Bab 6 Nisbah dan Graf Fungsi Trigonometri 41 – 46 Ratios and Graphs of Trigonometric Functions Bab 7 Sukatan Serakan Data Terkumpul 47 – 55 Measures of Dispersion for Grouped Data Bab 8 Pemodelan Matematik 56 – 58 Mathematical Modeling Bab 1 Ubahan 1 – 8 Variation Bab 2 Matriks 9 – 18 Matrices Bab 3 Matematik Pengguna: Insurans 19 – 25 Consumer Mathematics: Insurance Bab 4 Matematik Pengguna: Percukaian 26 – 34 Consumer Mathematics: Taxation Bab 5 Kekongruenan, Pembesaran dan Gabungan Transformasi 35 – 40 Congruency, Enlargement and Combined Transformations Penerbit Ilmu Bakti Sdn. Bhd. (732516-M) No. 18, Jalan PJS 5/26, Taman Desaria, 46150 Petaling Jaya, Selangor Darul Ehsan. Tel: 03-7783 3233, 7783 5233 Faks: 03-7783 7233 E-mel: [email protected] Laman web: www.penerbitilmubakti.com © Penerbit Ilmu Bakti Sdn. Bhd. (732516-M) 2024 Pertama kali diterbitkan 2024 ISBN 978- Cetakan: 9 8 7 6 5 4 3 2 1 Semua hak cipta terpelihara. Sebarang bahagian dalam buku ini tidak boleh diterbitkan semula, disimpan dalam cara yang boleh digunakan lagi, ataupun dipindahkan dalam sebarang bentuk atau cara, baik secara elektronik, mekanik, gambar, rakaman dan sebagainya,tanpa kebenaran terlebih dahulu daripada Penerbit Ilmu Bakti Sdn. Bhd. (732516-M). Penyunting: Aznani Hasnor Binti Ahmad Pereka kulit buku: Sarifuddin Yusof Pereka letak: Jessica Choo Text set in Utopia 10/12 points Printed in Malaysia by Kertas Model SPM 59 – 80 Jawapan J1 – J14 Kandungan Tk 5 24 PT Math kandungan.indd 1 2/6/2024 12:39:24 PM Penerbit Ilmu Bakti Sdn. Bhd. (732516-M) No. 18, Jalan PJS 5/26, Taman Desaria, 46150 Petaling Jaya, Selangor Darul Ehsan. Tel: 03-7783 3233, 7783 5233 Faks: 03-7783 7233 Emel: [email protected] Laman web: www.penerbitilmubakti.com © Penerbit Ilmu Bakti Sdn. Bhd. (732516-M) 2024 Pertama kali diterbitkan 2024 ISBN 978-629-473-334-3 Cetakan: 9 8 7 6 5 4 3 2 1 Semua hak cipta terpelihara. Sebarang bahagian dalam buku ini tidak boleh diterbitkan semula, disimpan dalam cara yang boleh digunakan lagi, ataupun dipindahkan dalam sebarang bentuk atau cara, baik secara elektronik, mekanik, gambar, rakaman dan sebagainya, tanpa kebenaran terlebih dahulu daripada Penerbit Ilmu Bakti Sdn. Bhd. (732516-M). Penyunting: Aznani Hasnor binti Ahmad Pereka kulit buku: Sarifuddin Yusof Pereka letak: Jessica Choo Teks diset dalam Utopia Std 10/12 poin Dicetak di Malaysia oleh Commercial Book Binders Sdn. Bhd.
1 1.1 Ubahan Langsung / Direct Variation 1 Diberi bahawa m berubah secara langsung dengan n2 dan m = 50 apabila n = 10. Ungkapkan m dalam sebutan n. It is given that m varies directly as n2 and m = 50 when n = 10. Express m in terms of n. A m = 1 2 n2 C m = 1 50n2 B m = n2 D m = 50n2 TP 3 BT ms.8 2 Diberi bahawa c berubah secara langsung dengan kuasa dua d dan c = 125 apabila d = 5. Ungkapkan c dalam sebutan d. It is given that c varies directly as the square of d and c = 125 when d = 5. Express c in terms of d. A c = 1 5 d2 C c = 2d2 B c = d2 D c = 5d2 TP 3 BT ms.8 3 Rajah 1 menunjukkan graf arus, I (miliampere, mA) melawan voltan V (volt, V) untuk sebuah perintang. Diagram 1 shows the graph of current, I (milliampere, mA) against voltage (volt, V) for a resistor. O I (mA) V (V) Rajah 1/Diagram 1 Diberi bahawa arus, I = 12 mA apabila V = 3 V. Berapakah nilai arus, I, apabila V = 4.5 V? Given that the current, I = 12 mA when V = 3 V. What is the value of current, I, when V = 4.5 V? A 0.25 mA C 18 mA B 4 mA D 36 mA TP 4 BT ms.11–12 1.2 Ubahan Songsang / Inverse Variation 4 Diberi bahawa p = 30 apabila q = 0.3. Ungkapkan p dalam sebutan q jika p berubah secara songsang dengan q3 . It is given that p = 30 when q = 0.3. Express p in terms of q if p varies inversely as q3 . A p = 0.81q2 C p = 0.81 q3 B p = 100q2 D m = 100 q3 TP 3 BT ms.19–22 5 Jadual manakah yang mewakili x ∝ 1 y 3 ? Which table represents x ∝ 1 y 3 ? A x 2 1 8 2 27 y 1 2 3 B x 1 27 1 32 3 125 y 3 4 5 C x 1 4 2 27 1 32 y 2 3 4 D x 3 64 2 4 1 108 y 4 5 6 TP 3 BT ms.22 6 Diberi bahawa m berubah secara songsang dengan punca kuasa dua n dan m = 1 apabila n = 100. Hitung nilai m apabila n = 4. It is given that m varies inversely as the square root of n and m = 1 when n = 100. Calculate the value of m when n = 4. A 0.25 C 2 B 1 D 5 TP 3 BT ms.22–23 7 Jadual 1 menunjukkan nilai pemboleh ubah p dan q dengan keadaan p berubah secara songsang dengan punca kuasa tiga q. Table 1 shows the values of variables p and q such that p varies inversely as the cube root of q. p 4 16 q 8 1 8 Jadual 1/Table 1 Bab 1 Ubahan Variation Bidang Pembelajaran: Perkaitan dan Algebra Tk 5 24 PT Math 1(1-8).indd 1 2/6/2024 12:33:35 PM
2 Ungkapkan p dalam sebutan q. Express p in terms of q. A p = 32 q C p = 2 q3 B p = 8 3 q D p = 83 q TP 3 BT ms.22–23 8 Diberi bilangan hari, n, yang diperlukan untuk menyiapkan suatu projek Matematik bagi setiap kumpulan berubah secara songsang dengan bilangan murid, m, dalam kumpulan itu. Jika projek itu dapat disiapkan dalam tempoh 14 hari oleh 5 orang murid, ungkapkan n dalam sebutan m. Given that the number of days, n, required to complete a Mathematics project for each group varies inversely as the number of students, m, in the group. If the project can be completed in 14 days by 5 students, express n in terms of m. A n = 70k m C n = 70m B n = 1 70m D n = 70 m TP 4 BT ms.22–23 9 Diberi bahawa m berubah secara songsang dengan punca kuasa tiga n dan m = 3 apabila n = 1 125 . Hitung nilai m apabila n = 216. Given that m varies inversely as the cube root of n and m = 3 when n = 1 125 . Calculate the value of m when n = 216. A 1 10 C 5 B 1 5 D 10 TP 3 BT ms.23 10 Jadual 2 menunjukkan beberapa nilai bagi pemboleh ubah x dan y. Table 2 shows some values of variables x and y. x 5 p y 1 2 2 Jadual 2/Table 2 Diberi bahawa y berubah secara songsang dengan kuasa dua x. Hitung nilai p. It is given that y varies inversely as the square of x. Calculate the value of p. A 10 C 2.5 B 5 D 0.5 TP 4 BT ms.23 1.3 Ubahan Bergabung / Combined Variation 11 Diberi bahawa p berubah secara langsung dengan punca kuasa tiga q dan secara songsang dengan kuasa