UASA TERKINI Berdasarkan Format Persediaan Awal Sebelum Ujian Akhir Sesi Akademik Demi Pentaksiran (Dwibahasa) MATEMATIK 3 TINGKATAN Tee Hock Tian KSSM
iii Kandungan 1 – 6 Praktis 1 Bab 1 Indeks 7 – 13 Praktis 2 Bab 2 Bentuk Piawai 14 – 20 Praktis 3 Matematik Pengguna: Simpanan dan Pelaburan, Kredit dan Hutang Bab 3 21 – 27 Praktis 4 Bab 4 Lukisan Berskala 28 – 34 Praktis 5 Bab 5 Nisbah Trigonometri 35 – 41 Praktis 6 Bab 6 Sudut dan Tangen bagi Bulatan 42 – 47 Praktis 7 Bab 7 Pelan dan Dongakan 48 – 54 Praktis 8 Bab 8 Lokus dalam Dua Dimensi 55 – 60 Praktis 9 Bab 9 Garis Lurus Jawapan J1 – J8 Ujian Akhir Sesi Akademik (UASA) 61 – 78 CONTOH
1 Nama: Tarikh: Praktis 1 Indeks Bab 1 Hal. Buku Teks: 1 – 29 Jawab semua soalan. Answer all questions. BAHAGIAN A Jawab semua soalan. Answer all questions. Nota / Note an = a × a × a × .... × a n faktor/n factors 1. (–6)3 = A –216 B –18 C 18 D 216 2. Cari nilai x, jika 5x = 15 625. Find the value of x, if 5x = 15 625. A 2 B 4 C 6 D 8 3. 85 × 812 = A 817 B 825 C 830 D 860 4. 6p4 × 3p2 × p = A 9p7 B 9p9 C 18p7 D 18p9 5. 82 × 32 = A 114 B 112 C 244 D 242 6. 64y6 ÷ 8y2 = A 8y3 B 8y4 C 512y3 D 512y4 7. Diberi x2m = x20 x6 , cari nilai m. Given that x2m = x20 x6 , find the value of m. A 6 B 7 C 13 D 14 8. Diberi 4x12 ÷ 12x–4 = 1 3 x 2k , cari nilai k. Given that 4x12 ÷ 12x–4 = 1 3 x 2k , find the value of k. A 4 B 5 C 6 D 8 9. (y4 ) 2 × y0 = A 0 B 1 C y6 D y8 10. Diberi (pr ) 4 = p20, cari nilai r. Given that (pr )4 = p20, find the value of r. A 4 B 5 C 10 D 80 11. (94 × 96 ) 2 = A 920 B 948 C 950 D 8120 CONTOH
2 Nota / Note Penyelesaian persamaan eksponen: Solving exponential equation: (a) Ungkapkan kedua-dua belah persamaan kepada asas yang sama. Express both sides of the equation to the same base. (b) Samakan indeks mereka. Equate their indices. ax = ay , ∴ x = y 12. Permudahkan: Simplify: (m3 n2 ) 2 ÷ mn6 A m4 n2 B m4 n2 C m5 n2 D m5 n4 13. Permudahkan: Simplify: ( a2 b3 ) 2 × b2 c × c2 a3 A ac b2 B ac b4 C ac2 b4 D a2 c b7 14. (p4 ) –3 = A 4 p3 B 3 p4 C 1 12p D 1 p12 15. 9 1 2 × 9 3 2 = A 9 3 4 B 9 4 3 C 92 D 94 16. Cari nilai bagi: Find the value of: 16– 1 4 × 27 2 3 A 4 1 2 B 6 1 2 C 18 D 36 17. Permudahkan: Simplify: √mn3 × 3√m6 × √m5 n A m2 n4 B m4 n2 C m5 n D m5 n2 18. (36– 3 4 ) 2 3 = A 1 36 B 1 6 C 6 D 36 19. Diberi m2 = 64– 2 3 × 81 1 2 , cari nilai m. Given that m2 = 64– 2 3 × 81 1 2 , find the value of m. A 3 4 B 9 16 C 4 3 D 36 9 20. Permudahkan: Simplify: 5n × 54 × 1252 A 54n + 2 B 5n + 8 C 5n + 10 D 58n CONTOH
