ii Mesti Tahu iii – viii Bab 1 Nombor Nisbah 1 – 11 Rational Numbers NOTA 1 Bahagian A 3 Bahagian B 4 Bahagian C 7 Bab 2 Faktor dan Gandaan 12 – 17 Factors and Multiples NOTA 12 Bahagian A 13 Bahagian B 14 Bahagian C 16 Bab 3 Kuasa Dua, Punca Kuasa Dua, Kuasa Tiga dan Punca Kuasa Tiga 18 – 25 Squares, Square Roots, Cubes and Cube Roots NOTA 18 Bahagian A 19 Bahagian B 20 Bahagian C 22 Bab 4 Nisbah, Kadar dan Kadaran 26 – 34 Ratios, Rates and Proportions NOTA 26 Bahagian A 28 Bahagian B 29 Bahagian C 32 Bab 5 Ungkapan Algebra 35 – 41 Algebraic Expressions NOTA 35 Bahagian A 36 Bahagian B 37 Bahagian C 39 Bab 6 Persamaan Linear 42 – 50 Linear Equations NOTA 42 Bahagian A 45 Bahagian B 46 Bahagian C 49 Bab 7 Ketaksamaan Linear 51 – 58 Linear Inequalities NOTA 51 Bahagian A 52 Bahagian B 54 Bahagian C 56 Kandungan Bab 8 Garis dan Sudut 59 – 73 Lines and Angles NOTA 59 Bahagian A 61 Bahagian B 63 Bahagian C 68 Bab 9 Poligon Asas 74 – 89 Basic Polygons NOTA 74 Bahagian A 77 Bahagian B 79 Bahagian C 85 Bab 10 Perimeter dan Luas 90 – 102 Perimeter and Area NOTA 90 Bahagian A 91 Bahagian B 93 Bahagian C 98 Bab 11 Pengenalan Set 103 – 115 Introduction of Set NOTA 103 Bahagian A 104 Bahagian B 106 Bahagian C 111 Bab 12 Pengendalian Data 116 – 132 Data Handling NOTA 116 Bahagian A 117 Bahagian B 121 Bahagian C 125 Bab 13 Teorem Pythagoras 133 – 140 The Pythagoras’ Theorem NOTA 133 Bahagian A 133 Bahagian B 135 Bahagian C 137 Pentaksiran Sumatif Ujian Akhir Sesi Akademik (UASA) 141 – 154 Jawapan 155 – 160
Definisi Penting (Bab 1) 1 © Pan Asia Publications Sdn. Bhd. Definisi Penting (Bab 3) 3 © Pan Asia Publications Sdn. Bhd. Definisi Penting (Bab 5) 5 © Pan Asia Publications Sdn. Bhd. Definisi Penting (Bab 7) 7 © Pan Asia Publications Sdn. Bhd. Definisi Penting (Bab 10) 9 © Pan Asia Publications Sdn. Bhd. Definisi Penting (Bab 12) 11 © Pan Asia Publications Sdn. Bhd. Integer terdiri daripada nombor bulat positif, nombor bulat negatif dan sifar. Integers consist of positive whole numbers, negative whole numbers and zero. ,QWHJHU SRVLWLI ialah integer yang lebih besar daripada sifar dengan atau tanpa tanda ‘+’ di hadapannya. Positive integers are integers more than zero with or without ‘+’ sign before it. ,QWHJHU QHJDWLI ialah integer yang kurang daripada sifar dengan tanda ‘–’ di hadapannya. Negative integers are integers less than zero with ‘–’ sign before it. 1RPERU QLVEDK ialah nombor yang boleh diungkap sebagai nisbah dua integer, iaitu p q dengan keadaan p dan q ialah integer dan q Rational numbers are numbers which can be expressed as a ratio of two integers, that is p q ZKHUHSDQGTDUHLQWHJHUVDQGT. Kuasa Dua, Punca Kuasa Dua, Kuasa Tiga dan Punca Kuasa Tiga Squares, Square Roots, Cubes and Cube Roots Perimeter dan Luas Perimeter and Area Integer dan Nombor Nisbah Integers and Rational Numbers Pemboleh Ubah, Sebutan Algebra dan Ungkapan Algebra Variables, Algebraic Terms and Algebraic Expressions Kekerapan dan Jadual Kekerapan Frequency and Frequency Table Ketaksamaan Inequalities .HWDNVDPDDQ ialah hubungan antara dua kuantiti yang berbeza. Inequality is a relationship between two different quantities. Simbol bagi ketaksamaan: Symbols of inequalities: (a) ‘’ bermaksud kurang daripada ‘’ means less than (b) ‘’ bermaksud kurang daripada atau sama dengan ‘’ means less than or equal to (c) ‘’ bermaksud lebih besar daripada ‘’ means greater than (d) ‘’ bermaksud lebih besar daripada atau sama dengan ‘’ means greater than or equal to .XDVD GXD suatu nombor ialah hasil darab nombor itu dengan dirinya sendiri. The square of a number is the product of the number with itself. 3XQFD NXDVD GXD suatu nombor positif ialah suatu nombor yang apabila didarab dengan dirinya sendiri akan menghasilkan nombor positif itu. Square root of a positive number is a number which will produce that positive number when the number is multiplied by itself. .XDVD WLJD suatu nombor ialah hasil darab nombor itu dengan dirinya sendiri sebanyak dua kali. The cube of a number is the product of the number with itself by two times. 3XQFD NXDVD WLJD suatu nombor ialah nombor yang kuasa tiganya menghasilkan nombor yang diberi. Cube root of a number is the number with power of 3 will produce the number given. 3HULPHWHU bagi suatu kawasan tertutup ialah jumlah panjang sisi yang mengelilingi kawasan itu. Perimeter of an enclosed region is the total length of sides surrounding the region. /XDV bagi suatu kawasan tertutup ialah ukuran saiz kawasan itu. Area of an enclosed region is the measurement of the size of the region. 