dua r. Jika ubahan itu diwakili oleh p ∝ qmr n, nyatakan nilai m dan nilai n. It is given that p varies directly as the cube root of q and varies inversely as the square of r. If the variation is represented as p ∝ qmr n, state the value of m and of n. A m = 1 3 , n = 2 B m = 1 3 , n = –2 C m = 3, n = 2 D m = 3, n = –2 TP 4 BT ms.27–28 12 Jadual 3 menunjukkan beberapa nilai pemboleh ubah x, y dan z dengan keadaan x berubah secara langsung dengan kuasa dua y dan secara songsang dengan z. Table 3 shows some values of variables x, y and z such that x varies directly as the square of y and inversely as z. x y z 8 6 9 p 3 6 Jadual 3/Table 3 Hitung nilai p. Calculate the value of p. A 2 C 5 B 3 D 9 TP 4 BT ms.27–28 13 Jadual 4 menunjukkan nilai P, M dan R. Diberi bahawa P berubah secara langsung dengan M dan berubah secara songsang dengan punca kuasa dua R. Table 4 shows the values of P, M and R. Given that P varies directly with M and varies inversely with the square root of R. P 5 2 M 6 4 R 9 k Jadual 4/Table 4 Hitung nilai k. Calculate the value of k. A 5 C 25 B 8 D 35 TP 4 BT ms.27–28 Tk 5 24 PT Math 1(1-8).indd 2 2/6/2024 12:33:35 PM
3 1 Tenaga kinetik suatu zarah, E, berubah secara langsung dengan kuasa dua kelajuannya, v. Tenaga kinetik zarah itu ialah 200 joule jika bergerak pada kelajuan 5 m s–1. Cari kelajuan zarah itu jika ia mempunyai tenaga kinetik 650 joule. TP 4 BT ms.8–9 The kinetic energy of a particle, E, varies directly as the square of its speed, v. The kinetic energy of the particle is 200 joules if it is moving at a speed of 5 m s–1. Find the speed of the particle if it has a kinetic energy of 650 joules. [4 markah/marks] Jawapan/Answer: 2 Luas sebuah sektor bulatan, A berubah secara langsung dengan sudut sektor, u dan kuasa dua jejari, r. Luas sektor bulatan berjejari 6 cm dengan sudut pada pusat 11 6 radian ialah 33 cm2 . BT ms.15–16 The area of a sector of a circle, A varies directly as the angle of the sector, u, and the square of the radius, r. The area of the sector with radius 6 cm and the angle at the centre of 11 6 radian is 33 cm2 . (a) Ungkapkan A dalam sebutan u dan r. TP 3 Express A in terms of u and r. (b) Cari luas sektor bagi suatu bulatan dengan jejari 7 cm dan sudut pada pusat 1.8 radian. TP 4 Find the area of a sector of a circle with the radius of 7 cm and the angle at the centre of 1.8 radian. [4 markah/marks] Jawapan/Answer: 1.1 Ubahan Langsung / Direct Variation Bahagian A / Section A Tk 5 24 PT Math 1(1-8).indd 3 2/6/2024 12:33:35 PM
4 1.2 Ubahan Songsang / Inverse Variation 3 Apabila suatu objek ditarik dengan satu daya malar, pecutan objek itu berubah secara songsang dengan jisimnya. Objek yang berjisim 4 kg akan bergerak dengan pecutan 1.5 m s–2. Cari pecutan objek itu jika jisimnya ialah 10 kg. TP 4 BT ms.25 When an object is pulled by a constant force, the acceleration of the object varies inversely with its mass. An object with a mass of 4 kg will move with an acceleration of 1.5 m s–2. Find the acceleration of the object if its mass is 10 kg. [4 markah/marks] Jawapan/Answer: 4 Rajah 1 menunjukkan suatu litar elektrik yang digunakan untuk mengkaji hubungan antara arus, I dengan panjang dawai nikrom, L. Jadual 1 menunjukkan nilai pemboleh ubah L dan I dengan keadaan I berubah secara songsang dengan L. TP 5 BT ms.25 Diagram 1 shows an electrical circuit used to study the relationship between current, I and the length of the nichrome wire, L. Table 1 shows the value of variables L and I such that I varies inversely as L. A 6V Bateri Battery Ammeter Ammeter P Q L Dawai nikrom Nichrome wire Rajah 1/Diagram 1 Jadual 1/Table 1 L (cm) 60 m I (A) 1.5 4.0 Cari nilai m. Find the value of m. [4 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 1(1-8).indd 4 2/6/2024 12:33:36 PM
5 1.3 Ubahan Bergabung / Combined Variation 5 Sebuah motor mengelilingi suatu selekoh semasa perlumbaan motor. Daya memusat yang bertindak berubah secara langsung dengan kuasa dua laju motor itu dan secara songsang dengan jarak motor dari pusat selekoh. Daya memusat F bertindak ke atas motor yang bergerak dengan laju v km/j pada jarak r km dari pusat selekoh. Hitung daya memusat, dalam sebutan F, yang bertindak jika motornya bergerak dengan laju 1 3 v km/j pada jarak 2r km dari pusat selekoh. KBAT Menilai TP 5 BT ms.28–29 A motorbike is going around a corner during a motor race. The centripetal force varies directly as the square of motorbike’s speed and varies inversely as the distance of the motorbike from the centre of the corner. The centripetal force, F acts on the motorbike moving at speed v km/h at a distance r km from the centre of the corner. Calculate the centripetal force, in terms of F acted if the motor is moving at a speed of 1 3 v km/j at a distance of 2r km from the centre of the corner. [5 markah/marks] Jawapan/Answer: Bahagian B / Section B 6 Frekuensi, f MHz, gelombang radio berubah secara songsang dengan panjang gelombang, λ m. Frekuensi gelombang radio yang mempunyai panjang gelombang 200 m ialah 100 MHz. Cari KBAT Mengaplikasi BT ms.25 The frequency, f MHz, of a radio wave varies inversely as its wavelength, λ m. The frequency of a radio wave that has a wavelength of 200 m is 100 MHz. Find (a) frekuensi gelombang radio yang mempunyai panjang gelombang 500 m, TP 4 the frequency of a radio wave that has a wavelength of 500 m, (b) panjang gelombang radio yang mempunyai frekuensi 80 MHz. TP 4 the wavelength of a radio wave that has a frequency of 80 MHz. [8 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 1(1-8).indd 5 2/6/2024 12:33:36 PM