3 1. (a) Isikan petak-petak di bawah dengan jawapan yang betul. Fill in the boxes below with the correct answers. SP 1.2.5 Jawapan/Answer: (i) 5 3 4 = ( √ 5 ) (ii) 9 = 1 (b) Rajah berikut menunjukkan dua kumpulan indeks. The following diagram shows two groups of indices. SP 1.2.4 m8 5√m 1 m4 m6 A m–4 (m4 ) 2 B m 1 5 m2 × m3 Berdasarkan contoh diberi, lengkapkan pasangan setara di bawah. Based on the example, complete the two equivalent pairs below. Contoh/Example: 5√m = m 1 5 Jawapan/Answer: (i) m8 = (ii) 1 m4 = 2. (a) Jadual berikut menunjukkan operasi melibatkan indeks. The following table shows the operations involving indices. SP 1.2.2 a2 × a5 (a5 ) 2 a4 ÷ a–6 a–8 × a–2 a20 a2 a14 a4 Berdasarkan jadual di sebelah, tulis operasi yang menghasilkan jawapan seperti diberikan dalam peta bulatan. Based on the table, write the operations that produce the answer as given in the circle map. Jawapan/Answer: a10 (a5 ) 2 (b) Padankan dengan jawapan yang betul./Match the correct answers. SP 1.2.1 Jawapan/Answer: (i) 58 × 5–5 (ii) 25– 3 2 3. (a) Jadual berikut menunjukkan beberapa indeks. The following table shows some indices. SP 1.2.2 x2 x 9 2 x4 x12 Lengkapkan operasi yang berikut dengan menggunakan indeks dalam jadual di atas. Complete the following operations by using the indices in the table above. Jawapan/Answer: (i) x16 ÷ x4 = (ii) x4 × x 1 2 = BAHAGIAN B Jawab semua soalan. Answer all questions. 1 125 1 5 125 CONTOH
4 (b) Rajah berikut menunjukkan indeks. The following diagram shows indices. SP 1.2.5 A B 3√ p 1 p4 p10 p 5 7 p–4 (p2 ) 5 7√ p p 5 1 3 Lengkapkan dua pasangan setara berdasarkan contoh yang diberi. Complete two equivalent pairs based on the given example. Contoh/Example: 3√ p = p 1 3 Jawapan/Answer: BAHAGIAN C Jawab semua soalan. Answer all questions. 1. (a) Permudahkan/Simplify: SP 1.2.3 (i) m6 × m3 (ii) k8 ÷ k2 (iii) (p–3) 2 Jawapan/Answer: (i) (ii) (iii) (b) (i) Cari nilai bagi 10–2. Find the value of 10–2. SP 1.2.4 (ii) Diberi bahawa 82x + 5 ÷ 83 = 4 096, cari nilai x. Given that 82x + 5 ÷ 83 = 4 096, find the value of x. SP 1.2.7 Jawapan/Answer: (i) (ii) 4. (a) Isikan petak dengan nombor yang betul. Fill in the box with the correct number. SP 1.1.1 Jawapan/Answer: (i) (–3) × (–3) × (–3) × (–3) × (–3) = (–3) (ii) 1 m = m–4 (b) Padankan dengan jawapan yang betul. Match the correct answers. SP 1.2.3 Jawapan/Answer: (i) 62 ÷ 6–3 (ii) (6–3 × 69 ) 1 2 65 63 6–6 CONTOH