3HPEROHK XEDK ialah suatu kuantiti tertentu yang belum diketahui nilainya. A variable is a certain quantity with an unknown value. 6HEXWDQ DOJHEUD ialah hasil darab suatu pemboleh ubah dengan suatu nombor. Algebraic term is the product of variables with numbers. 8QJNDSDQ DOJHEUD ialah dua atau lebih sebutan algebra yang digabungkan dengan operasi penambahan atau penolakan atau kedua-duanya. Algebraic expression is two or more algebraic terms combined by an addition or subtraction operation or both. .HNHUDSDQ sesuatu maklumat ialah bilangan kali maklumat itu muncul dalam suatu set data. Frequency of an information is the number of times the information appears in a data set. -DGXDO NHNHUDSDQ ialah satu jadual yang menunjukkan kekerapan bagi setiap kategori atau item data. Frequency table is a table that shows the frequency for each category or item of data. TAHU Definisi Penting AHU MESTI
Fakta Penting (Bab 1) 13 © Pan Asia Publications Sdn. Bhd. Fakta Penting (Bab 3) 15 © Pan Asia Publications Sdn. Bhd. Fakta Penting (Bab 7) 17 © Pan Asia Publications Sdn. Bhd. Fakta Penting (Bab 8) 19 © Pan Asia Publications Sdn. Bhd. Fakta Penting (Bab 10) 21 © Pan Asia Publications Sdn. Bhd. Fakta Penting (Bab 12) 23 © Pan Asia Publications Sdn. Bhd. Peraturan Pendaraban Integer Rules of Multiplication of Integers Sudut yang Berkaitan dengan Garis Bersilang Angles Related to Intersecting Lines Kuasa Dua, Punca Kuasa Dua dan Kuasa Tiga Squares, Square Roots and Cubes Sifat-sifat Ketaksamaan Properties of Inequalities Carta Palang Bar Chart Perimeter dan Luas Perimeter and Area (+) = (+) = (+) (+) = (–) = (–) (–) = (–) = (+) (–) = (+) = (–) Peraturan Pembahagian Integer Rules of Division of Integers (+) ÷ (+) = (+) (+) ÷ (–) = (–) (–) ÷ (–) = (+) (–) ÷ (+) = (–) c d a b Sudut bertentang bucu: Vertically opposite angles: (a) a = c (b) b = d Sudut bersebelahan pada garis bersilang: Adjacent angles on intersecting lines: (a) a + b fl (b) c + d fl (c) a + d fl (d) b + c fl 1RPERU NXDVD GXD VHPSXUQD ialah 1, 4, 9, 16, 25, … The perfect squares are 1, 4, 9, 16, 25, … Hasil darab punca kuasa dua bagi dua nombor yang sama: Multiplying the square root of two equal numbers: x = x = x Hasil darab punca kuasa dua bagi dua nombor yang berbeza: Multiplying the square root of two different numbers: x = y = xy 1RPERU NXDVD WLJD VHPSXUQD ialah 1, 8, 27, 64, 125, … The perfect cubes are 1, 8, 27, 64, 125, … A B D C E H F Bagi suatu gabungan bentuk ABCDEF, For a combined shape ABCDEF, Perimeter ABCDEF/Perimeter of ABCDEF = AB + BC + CD + DE + EF + AF Luas ABCDEF/Area of ABCDEF = luas trapezium ABCD + luas segi empat selari ADEF area of trapezium ABCD + area of parallelogram ADEF = 1 2 = (AB + CD) = AD + AD = EH Sifat akas/Converse property Jika a b, maka b a. If a b, then b a. Sifat transitif/Transitive property Jika a b c, maka a c. If a b c, then a c. Songsangan terhadap penambahan/Additive inverse Jika a b, maka –a –b. If a b, then –a –b. Songsangan terhadap pendaraban/Multiplicative inverse Jika a b, maka 1 a 1 b . If a b, then 1 a 1 b . &DUWD SDODQJ ialah sejenis perwakilan data dengan menggunakan palang segi empat tepat mengufuk atau mencancang. Bar chart is a type of data representation using horizontal or vertical rectangular bars. Panjang atau tinggi palang mewakili kekerapan yang sepadan dengan kategori atau item data. The length or height of bar represents the corresponding frequency with the category or item of data. Carta palang sesuai digunakan untuk membuat perbandingan antara kategori. Bar chart is suitable to use for the comparison between categories. TAHU Fakta Penting AHU MESTI
Kesalahan Umum (Bab 1) 25 © Pan Asia Publications Sdn. Bhd. Kesalahan Umum (Bab 4) 27 © Pan Asia Publications Sdn. Bhd. Kesalahan Umum (Bab 6) 29 © Pan Asia Publications Sdn. Bhd. Kesalahan Umum (Bab 8) 31 © Pan Asia Publications Sdn. Bhd. Kesalahan Umum (Bab 10) 33 © Pan Asia Publications Sdn. Bhd. Kesalahan Umum (Bab 12) 35 © Pan Asia Publications Sdn. Bhd. Sudut-sudut pada Garis Bersilang Angles at Intersecting Lines Perimeter suatu Kawasan Perimeter of a Region Persamaan Linear dalam Satu Pemboleh Ubah Linear Equations in One Variable Carta Palang Berpasangan Dual Bar Charts Gabungan Operasi bagi Integer Combined Basic Arithmetic Operations of Integer Nisbah yang Setara Equivalent Ratios Contoh/Example: Selesaikan 6 – 9 = 12. Solve 6 – 9 = 12. %HWXOCorrect 6DODKWrong 6 – 9 = 12 ±fl ± 6 – 9 = 12 = –3 = 12 = –36 Contoh/Example: Tentukan nilai x dalam rajah di bawah. Determine the value of x in the diagram below. 