BAB 1 Nombor Nisbah ........................................ 1 – 17 Rational Numbers 1.1 Integer Integers 1.2 Operasi Asas Aritmetik yang Melibatkan Integer Basic Arithmetic Operations Involving Integers 1.3 Pecahan Positif dan Pecahan Negatif Positive and Negative Fractions 1.4 Perpuluhan Positif dan Perpuluhan Negatif Positive and Negative Decimals 1.5 Nombor Nisbah Rational Numbers BAB 2 Faktor dan Gandaan .............................. 18 – 26 Factors and Multiples 2.1 Faktor, Faktor Perdana dan Faktor Sepunya Terbesar (FSTB) Factors, Prime Factors and Highest Common Factor (HCF) 2.2 Gandaan, Gandaan Sepunya dan Gandaan Sepunya Terkecil (GSTK) Multiples, Common Multiples and Lowest Common Multiple (LCM) BAB 3 Kuasa Dua, Punca Kuasa Dua, Kuasa Tiga dan Punca Kuasa Tiga............................ 27 – 37 Squares, Square Roots, Cubes and Cube Roots 3.1 Kuasa Dua dan Punca Kuasa Dua Squares and Square Roots 3.2 Kuasa Tiga dan Punca Kuasa Tiga Cubes and Cube Roots BAB 4 Nisbah, Kadar dan Kadaran................ 38 – 47 Ratios, Rates and Proportions 4.1 Nisbah Ratios 4.2 Kadar Rates 4.3 Kadaran Proportions 4.4 Nisbah, Kadar dan Kadaran Ratios, Rates and Proportions 4.5 Perkaitan antara Nisbah, Kadar dan Kadaran dengan Peratusan, Pecahan dan Perpuluhan Relationship between Ratios, Rates and Proportions, with Percentages, Fractions and Decimals BAB 5 Ungkapan Algebra................................. 48 – 54 Algebraic Expressions 5.1 Pemboleh Ubah dan Ungkapan Algebra Variables and Algebraic Expression 5.2 Ungkapan Algebra yang Melibatkan Operasi Asas Aritmetik Algebraic Expressions Involving Basic Arithmetic Operations BAB 6 Persamaan Linear.................................... 55 – 68 Linear Equations 6.1 Persamaan Linear dalam Satu Pemboleh Ubah Linear Equations in One Variable 6.2 Persamaan Linear dalam Dua Pemboleh Ubah Linear Equations in Two Variables 6.3 Persamaan Linear Serentak dalam Dua Pemboleh Ubah Simultaneous Linear Equations in Two Variables BAB 7 Ketaksamaan Linear............................... 69 – 78 Linear Inequalities 7.1 Ketaksamaan Inequalities 7.2 Ketaksamaan Linear dalam Satu Pemboleh Ubah Linear Inequalities in One Variable BAB 8 Garis dan Sudut....................................... 79 – 92 Lines and Angles 8.1 Garis dan Sudut Lines and Angles 8.2 Sudut yang Berkaitan dengan Garis Bersilang Angles Related to Intersecting Lines 8.3 Sudut yang Berkaitan dengan Garis Selari dan Garis Rentas Lintang Angles Related to Parallel Lines and Transversals BAB 9 Poligon Asas........................................... 93 – 103 Basic Polygons 9.1 Poligon Polygons 9.2 Sifat Segi Tiga dan Sudut Pedalaman serta Sudut Peluaran Segi Tiga Properties of Triangles and the Interior and Exterior Angles of Triangles 9.3 Sifat Sisi Empat dan Sudut Pedalaman serta Sudut Peluaran Sisi Empat Properties of Quadrilaterals and the Interior and Exterior Angles of Quadrilaterals BAB 10 Perimeter dan Luas............................ 104 – 112 Perimeter and Area 10.1 Perimeter Perimeter 10.2 Luas Segi Tiga, Segi Empat Selari, Lelayang dan Trapezium Area of Triangles, Parallelograms, Kites and Trapeziums 10.3 Perkaitan antara Perimeter dan Luas Relationship between Perimeter and Area BAB 11 Pengenalan Set..................................... 113 – 120 Introduction of Set 11.1 Set Set 11.2 Gambar Rajah Venn, Set Semesta, Pelengkap bagi suatu Set dan Subset Venn Diagrams, Universal Sets, Complement of a Set and Subsets BAB 12 Pengendalian Data.............................. 121 – 134 Data Handling 12.1 Proses Pengumpulan, Pengorganisasian dan Perwakilan Data, serta Pentafsiran Perwakilan Data Data Collection, Organisation and Representation Process, and Interpretation of Data Representation BAB 13 Teorem Pythagoras............................. 135 – 145 The Pythagoras’ Theorem 13.1 Teorem Pythagoras The Pythagoras’ Theorem 13.2 Akas Teorem Pythagoras The Converse of Pythagoras’ Theorem Pentaksiran Sumatif Ujian Akhir Sesi Akademik (UASA)........................................................................... 146 – 157 Jawapan.......................................................................... 158 – 166 Kandungan ii Kand_Topikal UASA A+ Maths Tg1.indd 2 07/03/2023 4:06 PM
