hingga susunan ke-7. Berapakah bilangan keping logam yang diperlukan untuk susunan itu? The arrangement of the metal pieces is continued until the 7th stack. How many pieces of metal are needed for the stack? [4 markah/marks] Jawapan/Answer: (i) Susunan/Stack 1 2 3 4 Bilangan keping logam/Number of pieces of metal (ii) (c) Rajah 10 menunjukkan beberapa batang mancis yang disusun mengikut suatu corak tertentu. Diagram 10 shows several matchsticks arranged according to a certain pattern. TP4 BT ms. 12 Corak 1/Pattern 1 Corak 2/Pattern 2 Corak 3/Pattern 3 Rajah 10/Diagram 10 (i) Cari bilangan batang mancis bagi corak 4 dan corak 5. Find the number of matchsticks for pattern 4 and pattern 5. (ii) Seterusnya, tulis pola bagi susunan batang mancis untuk corak ke-n dalam ungkapan algebra. Hence, write the pattern for the nth arrangement of matchsticks as an algebraic expression. [4 markah/marks] Jawapan/Answer: (i) (ii) 01 PT UASA MM Tg2.indd 8 25/01/2024 2:53 PM
9 2 BAB Pemfaktoran dan Pecahan Algebra Factorisation and Algebraic Fractions Bidang Pembelajaran: Perkaitan dan Algebra Bahagian A / Section A Kembangan Expansion 2.1 1 Kembangkan –4m(3m – 4). Expand –4m(3m – 4). A –12m2 – 16m B –12m2 + 16m C 12m2 + 16m D 12m2 – 16m TP3 BT ms. 21 – 22 2 (2a – 5b)2 = A 4a2 – 10ab + b2 B 4a2 – 20ab – 5b2 C 4a2 – 20ab + 25b2 D 4a2 + 20ab – 25b2 TP3 BT ms. 23 – 24 3 Permudahkan/Simplify m + 9 + (2m – 1)(m + 4) A 2m2 – 8m – 4 B 2m2 – 8m + 4 C 2m2 + 8m + 5 D 2m2 + 8m – 5 TP3 BT ms. 24 – 25 4 Sebuah segi tiga sama kaki mempunyai panjang tapak (12 – 4p) cm dan tinggi (10 + p) cm. Hitung luas, dalam cm2 , segi tiga sama kaki itu. An isosceles triangle has a base length of (12 – 4p) cm and a height of (10 + p) cm. Calculate the area, in cm2 , of the isosceles triangle. A 60 – 14p – 2p2 B 120 – 28p – 4p2 C 100 – 18p – p2 D 80 – 12p – 4p2 TP4 BT ms. 25 – 26 Pemfaktoran Factorisation 2.2 5 Antara berikut, yang manakah faktor sepunya bagi 6p2 q2 r dan 4p3 q? Which of the following is the common factor of 6p2 q2 r and 4p3 q? A 2p2 q C pq2 r B 3pq D pq2 TP2 BT ms. 28 6 Faktorkan 14kl – 8k2 l 3 . Factorise 14kl – 8k2 l 3 . A 7kl(7 – kl) C 2kl(7k – 4kl) B 4kl(3 – 2kl3 ) D 2kl(7 – 4kl2 ) TP3 BT ms. 29 – 30 7 Faktorkan selengkapnya x2 – 3x – 10. Factorise completely x2 – 3x – 10. A (x – 2)(x – 5) C (x – 3)(x – 10) B (x – 5)(x + 2) D (x + 5)(x – 2) TP3 BT ms. 30 – 31 8 Faktorkan 6pr + 3ps – 2qr – qs. Factorise 6pr + 3ps – 2qr – qs. A (2p + q)(3r – s) C (3p + q)(2r – s) B (2p – q)(3r – s) D (3p – q)(2r + s) TP3 BT ms. 32 9 Faktorkan ungkapan 49t 2 – 4. Factorise the expression 49t2 – 4. A (7t + 2)(7t – 2) C (7t + 2)(t – 2) B (7t + 4)(7t – 4) D (7t – 2)(7t – 2) TP3 BT ms. 30 – 31 10 Antara berikut, yang manakah faktor sepunya terbesar (FSTB) bagi 4mn dan 12mn2 ? Which of the following is the highest common factor (HCF) of 4mn and 12 mn2 ? A 12m C 4mn B 3mn