6 7 Panjang seutas dawai konstantan P ialah dua kali panjang dawai konstantan Q dan nisbah diameter dawai P kepada dawai Q ialah 1 : 3. Diberi bahawa rintangan dawai berubah secara langsung dengan panjang dan secara songsang dengan kuasa dua diameter, cari nisbah rintangan dawai P kepada dawai Q. KBAT Menilai TP 6 BT ms.28–29 The length of a constantan wire P is twice of the constantan wire Q and the ratio of the diameter of wire P to wire Q is 1 : 3. Given that the resistance of the wire varies directly as the length and inversely as the square of the diameter, find the resistance ratio of wire P to wire Q. [9 markah/marks] Jawapan/Answer: 8 Masa yang diambil untuk memotong rumput di sebuah padang berubah secara langsung dengan luas padang dan secara songsang dengan bilangan pekerja. Diberi bahawa lima orang pekerja memerlukan 3 jam untuk memotong rumput di padang seluas 4 × 104 m2 . BT ms.28–29 The time taken to mow a lawn varies directly as the field area and inversely as the number of workers. Given that five workers need 3 hours to mow the grass of a 4 × 104 m2 field area. (a) Hitung masa yang diambil oleh tiga orang pekerja untuk memotong rumput di padang seluas 2 × 104 m2 . TP 4 Calculate the time taken by three workers to mow the grass of a field of 2 × 104 m2 . (b) Hitung bilangan pekerja yang diperlukan untuk memotong rumput di padang seluas 8 × 104 m2 dalam masa 5 jam. TP 4 Calculate the number of workers required to mow the grass of a 8 × 104 m2 field in 5 hours. [8 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 1(1-8).indd 6 2/6/2024 12:33:36 PM
7 9 Sebuah roket dilancarkan menegak dari permukaan bumi. Apabila roket semakin jauh dari permukaan bumi, kekuatan medan graviti, g, semakin berkurang. Kekuatan medan graviti berubah secara songsang dengan kuasa dua jarak dari pusat bumi, r. Diberi kekuatan medan graviti di atas permukaan ialah 10 N kg–1 dengan jejari bumi 6 400 km. Hitung kekuatan medan graviti yang dikenakan terhadap roket yang berada 12 800 km dari pusat bumi. KBAT Menilai TP 5 BT ms.25 A rocket is launched straight up from the Earth's surface. As the rocket is farther from the Earth's surface, the gravitational field strength, g, decreases. The gravitational field strength varies inversely as the square of the distance from the centre of the Earth, r. Given that the gravitational field strength on the Earth's surface is 10 N kg–1 with the Earth's radius of 6 400 km. Calculate the the gravitational field strength acted on the rocket at 12 800 km from the centre of the earth. [8 markah/marks] Jawapan/Answer: Bahagian C / Section C 10 (a) Daya memusat, F yang bertindak ke atas suatu jasad yang bergerak dalam satu bulatan berubah secara langsung dengan kuasa dua lajunya, v dan secara songsang dengan jejari bulatan, r. Daya memusat 18 N bertindak ke atas jasad itu yang bergerak dengan laju 3 m s–1 pada bulatan berjejari 0.1 m. BT ms.28–29 Centripetal force, F which acts on a moving body in a circle varies directly to the square of its speed, v and inversely to the radius of the circle, r. P Q O r F v v fi The centripetal force of 18 N acts on the moving body at a speed of 3 m s–1 in a circle of radius of 0.1 m. (i) Ungkapkan F dalam sebutan v dan r. TP 3 Express F in terms of v and r. (ii) Cari laju jasad yang mengelilingi suatu bulatan berjejari 4 m dengan daya memusat 12.8 N. TP 5 Find the speed of the body that moves around a circle of radius 4 m with centripetal force of 12.8 N. [6 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 1(1-8).indd 7 2/6/2024 12:33:36 PM
8 (b) Tempoh ayunan, T, bagi suatu bandul ringkas berubah secara langsung dengan punca kuasa dua panjang tali bandul, l, dan secara songsang dengan punca kuasa dua pecutan graviti, g. Suatu bandul ringkas dengan panjang 0.4 m berayun dengan tempoh 1.26 saat pada permukaan bumi. Jika bandul ringkas yang panjangnya 0.9 m berayun di permukaan bulan, tempoh ayunannya ialah 4.73 saat. Hitung pecutan graviti di permukaan bulan. [Pecutan graviti di permukaan bumi ialah 10 m s–2] KBAT Menilai TP 5 BT ms.28–29 The oscillation period, T, of a simple pendulum varies directly as the square root of the length of pendulum l, and inversely as square root of gravitational acceleration, g. A simple pendulum of length 0.4 m oscillates at a period of 1.26 seconds on the Earth's surface. If a simple pendulum of length 0.9 m oscillates on the moon's surface, the period of oscillation is 4.73 seconds. Calculate the acceleration of gravity on the surface of the moon. [Acceleration of gravity on the earth's surface is 10 m s–2] [9 markah/marks] Jawapan/Answer: Zon KBAT 1 Rajah di sebelah menunjukkan sebuah piramid bertapak segi empat sama. The diagram on the right shows a square base pyramid. Tinggi piramid itu, h, berubah secara songsang dengan kuasa dua panjang sisi tapak, x. Diberi bahawa tinggi dan panjang tapak itu masing-masing ialah 9 cm dan 6 cm. Hitung panjang tapak piramid yang mempunyai tinggi 4 cm. KBAT Menilai TP 5 BT ms.25 The height of the pyramid, h, varies inversely as the square of the length of the base, x. Given that the height and the length of base is 9 cm and 6 cm respectively. Calculate the base dimension of the pyramid having a height of 4 cm. x cm h cm l Tk 5 24 PT Math 1(1-8).indd 8 2/6/2024 12:33:36 PM
9 2.1 Matriks / Matrices 1 Antara yang berikut, yang manakah merupakan matriks 1 × 3? Which of the following is a 1 × 3 matrix? A [4 2 3] C 1 2 3 6 5 4 B – 5 7 8 D – 12 14 11 8 7 9 TP 2 BT ms.38–39 2 Jadual 1 menunjukkan skor yang diperoleh tiga buah pasukan. Table 1 shows the scores obtained by three groups. Pasukan Group P Q R Skor Score 115 121 108 Jadual 1/Table 1 Wakilkan maklumat di atas dalam bentuk matriks. Represent the data above in matrix form. A P Q R 115 121 108 C – 108 121 115 B [115 121 108] D – 15 121 108 TP 1 BT ms.36–37 3 Diberi bahawa A = 4 7 dan B = 3 1 0 10 5 –4 . Hitung A21 × B12. It is given that A = 4 7 and B = 3 1 0 10 5 –4 . Calculate A21 × B12. A 4 C 20 B 7 D 35 TP 3 BT ms.39-40 4 Diberi bahawa matriks P = 3x 10 2 5x – y dan matriks Q = 27 10 2 32 . Tentukan nilai y jika P = Q. Given that matrix P = 3x 10 2 5x – y and matrix Q = 27 10 2 32 . Determine the value of y if P = Q. A 6 C 13 B 9 D 15 TP 2 BT ms.40–41 2.2 Operasi Asas Matriks Basic Operation on Matrices 5 Diberi V = 7 1 2 3 , hitung V2 . Given V = 7 1 2 3 , calculate V 2. A 14 2 4 6 C 51 10 20 11 B 49 1 16 9 D 49 7 14 2 TP 3 BT ms.48–49 6 Diberi bahawa R = –3 –5 6 4 , S = 0 1 7 5 dan I = 1 0 0 1 . Hitung 2R + SI. KBAT Menilai Given that R = –3 –5 6 4 , S = 0 1 7 5 and I = 1 0 0 1 . Calculate 2R + SI. A –3 –4 13 9 C –6 –9 19 13 B –6 –10 12 8 D –2 –5 13 10 TP 4 BT ms.58–60 7 Diberi bahawa A = 6 3 9 3 dan I = 1 0 0 1 . Cari AI + IA. Given that A = 6 3 9 3 and I = 1 0 0 1 . Find AI + IA. A 6 3 9 3 C 5 3 9 2 B 12 6 18 6 D –6 –3 –9 –3 TP 3 BT ms.58–60 Bab 2 Matriks Matrices Bidang Pembelajaran: Perkaitan dan Algebra Tk 5 24 PT Math 2(9-18).indd 9 2/6/2024 12:34:19 PM