BAB 1 Nombor Nisbah Rational Numbers Nota Ekspres Buku Teks: m.s. 2 – 7 Integer Integers 1.1 Nota Ekspres 1. Nombor positif ialah nombor yang boleh ditulis dengan tanda ‘+’ atau tanpa tanda. Contohnya, +3, +46 atau 3, 46. A positive number is a number that can be written with or without ‘+’ sign. For example, +3, +46 or 3, 46. 2. Nombor negatif ialah nombor yang ditulis dengan tanda ‘–’. Contohnya, –5, –10. A negative number is a number that is written with ‘–’ sign. For example, –5, –10. 3. Integer ialah suatu nombor yang merupakan nombor bulat positif atau nombor bulat negatif termasuk sifar. An integer is a number that is a positive whole number or a negative whole number including zero. 4. Integer positif ialah integer yang lebih daripada sifar. A positive integer is an integer that is greater than zero. 5. Integer negatif ialah integer yang kurang daripada sifar. A negative integer is an integer that is less than zero. 1. Gariskan nombor yang betul berdasarkan situasi berikut. TP 1 Underline the correct number based on the following situations. Contoh Keuntungan RM2 000 daripada perniagaan dalam sebulan. A profit of RM2 000 from a business in a month. +RM2 000 –RM2 000 (a) +30 m –30 m (b) +100°C –100°C 2. Lengkapkan rajah berikut. TP 1 Complete the following diagram. 55, – 3 4 , –4.06, –26, +3 627, 31 2 5 , 0.07, –321 Positif/Positive Contoh 55 (a) +3 627 (b) 31 2 5 (c) 0.07 Negatif/Negative (d) – 3 4 (e) –4.06 (f) –26 (g) –321 Nombor/Numbers TP1 Menguasai Belum menguasai 1Bab 1 01 Topikal UASA A+ Maths Tg1.indd 1 14/03/2023 9:38 AM
3. Padankan nombor berikut. TP 1 Match the following numbers. Contoh – 9 7 (a) 0 (b) +25.8 (c) 8 13 (d) –1 002 (e) 24 685 4. Tandakan nombor berikut pada garis nombor yang diberi. TP 1 Mark the following numbers on the given number lines. Contoh –11, –4, –7, –3, –6 –11 –7 –6 –4 –3 (a) 9, 7, 5, 11, 13 5 7 9 11 13 (b) 1, –2, –1, –3, –6 –6 –3 –2 –1 1 5. Banding dan susun nombor berikut dalam tertib menaik. TP 2 Compare and arrange the following numbers in ascending order. Contoh –6, –8, 5, 9, –21 Tertib menaik: Ascending order: –21, –8, –6, 5, 9 (a) 3, 8, –10, 24, –23 Tertib menaik: Ascending order: –23, –10, 3, 8, 24 (b) 13, –113, –133, 3 003, –3 030 Tertib menaik: Ascending order: –3 030, –133, –113, 13, 3 003 6. Banding dan susun nombor berikut dalam tertib menurun. TP 2 Compare and arrange the following numbers in descending order. Contoh –5, 3, 1, –11, –9 Tertib menurun: Descending order: 3, 1, –5, –9, –11 (a) 88, –880, 8 008, –8 808, –8 888 Tertib menurun: Descending order: 8 008, 88, –880, –8 808, –8 888 (b) 2, –22, –2, 2 002, 222 Tertib menurun: Descending order: 2 002, 222, 2, –2, –22 Integer Integer Bukan integer Non-integer TP1 Menguasai Belum menguasai TP2 Menguasai Belum menguasai –11 ialah nilai terkecil. Maka, –11 berada di sebelah paling kiri. –11 is the smallest value. Thus, –11 is located the furthest to the left. 2Bab 1 01 Topikal UASA A+ Maths Tg1.indd 2 14/03/2023 9:38 AM
13. Selesaikan masalah berikut. TP 4 Solve the following problems. Contoh Dalam suatu kuiz, 2 markah akan ditolak bagi setiap jawapan yang salah. Jika Razak menjawab 20 daripada 25 soalan dengan betul, berapakah markah yang akan ditolak? In a quiz, 2 marks will be deducted for each of the incorrect answer. If Razak answered 20 out of 25 questions correctly, how many marks will be deducted? (25 – 20) × (–2) = 5 × (–2) = –10 10 markah akan ditolak. 10 marks will be deducted. (a) Harga sebuah televisyen menurun RM225 setiap tahun. Jika harga asal ialah RM4 100, berapakah harga televisyen itu selepas 6 tahun? The price of a television drops RM225 each year. If the original price was RM4 100, what is the price of the television after 6 years? 4 100 – (225 × 6) = 4 100 – 1 350 = 2 750 Harga televisyen itu selepas 6 tahun ialah RM2 750. The price of the television after 6 years is RM2 750. (b) Jisim Encik Tan ialah 180 kg. Dia mengambil bahagian dalam program melangsingkan badan dan berjaya mengurangkan jisimnya sebanyak 7 kg setiap minggu. Berapakah jisim baharunya selepas 10 minggu? Mr. Tan’s mass was 180 kg. He took part in a slimming programme and lost 7 kg every week. What would be his new mass after 10 weeks? 