D 4n TP3 BT ms. 28 – 29 11 Helen membeli (2x + 4) set alat tulis. Harga setiap set alat tulis itu ialah RM(6x + 2). Helen berkongsi wang secara sama rata dengan tiga orang kawannya untuk membayar set alat tulis itu. Hitung harga yang perlu dibayar oleh setiap orang. Helen bought (2x + 4) stationery sets. The price of each stationery set is RM(6x + 2). Helen shared the money equally with her three friends to pay for the stationery sets. Calculate the price each person has to pay. A RM(3x2 + 8x + 3) B RM(4x2 + 9x + 3) C RM(3x2 + 7x + 2) D RM(4x2 + 7x + 2) TP4 BT ms. 32 02 PT UASA MM Tg2.indd 9 25/01/2024 2:53 PM
10 12 Aznim makan (16q + 200) keping biskut. Hanim pula makan tiga kali bilangan biskut yang dimakan oleh Aznim. Jijah makan suku daripada bilangan biskut yang dimakan oleh Hanim. Hitung bilangan biskut yang dimakan oleh Jijah. Aznim eats (16q + 200) cookies. Hanim eats three times the number of cookies eaten by Aznim. Jijah eats a quarter of the number of cookies that Hanim ate. Calculate the number of cookies eaten by Jijah. A 10q + 150 C 8q + 100 B 48q + 600 D 12q + 150TP4 BT ms. 32 Ungkapan Algebra dan Hukum Operasi Asas Aritmetik Algebraic Expression and Laws of Basic Arithmetic Operations 2.3 13 Permudahkan ungkapan berikut. Simplify the following expression. 30x + 12y 25x2 – 4y2 A 6 5x + 2y C 6 5x – y B 6 5x + y D 6 5x – 2y TP3 BT ms. 36 14 Permudahkan 5 m + 4 – m – 2 m2 – 16 . Simplify 5 m + 4 – m – 2 m2 – 16 . A 2(2m – 9) m2 – 16 B 2m + 9 m2 – 16 C 2(2m – 11) m2 – 16 D 2m + 18 m2 – 16 TP3 BT ms. 35 15 Permudahkan k + 2 m2 ÷ 3k + 6 m sebagai satu pecahan tunggal. Simplify k + 2 m2 ÷ 3k + 6 m as a single fraction. A m 3 B 1 3m C 3m D 3 m TP3 BT ms. 36 Bahagian B / Section B 16 (a) Bulatkan semua faktor bagi 4f 2 gh. TP2 BT ms. 28 Circle all the factors of 4f 2 gh. [2 markah/marks] Jawapan/Answer: 2gh 4fg2 2gh3 4fgh 6fgh 8gh (b) Tentukan Benar atau Palsu bagi setiap kembangan yang berikut. TP3 BT ms. 21 – 24 Determine True or False for each of the following expansions. [2 markah/marks] Jawapan/Answer: Ungkapan Expressions Benar/Palsu True/False (i) 9m(m – 5) = 9m2 – 45m (ii) (2r + 3)2 = 4r2 + 12r + 6 02 PT UASA MM Tg2.indd 10 25/01/2024 2:53 PM
11 17 Padankan setiap ungkapan algebra dengan kembangan yang betul. TP3 BT ms. 21 – 22 Match each algebraic expression with the correct expansion. [4 markah/marks] Jawapan/Answer: 2d(e + 4) d(d + 5e) 2d(3d – e) d(3d + 2e) d2 + 5de 5d2 – 2de 2de + 8d 3d2 + 2de 2de + 4e 6d2 – 2de 18 Lengkapkan peta buih dengan faktor-faktor bagi 8k. TP3 BT ms. 28 Complete the bubble map with the factors of 8k. [4 markah/marks] Jawapan/Answer: 8k 8 4 2 k i-THINK Peta Buih Bahagian C / Section C 19 (a) Tentukan faktor sepunya terbesar (FSTB) bagi 15gh, 9fgh3 dan 12g3 . TP3 BT ms. 28 – 29 Determine the highest common factor (HCF) of 15gh, 9fgh3 and 12g3 . [3 markah/marks] Jawapan/Answer: 02 PT UASA MM Tg2.indd 11 25/01/2024 2:53 PM