4x 72° x %HWXOCorrect 6DODKWrong 4x = x + 72 3x = 72 x = 24 4x = 72 x = 18 Contoh/Example: 7XOLVQLVEDK\DQJVHWDUDEDJLFPfflFPfflPP Write the equivalent ratios of FPfflFPfflPP %HWXOCorrect 6DODKWrong FPfflFPfflPP 3.6 cm : 1.2 cm : 6 cm 3 : 1 :5 FPfflFPfflPP ffl ffl Contoh/Example: Hitung perimeter, dalam cm, bagi seluruh rajah di bawah. Calculate the perimeter, in cm, for the whole diagram below. 11 cm 5 cm 4 cm 7 cm C D A B E %HWXOCorrect 6DODKWrong Perimeter ABCDE Perimeter of ABCDE = 5 + 4 + 7 + 7 + 4 = 27 cm Perimeter ABCDE Perimeter of ABCDE = 5 + 4 + 7 + 7 + 11 + 4 = 38 cm Contoh/Example: Selesaikan persamaan 4(p – 5) = p. Solve the equation 4(p – 5) = p. %HWXOCorrect 6DODKWrong 4(p – 5) = p 4p± p 3p p = 3 4(p – 5) = p 4p – 5 = p 3p = 5 p = 5 3 Contoh/Example: Cari nisbah simpanan tetap kepada simpanan akaun semasa di bank Y. )LQGWKHUDWLRRI¿[HG deposit to current account deposit in bank Y. %HWXOCorrect 6DODKWrong Nisbah/Ratio ffl = 3 : 1 Nisbah/Ratio ffl = 4 : 1 500 X 0 Y Z 1 000 1 500 2 000 2 500 3 000 Bank/Bank Simpanan (RM) Deposit (RM) Akaun semasa Current account Simpanan tetap Fixed deposit TAHU Kesalahan Umum U MESTI
1 NOTA 1.1 Integer Integers 1. Integer terdiri daripada nombor bulat positif, nombor bulat negatif dan sifar. Integers consist of positive whole numbers, negative whole numbers and zero. 2. Integer positif ialah integer yang lebih besar daripada sifar dengan atau tanpa tanda ‘+’ di hadapannya. Positive integers are integers more than zero with or without ‘+’ sign before it. 3. Integer negatif ialah integer yang kurang daripada sifar dengan tanda ‘–’ di hadapannya. Negative integers are integers less than zero with ‘–’ sign before it. 4. Contoh dalam situasi harian: Examples in daily situation: (a) 5°C mewakili suhu di atas takat beku manakala –5°C mewakili suhu di bawah takat beku. 5°C represents the temperature above freezing point while –5°C represents the temperature below freezing point. (b) 10 mewakili pergerakan 10 unit ke kanan manakala –10 mewakili pergerakan 10 unit ke kiri. 10 represents moving 10 units to the right while –10 represents moving 10 units to the left. (c) 3 mewakili lif naik tiga tingkat ke atas manakala –3 mewakili lif turun tiga tingkat ke bawah. 3 UHSUHVHQWVWKHOLIW JRLQJ XSWKUHH ÀRRUVZKLOH–3 UHSUHVHQWVWKHOLIWJRLQJGRZQWKUHHÀRRUV 5. Integer boleh diwakilkan pada garis nombor mengufuk atau garis nombor mencancang. Integers can be represented on a horizontal number line or a vertical number line. (a) Garis nombor mengufuk Horizontal number line –3 –2 –1 0 1 2 3 Integer negatif Negative integers Integer positif Sifar Positive integers Zero (b) Garis nombor mencancang Vertical number line 3 2 1 0 –1 –2 –3 Integer negatif Negative integers Integer positif Positive integers Sifar/Zero 6. Garis nombor boleh digunakan untuk membandingkan nilai dua integer. Number lines can be used to compare the values of two integers. –3 –2 –1 0 1 2 3 4 5 –2 berada di sebelah kiri 2 –2 lies on the left of 2 –2 2 5 berada di sebelah kanan 2 5 lies on the right of 2 5 2 1.2 Operasi Asas Aritmetik yang Melibatkan Integer Basic Arithmetic Operations Involving Integers 1. Penambahan integer boleh dilakukan dengan menggunakan garis nombor. Addition of integers can be performed by using a number line. (a) Penambahan integer positif: Addition of positive integers: Pergerakan ke arah positif (ke kanan) sepanjang garis nombor. Moving to the positive direction (to the right) along the number line. (b) Penambahan integer negatif: Addition of negative integers: Pergerakan ke arah negatif (ke kiri) sepanjang garis nombor. Moving to the negative direction (to the left) along the number line. Arah negatif Negative direction Arah positif Positive direction –3 –2 –1 0 1 2 3 Bab 1 Nombor Nisbah Rational Numbers