180 – (7 × 10) = 180 – 70 = 110 Jisim baharunya ialah 110 kg. His new mass is 110 kg. (c) Selepas pemanasan, suhu suatu bahan kimia meningkat daripada –6°C ke 15°C dalam masa 3 minit. Cari purata perubahan suhu bahan kimia dalam masa 1 minit. After heating, the temperature of a chemical increases from –6°C to 15°C in 3 minutes. Find the average change in temperature of the chemical in 1 minute. [15 – (–6)] ÷ 3 = (15 + 6) ÷ 3 = 21 ÷ 3 = 7 Purata perubahan suhu bahan kimia dalam masa 1 minit ialah 7°C. The average change in temperature of the chemical in 1 minute is 7°C. Nota Ekspres Buku Teks: m.s. 14 – 18 Pecahan Positif dan Pecahan Negatif Positive and Negative Fractions 1.3 Nota Ekspres 1. Pecahan positif ialah pecahan yang lebih besar daripada sifar. Contohnya, + 1 2 , 3 7 , 15 16. A positive fraction is a fraction that is greater than zero. For example, + 1 2 , 3 7 , 15 16. 2. Pecahan negatif ialah pecahan yang kurang daripada sifar. Contohnya, – 1 2 , – 3 7 , – 15 16. A negative fraction is a fraction that is less than zero. For example, – 1 2 , – 3 7 , – 15 16. 14. Tandakan pecahan berikut pada satu garis nombor. TP 1 Mark the following fractions on a number line. Contoh – 4 5 , – 2 5 , 1 5 , 3 5 –1 – 4 5 – 2 5 0 1 5 3 5 1 TP1 Menguasai Belum menguasai TP4 Menguasai Belum menguasai 6Bab 1 01 Topikal UASA A+ Maths Tg1.indd 6 14/03/2023 9:38 AM
(a) – 3 4 , – 1 2 , 1 2 , 1 4 –1 – 3 4 – 1 2 0 1 4 1 2 1 (b) 3 4 , – 3 8 , – 1 2 , 1 4 –1 – 1 2 – 3 8 0 1 4 3 4 1 15. Lengkapkan garis nombor berikut. TP 1 Complete the following number lines. Contoh –2 1 2 –2 –1 1 2 –1 – 1 2 0 1 2 (a) –2 1 5 –1 3 5 –1 2 5 –1 1 5 –1 – 4 5 – 3 5 (b) – 1 7 0 1 7 2 7 4 7 5 7 6 7 1 16. Banding dan susun pecahan berikut dalam tertib menaik. TP 2 Compare and arrange the following fractions in ascending order. Contoh – 1 4 , 1 2 , – 1 2 –1 – 1 2 – 1 4 0 1 2 1 Tertib menaik/Ascending order: – 1 2 , – 1 4 , 1 2 (a) –2 2 3 , –1 1 3 , 2 3 –3 –2 2 3 –2 –1 1 3 –1 0 2 3 1 Tertib menaik/Ascending order: –2 2 3 , –1 1 3 , 2 3 (b) – 1 4 , –1 1 2 , –2 1 2 , 1 2 –2 1 2 –2 –1 1 2 –1 – 1 4 0 1 2 1 Tertib menaik/Ascending order: –2 1 2 , –1 1 2 , – 1 4 , 1 2 TP1 Menguasai Belum menguasai TP2 Menguasai Belum menguasai 7Bab 1 01 Topikal UASA A+ Maths Tg1.indd 7 14/03/2023 9:38 AM
1. Rajah berikut menunjukkan satu garis nombor. The following diagram shows a number line. 1.75 p 2.45 q 3.50 Cari nilai q − p. Find the value of q − p. A 1.05 B 2.15 C 3.10 D 3.15 2. 9 × (–0.7) + 8.5 – 1 2 = A −1.7 B 1.0 C 1.7 D 1.9 3. Rajah berikut menunjukkan satu garis nombor. The following diagram shows a number line. –4 –3 –2 –1 0 1 2 3 4 Apakah operasi yang diwakili oleh garis nombor itu? What is the operation represented by the number line? A −2 + 4 − 4 B −2 + 6 − 8 C −2 − 6 − 4 D −2 − 4 + 4 Azyra had savings of RM480 in the bank. She donated 1 3 of her savings to orphanage. Then she spent RM120 for daily necessities. She wants to buy four pairs of school shoes which cost RM35 a pair for her children. Does Azyra have enough money to buy school shoes? How many pairs of school shoes that can be purchased by Azyra? Derma/Donation = 1 3 × RM480 = RM160 Baki wang/Balance of money = RM480 – RM160 – RM120 = RM200 RM200 ÷ RM35 = 5.71 Ya, Azyra mempunyai wang yang mencukupi untuk membeli kasut sekolah itu. Dia boleh membeli 5 pasang kasut sekolah. Yes, Azyra has enough money to buy the school shoes. She can buy 5 pairs of school shoes. (a) Aziah membayar 2 7 daripada gaji bulanannya untuk pinjaman kereta. Dia membelanjakan RM11 520 untuk pinjaman kereta dalam setahun. Hitung gaji bulanannya jika dia menerima amaun gaji bulanan yang sama pada setiap bulan. Aziah pays 2 7 of her monthly salary for a car loan. She spend RM11 520 for the car loan in a year. Calculate her monthly salary if she receives the same amount of monthly salary for each month. RM11 520 ÷ 12 = RM960 7 2 × 960 = RM3 360 Soalan Objektif TP4 Menguasai Belum menguasai 13Bab 1 01 Topikal UASA A+ Maths Tg1.indd 13 14/03/2023 9:38 AM