10 8 Diberi bahawa penentu kepada matriks a 10 11 10 ialah 30. Cari nilai a. Given that the determinant of matrix a 10 11 10 is 30. Find the value of a. A 11 B 12 C 13 D 14 TP 3 BT ms.60–62 9 Diberi bahawa [h 3] – [2 k] = [–4 –6], cari nilai h + k. Given that [h 3] – [2 k] = [–4 –6], find the value of h + k. A 5 C 7 B 6 D 10 TP 4 BT ms.44 10 Diberi persamaan serentak 2x = y + 6 dan 3y = 4x – 8 . Susun persamaannya dalam bentuk matriks. Given the simultaneous equations 2x = y + 6 and 3y = 4x – 8. Arrange the equation in the form of matrix. A 2 –1 –4 3 x y = 6 8 B 2 –1 4 –3 x y = 6 –8 C 2 1 –4 3 x y = 6 –8 D 2 –1 4 –3 x y = 6 8 TP 3 BT ms.62–64 11 Kedai Adam membeli 12 karton minuman anggur dan 15 karton minuman strawberi. Kedai Basri membeli 18 karton minuman anggur dan 9 karton minuman strawberi. Setiap karton minuman anggur berharga RM28 dan setiap karton minuman strawberi berharga RM25. Antara berikut, yang manakah kaedah yang betul untuk mengira jumlah bayaran bagi kedai Adam, x dan kedai Basri, y? Adam’s shop bought 12 cartons of grape drinks and 15 cartons of strawberry drinks. Basri’s shop bought 18 cartons of grape drinks and 9 cartons of strawberry drinks. Each carton of grape drink costs RM28 and each carton of strawberry drink costs RM25. Which of the following is the correct method to calculate the total payment to be made by Adam’s shop, x and Basri’s shop, y? A 12 18 15 9 28 25 = x y B 12 15 18 9 25 28 = x y C 12 18 15 9 25 28 = x y D 12 15 18 9 28 25 = x y TP 3 BT ms.62–64 12 7 4 –3 2 – 3 k 3 1 0 = 1 –5 –6 2 . Cari nilai k. Find the value of k. A –2 C 4 B 2 D 6 TP 4 BT ms.53 13 Diberi bahawa [2k 5] 4 –3k = [ –21 ], cari nilai k. Given that [2k 5] 4 –3k = [ –21 ], find the value of k. A 1 C 3 B 2 D 4 TP 4 BT ms.53 14 [5 –6 3] – [2 5 –8] + 3[–1 4 3] = A [2 –7 14] C [0 1 20] B [2 3 –2] D [0 11 4] TP 3 BT ms.46–49 15 – 3 2 –4 0 5 1 2 –6 = A – –6 –8 4 C – 6 –12 –8 0 10 –6 B – 5 –8 4 D – 6 4 24 0 10 2 TP 3 BT ms.50–53 16 6 1 4 3 –3 5 = A –13 3 C –18 5 –12 15 B –21 35 D –18 –3 20 15 TP 3 BT ms.50–53 17 [4 9] – [–3 2] + 1 2 [8 6] = A [15 13] C [5 13] B [11 10] D [11 12] TP 3 BT ms.48–49 18 Jika [2 3] 3k –k = [ 12 ], maka k = If [2 3] 3k –k = [ 12 ], then k = Tk 5 24 PT Math 2(9-18).indd 10 2/6/2024 12:34:19 PM
11 A 1 4 C 4 B 4 3 D 6 TP 3 BT ms.51–53 19 Diberi bahawa [2m 5] 4 –3 = [9], cari nilai m. Given that [2m 5] 4 –3 = [9], find the value of m. A 1 C 3 B 2 D 4 TP 4 BT ms.53 20 Jika [2m –4] 3 –m = [ 70 ], maka m = If [2m –4] 3 –m = [ 70 ], then m = A 35 C 7 B 8 D –7 TP 4 BT ms.53 21 [5 x] 8 –1 = [19 + 2x] Cari nilai x. Find the value of x. A 7 C –7 B 5 D 21 TP 3 BT ms.53 22 Diberi bahawa 3[4 p] + q[–1 5] = [14 5], cari nilai p + q. Given that 3[4 p] + p[–1 5] = [14 5], find the value of p + q. A –7 C 3 B –3 D 7 TP 4 BT ms.53 23 Diberi 5 –2 –7 3 L = 1 0 0 1 . Cari matriks L. Given 5 –2 –7 3 L = 1 0 0 1 . Find the matrix L. A 3 2 7 5 C 3 –7 –2 5 B 5 2 7 3 D –5 –7 –2 –3 TP 3 BT ms.59–61 24 Diberi matriks songsang bagi 6 m –2 –1 ialah 1 k –1 –4 2 n . Cari nilai m dan k. Given the inverse of 6 m –2 –1 is 1 k –1 –4 2 n . Find the values of m and k. A m = 4, k = –14 C m = –4, k = 2 B m = 4, k = 2 D m = –4, k = –2 TP 3 BT ms.59–61 25 Diberi bahawa P 8 –3 4 –2 = 1 0 0 1 , dan P ialah matriks 2 × 2. Cari matriks P. It is given that P 8 –3 4 –2 = 1 0 0 1 , and P is a 2 × 2 matrix. Find the matrix P. A 1 4 –2 3 –4 8 C – 1 4 –2 3 –4 8 B 1 4 2 –4 3 –8 D – 1 4 2 –4 3 –8 TP 3 BT ms.59–61 26 Matriks songsang bagi 3 –5 5 –9 ialah k –9 5 –5 p . Cari nilai k dan p. The inverse matrix of 3 –5 5 –9 is k –9 5 –5 p . Find the values of k and p. A k = – 1 2 , p = –3 C k = 1 2 , p = –3 B k = – 1 2 , p = 3 D k = 1 2 , p = 3 1 SMK Pekan mempunyai tiga buah kelas Tingkatan 5 aliran Sains. Tingkatan 5 Amanah terdiri daripada 26 orang murid lelaki dan 20 orang murid perempuan, Tingkatan 5 Bestari terdiri daripada 17 orang murid lelaki dan 26 orang murid perempuan, dan Tingkatan 5 Cekal pula terdiri daripada 20 orang murid lelaki dan 18 orang murid perempuan. Bentukkan satu matriks yang mewakili maklumat yang diberi. TP 3 BT ms.37 SMK Pekan has three Form 5 Science stream classes. Form 5 Amanah has 26 boys and 20 girls, Form 5 Bestari has 17 boys and 26 girls, and Form 5 Cekal has 20 boys and 18 girls. Form a matrix to represent the given information. [2 markah/marks] 2.1 Matriks / Matrices Bahagian A / Section A Tk 5 24 PT Math 2(9-18).indd 11 2/6/2024 12:34:20 PM
12 Jawapan/Answer: 2.2 Operasi Asas Matriks / Basic Operation on Matrices 2 Semasa hari kantin sekolah, sekolah itu menjual kupon makanan berharga RMx sekeping dan kupon minuman berharga RMy sekeping. Hui Thing membelanjakan RM28 untuk 5 kupon makanan dan 6 kupon minuman. Xin Yee membelanjakan RM41 untuk 7 kupon makanan dan 9 kupon minuman. Dengan menggunakan kaedah matriks, hitung nilai x dan nilai y. KBAT Menilai TP 4 BT ms.64–65 During the school canteen day, the school was selling food coupons of RMx each and drink coupons of RMy each. Hui Thing spent RM28 on 5 food coupons and 6 drink coupons. Xin Yee spent RM41 on 7 food coupons and 9 drink coupons. Using the matrix method, calculate the value of x and of y. [4 markah/marks] Jawapan/Answer: 3 Jumlah umur Jerrine dan ibunya ialah 56 tahun. Dua tahun lalu umur ibu Jerrine ialah tiga kali umur Jerrine. Diberi umur Jerrine dan ibunya kini masing-masing ialah x tahun dan y tahun. TP 4 BT ms.64–65 The sum of the ages of Jerrine and her mother is 56 years. Two years ago, Jerrine’s mother was three times as old as Jerrine. Given that Jerrine and her mother present ages are x years and y years respectively. (a) Tulis dua persamaan linear dalam sebutan x dan y. Write two linear equations in terms of x and y. (b) Seterusnya, selesaikan persamaan serentak dengan menggunakan matriks. KBAT Menilai Hence, solve the simultaneous equations using matrices. [5 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 2(9-18).indd 12 2/6/2024 12:34:20 PM