3TIP SOS 1.2 Operasi Asas Aritmetik yang Melibatkan Integer Basic Arithmetic Operations Involving Integers 1. Rajah di bawah menunjukkan satu garis nombor. The diagram below shows a number line. –10 T Q R 15 Hitung nilai T + Q + R. Calculate the value of T + Q + R. A 0 C 8 B 5 D 10 2. –100 + 99 – (–8) = A 7 C 191 B –9 D 207 1.3 Pecahan Positif dan Pecahan Negatif Positive and Negative Fractions 3. í—2 3 ÷ —3 4 = A –5 C ífl—8 9 B í—– 11 12 D 7—– 5 12 4. 7—4 5 – –2— 1 3 = A 5—–7 15 C 10—–2 15 B í—–7 15 D í—–2 15 1.4 Perpuluhan Positif dan Perpuluhan Negatif Positive and Negative Decimals 5. 0.7 – 1.168 = A – 0.468 B 1.868 C 1.098 D 1.238 6. –0.5 = 1.2 ÷ 0.9 = A í— 1 3 C — 3 4 B – —2 3 D —5 6 1.5 Nombor Nisbah Rational Numbers 7. Rajah di bawah menunjukkan dua nombor. The diagram below shows two numbers. T = 50 – 28—1 3 – 1—2 3 Q = (–28) ÷ (– 4) Cari nilai T ÷ (–Q). Find the value of T ÷ (–Q). A í—1 6 C – 4—3 7 B – —5 7 D –2—6 7 8. Hitung: Calculate: 1.5 = 6 ÷ 0.1 10 A —–9 100 C 9 B —1 4 D 90 9. Nilaikan: Evaluate: 1 5 í = – 5 6 ÷ 1 2 A íffi 2 15 B –5 C 5 D 27 14 15 BAHAGIAN A Soalan 2/Question 2: – (–a) = +a Soalan 3/Question 3: (–) ÷ (+) = (–)
4 TIP SOS 1. Isikan tempat kosong. Fill in the blanks. [4 markah/4 marks] Jawapan/Answer: Situasi Situation Integer Integer (a) (i) Lari ke depan. Run forward. (ii) Lari 100 m ke belakang. Run 100 m backward. +100 m (b) (i) 500 m di atas paras laut. 500 m above the sea level. (ii) 950 m di bawah paras laut. 950 m below the sea level. 2. (a) Bulatkan integer terbesar. Circle the largest integer. [2 markah/2 marks] Jawapan/Answer: (i) 10 –15 –4 –89 2 (ii) –13 –14 –17 –21 –28 (b) Nyatakan integer yang diwakili oleh huruf pada garis nombor berikut. State the integer represented by the letters on the following number line. –30 R –18 S –6 [2 markah/2 marks] Jawapan/Answer: R = S = 3. (a) Senaraikan semua integer daripada –10 hingga 2. List all the integers from –10 to 2. [1 markah/1 mark] Jawapan/Answer: (b) Rajah di bawah menunjukkan satu garis nombor. The diagram below shows a number line. –18 –14 –10 p –2 q 6 Tandakan () bagi nilai yang betul. Mark () for the correct value. [3 markah/3 marks] Jawapan/Answer: (i) p = –6 p = –4 (ii) q = 0 q = 2 (iii) p – q = –8 p – q = –4 4. Lengkapkan garis nombor pada ruang jawapan. Complete the number lines on the answer space. [4 markah/4 marks] Jawapan/Answer: (a) –4 –1 0 1 2 (b) –100 0 100 150 200 BAHAGIAN B Soalan 3/Question 3: (a) Integer merangkumi nombor bulat positif, nombor bulat negatif dan sifar. Integers include positive whole numbers, negative whole numbers and zero.
7TIP SOS (b) Pilih operasi aritmetik bagi nombor nisbah mengikut tertib yang betul. Choose the correct order of arithmetic operations on the rational numbers. KBAT Menganalisis [2 markah/2 marks] Jawapan/Answer: (i) 3– 1 2 + 4 = 5.6 ÷ (–4) = I 10 1 2 = (–1.4) II 3– 7 2 = 5.6 = – 1 4 III – 3 2 + 22.4 ÷ (–4) IV 10 1 2 = (–22.4) (ii) 20 – – 3 20 = 20 + — 1 4 ÷ – 1 2 = I 20 3 20 = 20 + – 1 2 II 20 – – 3 20 = 20 1 4 = (–2) III 20 – (–3) + – 1 2 IV 20 – (–3) + – 1 8 15. Bulatkan jawapan yang betul. Circle the correct answer. [4 markah/4 marks] Jawapan/Answer: (a) 2 1 6 + (–0.4) = —– 53 30 –—– 77 30 (b) –1 1 8 + 2 3 = –1 1 2 = 1 8 –2 1 8 (c) –3 1 4 = –6 2 9 – 20 = 2 9 –40 2 9 (d) – 2 5 + 1 2 = 100 ——————— 0.2 = 248 252 BAHAGIAN C 1. (a) Selesaikan setiap yang berikut. Solve each of the following. (i) 100 ÷ (–2) × (94 – 99) (ii) [(–52 – 18) + (–50)] × 16 [4 markah/4 marks] Jawapan/Answer: (i) (ii) (b) Hitung setiap yang berikut. Calculate each of the following. (i) –42 – (–18 + 14) (ii) 28 + (–6) – (–12) [4 markah/4 marks] Jawapan/Answer: (i) (ii) Soalan 14(b), 15 dan 1/Question 14(b), 15 and 1: B Brackets (Tanda kurung) 10 = (2 + 3) = 10 = 5 = 50 M Multiplication (Pendaraban) 12 – 3 = 2 = 12 – 6 = 6 O Order of power (Kuasa/Punca kuasa) 3 + 23 = 3 + 8 = 11 A Addition (Penambahan) 4 = 5 + 3 = 20 + 3 = 23 D Division (Pembahagian) 10 + 9 ÷ 3 = 10 + 3 = 13 S Subtraction (Penolakan) 4 = 5 – 3 = 20 – 3 = 17
8 TIP SOS (c) Selesaikan: Solve: [899 – 72 + (–27)] ÷ 25 [2 markah/2 marks] Jawapan/Answer: 2. (a) Selesaikan setiap yang berikut. Solve each of the following. (i) 5 = (–2) = 9 (ii) (–8) = 12 = (–11) [4 markah/4 marks] Jawapan/Answer: (i) (ii) (b) Cari hasil bahagi bagi setiap yang berikut. Find the quotient for each of the following. (i) (–81) ÷ (–9) (ii) 6 960 ÷ (–87) ÷ (–2) [4 markah/4 marks] Jawapan/Answer: (i) (ii) (c) Suhu di sebuah bandar ialah 6°C pada waktu siang dan –2°C pada waktu malam. Hitung beza suhu antara waktu siang dengan malam. The temperature of a town is 6°C during day time and –2°C at night. Calculate the difference in the temperature between day time and night. [2 markah/2 marks] Jawapan/Answer: 3. (a) Hitung setiap yang berikut. Calculate each of the following. (i) — 3 4 + –— 2 5 + 1— 3 5 (ii) 3—2 9 – –—4 5 (iii) 10 – 5— 1 2 – 1— 2 3 [6 markah/6 marks] Jawapan/Answer: (i) (ii) (iii) Soalan 2/Question 2: (a) (+) = (–) = (–) (–) = (–) = (+) (b) (+) ÷ (–) = (–) (–) ÷ (–) = (+)