1. Tentukan nilai A, B dan C. TP 2 Determine the values of A, B and C. A – 3 4 B 0 1 4 1 2 C 1 A: –1 B: – 1 2 C: 3 4 4. Antara senarai pecahan berikut, yang manakah disusun mengikut tertib menurun? Which of the following list of fractions is arranged in descending order? A 1 5 , 3 8 , 3 4 B 1 7 , 2 5 , 1 3 C 1 2 , 3 7 , 4 5 D 3 5 , 2 7 , 1 8 5. Antara berikut, yang manakah menunjukkan langkah yang betul untuk menyelesaikan 5 6 – 1 5 ? Which of the following shows the correct steps for solving 5 6 – 1 5 ? A 5 6 – 1 5 = 5 – 1 6 – 5 B 5 6 – 1 5 = 5 – 1 6 × 5 C 5 6 – 1 5 = 5 × 6 – 1 × 5 6 × 5 D 5 6 – 1 5 = 5 × 5 – 1 × 6 6 × 5 6. Antara garis nombor berikut, yang manakah mewakili operasi bagi –3 – (–6)? Which of the following number lines represents the operation for –3 – (–6)? A –9 –8 –7 –6 –5 –4 –3 –2 –1 0 B –3 –2 –1 0 1 2 3 C –3 –2 –1 0 1 2 3 D –3 –2 –1 0 1 2 3 4 5 6 7. Antara berikut, yang manakah sama dengan 3 – (–9)? Which of the following is equivalent to 3 – (–9)? A –6 + (–6) B –5 + (–7) C –9 + (–3) D –2(–4) + 4 8. Antara berikut, yang manakah mempunyai nilai terkecil? Which of the following gives the smallest value? A 14 × [–20 ÷ (–5)] B 200(–15 + 7) C –20 + 7 D 9 + (–6) + (–2) 9. Antara langkah pengiraan berikut, yang manakah betul? Which of the following steps of calculation is correct? 5(–4 + 10) × 3.2 ÷ 2 2 3 = A 30 × 1.2 B –20 + 32 × 3 8 C 30 × 3.2 × 8 3 D 5(–6) × 1.2 Soalan Subjektif TP2 Menguasai Belum menguasai 14Bab 1 01 Topikal UASA A+ Maths Tg1.indd 14 14/03/2023 9:38 AM
2. Rajah berikut menunjukkan peraturan pemarkahan bagi suatu ujian Matematik. TP 3 The following diagram shows the marking scheme of a Mathematics test. Peraturan Pemarkahan Ujian Matematik Marking Scheme of Mathematics Test Setiap soalan dijawab dengan betul Each question answered correctly Diberi 2 markah Award 2 marks Setiap soalan dijawab dengan salah Each question answered incorrectly Ditolak 1.5 markah Deduct 1.5 marks Jermine menduduki ujian Matematik yang mengandungi 60 soalan. Markah Jermine telah ditolak sebanyak 12. Hitung jumlah markah yang diperoleh Jermine dalam ujian itu. Jermine sat for Mathematics test consisting of 60 questions. Jermine’s marks had been deducted by 12. Calculate the total marks obtained by Jermine in that test. Bilangan soalan yang dijawab dengan salah/Number of questions answered incorrectly = 12 ÷ 1.5 = 8 Bilangan soalan yang dijawab dengan betul/Number of questions answered correctly = 60 – 8 = 52 Jumlah markah Jermine/Jermine’s total marks = 52 × 2 – 12 = 92 3. (a) Isikan petak kosong dengan simbol “” atau “” yang betul. TP 2 Fill in the box with the correct symbol “” or “”. –7 –9 (b) Susun semula integer berikut mengikut tertib menaik. TP 2 Rearrange the following integers in ascending order. –10, 7, 15, –1, 0, –25 –25, –10, –1, 0, 7, 15 4. Dalam satu kumpulan murid, 2 5 daripada mereka ialah ahli Kelab Sains dan selebihnya ialah ahli Kelab Matematik. 2 3 daripada ahli Kelab Sains atau 24 orang ialah murid lelaki. Cari jumlah bilangan ahli Kelab Matematik. TP 3 In a group of students, 2 5 of them are Science Club members and the rest are Mathematics Club members. 2 3 of the Science Club members or 24 of them are boys. Find the total number of the Mathematics Club members. Sains Science Matematik Mathematics Lelaki Boys Perempuan Girls Jumlah ahli perempuan Kelab Sains/Total number of female members of Science Club = 24 ÷ 2 = 12 Jumlah ahli Kelab Sains/Total number of members of Science Club = 12 × 3 = 36 Jumlah ahli Kelab Matematik/Total number of members of Mathematics Club = 36 2 × 3 = 54 TP2 Menguasai Belum menguasai TP3 Menguasai Belum menguasai 15Bab 1 01 Topikal UASA A+ Maths Tg1.indd 15 14/03/2023 9:38 AM