5 (c) Diberi y2 = 729 1 3 × 64– 2 3 , tentukan nilai y. Given that y2 = 729 1 3 × 64– 2 3 , determine the value of y. SP 1.2.7 Jawapan/Answer: 2. (a) (i) Permudahkan/Simplify: g–3 ÷ g4 . SP 1.2.2 (ii) Cari nilai bagi 125 2 3 × 4 1 2 . Find the value of 125 2 3 × 4 1 2 . SP 1.2.6 Jawapan/Answer: (i) (ii) (b) Diberi p ÷ 12 × 48 = 8 dan q–3 × 6 ÷ p2 = 3 1 024, hitung nilai p dan q. Given that p ÷ 12 × 48 = 8 and q–3 × 6 ÷ p2 = 3 1 024 , calculate the value of p and q. SP 1.2.7 Jawapan/Answer: (c) Rajah berikut menunjukkan satu segi empat tepat, ABCD. The following diagram shows a rectangle, ABCD. SP 1.2.7 A D x 2 y 5 cm B C Diberi luas bagi ABCD ialah x 5 2 y7 cm2 , hitung panjang, dalam cm, bagi CD. Given that the area of ABCD is x 5 2 y7 cm2 , calculate the length, in cm, of CD. Jawapan/Answer: CONTOH
6 3. (a) Diberi 163 × 42n – 5 = 214, hitung nilai n. Given that 163 × 42n – 5 = 214, calculate the value of n. SP 1.2.7 Jawapan/Answer: (b) Diberi (√x ) 7 × y3 = 3 125 dan y√x = 5, hitung nilai x dan y. Given that (√x ) 7 × y3 = 3 125 and y√x = 5, calculate the value of x and y. SP 1.2.7 Modul hebat 31 Jawapan/Answer: (c) Diberi bahawa 4x × 162x – 3y = 32, ungkapkan x dalam sebutan y. Given that 4x × 162x – 3y = 32, express x in terms of y. SP 1.2.7 Jawapan/Answer: 4. (a) Permudahkan/Simplify: SP 1.2.6 Modul hebat 31 (4p2 q3 ) 2 × (p3 ) –2 ÷ 2p5 q2 Jawapan/Answer: (b) Cari nilai bagi/Find the value of : 4 2 3 × 2 5 3 128 2 7 SP 1.2.6 Jawapan/Answer: (c) Diberi 25x × 1251 – x = 625, hitung nilai x. Given that 25x × 1251 – x = 625, calculate the value of x. SP 1.2.7 Jawapan/Answer: CONTOH
61 1. Rajah 1 menunjukkan O ialah pusat bagi bulatan. PRU dan QRS adalah garis lurus. Diagram 1 shows O is the centre of the circle. PRU and QRS are straight lines. O x P Q R S U T 42° Rajah/Diagram 1 Cari nilai x. Find the value of x. A 254° B 276° C 296° D 318° 2. 128x 20y 7 32x 12y = A 8x 32y 7 B 4x 32y 8 C 4x 8 y 6 D 2x 8 y 7 3. Rajah 2 menunjukkan lukisan berskala bagi suatu padang yang berbentuk segi empat tepat. Diagram 2 shows a scale drawing of a rectangular field. Jika skala yang digunakan ialah 1 : 500, hitung luas sebenar, dalam m2 , padang itu. If the scale used is 1 : 500, calculate the actual area, in m2 , of the field. A 216 B 2 160 C 4 500 D 5 400 4. Bundarkan 27.039 betul kepada 3 angka bererti./Round off 27.039 correct to 3 significant figures. A 27 B 27.0 C 27.1 D 27.04 5. Henry mendapat satu pinjaman peribadi sebanyak RMy daripada bank dengan kadar faedah 4.5% setahun. Dia dikehendaki membayar balik pinjaman bersama dengan faedah dalam 5 tahun. Cari nilai y jika ansuran bulanannya ialah RM1 470. Henry got a personal loan of RMy from the bank with an interest rate of 4.5% per annum. He has to repay the loan along with interest in 5 years. Find the value of y if the monthly instalment is RM1 470. A RM72 000 B RM74 000 C RM75 200 D RM80 500 6. Rajah 3 