13 4 RM150 dibahagikan antara Hui Ting dengan Hui Kiam dengan keadaan satu perempat daripada bahagian Hui Ting adalah bersamaan dengan satu perenam daripada bahagian Hui Kiam. TP 4 BT ms.64–65 RM150 is divided between Hui Ting and Hui Kiam such that one quarter of Hui Ting’s share is equal to one sixth of Hui Kiam’s share. (a) Tulis dua persamaan linear dalam sebutan x dan y jika Hui Ting dan Hui Kiam masing-masing menerima RMx dan RMy. Write two linear equations in terms of x and y if Hui Ting and Hui Kiam received RMx and RMy respectively. (b) Seterusnya, selesaikan persamaan serentak dengan menggunakan matriks. KBAT Menilai Hence, solve the simultaneous equations using matrices. [5 markah/marks] Jawapan/Answer: 5 Jadual 1 menunjukkan bilangan buku yang dibeli oleh Fitri. TP 5 BT ms.64–65 Table 1 shows the number of books bought by Fitri. Jenis buku Type of books Bilangan buku Number of books Harga per buku (RM) Price per book (RM) Buku cerita Story books x 3.5 Buku rujukan Reference books y 21 Jadual 1/Table 1 Fitri membeli 11 buah buku yang terdiri daripada x buah buku cerita dan y buah buku rujukan. Jumlah harga buku-buku itu ialah RM126. Fitri bought 11 books that consists of x story books and y reference books. The total price of the books is RM126. (a) Tulis dua persamaan linear dalam sebutan x dan y berdasarkan maklumat di atas. Write two linear equations in terms of x and y based on the above information. (b) Seterusnya, hitung nilai x dan y dengan menggunakan kaedah matriks. KBAT Menilai Hence, calculate the values of x and y by using matrix method. [5 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 2(9-18).indd 13 2/6/2024 12:34:20 PM
14 6 Perimeter bagi suatu permukaan meja yang berbentuk segi empat tepat ialah 420 cm. Diberi panjangnya ialah 30 cm lebih daripada lebarnya. Dengan menggunakan kaedah matriks, cari panjang dan lebar permukaan meja itu. TP 5 BT ms.64–65 The perimeter of a rectangular table surface is 420 cm. Given its length is 30 cm more than its width. Using the matrix method, find the length and the width of the table surface. [5 markah/marks] Jawapan/Answer: 7 Li Min membeli 2 batang pen dan 7 batang pensel dengan jumlah harga RM12. Di Shen pula membeli 6 batang pen dan 5 batang pensel dengan jumlah harga RM20. Dengan menggunakan kaedah matriks, cari harga bagi sebatang pen dan sebatang pensel. TP 4 BT ms.64–65 Li Min bought 2 pens and 7 pencils for a total price of RM12. Di Shen bought 6 pens and 5 pencils for a total price of RM20. By using the matrix method, find the price of a pen and a pencil. [5 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 2(9-18).indd 14 2/6/2024 12:34:20 PM
15 Bahagian B / Section B 8 (a) Cari matriks songsang bagi 5 6 3 4 . TP 3 BT ms.59–61 Find the inverse matrix of 5 6 3 4 . [3 markah/marks] (b) Adila dan Hanie pergi ke sebuah pasar raya untuk membeli oren dan epal. Adila membeli 5 biji oren dan 6 biji epal dengan harga RM19. Hanie membeli 3 biji oren dan 4 biji epal dengan harga RM12. Cari harga sebiji oren dan sebiji epal. KBAT Menilai TP 5 BT ms.64–65 Adila and Hanie went to a supermarket to buy oranges and apples. Adila bought 5 oranges and 6 apples for RM19. Hanie bought 3 oranges and 4 apples for RM12. Find the price of an orange and an apple. [5 markah/marks] Jawapan/Answer: 9 (a) Diberi P = 3 –2 4 –5 , Q = m –5 n –4 3 dan I = 1 0 0 1 . Cari nilai m dan nilai n jika PQ = I. KBAT Menilai TP 3 BT ms.57–61 Given that P = 3 –2 4 –5 , Q = m –5 n –4 3 dan I = 1 0 0 1 . Find the values of m and n if PQ = I. [3 markah/marks] (b) Dengan menggunakan kaedah matriks, hitung nilai x dan y yang memuaskan persamaan matriks yang berikut: TP 3 BT ms.62–63 By using the matrix method, calculate the values of x and y that satisfy the following matrix equations: 3x – 2y = 12 4x – 5y = 23 [5 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 2(9-18).indd 15 2/6/2024 12:34:20 PM
16 10 Transformasi matriks 0 –1 –1 0 memetakan (p, q) kepada (3 , 2) dan transformasi matriks –1 0 0 1 pula memetakan (3 , 2) kepada (r, s). KBAT Menilai TP 6 BT ms.64–65 A matrix transformation 0 –1 –1 0 maps (p, q) to (3, 2) and another matrix transformation –1 0 0 1 maps (3, 2) to (r, s). (a) Hitung nilai p, q, r dan s. Calculate the values of p, q, r and s. (b) Cari transformasi matriks tunggal yang memetakan (p, q) kepada (r, s). Find the transformation of a single matrix mapping (p, q) to (r, s). [8 markah/marks] Jawapan/Answer: 11 M ialah matriks 2 × 2 dengan keadaan M 7 –4 3 –2 = 1 0 0 1 . TP 3 BT ms.61 M is a 2 × 2 matrix such that M 7 –4 3 –2 = 1 0 0 1 . (a) Cari matriks M. Find the matrix M. (b) Tulis persamaan linear serentak berikut sebagai suatu persamaan matriks: TP 4 BT ms.62–63 Write the following simultaneous linear equations as matrix equation: 7x – 4y = 5 3x – 2y = 2 Seterusnya, dengan menggunakan matriks, hitung nilai x dan y. Hence, using matrices, calculate the values of x and y. [8 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 2(9-18).indd 16 2/6/2024 12:34:20 PM
17 12 (a) Diberi bahawa 1 k –3 4 –5 8 h –4 5 –3 = 1 0 0 1 , cari nilai k dan h. TP 4 BT ms.59–61 Given that 1 k –3 4 –5 8 h –4 5 –3 = 1 0 0 1 , find the value of k and of h. (b) Menggunakan matriks, hitung nilai x dan y yang memuaskan persamaan matriks berikut: TP 4 BT ms.62–63 Using matrices, calculate the value of x and of y that satisfy the following matrix equation: –3 4 –5 8 x y = 7 12 [8 markah/marks] Jawapan/Answer: 13 Matriks songsang bagi 4 3 9 8 ialah 1 m 8 –3 k 4 . TP 3 BT ms.59–61 The inverse matrix of 4 3 9 8 is 1 m 8 –3 k 4 . (a) Cari nilai m dan k. Find the value of m and of k. (b) Tulis persamaan linear serentak berikut sebagai suatu persamaan matriks: TP 4 BT ms.62–63 Write the following simultaneous linear equations as a matrix equation: 4x + 3y = 6 9x + 8y = 11 Seterusnya, dengan menggunakan matriks, hitung nilai x dan y. Hence, using matrices, calculate the value of x and of y. [8 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 2(9-18).indd 17 2/6/2024 12:34:20 PM