1. Hitung perimeter bagi setiap rajah berikut. TP 3 Calculate the perimeter for each of the following diagrams. Contoh 5 cm 2.5 cm Perimeter/Perimeter = 5 + 5 + 5 + 2.5 + 2.5 + 2.5 + 2.5 = 25 cm (a) 2 cm Perimeter/Perimeter = 8 × 2 = 16 cm (b) 3 cm Perimeter/Perimeter = 11 × 3 = 33 cm 2. Anggarkan perimeter dan ukur setiap bentuk berikut dengan menggunakan pembaris atau benang. Estimate the perimeter and measure each of the following shapes by using a ruler or a thread. TP 3 Contoh 1 cm 1 cm Anggaran/Estimation = 6 cm Perimeter/Perimeter = 6.1 cm (a) 1 cm 1 cm Anggaran/Estimation = 14 cm Perimeter/Perimeter = 13.8 cm (b) 1 cm 1 cm Anggaran/Estimation = 16 cm Perimeter/Perimeter = 18.1 cm 3. Selesaikan masalah berikut. TP 4 Solve the following problems. Contoh Dalam rajah di sebelah, BCD dan GFE ialah segi tiga sama sisi, BDEG ialah segi empat sama dan ABGH ialah segi empat tepat. In the diagram on the right, BCD and GFE are equilateral triangles, BDEG is a square and ABGH is a rectangle. BAB 10 Perimeter dan Luas Perimeter and Area Nota Ekspres Buku Teks: m.s. 226 – 230 Perimeter Perimeter 10.1 Nota Ekspres Perimeter ialah jumlah panjang sisi yang mengelilingi suatu kawasan tertutup. Perimeter is the total length of all the sides that enclosed a region. TP3 Menguasai Belum menguasai TP4 Menguasai Belum menguasai 8 cm A B C F D E H G 104Bab 10 10 Topikal UASA A+ Maths Tg1.indd 104 14/03/2023 10:17 AM
Diberi perimeter rajah itu ialah 37 cm, cari panjang EF, dalam cm. It is given that the perimeter of the diagram is 37 cm, find the length of EF, in cm. HG = AB = 8 cm AH = DE = BC = DC = GF = EF Katakan/Let EF = x 8 + 8 + AH + DE + BC + DC + GF + EF = 37 8 + 8 + x + x + x + x + x + x = 37 16 + 6x = 37 6x = 37 – 16 6x = 21 x = 21 6 x = 3.5 Maka/Thus, EF = 3.5 cm (a) Rajah di sebelah menunjukkan dua segi empat sama yang bertindih. Hitung perimeter, dalam cm, bagi rajah itu. The diagram on the right shows two overlapped squares. Calculate the perimeter, in cm, of the diagram. Perimeter/Perimeter = 10 + 10 + 6 + 3 + 8 + 8 + 4 + 5 = 54 cm Nota Ekspres Buku Teks: m.s. 231 – 238 Luas Segi Tiga, Segi Empat Selari, Lelayang dan Trapezium Area of Triangles, Parallelograms, Kites and Trapeziums 10.2 Nota Ekspres 1. Luas ialah ukuran jumlah keseluruhan permukaan tertutup. Area is a measurement of the total amount of surface covered. 2. Jadual berikut menunjukkan rumus luas bagi bentuk yang berbeza. The following table shows the fomulae of area for different shapes. Bentuk/Shape Luas/Area Segi tiga/Triangle Tinggi/Height Tapak/Base 1 —2 × panjang tapak × tinggi 1 — 2 × length of base × height 8 cm 8 cm 5 cm 5 cm 4 cm 4 cm 10 cm 10 cm 6 cm 3 cm 8 cm 6 cm TP4 Menguasai Belum menguasai 105Bab 10 10 Topikal UASA A+ Maths Tg1.indd 105 14/03/2023 10:17 AM
Segi empat selari/Parallelogram panjang tapak × tinggi length of base × height Lelayang/Kite 1 —2 × hasil darab panjang dua pepenjuru 1 — 2 × product of the lengths of the two diagonals Trapezium/Trapezium 1 —2 × (hasil tambah dua sisi selari) × tinggi 1 — 2 × (sum of the lengths of the two parallel sides) × height 4. Anggarkan luas bagi setiap rajah berikut. TP 2 Estimate the area for each of the following diagrams. Contoh 1cm 1cm Anggaran luas Estimated area = 12 cm2 (a) 1cm 1cm Anggaran luas Estimated area = 13 cm2 (b) 1cm 1cm Anggaran luas Estimated area = 12 cm2 5. Tulis satu ungkapan untuk mewakili luas bagi setiap rajah berikut. TP 2 Write an expression to represent the area for each of the following diagrams. Contoh p q Luas/Area = 1 —2 × p × q = 1 —2 pq (a) p h n m Luas/Area = 1 —2 × (m + n) × h = 1 —2 (m + n)h (b) p r q s Luas/Area = p × r = pr TP2 Menguasai Belum menguasai Hanya bilangan meliputi 1 cm2 penuh, setengah atau lebih setengah yang dihitung. Only numbers of full 1 cm2 , half or more than half are counted. 106Bab 10 10 Topikal UASA A+ Maths Tg1.indd 106 14/03/2023 10:17 AM