12 (b) Faktorkan setiap yang berikut: TP3 BT ms. 29 – 31 Factorise each of the following: (i) 8m2 − 50n2 (ii) (s − 4)2 − 4 [3 markah/marks] Jawapan/Answer: (i) (ii) (c) Rajah 1 menunjukkan sebuah segi tiga bersudut tegak ABC. Diberi bahawa YC = 2h cm, AY = CZ = 4 cm dan BZ adalah separuh daripada panjang YC. TP4 BT ms. 32 Diagram 1 shows a right-angled triangle ABC. It is given that YC = 2h cm, AY = CZ = 4 cm and BZ is half the length of YC. A C 4 cm 4 cm 2h cm Z B Y Rajah 1/Diagram 1 (i) Hitung luas, dalam cm2 , kawasan berlorek. Calculate the area, in cm2 , of the shaded region. (ii) Diberi bahawa h = 2. Cari luas, dalam cm2 , kawasan berlorek. It is given that h = 2. Find the area, in cm2 , of the shaded region. [4 markah/marks] Jawapan/Answer: (i) (ii) 20 (a) Faktorkan setiap yang berikut: TP3 BT ms. 28 – 31 Factorise each of the following: (i) 3 – 12p2 (ii) 2y2 – 11y + 12 [3 markah/marks] Jawapan/Answer: (i) (ii) 02 PT UASA MM Tg2.indd 12 25/01/2024 2:53 PM
13 (b) Permudahkan setiap yang berikut: TP3 BT ms. 34 – 35 Simplify each of the following: (i) 2p 3 + 3q 7 (ii) p – 1 p – 2 – 3p2 p2 – 4 [4 markah/marks] Jawapan/Answer: (i) (ii) (c) Sebuah segi empat sama mempunyai luas (4x2 + 12x + 9) cm2 . Hitung perimeter, dalam cm, segi empat sama itu. TP4 BT ms. 32 A square has an area of (4x2 + 12x + 9) cm2 . Calculate the perimeter, in cm, of the square. [3 markah/marks] Jawapan/Answer: 21 (a) Permudahkan/Simplify: TP3 BT ms. 36 c – 3d 2b ÷ 3c2 – 9cd 4b2 – 10ab [3 markah/marks] Jawapan/Answer: 02 PT UASA MM Tg2.indd 13 25/01/2024 2:53 PM
14 (b) Siew Lin dapat menyiapkan (12 + 36x) soalan Matematik dalam masa 4 jam. Jika setiap soalan dijawab dalam tempoh masa yang sama, berapa lamakah masa yang diambil oleh Siew Lin untuk menyiapkan (21 + 63x) soalan? TP4 BT ms. 32 KBAT Mengaplikasi Siew Lin can complete (12 + 36x) Mathematics questions in 4 hours. If each question is completed within the same duration, how long does it take her to answer (21 + 63x) questions? [3 markah/marks] Jawapan/Answer: (c) Rajah 2 menunjukkan lakaran sebuah laman rumah oleh Encik Amri. TP4 BT ms. 32 Diagram 2 shows a sketch of the front yard designed by Encik Amri. Kolam ikan Fish pond 10 m r m p m Taman bunga Flower garden 30 m Rajah 2/Diagram 2 (i) Encik Amri ingin memagari sekeliling kolam ikan itu. Hitung perimeter, dalam m, pagar yang diperlukan. Encik Amri wants to fence up the fish pond. Calculate the perimeter, in m, of the fence needed. (ii) Kawasan taman bunga akan dipasang rumput tiruan. Jika harga rumput tiruan ialah RM15 per meter persegi, berapakah jumlah kos yang akan ditanggung oleh Encik Amri? Ungkapkan jawapan dalam bentuk ungkapan algebra. Artificial grass will be installed in the flower garden area. If the price of the artificial grass is RM15 per square metre, how much will Encik Amri incur? Express the answer in the form of algebraic expression. [4 markah/marks] Jawapan/Answer: (i) (ii) 02 PT UASA MM Tg2.indd 14 25/01/2024 2:53 PM