18 14 Jadual 2.1 menunjukkan markah yang diperoleh tiga orang murid dalam suatu ujian yang terdiri daripada dua kertas. Jadual 2.2 menunjukkan pemberat bagi dua kertas dalam ujian itu. Table 2.1 below shows the marks obtained by three students in a test consisting of two papers. Table 2.2 shows the weightages of the two papers in the test. Murid/Student Kertas 1/Paper 1 Kertas 2/Paper 2 Adam 80 70 Bella 60 85 Christ 85 90 Jadual 2.1/Table 2.1 Ujian/Test Kertas 1/Paper 1 Kertas 2/Paper 2 Pemberat/Weightage 40% 60% Jadual 2.2/Table 2.2 Dengan menggunakan kaedah matriks, cari peratusan markah yang diperoleh tiga orang murid tersebut dalam ujian itu. TP 4 BT ms.64–65 By using matrix method, find the percentage of marks obtained by the three students in the test. [9 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 2(9-18).indd 18 2/6/2024 12:34:20 PM
19 3.1 Risiko dan Perlindungan Insurans Risk and Insurance Coverage 1 Antara berikut, yang manakah menerangkan maksud ‘premium’? Which of the following defi nes the word ‘premium’? A Pihak yang akan menuntut dan menerima pampasan atas kerugian yang telah diinsuranskan. Th e individual who will claim and receive compensation for the loss insured. B Jumlah wang yang dibayar oleh pemegang polisi kepada syarikat insurans. An amount of money payable by the policyholder to the insurance company. C Pihak yang bersetuju untuk membayar pampasan ke atas kerugian yang telah diinsuranskan. Th e party that agrees to pay compensation for the loss insured. D Suatu polisi dan bukti perjanjian antara syarikat insurans dan pemegang polisi. A policy and evidence of an agreement made between the insurance company and the policyholder. TP 2 BT ms.75 2 Insurans yang manakah menawarkan polisi penyakit kritikal dan polisi pendapatan hospital? Which insurance off ers the critical illness policy as well as the hospital income policy? A Insurans kebakaran Fire insurance B Insurans perjalanan Travel insurance C Insurans kemalangan diri Personal accident insurance D Insurans perubatan dan kesihatan Medical and health insurance TP 2 BT ms.78 3 Sharif menginsuranskan keretanya di bawah polisi komprehensif sebanyak RM70 000. Kadar yang dikenakan untuk RM1 000 pertama ialah RM339.10. Hitung premium asas yang perlu dibayar oleh Sharif jika dia tinggal di Perak. Bab 3 Matematik Pengguna: Insurans Consumer Mathematics: Insurance Bidang Pembelajaran: Nombor dan Operasi Sharif insured his car under a comprehensive policy at a sum of RM70 000. Th e rate charged for the fi rst RM1 000 is RM339.10. Calculate the basic premium payable by Sharif if he stays in Perak. A RM1 599.83 C RM1 820.10 B RM1 794.00 D RM2 133.10 TP 5 BT ms.83–84 4 Jadual 1 menunjukkan jadual pengiraan premium yang tidak lengkap untuk polisi insurans komprehensif yang dibeli oleh Mei Lin. Nilai yang diinsuranskan untuk kenderaannya ialah RM50 000. Table 1 shows an incomplete table for the calculation of the premium for comprehensive motor insurance policy bought by Mei Lin. Th e sum insured for her vehicle is RM50 000. RM1 000 yang pertama Th e fi rst RM1 000 RM305.50 RM26 × (setiap baki RM1 000) RM26 × (each RM1 000 balance) Premium asas Basic premium NCD 25% Jadual 1/Table 1 Hitung premium kasar. Calculate the gross premium. A RM394.90 C RM1 274.00 B RM1 184.60 D RM1 579.50 TP 5 BT ms.83– 84 5 Encik Amin telah membeli polisi insurans kebakaran dengan deduktibel sebanyak RM3 000. Semasa tempoh perlindungan insurans, rumahnya mengalami kebakaran. Berapakah jumlah pampasan yang akan diterima jika jumlah kerugian yang dialami oleh Encik Amin ialah RM20 000? Encik Amin has bought a fi re insurance policy with a deductible of RM3 000. During the insurance coverage period, his house caught on fi re. What is the amount of compensation he will receive if the amount of loss is RM20 000? Tk 5 24 PT Math 3(19-25).indd 19 2/6/2024 12:35:01 PM
20 A RM3 000 C RM20 000 B RM17 000 D RM23 000 TP 5 BT ms.87– 88 6 Catherine telah membeli insurans perubatan dengan deduktibel tahunan sebanyak RM2 500. Baru-baru ini, dia mengalami pembedahan batu ginjal. Bil perubatannya ialah RM4 800. Berapakah yang dibayar oleh Catherine menggunakan wangnya sendiri? 3.1 Risiko dan Perlindungan Insurans / Risk and Insurance Coverage 1 Manisha membeli polisi insurans daripada TAKAFUL Insurance bernilai RM300 000 dengan bayaran bulanan RM200. Dia mengambil insurans itu untuk melindungi dirinya sekiranya menghidapi penyakit kritikal. TP 3 BT ms.79–80 Manisha buys an insurance policy from TAKAFUL Insurance worth RM300 000 with a monthly payment of RM200. She takes the insurance to cover herself in case of critical illnesses. (a) Siapakah syarikat insurans dan pemegang polisi? Who is the insurance company and the policyholder? (b) Berapakah had perlindungan? How much is the coverage limit? (c) Berapakah premium bulanan? How much is the monthly premium? (d) Apakah risiko yang diinsuranskan? What is the risk to be insured? [4 markah/marks] Jawapan/Answer: 2 Puan Alyah memiliki sebuah kereta di Kuching. Maklumat kereta tersebut diberikan dalam Jadual 1.1. Tarif Motor untuk polisi motor yang dikeluarkan di Sabah dan Sarawak ditunjukkan dalam Jadual 1.2. TP 4 BT ms.82–84 Puan Alyah owns a car in Kuching. The information of the car is given in Table 1.1. The Motor Tariff for motor policies issued in Sabah and Sarawak is shown in Table 1.2. Bahagian A / Section A Catherine has purchased a medical insurance with an annual deductible of RM2 500. Recently, she underwent a surgery for kidney stones. The surgery costs RM4 800. How much does Catherine pay using her own money? A RM4 800 B RM2 500 C RM2 300 D RM0 TP 4 BT ms.86–87 Tk 5 24 PT Math 3(19-25).indd 20 2/6/2024 12:35:01 PM