103 NOTA 11.1 Set Set 1. Set ialah pungutan objek-objek dengan setiap objek itu dikenali sebagai unsur. Set is the collection of objects where each object is known as element. 2. Suatu set yang terdiri daripada nombor 1, 3, 5, 7, 9 boleh dihuraikan dengan menggunakan A set consisting of the numbers 1, 3, 5, 7, 9 can be described by using (a) perihalan/description Set nombor ganjil kurang daripada 10. Set of odd numbers less than 10. (b) penyenaraian/listing {1, 3, 5, 7, 9} (c) tatatanda pembina set/set builder notation {x : x 10, x ialah nombor ganjil} {x : x 10, x is an odd number} 3. Simbol Symbol Penerangan Description { } atau { } or Set kosong ialah set yang tidak mengandungi sebarang unsur. Empty set is a set that does not contain any elements. Misalnya, {nombor perdana di antara 31 dengan 37}. For example, {prime numbers between 31 and 37}. ialah unsur bagi is an element of Misalnya,/For example, 3 {1, 2, 3, 4} bukan unsur bagi not an element of Misalnya,/For example, 6 {1, 2, 3, 4} n(A) bilangan unsur bagi A number of elements of A Misalnya,/For example, A = {2, 4, 6, 8, 10} n(A) = 5 4. Set sama mengandungi unsur-unsur yang sama. Equal sets contain the same elements. 11.2 Gambar Rajah Venn, Set Semesta, Pelengkap bagi Suatu Set dan Subset Venn Diagrams, Universal Sets, Complement of a Set and Subsets 1. Gambar rajah Venn ialah sebuah rajah yang mewakili satu atau lebih set dengan menggunakan bentuk geometri seperti bulatan, bujur, segi empat tepat dan sebagainya. Venn diagram is a diagram representing one or more sets by using geometry shapes such as circles, ovals, rectangles and so on. 2. Simbol Symbol Makna Meaning Gambar rajah Venn Venn diagram x Set semesta Universal set j Av Pelengkap bagi set A Complement of set A A A′ j Subset Subset A B A B 3. Subset bagi set {1, 2, 3} ialah { }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}. The subsets of the set {1, 2, 3} are { }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}. Bab 11 Pengenalan Set Introduction of Set
104TIP SOS 11.1 Set Set 1. Set S = {x : 5 x 24, x ialah nombor perdana}. Antara berikut, yang manakah betul? Set S = {x : 5 x 24, x is a prime number}. Which of the following is correct? A S = {7, 11, 13, 17, 19, 21} B S = {7, 11, 13, 17, 19, 23} C S = {5, 7, 11, 13, 15, 19, 21} D S = {5, 7, 11, 13, 17, 19, 23} 2. Diberi set M = {faktor bagi 51}. Antara berikut, yang manakah tidak betul? Given set M = {factors of 51}. Which of the following is not correct? A 3 M C 21 M B 19 M D 51 M 3. Jika set P = {x : 20 x 100, x ialah kuasa dua sempurna}, tentukan n(P). If set P = {x : 20 x 100, x is a perfect square}, determine n(P). A 4 C 6 B 5 D 7 4. Diberi T = {huruf dalam perkataan ‘makmur’}, P = {a, e, u}, Q = {huruf dalam perkataan ‘rumahku’}, R = {a, k, m, r, u} dan S = {huruf vokal}. Antara berikut, yang manakah betul? Given T = {letters in the word ‘makmur’}, P = {a, e, u}, Q = {letters in the word ‘rumahku’}, R = {a, k, m, r, u} and S = {vowels}. Which of the following is correct? A P = S C Q = T B Q = R D R = T 11.2 Gambar Rajah Venn, Set Semesta, Pelengkap bagi Suatu Set dan Subset Venn Diagrams, Universal Sets, Complement of a Set and Subsets 5. P, Q dan R ialah tiga set dengan keadaan P Q dan Q R. P, Q and R are three sets such that P Q and Q R. Gambar rajah Venn yang manakah menunjukkan hubungan antara tiga set itu? Which Venn diagram shows the relationship among the three sets? A P Q R C Q R P B R Q P D Q R P 6. Diberi set semesta = {x : 1 x 100, x ialah integer} dan set H = {x : x ialah kuasa tiga sempurna}. Cari n(Hv). Given the universal set = {x : 1 x 100, x is an integer} and set H = {x : x is a perfect cube}. Find n(Hv). A 94 B 95 C 96 D 97 7. Diberi set semesta = {2, 5, 6, 7, 9, 11, 12} dan set N = {nombor ganjil}. Cari pelengkap set N. Given the universal set = {2, 5, 6, 7, 9, 11, 12} and set N = {odd numbers}. Find the complement of set N. A {2, 6, 9} B {2, 6, 12} C {5, 6, 12} D {6, 9, 12} 8. Diberi set T = {huruf dalam perkataan ‘HARMONI’}. Antara berikut, yang manakah tidak betul? Given set T = {letters in the word ‘HARMONI’}. Which of the following is not correct? A {A, R, M} T B {H, A, R, I} T C {A, E, I} T D {M, N} T BAHAGIAN A Soalan 3/Question 3: Senaraikan semua kuasa dua sempurna bagi set P dan tentukan bilangannya, n(P) secara membilang. List all the perfect squares of set P and determine its number, n(P) by counting.