15 Bahagian A / Section A Rumus Algebra Algebraic Formulae 3.1 1 Diberi q2 = 1 9 p + r2 , maka r = Given that q2 = 1 9 p + r2 , then r = A q2 + 1 3 p C q2 – 1 3 p B q2 + 1 9 p D q2 – 1 9 p TP2 BT ms. 46 – 47 2 Diberi 4(5r – t) t = 3, maka t = Given that 4(5r – t) t = 3, then t = A 20r 7 C 7r 4 B 5r 7 D 5r 4 TP2 BT ms. 46 – 47 3 Diberi bahawa x = 3 + y z . Ungkapkan z sebagai perkara rumus. It is given that x = 3 + y z . Express z as the subject of the formula. A z = 3 + y x2 C z = 3 + y x B z = 3 + y x D z = 3 + y x2 TP2 BT ms. 46 – 47 4 Diberi bahawa p = 9 q2 + 1. Ungkapkan q dalam sebutan p. It is given that p = 9 q2 + 1. Express q in terms of p. A q = 9 p – 1 C q = 3 p – 1 B q = 3 p – 1 D q = 3 p – 1 TP2 BT ms. 46 – 47 5 Diberi bahawa 4q = 8p – 4pq. Ungkapkan q sebagai perkara rumus. It is given that 4q = 8p – 4pq. Express q as the subject of the formula. A q = 2p 1 + p C q = 1 + p 2p B q = 2p 1 – p D q = 1 – p 2p TP2 BT ms. 46 – 47 6 Diberi 2x – 4 3y = 2, ungkapkan y dalam sebutan x. Given that 2x – 4 3y = 2, express y in terms of x. A y = x – 4 12 C y = x – 2 6 B y = 2x – 4 12 D y = 2x – 4 6 TP2 BT ms. 46 – 47 7 Diberi bahawa p + 5q q – 3 = 8. Ungkapkan q sebagai perkara rumus. It is given that p + 5q q – 3 = 8. Express q as the subject of the formula. A q = p + 8 3 C q = p – 24 3 B q = p – 8 3 D q = p + 24 3 TP2 BT ms. 46 – 47 8 Sempena Pesta Buku Antarabangsa, sebuah buku rujukan Matematik yang berharga RMx diberi diskaun sebanyak RM2. Salmi membeli 6 buah buku rujukan tersebut dan membayar sebanyak RMQ, maka In conjunction with the International Book Fair, a Mathematics reference book that cost RMx is sold at a discount of RM2. Salmi buys 6 reference books and pays RMQ, then A Q = x – 12 C Q = 6x – 2 B Q = 6(x – 2) D Q = 2x – 6 TP2 BT ms. 44 – 45 3 BAB Rumus Algebra Algebraic Formulae Bidang Pembelajaran: Perkaitan dan Algebra 03 PT UASA MM Tg2.indd 15 25/01/2024 2:54 PM
16 9 Diberi E = mc2 , cari nilai c jika E = 250 dan m = 10. Given that E = mc2 , find the value of c if E = 250 and m = 10. A 2 B 3 C 5 D 25 TP3 BT ms. 47 – 48 10 Diberi bahawa 2m – 1 = n. Ungkapkan m dalam sebutan n. It is given that 2m – 1 = n. Express m in terms of n. A m = n2 2 + 1 C m = n2 + 1 4 B m = n2 4 + 1 D m = ( n 2 + 1) 2 TP2 BT ms. 46 – 47 11 Rajah 1 menunjukkan sebuah segi empat tepat. Diagram 1 shows a rectangle. (y + 1) cm (y – 3) cm Rajah 1/Diagram 1 Ungkapkan perimeter, P, dalam cm, bagi segi empat tepat itu dalam sebutan y. Express the perimeter, P, in cm, of the rectangle in terms of y. A P = 4y – 4 C P = 4y – 2 B P = 4y + 4 D P = 4y + 2 TP2 BT ms. 44 – 45 12 Bayaran tiket masuk ke sebuah taman tema untuk seorang kanak-kanak dan seorang dewasa masing-masing ialah RMx dan