21 Jumlah yang diinsuranskan Sum insured RM58 000 Usia kenderaan Age of vehicle 6 tahun 6 years Kapasiti enjin Engine capacity 1 500 cc NCD 50% Kapasiti enjin tidak melebihi Engine capacity not exceeding (cc) Sabah dan/ and Sarawak Polisi komprehensif Comprehensive policy (RM) Polisi pihak ketiga Third party policy (RM) 1 400 196.20 67.50 1 650 220.00 75.60 2 200 243.90 85.20 3 050 266.50 93.60 4 100 290.00 101.70 4 250 313.00 110.10 4 400 336.90 118.20 Melebihi 4 400 Over 4 400 359.50 126.60 Jadual 1.1 / Table 1.1 Jadual 1.2 / Table 1.2 Hitung premium kasar untuk kereta Puan Alyah berdasarkan polisi komprehensif. Calculate the gross premium for Puan Alyah’s car under the comprehensive policy. [3 markah/marks] Jawapan/Answer: 3 Encik Lim merupakan seorang jurutera awam berusia 30 tahun yang merokok. Dia berhasrat untuk membeli satu pelan insurans untuk dirinya. TP 4 BT ms.81–82 Mr. Lim is a 30-year-old civil engineer who smokes. He intends to purchase an insurance plan for himself. Kos insurans tahunan bagi setiap RM100 nilai muka The annual cost of insurance per RM100 face value Julat umur Range of ages (Tahun /Years) Bukan perokok / Non-smoker (RM) Perokok / Smoker (RM) Lelaki /Male Perempuan/Female Lelaki /Male Perempuan/Female < 30 1.176 1.138 1.285 1.249 30 – 34 1.322 1.221 1.321 1.306 35 – 39 1.384 1.303 1.426 1.382 40 – 44 1.438 1.398 1.580 1.447 45 – 49 1.629 1.608 1.890 1.651 50 – 54 2.116 1.988 2.469 2.258 55 – 59 2.792 2.627 3.426 3.056 60 – 64 3.988 3.582 4.670 4.328 Jadual 2 / Table 2 Tk 5 24 PT Math 3(19-25).indd 21 2/6/2024 12:35:01 PM
22 Menggunakan Jadual 2, anggarkan premium tahunan yang Encik Lim perlu bayar untuk nilai muka sebanyak RM250 000. Using Table 2, estimate the annual premium that Mr. Lim has to pay for a face value of RM250 000. [3 markah/marks] Jawapan/Answer: Bahagian B / Section B 4 Encik Yong ingin membeli satu insurans kebakaran untuk kilang baharunya yang terletak di Taman Perindustrian Bahagia. Nilai boleh insurans kilang itu ialah RM1 000 000. Encik Yong ingin membeli satu polisi insurans kebakaran dengan peruntukan ko-insurans untuk menginsuranskan 70% daripada nilai yang boleh insurans hartanya dan deduktibel sebanyak RM20 000. BT ms.87–88 Mr. Yong wants to buy a fire insurance for his new factory located in Taman Perindustrian Bahagia. The insurable value of the factory is RM1 000 000. Mr. Yong intends to buy a fire insurance policy with a co-insurance provision to insure 70% of its insurable value and a deductible of RM20 000. (a) Hitung jumlah insurans yang harus dibeli oleh Encik Yong untuk kilangnya. TP 4 Calculate the amount of insurance required by Mr. Yong for his factory. (b) Andaikan berlakunya letupan di kilang Encik Yong dan menyebabkan kerosakan. Jumlah kerugian ialah RM50 000. Hitung jumlah pampasan yang akan diterima oleh Encik Yong sekiranya dia menginsuranskan kilangnya TP 5 Assume there is an explosion in Mr. Yong’s factory and caused some damage. The amount of loss is RM50 000. Calculate the amount of compensation that Mr. Yong will receive if he insured his factory (i) pada jumlah insurans yang harus dibelinya, at the amount of required insurance, (ii) dengan jumlah RM600 000. Seterusnya, hitung nilai penalti ko-insurans. at a sum of RM600 000. Hence, calculate the co-insurance penalty. [8 markah/marks] Jawapan/Answer: Tk 5 24 PT Math 3(19-25).indd 22 2/6/2024 12:35:01 PM
23 Bahagian C / Section C 5 Puan Reena merupakan seorang guru sekolah yang berusia 31 tahun. Beliau seorang yang sihat dan tidak merokok. Beliau ingin membeli satu insurans tetapi tidak pasti mana satu yang bersesuaian untuk dirinya. BT ms.81–82, 89 Puan Reena is a 31-year-old school teacher. She is healthy and does not smoke. She wants to buy an insurance but not sure how to choose which is the best for herself. (a) Senaraikan panduan untuk Puan Reena memilih insurans yang terbaik bagi dirinya. TP 3 List the guidelines for Puan Reena to choose the best insurance for herself. (b) Setelah mempertimbangkan pelbagai faktor, Puan Reena telah memutuskan untuk membeli satu polisi insurans bernilai RM200 000 daripada Canggih Insurance Sdn. Bhd. Jadual 3 menunjukkan jadual kadar premium tahunan bagi setiap RM1 000 nilai muka insurans sementara boleh baharu tahunan yang ditawarkan oleh Canggih Insurance Sdn. Bhd. After considering different factors, Madam Reena has decided to purchase an insurance policy worth RM200 000 from Canggih Insurance Sdn. Bhd. Table 3 shows the annual premium rate schedule per RM1 000 face value of a yearly renewable term insurance offered by Canggih Insurance Sdn. Bhd. Umur Ages Lelaki/ Male (RM) Perempuan/ Female Bukan perokok Non-smoker (RM) Perokok Smoker (RM) Bukan perokok Non-smoker (RM) Perokok Smoker (RM) 30 1.82 2.40 1.14 1.41 31 1.89 2.46 1.21 1.48 32 1.95 2.52 1.27 1.55 33 2.00 2.60 1.32 1.62 34 2.06 2.68 1.38 1.70 35 2.12 2.72 1.45 1.78 Jadual 3 / Table 3 (i) Hitung premium tahunan untuk Puan Reena. TP 4 Calculate the annual premium for Puan Reena. (ii) Andaikan Puan Reena ingin menambah polisi penyakit kritikal. Canggih Insurance Sdn. Bhd. menawarkan polisi penyakit kritikal dengan memberikan perlindungan sebanyak 25% nilai muka asas dan kadar premium bagi setiap RM1 000 ialah RM1.50 mengikut umur dan status kesihatan Puan Reena. Hitung jumlah premium tahunan yang harus dibayar oleh Puan Reena, termasuk premium tambahan untuk penyakit kritikal. KBAT Menilai TP 5 Suppose Puan Reena wants to add on a critical illness policy. Canggih Insurance Sdn. Bhd offers a critical illness policy with a coverage of 25% of basic face value and the premium rate is RM1.50 per RM1 000 based on Puan Reena’s age and health status. Calculate the total annual premium that Puan Reena has to pay, including the additional premium for critical illness. (c) Encik Jaya, suami Puan Reena, ialah seorang usahawan yang berusia 35 tahun. Dia merupakan seorang perokok. Dia ingin membeli satu polisi insurans bernilai sama dengan isterinya. Hitung premium tahunan untuk Encik Jaya. TP 4 Encik Jaya, Puan Reena’s husband, is a 35-year-old businessman. He is a smoker. He wants to buy an insurance policy worth the same amount as his wife. Calculate the annual premium for Encik Jaya. (d) Bandingkan premium tahunan yang harus dibayar oleh Puan Reena dan Encik Jaya. TP 3 Compare the annual premiums that Puan Reena and Encik Jaya have to pay. [15 markah/marks] Tk 5 24 PT Math 3(19-25).indd 23 2/6/2024 12:35:01 PM