106TIP SOS 1. D .ODVL¿NDVLNDQ QHJHULQHJHUL 0DOD\VLD yang diberi dalam kumpulan set di ruang jawapan. Classify the given states of Malaysia in the groups of set in the answer space. Perlis Kelantan Sarawak Selangor Melaka Sabah [2 markah/2 marks] Jawapan/Answer: (i) Set negeri-negeri di Malaysia Barat Set of states in West Malaysia (ii) Set negeri-negeri di Malaysia Timur Set of states in East Malaysia (b) Huraikan huruf-huruf di bawah dengan menggunakan Describe the letters below by using (i) perihalan,/description, (ii) penyenaraian./listing. a, e, i, o, u [2 markah/2 marks] Jawapan/Answer: (i) (ii) 2. D .ODVL¿NDVLNDQ REMHNREMHN \DQJ GLEHUL mengikut set berikut. Classify the given objects according to the following sets. (i) Set mata pelajaran sekolah Set of school subjects (ii) Set peralatan pejabat 6HWRIRI¿FHHTXLSPHQWV Sains Science Bahasa Inggeris Bahasa Inggeris Telefon Telephone Komputer Computer Sejarah History Almari Cupboard Matematik Mathematics Bahasa Melayu Bahasa Melayu Mesin cetak Printer [2 markah/2 marks] Jawapan/Answer: (i) (ii) (b) Lengkapkan jadual di ruang jawapan. Complete the table in the answer space. [2 markah/2 marks] Jawapan/Answer: Set Set Bilangan unsur Number of elements (i) H = {huruf dalam perkataan ‘JUJUR’} H = {letters in the word ‘JUJUR’} (ii) S = {x : 7 x 16, x ialah integer} S = {x : 7 x 16, x is an integer} 3. (a) Isikan tempat kosong pada rajah di ruang jawapan untuk menghuraikan set nombor yang diberi. Fill in the blanks on the diagram in the answer space to describe the given set of numbers. [3 markah/3 marks] BAHAGIAN B Soalan 2/Question 2: E 6HQDUDLNDQ XQVXUXQVXU GDODP VHW H dan set S. List down the elements in the sets H and S. %LODQJ ELODQJDQ XQVXUXQVXU GDODP VHW H dan set S. Count the elements in the sets H and S.
111TIP SOS BAHAGIAN C 1. (a) Diberi set S = {x : x ialah nombor tiga digit dengan keadaan hasil tambah digitdigitnya ialah 4}. Given set S = {x : x is a three-digit number such that the sum of its digits is 4}. (i) Tulis set S dengan menyenaraikan unsur-unsurnya. Write down set S by listing its elements. (ii) Nyatakan n(S). State n(S). [3 markah/3 marks] Jawapan/Answer: (i) (ii) (b) (i) Diberi set semesta, x = {x : 25 x 40, x ialah integer} dan H = {x : x ialah nombor dengan keadaan hasil tambah digit-digitnya ialah kuasa dua sempurna}. Cari n(Hv). Given the universal set, x = {x : 25 x 40, x is an integer} and H = {x : x is a number such that the sum of its digits is a perfect square}. Find n(Hv). (ii) Diberi set semesta, x = {x : 10 x 20, x ialah integer} dan set A = {nombor perdana}. Wakilkan set pelengkap bagi A pada gambar rajah Venn di ruang jawapan. Given the universal set, x = {x : 10 x 20, x is an integer} and set A = {prime numbers}. Represent the complement set of A on the Venn diagram in the answer space. [4 markah/4 marks] Jawapan/Answer: (i) (ii) A j (c) Gambar rajah Venn di bawah menunjukkan set P, set Q, set R dan set semesta x. The Venn diagram below shows sets P, Q, R and the universal set x. ffi fl P Q R j (i) Tulis satu hubungan antara set P dengan set Q. Write the relationship between sets P and Q. (ii) Cari/Find (a) n(P), (b) n(Rv). [3 markah/3 marks] Jawapan/Answer: (i) (ii) (a) (b) 2. (a) Diberi A = {nombor dua digit yang mempunyai digit-digit yang sama}, B = {x : 1 x 100, x ialah gandaan bagi 11} dan C = {faktor bagi 55}. Given A = {two-digit numbers with the same digits}, B = {x : 1 x 100, x is a multiple of 11} and C = {factors of 55}. (i) Tentukan n(C). Determine n(C). (ii) Nyatakan dua set yang sama. State the two equal sets. [3 markah/3 marks] Soalan 1/Question 1: D 6XDWXQRPERUWLJDGLJLWabcWHUOHWDNGLDQWDUDffiffiGHQJDQ A three-digit number abc lies between 99 and a + b + c = 4 (c) (i) Set Q terletak dalam set P. Set Q lies inside set P. (ii) (a) n(P) ialah bilangan unsur dalam set P. n(P) is the number of elements in set P. (b) n(Rv) ialah bilangan unsur di luar set R. n(Rv) is the number of elements outside set R.