RMy. Ungkapkan jumlah bayaran tiket masuk, RMJ bagi 5 orang kanak-kanak dan 10 orang dewasa dalam sebutan x dan y. The price of an entry ticket to a theme park for a child and an adult are RMx and RMy respectively. Express the total entry ticket price, RMJ for 5 children and 10 adults in terms of x and y. A J = 5xy C J = 10x + 5y B J = 5x + 10y D J = 50xy TP2 BT ms. 44 – 45 13 Diberi k = 4 + m 4 – m , maka m = Given that k = 4 + m 4 – m , then m = A k + 1 1 – k C 4k – 4 1 + k B k – 1 1 + k D 4k + 4 1 – k TP2 BT ms. 46 – 47 Bahagian B / Section B 14 Tandakan ( ✓ ) pada perkara rumus yang betul dan ( ✗ ) pada perkara rumus yang salah bagi persamaan 2pr = (9q – 4r)s. TP2 BT ms. 46 – 47 Tick ( ✓ ) for the correct subject of the formula and ( ✗ ) for the incorrect subject of the formula for the equation 2pr = (9q – 4r)s. [4 markah/marks] Jawapan/Answer: (a) p = (9q – 4r)s 2r (b) q = 2r(p + 2) 9s (c) r = 9qs 2(p + 4s) (d) s = 2pr 9q – 4r 03 PT UASA MM Tg2.indd 16 25/01/2024 2:54 PM
17 15 Tulis Benar atau Palsu bagi rumus algebra yang diberi. TP2 BT ms. 44 – 45 Write True or False for the given algebraic formula. [4 markah/marks] Jawapan/Answer: Pernyataan Statement Rumus algebra Algebraic formula Jawapan Answer (a) r ialah hasil darab a dan x . r is the product of a and x . r = a x (b) w adalah kurang 5 daripada 2 kali jumlah x dan y. w is 5 less than 2 times the total of x and y. w = 2(x + y) – 5 (c) Hasil tambah dua nombor, m dan n ialah 12. The sum of two numbers, m and n is 12. m + n = 12 (d) Kuasa dua bagi x ialah 25. The square of x is 25. x = 25 Bahagian C / Section C 16 (a) Diberi m = 4n – 5 3 , Given that m = 4n – 5 3 , (i) ungkapkan n sebagai perkara rumus, TP2 BT ms. 46 – 47 express n as the subject of the formula, (ii) seterusnya, cari nilai n jika m = 3. TP3 BT ms. 47 – 48 hence, find the value of n if m = 3. [3 markah/marks] Jawapan/Answer: (i) (ii) (b) Jadual 1 menunjukkan kos petrol yang digunakan oleh tiga jenis kenderaan untuk jarak perjalanan yang sama. Table 1 shows the cost of petrol used by three types of vehicles travelling over the same distance. Jenis kenderaan Type of vehicle Motosikal Motorcycle Van Van Kereta Car Kos petrol (RM) Cost of petrol (RM) m t k Jadual 1/Table 1 03 PT UASA MM Tg2.indd 17 25/01/2024 2:54 PM
18 Jumlah kos petrol yang digunakan oleh sebuah kereta dan dua buah motosikal adalah sama dengan kos petrol yang digunakan oleh dua buah van. TP4 BT ms. 48 – 49 The total cost of petrol used by a car and two motorcycles is the same as the cost of petrol used by two vans. (i) Jika kos petrol yang digunakan oleh sebuah kereta ialah RM20 dan sebuah motosikal ialah RM5, cari kos petrol yang digunakan oleh sebuah van. If the cost of petrol used by a car is RM20 and a motorcycle is RM5, find the cost of petrol used by a van. (ii) Ungkapkan m dalam sebutan t dan k. Express m in terms of t and k. [4 