13. Selesaikan masalah berikut. TP 4 Solve the following problems. Contoh Rajah berikut menunjukkan sebuah segi empat sama. The following diagram shows a square. 6 cm Hitung peratusan luas kawasan berlorek itu. Calculate the percentage of area of the shaded region. Luas kawasan berlorek/Area of shaded region = 1 —2 × 3 × 6 × 2 = 18 cm2 Peratusan luas kawasan berlorek Percentage of area of the shaded region = 18 —36 × 100% = 50% (a) Rajah di sebelah menunjukkan sebuah segi empat tepat ABCD. Diberi AE = BG dan BC = 20 cm. Jika luas kawasan berlorek ialah 46 cm2 , cari perimeter, dalam cm, bagi seluruh rajah. The diagram on the right shows a rectangle ABCD. It is given that AE = BG and BC = 20 cm. If the area of the shaded region is 46 cm2 , find the perimeter, in cm, of the whole diagram. Luas kawasan berlorek = 1 —2 × luas segi empat tepat ABCD Area of shaded region = 1 —2 × area of rectangle ABCD Luas segi empat tepat ABCD Area of rectangle ABCD = 2 × 46 = 92 cm2 BC × CD = 92 20 × CD = 92 CD = 92 —20 CD = 4.6 cm Perimeter/Perimeter = 20 + 20 + 4.6 + 4.6 = 49.2 cm A D E H C B G F 1. Antara segi tiga berikut, yang manakah mempunyai luas yang terbesar? Which of the following triangles has the largest area? A 8 cm 6 cm B 6 cm 9 cm C 7 cm 8 cm D 8 cm 9 cm 2. Dalam rajah berikut, ABCE ialah segi empat tepat dan DFC ialah segi tiga tak sama kaki. Diberi ED = EF = FA. In the following diagram, ABCE is a rectangle and DFC is a scalene triangle. Given ED = EF = FA. 21 cm 14 cm A B E F D C Cari luas, dalam cm2 , kawasan berlorek itu. Find the area, in cm2 , of the shaded region. A 49 B 98 C 215 D 245 Soalan Objektif TP4 Menguasai Belum menguasai 110Bab 10 10 Topikal UASA A+ Maths Tg1.indd 110 14/03/2023 10:17 AM
1. Rajah di sebelah menunjukkan sebidang tanah berbentuk segi empat tepat ABCD berukuran 100 m panjang dan 80 m lebar. Rombus AEFG diperuntukkan untuk membina sebuah kolam renang. Segi tiga BCH dicadangkan untuk pembinaan taman rekreasi. TP 4 The diagram on the right shows a piece of rectangular land ABCD measures 100 m in length and 80 m in width. Rhombus AEFG is allocated to build a swimming pool. Triangle BCH is proposed for recreational park. Hitung perimeter, dalam m, kawasan yang belum dirancang untuk pembangunan projek. Calculate the perimeter, in m, of the region which has not been planned for project development. Perimeter/Perimeter = EB + BH + HD + DA + AG + GF + FE = 50 + 100 + 40 + 80 + 50 + 50 + 50 = 420 m 2. Rajah di sebelah menunjukkan sebuah trapezium ACDE. Luas segi tiga ABF ialah 32 cm2 . TP 4 The diagram on the right shows a trapezium ACDE . The area of triangle ABF is 32 cm2 . Hitung luas, dalam cm2 , kawasan berlorek. Calculate the area, in cm2 , of the shaded region. AB = AF = x 1 —2 × x × x = 32 x2 = 64 x = 64 x = 8 cm ED = 8 + 8 = 16 cm AC = 8 + 20 = 28 cm AE = 4 + 8 = 12 cm Luas kawasan berlorek Area of shaded region = 1 —2 × (28 + 16) × 12 – 32 = 232 cm2 3. Rajah di sebelah menunjukkan sebuah trapezium ABCD. TP 4 The diagram on the right shows a trapezium ABCD. Hitung luas, dalam cm2 , kawasan berlorek. Calculate the area, in cm2 , of the shaded region. Luas kawasan berlorek Area of shaded region = 1 —2 × (24 + 18) × 12 – 6 × 6 = 252 – 36 = 216 cm2 4. Rajah di sebelah menunjukkan sebuah segi empat tepat dengan perimeter 20 cm dan luas 24 cm2 . TP 5 The diagram on the right shows a rectangle with a perimeter of 20 cm and an area of 24 cm2 . Nyatakan ukuran bagi sebuah segi empat tepat dengan luas yang sama tetapi mempunyai perimeter yang lebih besar. Cari perimeter, dalam cm, segi empat tepat itu. State the measurement of a rectangle with the same area but larger perimeter. Find the perimeter, in cm, of the rectangle. KBAT Menganalisis (i) Ukuran/Measurement: 2 cm × 12 cm Perimeter/Perimeter = 2 + 2 + 12 + 12 = 28 cm (ii) Ukuran/Measurement: 3 cm × 8 cm Perimeter/Perimeter = 3 + 3 + 8 + 8 = 22 cm (iii) Ukuran/Measurement: 1 cm × 24 cm Perimeter/Perimeter = 1 + 1 + 24 + 24 = 50 cm (Mana-mana satu jawapan) (Any one of the answer) A B C E D F 4 cm 20 cm A E B G F D H C 50 m 100 m 80 m 60 m A B C D 18 cm 24 cm 12 cm 6 cm 4 cm Soalan Subjektif TP4 Menguasai Belum menguasai TP5 Menguasai Belum menguasai 112Bab 10 10 Topikal UASA A+ Maths Tg1.indd 112 14/03/2023 10:17 AM