141 1. 1— 3 4 + 5.48 = 5 = A 16.44 C 36.15 B 29.15 D 47.95 2. Diberi bahawa n – 3 ialah faktor sepunya terbesar bagi 28 dan 42. Cari nilai n. Given that n – 3 is the highest common factor of 28 and 42. Find the value of n. A 6 C 14 B 12 D 17 3. Tentukan dua gandaan sepunya pertama bagi 5, 10 dan 15. 'HWHUPLQHWKH ¿UVWWZRFRPPRQPXOWLSOHV RI5, 10 and 15. A 15 dan/and 30 C 30 dan/and 60 B 30 dan/and 45 D 60 dan/and 90 4. Diberi bahawa 7.842 = 61.47. Cari nilai bagi 10 = 78.42 . Given that 7.842 = 61.47. Find the value of 10 = 78.42 . A 6 147 C 614 700 B 61 470 D 6 147 000 5. 3 – 3 –64 = A –5 C 7 B –1 D 11 6. Ahmad menerima sejumlah dividen RM3 500 bagi tiga amanah saham P, Q dan R yang dia laburkan. Amanah saham Q dan R membayar dividen mengikut nisbah 5 : 2. Jika amanah saham P membayar dividen RM2 100, cari dividen, dalam RM, yang dibayar oleh amanah saham R. Ahmad received a total dividend of RM3 500 for three unit trusts P, Q and R that he invested in. Unit WUXVWV4DQG5SDLGDGLYLGHQGLQWKHUDWLR5 : 2. If XQLWWUXVW 3 SDLG D GLYLGHQG RIRM2 100 ¿QGWKH dividend, in RMSDLGE\XQLWWUXVW5 A 400 C 1 000 B 600 D 1 400 7. Permudahkan: 6LPSOLI\ffl (12x2 \2 + 17SVW) + (6SVW – 15x2 \2 ) A –27x2 \2 + 23SVW C 3x2 \2 – 9SVW B –3x2 \2 + 23SVW D 29x2 \2 – 9SVW 8. Rajah 1 menunjukkan segi tiga PQR. Diagram 1VKRZVDWULDQJOH345 R P Q 32° x y Rajah 1/Diagram 1 Sudut \ adalah 13° lebih besar daripada 4x. Tentukan nilai x dan nilai \. $QJOH\LV13° more than 4x. Determine the values RI[DQG\ A x = 25°, \ = 123° C x = 29°, \ = 119° B x = 27°, \ = 121° D x = 34°, \ = 114° 9. Selesaikan ketaksamaan linear serentak: 6ROYHWKHVLPXOWDQHRXVOLQHDULQHTXDOLWLHVffl 1 —3 4 x – 5 dan/and 1 – 2x x + 10 A x –3 C –9 x 4 B x 8 D –3 x 8 10. Dalam Rajah 2, PQ dan RS ialah garis lurus. In Diagram 2, PQ and RS are straight lines. 36° 50° 2x x y S Q R P Rajah 2/Diagram 2 Cari nilai x dan nilai \. )LQGWKHYDOXHVRI[DQG\ A x = 14°, \ = 102° C x = 18°, \ = 108° B x = 16°, \ = 112° D x = 24°, \ = 112° Pentaksiran Sumatif Ujian Akhir Sesi Akademik (UASA) Bahagian A / Section A [20 markah / 20 marks] Jawab semua soalan. $QVZHUall questions.
144 1. (a) Tandakan () untuk menunjukkan hukum operasi aritmetik yang digunakan dalam pengiraan di bawah. Mark ()WRVKRZWKHODZRIDULWKPHWLFRSHUDWLRQXVHGLQWKHFDOFXODWLRQEHORZ 9 = 4.8 = 9 = (4 + 0.8) = 9 = 4 + 9 = 0.8 = 36 + 7.2 = 43.2 [1 markah/1 mark] Jawapan/$QVZHU: Hukum Kalis Tukar Tertib &RPPXWDWLYH/DZ Hukum Kalis Agihan 'LVWULEXWLYH/DZ Hukum Kalis Sekutuan $VVRFLDWLYH/DZ (b) Rajah 11 menunjukkan beberapa faktor bagi 21 dan 54. Lengkapkan bulatan-bulatan dengan faktorfaktor yang lain. Diagram 11 VKRZVVRPHIDFWRUVRI21 and 54&RPSOHWHWKHFLUFOHVZLWKWKHRWKHUIDFWRUV [3 markah/3 marks] Jawapan/$QVZHU: 54 9 54 1 2 6 18 21 7 Rajah 11/Diagram 11 2. (a) Padankan. Match. [2 markah/2 marks] Jawapan/$QVZHU: (i) 27 64 529 Kuasa dua sempurna Perfect square Kuasa tiga sempurna 3HUIHFWFXEH (ii) (iii) Bahagian B / Section B [20 markah / 20 marks] Jawab semua soalan. Answer all questions.
147 1. (a) Dengan menggunakan hukum operasi aritmetik yang sesuai, tentukan nilai bagi 10.9 = 8 + 8 = 4.1. %\XVLQJVXLWDEOHODZVRIDULWKPHWLFRSHUDWLRQGHWHUPLQHWKHYDOXHRI10.9 = 8 + 8 = 4.1. [3 markah/3 marks] Jawapan/$QVZHU: (b) Cari nilai bagi 3— 1 2 – — 3 5 ÷ 0.8. Find the value of 3—1 2 – —3 5 ÷ 0.8. [3 markah/3 marks] Jawapan/$QVZHU: (c) (i) Tentukan tiga gandaan sepunya pertama bagi 4, 5 dan 8. 'HWHUPLQHWKH¿UVWWKUHHFRPPRQPXOWLSOHVRI4, 5 and 8. [2 markah/2 marks] (ii) Cari gandaan sepunya terkecil bagi 6 dan 70. )LQGWKHORZHVWFRPPRQPXOWLSOHRI6 and 70. [2 markah/2 marks] Jawapan/$QVZHU: (i) (ii) Bahagian C / Section C [60 markah / 60 marks] Jawab semua soalan. Answer all questions.