markah/marks] Jawapan/Answer: (i) (ii) (c) Rajah 2 menunjukkan harga sebuah alat muzik yang ingin dibeli oleh Hafiy. Ibunya memberi wang sebanyak RM55 dan dia menyimpan sebanyak RM5 setiap minggu. TP4 BT ms. 48 – 49 Diagram 2 shows the price of a musical instrument that Hafiy wants to buy. His mother gives him RM55 and he saves RM5 every week. RM165 Rajah 2/Diagram 2 (i) Tulis rumus algebra untuk mewakili jumlah wang yang Hafiy ada selepas W minggu. Write an algebraic formula to represent the amount of money that Hafiy has after W weeks. (ii) Jika Hafiy ingin membeli alat muzik itu dalam masa 20 minggu, berapakah jumlah wang yang perlu disimpan oleh Hafiy pada setiap minggu? Tunjukkan jalan kerja anda dan nyatakan pemboleh ubah yang digunakan. If Hafiy wants to buy the musical instrument in 20 weeks, how much money must he save each week? Show your working and state the variables used. [3 markah/marks] Jawapan/Answer: (i) (ii) 03 PT UASA MM Tg2.indd 18 25/01/2024 2:54 PM
19 17 (a) Jumlah harga yang perlu dibayar oleh Melvin apabila membeli m kg durian dan n kg mangga ialah RMx. Harga bagi sekilogram durian dan sekilogram mangga masing-masing ialah RM10.90 dan RM4.30. TP4 BT ms. 48 – 49 The total price to be paid by Melvin for m kg of durians and n kg of mangoes is RMx. The price of 1 kg of durians and 1 kg of mangoes are RM10.90 and RM4.30 respectively. (i) Tulis satu rumus algebra berdasarkan situasi di atas. Write an algebraic formula based on the above situation. (ii) Melvin membuat bayaran dengan dua keping wang kertas RM50 dan menerima baki sebanyak RM22. Jika dia membeli 8 kg mangga, hitung jisim durian yang dibelinya. Melvin pays with two RM50 notes and receives RM22 in change. If he buys 8 kg of mangoes, calculate the mass of durians that he bought. [3 markah/marks] Jawapan/Answer: (i) (ii) (b) Diberi bahawa k = 10m2 n – 315./It is given that k = 10m2 n – 315. (i) Ungkapkan m sebagai perkara rumus./Express m as the subject of the formula. TP2 BT ms. 46 – 47 (ii) Cari nilai positif m apabila k = 165 dan n = 3. TP3 BT ms. 47 – 48 Find the positive value of m when k = 165 and n = 3. [4 markah/marks] Jawapan/Answer: (i) (ii) (c) Rajah 3 menunjukkan jisim bagi tiga buah buku. Diagram 3 shows the mass of three books. Cari nilai n jika n = 0.8m. TP4 BT ms. 48 – 49 Find the value of n if n = 0.8m. [3 markah/marks] Jawapan/Answer: 1.2m kg n kg 1.8 kg 0 3 4 2 1 kg 5 6 7 8 9 Rajah 3/Diagram 3 03 PT UASA MM Tg2.indd 19 25/01/2024 2:54 PM