1. Diberi (16 × Q – 8) ÷ (–15 + 20) = 8, cari nilai Q. Given (16 × Q – 8) ÷ (–15 + 20) = 8, find the value of Q. A 1 B 3 C 5 D 6 2. Dua perlima daripada tetamu yang hadir awal ke suatu majlis hari jadi adalah lelaki. Tiada seorang pun daripada mereka meninggalkan majlis itu, tetapi 20 orang tetamu lelaki dan 20 orang tetamu perempuan lagi hadir ke majlis tersebut. Antara pernyataan berikut, yang manakah benar? Two fifths of the guests that present early in a birthday party are males. None of them leave the party, but 20 males and 20 females arrive at that party. Which of the following statements is true? A Bilangan tetamu lelaki adalah lebih banyak berbanding dengan bilangan tetamu perempuan The number of males is more than females B Bilangan tetamu lelaki adalah sama dengan bilangan tetamu perempuan The number of males is equal to females C Bilangan tetamu perempuan adalah lebih banyak berbanding dengan bilangan tetamu lelaki The number of females is more than males D Bilangan tetamu lelaki dan perempuan tidak dapat diketahui The number of males and females are unknown Bahagian A/Section A [20 markah/20 marks] Jawab semua soalan. Answer all questions. 3. Rajah 1 menunjukkan satu set nombor. Diagram 1 shows a set of numbers. 2 3 4 10 17 Rajah 1 Diagram 1 Antara berikut, yang manakah faktor perdana bagi 170? Which of the following are the prime factors of 170? A 4 dan 17 B 3 dan 17 4 and 17 3 and 17 C 2 dan 17 D 2 dan 3 2 and 17 2 and 3 4. Antara berikut, yang manakah bukan gandaan sepunya bagi 6 dan 8? Which of the following is not a common multiple of 6 and 8? A 144 B 48 C 36 D 24 5. Anggarkan nilai 14.8 × 10 000 dengan menentukan julatnya. Estimate the value of 14.8 × 10 000 by determining its range. A 20 dan 30 B 30 dan 40 20 and 30 30 and 40 C 200 dan 300 D 300 dan 400 200 and 300 300 and 400 6. Diberi k2 270 (k + 1)2 dengan keadaan k ialah integer, cari nilai k. Given k2 270 (k + 1)2 such that k is an integer, find the value of k. A 15 B 16 C 17 D 18 Pentaksiran Sumatif Ujian Akhir Sesi Akademik (UASA) 146 Pentaksiran Sumatif PSumatif Topikal UASA A+ Maths Tg1.indd 146 14/03/2023 5:07 PM
Bahagian B/Section B [20 markah/20 marks] Jawab semua soalan. Answer all questions. 21. Padankan setiap yang berikut. Match each of the following. [4 markah/4 marks] Jawapan/Answer: Nama poligon Name of polygons Bilangan sisi Number of sides Oktagon Octagon • Nonagon Nonagon • Pentagon Pentagon • Heksagon Hexagon • 22. Isi petak kosong dengan simbol ‘=’ atau ‘≠’. Fill in the blanks with the symbol ‘‘=’ or ‘≠’. [4 markah/4 marks] Jawapan/Answer: (a) 25 = (5 )2 (b) k + k + k ≠ k3 (c) 3x – 2 ≠ 3(x – 2) (d) (–x)2 ≠ –x2 5 6 7 8 9 149Pentaksiran Sumatif PSumatif Topikal UASA A+ Maths Tg1.indd 149 14/03/2023 5:08 PM
Bahagian C/Section C [60 markah/60 marks] Jawab semua soalan. Answer all questions. 26. (a) Bulatkan integer yang lebih besar. Circle the greater integer. [3 markah/3 marks] Jawapan/Answer: (i) 3 –3 (ii) –7 –10 (iii) 0 –4 (b) Lengkapkan operasi berikut dengan mengisi petak kosong dengan nombor yang sesuai. Complete the following operations by filling in the boxes using suitable numbers. [4 markah/4 marks] Jawapan/Answer: 3 8 –—125 –3 6 —25 2 = 2 5 – 81 25 2 = –7 5 2 = 49 —– 25 (c) Diberi a : b : c = 4 : 5 : m dan m adalah 40% daripada jumlah, cari nilai m. Given that a : b : c = 4 : 5 : m and m is 40% of the total, find the value of m. [3 markah/3 marks] Jawapan/Answer: 9 unit/units 60% m unit/units 40% 9 —m = 60 —40 60 × m = 40 × 9 m = — 40 × 9 60 m = 6 152 Pentaksiran Sumatif PSumatif Topikal UASA A+ Maths Tg1.indd 152 14/03/2023 5:08 PM
159 BAB 1 1. (a) –30 m (b) +100°C 2. Nombor positif/Positive numbers: +3 627, 31 2 5 , 0.07 Nombor negatif/Negative numbers: – 3 4 , –4.06, –26, –321 3. Integer/Integers: 0, –1 002, 24 685 Bukan integer/Non-integers: +25.8, 8 13 4. (a) 5 7 9 11 13 (b) –6 –3 –2 –1 1 5. (a) –23, –10, 3, 8, 24 (b) –3 030, –133, –113, 13, 3 003 6. (a) 8 008, 88, –880, –8 808, –8 888 (b) 2 002, 222, 2, –2, –22 7. (a) 12 + (–9) = 3 (b) –2 + 4 = 2 8. (a) –19 (b) 16 (c) 16 (d) –8 (e) –1 9. (a) 42 (b) –4 (c) 24 (d) 3 (e) 20 10. (a) –4 (b) –10 (c) –10 (d) 14 (e) –8 11. (a) 40 (b) 30 (c) 112 12. (a) 144 (b) 47 988 (c) 4 600 13. (a) RM2 750 (b) 110 kg (c) 7°C 14. (a) –1 – 3 4 – 1 2 0 1 4 1 2 1 (b) –1 – 1 2 – 3 8 0 1 4 3 4 1 15. (a) –2 1 5 , –1 3 5 , –1 1 5 , – 3 5 (b) – 1 7 , 1 7 , 4 5 , 6 7 16. (a) –2 2 3 , –1 1 3 , 2 3 (b) –2 1 2 , –1 1 2 , – 1 4 , 1 2 17. (a) 1 2 , 1 4 , – 3 4 , –1 1 2 (b) 2 3 , 1 6 , –1 1 6 , –1 1 2 18. (a) 8 45 (b) 1 4 (c) 2 5 9 19. (a) Juliana: RM492, Faizul: RM508 20. (a) –3.0 –2.4–2.2–2.0 –1.6 –1.2–1.0 –0.6 0 (b) –1.0 –0.6 –0.2 0 0.1 0.5 0.7 1.0 21. (a) –4.5, –2.5, –1.5, –0.5 (b) –2.4, –1.6, –0.8, 0.4 22. (a) 0.01, 0.03, 0.07, 0.10, 0.15 (b) –2.7, –2.5, –2.0, –1.7, –1.3 23. (a) 7.8, 7.4, 7.0, 6.8, 6.0 (b) 3.0, 2.5, –0.5, –1.5, –2.5, –4.5 24. (a) –0.41 (b) –22.33 (c) –3.51 (d) 12.85 (e) –0.6 25. (a) 6.5 26. (a) ✓ (b) ✓ (c) ✗ 27. (a) 11 4 (b) 31 25 (c) 3 8 28. (a) –0.1 (b) –4.25 29. (a) RM3 360 Soalan Objektif 1. A 2. C 3. B 4. D 5. D 6. B 7. D 8. B 9. A Soalan Subjektif 1. A: –1, B: – 1 2 , C: 3 4 2. 