155 BAB 1 Bahagian A 1. D 2. A 3. C 4. C 5. A 6. B 7. D 8. C 9. B Bahagian B 1. (a) (i) 100 m (ii) –100 m (b) (i) +500 m (ii) –950 m 2. (a) (i) 10 (ii) –13 (b) R = –24, S = –12 3. (a) –10, –9, –8, –7, –6, –5, –4, –3, –2, –1, 0, 1, 2 (b) (i) p = –6 (ii) q = 2 (iii) p – q = –8 4. (a) –4 –3 –2 –1 0 1 2 (b) –100 –50 0 50 100 150 200 5. (a) –5 + (+8) + 1 (b) (i) 0 (ii) –16 (iii) –2 6. (a) (i) Palsu/False (ii) Benar/True (b) (i) –15 = (–4) = 8 (ii) –8 = (–20) = (–3) 7. (a) –16 (b) –107 (c) 63 (d) –120 8. (a) i , iv (b) i , iii 9. – 4 —3 – 2 —3 – 1 —3 5 —3 2 —3 0 1 10. (a) 6 —7 , 2 —3 , 1 —2 , 1 —3 , – 1 —5 , – 1 —4 , – 1 —2 (b) (i) 9 1 –—21 (ii) –3 25 –—27 (iii) – 1 —7 11. (a) Palsu/False (b) Benar/True (c) Benar/True (d) Palsu/False 12. (a) (b) (c) (d) 13. (a) 5.555 (b) 6.666 (c) 22.1062 (d) 3.24 14. (a) 1 —2 , – 3 —7 (b) (i) I (ii) III 15. (a) 53 –—30 (b) –2 1 —8 (c) 2 —9 (d) 248 Bahagian C 1. (a) (i) 250 (ii) –1 920 (b) (i) –38 (ii) 34 (c) 32 2. (a) (i) –90 (ii) 1 056 (b) (i) 9 (ii) 40 (c) 8°C 3. (a) (i) 1 19 20 (ii) 4 1 45 (iii) 2 5 6 (b) 2 1 2 4. (a) (i) –617 24 (ii) 17 1 5 (iii) –62 (b) RM35 5. (a) 10 140.48 (b) (i) 9.316 (ii) –1.726 (c) 925.82 kg 6. (a) (i) 0.00312 (ii) 316 (b) 4.4 (c) (i) 0.003 (ii) 220 7. (a) 3 (b) RM276 (c) RM2.50 BAB 2 Bahagian A 1. D 2. B 3. A 4. C 5. D 6. A 7. D 8. C 9. D 10. B Bahagian B 1. (a) (i) (ii) (b) 2 = 3 = 5 = 5 2. 45 15 5 9 3 1 18 6 2 3. 1, 3, 9, 27 4. (a) 10 (b) 4 (c) 27 (d) 12 5. (a) (i) 72, 80, 88, 96 (ii) 36, 48, 60, 72 (iii) 38, 57, 76, 95 (b) 3, 4, 6 6. (a) 125, 250, 375, 500 (b) (ii) (iv) 7. (a) (i) Ya/Yes (ii) Tidak/No (b) (i) 21 (ii) 24 Bahagian C 1. (a) (i) 28 (ii) 23 (b) 95 (c) 3 2. (a) (i) 2 (ii) 1, 2, 4, 8 (b) 2 (c) 8 3. (a) 1, 2, 3, 6, 9, 18, 27, 54 (b) (i) 4, 8, 12, 16, 20, 24, 28 (ii) 56, 64, 72, 80, 88, 96 (c) 3, 6, 9, 18, 27, 54 4. (a) 48 (b) 8 (c) 10, 20, 30 BAB 3 Bahagian A 1. B 2. C 3. D 4. B 5. C 6. C 7. A 8. D 9. A 10. D Bahagian B 1. (a) 64 (b) (i) 9 025 (ii) 1 156 (iii) 2 401 2. (a) 4 (b) (i) 100 49 (ii) 4 81 (iii) 441 64 3. (a) 360 000 (b) (i) Benar/True (ii) Palsu/False (iii) Benar/True 4. (a) 0.9 (b) (i) 14 (ii) 35 (iii) 2 5. (a) 0.03 (b) (i) 11.75 (ii) 10.68 (iii) 9.67 6. 729, 343, 1 728, 216 7. (a) (i) –0.6 (ii) 12 –—13 (b) (i) 0.000125 (ii) 125 –—– 27 8. (a) (i) 9 (ii) 8.5 (iii) 0.8 (b) 0.4 9. (a) 8 —7 (b) 5 —2 (c) 21 (d) 2 Bahagian C 1. (a) (i) 225 (ii) 5 41 –—64 (b) (i) 0.25 (ii) 3 600 (c) 100, 121, 144, 169, 196, 225, 256, 289 2. (a) (i) 8 431 (ii) 0.8431 (b) (i) 5 6 (ii) 4 5 (iii) 2 1 5 3. (a) (i) 2.5 (ii) 0.9 (b) 48 m (c) 38.1 cm 4. (a) (i) –343 (ii) 1 91 –—– 125 (b) (i) –6 (ii) 9 (c) 0.3 5. (a) 3.302 (b) 0.00053539 (c) 51.11 6. (a) 3 1 3 (b) 2 (c) 100 BAB 4 Bahagian A 1. B 2. A 3. A 4. C 5. C 6. B 7. A 8. C 9. B 10. B Bahagian B 1. (a) (i) 2 : 5 : 10 (ii) 7 : 6 : 10 (b) (i) 1 : 2 (ii) 4 : 5 Jawapan Bab 1 – Bab 4 Sila imbas kod QR ini untuk jawapan lengkap Bahagian A dan Bahagian C. Scan the QR code for complete answers Bahagian A and Bahagian C. https://bit.ly/46OgDFe