24 Jawapan/Answer: 6 Tat Yang tinggal di Melaka. Dia mahu membeli polisi insurans motor untuk keretanya. Maklumat keretanya diberikan dalam Jadual 4.1. Tat Yang stays in Melaka. He wants to buy a motor insurance policy for his car. The information for his car is given in Table 4.1. Jumlah yang diinsuranskan/ Sum insured RM84 000 Usia kenderaan/Age of vehicle 1 bulan/ month Kapasiti enjin/Engine capacity 1 377 cc NCD 30% Jadual 4.1 / Table 4.1 Hitung premium kasar untuk kereta Tat Yang berdasarkan polisi komprehensif, polisi pihak ketiga, kebakaran dan kecurian, dan polisi pihak ketiga. Anda boleh merujuk harga premium separa untuk Tarif Motor dalam Jadual 4.2. KBAT Menilai TP 5 BT ms.82–84 Calculate the gross premium for Tat Yang’s car under the comprehensive policy, the third party, fire and theft policy, and the third-party policy. You can refer to the partial premium rates for Motor Tariff in Table 4.2. Kapasiti enjin tidak melebihi Engine capacity not exceeding (cc) Semenanjung Malaysia Peninsular Malaysia Sabah dan Sarawak Sabah and Sarawak Polisi komprehensif Comprehensive policy Polisi pihak ketiga Third party policy (RM) Polisi komprehensif Comprehensive policy Polisi pihak ketiga Third party policy (RM) 1 400 273.80 120.60 196.20 67.50 1 650 305.50 135.00 220.00 75.60 2 200 339.10 151.20 243.90 85.20 3 050 372.60 167.40 266.50 93.60 Jadual 4.2 / Table 4.2 [15 markah/marks] Tk 5 24 PT Math 3(19-25).indd 24 2/6/2024 12:35:01 PM
25 Jawapan/Answer: Zon KBAT 1 Santosh mengalami kemalangan dua bulan lepas. Dia membuat tuntutan sebanyak RM2 400 daripada syarikat insurans yang menanggung polisi insurans motornya dengan peruntukan deduktibel dalam suatu jumlah tertentu. Tetapi, dia hanya menerima pampasan sebanyak RM2 100. Berapakah jumlah deduktibelnya? Santosh had involved in an accident last two months. He made a claim of RM2 400 from the insurance company that covered his motor insurance policy with a certain amount of deductible allocation. However, he only received a compensation of RM2 100. What is the deductible amount? TP 4 BT ms.86 Jawapan/Answer: Tk 5 24 PT Math 3(19-25).indd 25 2/6/2024 12:35:02 PM
J1 Praktis Topikal SPM Matematik (Dwibahasa) Tingkatan 5 – Jawapan Bab 1 Ubahan Kertas 1 1 A 2 D 3 C 4 C 5 C 6 D 7 B 8 D 9 A 10 C 11 B 12 B 13 C Kertas 2 Bahagian A 1 E ∝ v2 E = kv2 200 = k(52 ) k = 8 E = 8v2 650 = 8v2 v2 = 81.25 v = 81.25 = 9.014 m s–1 2 (a) A∝ θr 2 A = k θr 2 33 = k(11 6 )(62 ) 33 = 66k k = 0.5 A = 0.5 θr 2 (b) A = 0.5(1.8)(72 ) = 44.1 cm2 3 Andaikan a = pecutan dan m = jisim Assume that a = acceleration and m = mass a∝ 1 m a = k m 1.5 = k 4 k = 6 a = 6 m a = 6 10 = 0.6 4 I ∝ 1 L I = k L 1.5 = k 60 k = 90 I = 90 L 4 = 90 m m = 22.5 cm 5 F ∝ v 2 r F = kv 2 r F = k( 1 3 v) 2 2r = k 1 9 v 2 2r = kv 2 18r = 1 18 F Bahagian B 6 f ∝ 1 λ f = k λ 100 = k 200 (a) f = 20 000 λ = 20 000 500 = 40 MHz (b) f = 20 000 λ 80 = 20 000 λ = 20 000 80 = 250 m 7 R ∝ 1 d2 , l p = 2l Q dan/and dp dQ = 1 3 R = kl d2 dP = 1 3 dQ RP = klp dp RQ = klQ dQ 2 RP = klP dQ 2 = k(2l Q) k( 1 3 dQ) 2 = 18klQ dQ 2 = 18 RQ RP RQ = 18 1 [ RP : RQ = 18 : 1 8 T = Masa yang diambil/Time taken A = Luas padang/Area of the fi eld m = Bilangan pekerja/Number of workers T ∝ A m T = k A m 3 = k 4 × 104 5 k = 15 4 × 104 = 3.75 × 10–4 T = 3.75 × 10–4 A m (a) T = 3.75 × 10–4 × 2× 104 3 = 2.5 jam/hours (b) 5 = 3.75 × 10–4 × 8× 104 m m = 6 9 g ∝ 1 r 2 g = k r 2 10 = k 6 4002 = 4.096 × 108 g = 4.096 × 108 12 8002 = 2.5 N kg–1 Bahagian C 10 (a) (i) F ∝ v 2 r (b) (ii) 12.8 = 0.2v 2 4 v 2 = 12.8 × 4 0.2 = 256 v = 16 m s–1 F = kv 2 r 18 = k(3)2 0.1 1.8 = 9k k = 0.2 F = 0.2v 2 r (b) T = tempoh ayunan/oscillation period l = panjang bandul/length of pendulum g = pecutan graviti/gravitational acceleration Diberi/Given that T ∝ l g T = l g k dengan k ialah pemalar/where k is a constant Jawapan Tk 5 24 PT Math J(J1-14).indd 1 2/6/2024 12:38:09 PM
Penerbit Ilmu Bakti Sdn. Bhd. (732516-M) 2024 J2 Apabila/When l = 0.4 dan/and g = 10, T = 1.26 1.26 = 0.4 10 k 1.26 = 0.2k k = 1.26 0.2 = 6.3 Maka/Therefore T = l g 6.3 Apabila/When l = 0.9 dan/and T = 4.73 4.73 = 0.9 g 6.3 4.73 g = 6.3 0.9 g = 0.9 4.73 6.3 = 1.264 g = 1.2642 = 1.598 [ Pecutan graviti di permukaan bulan ialah 1.598 m s–2. The gravitational acceleration on the surface of the moon is 1.598 m s–2. Zon KBAT 1 h ∝ 1 x2 h = k x2 9 = k 62 k = 324 h = 324 x2 4 = 324 x2 x2 = 81 x = 9 cm Bab 2 Matriks Kertas 1 1 A 2 B 3 B 4 C 5 C 6 C 7 B 8 D 9 C 10 D 11 D 12 B 13 C 14 C 15 A 16 A 17 B 18 C 19 C 20 C 21 A 22 C 23 A 24 B 25 C 26 B Kertas 2 Bahagian A 1 Tingkatan/ Form Lelaki/ Boys Perempuan/ Girls 5 Amanah 26 20 5 Bestari 17 26 5 Cekal 20 18 Matriks yang terbentuk ialah/The matrix formed is 26 20 17 26 20 18 . 2 5x + 6y = 28 7x + 9y = 41 5 6 7 9 x y = 28 41 x y = 1 5(9) – 6(7) 9 –6 –7 5 28 41 = 1 3 9 × 28 + (–6) × 41 –7 × 28 + 5 × 41 = 1 3 6 9 = 2 3 [ x = 2, y = 3 3 (a) x + y = 56 .......... 1 y – 2 = 3(x – 2) y – 2 = 3x – 6 –3x + y = –4 atau/or y – 3x = –4 .......... 2 (b) x + y = 56 –3x + y = –4 1 –3 1 1 x y = 56 –4 x y = 1 1 – [–3] 1 3 –1 1 56 –4 = 1 4 60 164 = 15 41 [ x = 15 dan/and y = 41 4 (a) x + y = 150 .......................... 1 1 4 x = 1 6 y 3x = 2y 3x – 2y = 0 .............................. 2 (b) x + y = 150 3x – 2y = 0 1 3 1 –2 x y = 150 0 x y = 1 –2 – 3 –2 –3 –1 1 150 0 = 1 –5 –300 –450 = 60 90 [ x = 60 dan/and y = 90 5 (a) x + y = 11 3.5x + 21y = 126 (b) x + y = 11 3.5x + 21y = 126 1 3.5 1 21 x y = 11 126 x y = 1 21 – 3.5 21 –3.5 –1 1 11 126 = 1 17.5 105 87.5 = 6 5 [ x = 6 dan/and y = 5 6 Panjang/Length = x, lebar/width = y x + y = 420 x – y = 30 1 1 1 –1 x y = 420 30 x y = 1 –1 – 1 –1 –1 –1 1 420 30 = – 1 2 –450 –390 = 225 195 [ Panjang/Length = 225 cm Lebar/Width = 195 cm 7 Harga sebatang pen/Price of a pen = RMx Harga sebatang pensel/Price of a pencil = RMy 2x + 7y = 12 6x + 5y = 20 Tk 5 24 PT Math J(J1-14).indd 2 2/6/2024 12:38:10 PM