92 3. (a) (b) –25, –10, –1, 0, 7, 15 4. 54 5. (a) 81 m (b) 15 m 6. (a) 7 (b) –9 (c) 1 7 (d) – 5 8 (e) 0.89 (f) –7.55 7. (a) 2 370 (b) 16 555 BAB 2 1. (a) Ya/Yes (b) Bukan/No 2. (a) 1, 2, 3, 4, 9, 12, 18, 36 (b) 1, 3, 9, 27, 81 3. 3, 23 4. (a) Faktor/Factors: 1, 2, 3, 4, 6, 8, 12, 24 Faktor perdana/Prime factors: 2, 3 24 = 2 × 2 × 2 × 3 (b) Faktor/Factors: 1, 2, 3, 6, 7, 14, 21, 42 Faktor perdana/Prime factors: 2, 3, 7 42 = 2 × 3 × 7 5. (a) 1, 2, 4 (b) 1, 3 6. (a) 6 7. (a) 3 8. (a) 8 9. (a) 12 10. (a) (i) ✓ (ii) ✗ (iii) ✓ (b) (i) ✓ (ii) ✗ (iii) ✓ 11. (a) 150, 300, 450 (b) 24, 48, 72 12. (a) 60 13. (a) 126 14. (a) 48 15. (a) 12:20 p.m. Soalan Objektif 1. A 2. B 3. C 4. D 5. D 6. C 7. C 8. C Soalan Subjektif 1. 5, 17, 29 2. 4, 5, 40 3. Terima sebarang jawapan yang munasabah. Accept any reasonable answers. 4. 132 Jawapan Jaw Topikal UASA A+ Maths Tg1.indd 159 14/03/2023 10:26 AM
160 BAB 3 1. 64, 81, 144, 169, 256, 324 2. (a) 3.5 × 3.5 (b) (– 3 5 ) × (– 3 5 ) 3. (a) 0.9 × 0.9 (b) 4 5 × 4 5 4. (a) 49 (b) 16 25 (c) 0.64 5. (a) 5.76 (b) 361 484 (c) –44.89 6. (a) 0.5 (b) 1 4 (c) 12 7. (a) 22.72 (b) 0.06 (c) 0.77 8. (a) 25 (b) 256 (c) 0.01 9. (a) 8 (b) 9 (c) 7 10. (a) 336 cm 11. (a) ✓ (b) ✗ (c) ✗ 12. (a) 3 4 × 3 4 × 3 4 (b) (–0.2) × (–0.2) × (–0.2) 13. (a) 3 – 1 2 × – 1 2 × – 1 2 (b) 3 0.3 × 0.3 × 0.3 14. (a) –216 (b) –0.027 (c) – 125 27 15. (a) 4.49 (b) –91.13 (c) –0.67 16. (a) 0.2 (b) 0.5 (c) –0.3 17. (a) 4.19 (b) 0.82 (c) –6.28 18. (a) 729 (b) 0.125 (c) –27 19. (a) 4 (b) –7 (c) 0.3 20. (a) 5 400 cm2 21. (a) 65 (b) –31 (c) 12 (d) – 2 5 (e) 0.35 Soalan Objektif 1. C 2. C 3. B 4. D 5. D 6. B 7. C 8. A Soalan Subjektif 1. 3 125 8 – 144 49 = 5 2 – 12 7 = 11 14 2. 1, 4, 7, 10, 12 3. (a) –64 (b) –7 (c) 11 4. 1 647 cm3 5. M: 1, 8, 27, 64, 125; N: 54, 59, 64, 69, 74 6. 576 BAB 4 1. (a) 1 : 3 (b) 10 : 7 2. (a) 1 : 15 : 3 (b) 3 : 2 : 7 3. (a) ✓ (b) ✗ 4. (a) 1 : 3 (b) 7 : 10 5. (a) 12 unit per hari/12 units per day (b) RM0.65 per biji/RM0.65 per egg (c) 0.08 km per minit/0.08 km per minute 6. (a) 12 1 2 m/s (b) 200 m/minit 200 m/minute 7. (a) 50 km 1 j = 25 km 30 minit / 50 km 1 h = 25 km 30 minutes (b) 4.6 kg 4 pasang/pairs = 6.9 kg 6 pasang/pairs 8. (a) 51 600 unit/units (b) RM39 (c) RM360 9. (a) 21 : 6 : 11 (b) 56 : 35 : 15 10. (a) 42 (b) 30 11. (a) RM6 875 12. (a) 1 : 5 (b) 70% 13. (a) 30% 14. (a) 180 Soalan Objektif 1. C 2. B 3. D 4. D 5. B 6. D 7. A Soalan Subjektif 1. 9 2. (a) 7 : 9 (b) 27 3. 2 : 6 : 7 4. (a) 8 : 5 (b) 1 : 4 (c) 2 : 1 (d) 1 : 3 5. (a) Tahir. Tahir menghasilkan produk M yang paling sedikit dalam masa 1 jam. Tahir. He produced the least product M in 1 hour. (b) Naveen dan/and Tahir: 78 produk per jam/ 78 products per hour; 39 58 ; 67.24% Chong: 38 produk per jam/38 products per hour; 19 58 ; 32.76% BAB 5 1. (a) Harga pasaran petrol/Market price of petrol; p; Nilai yang berubah/Varied value; Harga pasaran petrol adalah tidak tentu dan bergantung pada harga pasaran dunia/The market price of petrol is irregular and depends on the world market price. (b) Masa/Time; t; Nilai yang berubah/Varied value; Masa yang diambil oleh setiap murid untuk menamatkan larian merentas desa adalah berbeza/The time taken by each student to complete the cross-country run is different. 2. (a) 10xy (b) 50 h 3. (a) (i) 22 (ii) –16 (b) (i) 16 (ii) –11 4. (a) RM12.50 (b) 128 cm 5. (a) bc, 3b2 , 2c dan/and 1 (b) m 4 , 6n dan/and 4 6. (a) 2 (b) 4 7. (a) (i) 2t (ii) 2v2 (iii) 2 (iv) vt 8. (a) ✗ (b) ✓ (c) ✗ 9. (a) 15p – 5q (b) 11fg + 2g 10. (a) (x + 2)3 (b) (2 – y)4 (c) (a – b)5 11. (a) (2 + 3b) × (2 + 3b) × (2 + 3b) Jaw Topikal UASA A+ Maths Tg1.indd 160 14/03/2023 10:26 AM