J1 Praktis Topikal UASA Matematik Tingkatan 2 – Jawapan BAB 1 Pola dan Jujukan BAHAGIAN A 1 A –16, 8, –4, 2, –1, 0.5, … ÷(–2) ÷(–2) ÷(–2) ÷(–2) ÷(–2) 2 C M = 1 + 3 = 4 N = 4 + 6 = 10 M + N = 4 + 10 = 14 3 D p = 2 + 3 = 5 q = 5 + 8 = 13 q – p = 13 – 5 = 8 4 C 3, 8, 13, 18, … +5 +5 +5 16, 21, 26, 31, … +5 +5 +5 5 D 2, 3, 5, 8, 13, ... 2 + 3 3 + 5 5 + 8 6 C 11, 16, 21, 26, 31, 36, 41, 46 … +5 +5 +5 +5 +5 +5 +5 Nombor ganjil/Odd numbers: 11, 21, 31, 41, … +10 +10 +10 7 A +2 +2 +2 +2 +2 +2 2, 4, 6, 8, 10, 12, 14, … Maka, bilangan segi tiga sama sisi = 14 Thus, the number of equilateral triangles = 14 8 C –4 –4 –4 –4 10, 6, 2, –2, –6, … 9 A +4 +4 +4 +4 +4 –27, –23, –19, –15, –11, –7, … 10 D 2.3, 2.7, 3.1, 3.5, 3.9, … +0.4 +0.4 +0.4 +0.4 11 B 89, 83, 77, 71, 65, 59, 53, 47, 41, ... –6 –6 –6 –6 –6 –6 –6 –6 T9 = 41 12 C 9, 2, –5, –12, –19, –26, –33, –40, –47, –54... –7 –7 –7 –7 –7 –7 –7 –7 –7 T4 – T6 = –12 – (–26) = 14 13 D 1 2 , 1 4 , 1 8 , 1 16, 1 32, 1 64, 1 128 , 1 256 , … × 1 2 × 1 2 × 1 2 × 1 2 × 1 2 × 1 2 × 1 2 T8 = 1 256 (b) × (–2) × (–2) × (–2) 1.3, –2.6, 5.2, –10.4, … Mendarab nombor sebelumnya dengan –2. Multiply the previous number by –2. BAHAGIAN C 23 (a) (i) Menambah 7 kepada nombor sebelumnya Add 7 to the previous number (ii) Menolak 10 daripada nombor sebelumnya Subtract 10 from the previous number (b) (i) –23, –16, –9, –2, 5, 12, 19, … +7 +7 +7 +7 +7 +7 (ii) 78, 66, 54, 42, 30, 18, … –12 –12 –12 –12 –12 –12 (c) (i) (ii) 2, 5, 8, 11, 14, 17, 20, … +3 +3 +3 +3 +3 +3 Bilangan butang pada corak ke-7 = 20 Number of buttons in the 7th pattern = 20 (iii) 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, ... +3 +3 +3 +3 +3 +3 +3 +3 +3 +3 +3 Maka, bilangan butang ialah 35 pada corak ke-12. The number of buttons is 35 in the 12th pattern. 24 (a) (i) 5 + 8 = 13 (ii) 2 + 4 = 6 (iii) 4 + 7 = 11 (iv) 25 + 39 = 64 (b) Beza bilangan jubin: Difference of the number of tiles: Corak 1/Pattern 1 = 2 – 1 = 1 Corak 2/Pattern 2 = 4 – 2 = 2 Corak 3/Pattern 3 = 6 – 3 = 3 Corak 4/Pattern 4 = 8 – 4 = 4 Corak 32/Pattern 32 = 64 – 32 = 32 Maka, beza bilangan jubin bagi corak ke-32 ialah 32. Thus, the difference of the number of tiles in the 32nd pattern is 32. (c) (i) T1 = 1 = 12 T2 = 4 = 22 T3 = 9 = 32 Tn = n2 , n = 1, 2, 3, … (ii) 8n = n2 8n = n × n n = 8 14 C 34, 42, 50, 58, 66, 74, 82, … +8 +8 +8 +8 +8 +8 T5 + T7 = 66 + 82 = 148 15 A –5, –1, 3, 7, 11, 15, 19, 23, 27, 31, … +4 +4 +4 +4 +4 +4 +4 +4 +4 T10 = 31 16 B T9 = 9[5(9) – 7] = 342 17 D 24 3 = 8 jam/hours T1 = 7:30 a.m. T2 = 7: 30 a.m. + 8 jam/hours = 3:30 p.m. T3 = 3: 30 a.m. + 8 jam/hours = 11:30 p.m. 18 D T1 = 10 – 3(1) = 7 T2 = 10 – 3(2) = 4 T3 = 10 – 3(3) = 1 19 B Tn = 500 + 13(n − 1 ) dengan keadaan/ where n = 1, 2, 3, … 760 = 500 + 13n − 13 13n = 273 n = 21 BAHAGIAN B 20 (a)+9 +9 +9 +9 +9 –53, –44, –35 , –26, –17 , –8, … (b) +3 +3 +3 +3 1, 4, 7, 10, 13, … ×3 ×3 ×3 ×3 2, 6, 18, 54, 162, … 21 3, 5, 7, 9, 11, … n − 1, n = 1, 2, 3, … 5n − 1, n = 1, 2, 3, … –3, 9, –27, 81, … 2(n – 1), n = 1, 2, 3, ... 0, 2, 4, 6, 8, … n + 2, n = 1, 2, 3, ... 4, 9, 14, 19, 24, … (–3)n, n = 1, 2, 3, ... 1 + 2n, n = 1, 2, 3, ... 22 (a) +5 +5 +5 9, 14, 19, 24, … Menambah 5 kepada nombor sebelumnya. Add 5 to the previous number. Jawapan 15 JAW_PT UASA MM Tg2.indd 1 25/01/2024 2:57 PM