menunjukkan suatu prisma. Diagram 3 shows a prism. T P 9 cm 8 cm V W 3 cm S U Q R X Rajah/Diagram 3 Nyatakan panjang, dalam cm, bagi PR, dalam unjuran ortogonnya dari X. State the length, in cm, of PR in its orthogonal projection as viewed from X. A 9 B 10 C 12 D 13 12 cm 18 cm Rajah/Diagram 2 Markah: Ujian Akhir Sesi Akademik (UASA) 100 Nama: Tarikh: Masa: 2 jam [20 markah/marks] Jawab semua soalan. Answer all questions. Bahagian A CONTOH
62 7. Rajah 4 menunjukkan dua buah bulatan. Diagram 4 shows two circles. Rajah/Diagram 4 Berapakah bilangan tangen sepunya boleh dilukis bagi bulatan itu? How many common tangents can be drawn for the circles? A 1 B 2 C 3 D 4 8. Rajah 5 menunjukkan suatu segi empat sama, PQRS. Diagram 5 shows a square, PQRS. P Q S R Rajah/Diagram 5 Bina lokus bagi satu titik bergerak yang sentiasa berjarak sama dari PQ dan QR. Construct the locus of a moving point which is always equidistant from PQ and QR. A P Q S R B P Q S R C P Q S R D P Q S R 9. Diberi 625 = 5x , cari nilai x. Given 625 = 5x , find the value of x. A 3 B 4 C 5 D 6 10. Tukar 348 mikrometer kepada meter. Convert 348 micrometres to metres. A 3.48 × 10–6 B 3.48 × 10–5 C 3.48 × 10–4 D 3.48 × 10–3 11. Rajah 6 menunjukkan suatu segi tiga bersudut tegak. Diagram 6 shows a right-angled triangle. x 13 cm 5 cm Rajah/Diagram 6 Cari nilai tan x. Find the value of tan x. A 5 13 B 5 12 C 12 13 D 12 5 12. Tentukan kecerunan dan pintasan-y bagi 3x + 4y = 24. Determine the gradient and y-intercept of 3x + 4y = 24. Kecerunan Gradient Pintasan-y y-intercept A – 4 3 6 B – 3 4 6 C 3 4 8 D 4 3 12 13. Rajah 7 menunjukkan suatu prisma. Diagram 7 shows a prism. Rajah/Diagram 7 5 cm 12 cm 8 cm Antara berikut, yang manakah ialah pelannya? Which of the following is the plan? A 5 cm 12 cm B 5 cm 8 cm C 12 cm 8 cm D 13 cm 8 cm CONTOH
63 14. Nyatakan 6.75 × 108 3 × 102 dalam bentuk piawai. State 6.75 × 108 3 × 102 in standard form. A 2.25 × 106 B 2.25 × 107 C 2.25 × 109 D 2.25 × 1010 15. Rajah 8 menunjukkan sekeping gambar yang diambil oleh Nabila. Diagram 8 shows a picture captured by Nabila. 35 cm 28 cm 7 cm Rajah/Diagram 8 Nabila mencetak satu salinan gambar yang lebih kecil. Jika salinan gambar yang dibuatnya serupa dengan gambar asal dan tinggi salinan gambar ialah 7 cm, hitungkan lebarnya. Nabila printed a reduced copy of the picture. If the copy of the picture was similar to the original picture and the height of the copy was 7 cm, calculate its breadth. A 7.5 cm B 8.75 cm C 14.5 cm D 16.75 cm 16. Cari nilai x bagi persamaan Find the value of x for equation 3x ÷ 92x – 1 = 27x + 1 A – 1 6 B – 1 2 C 2 3 D 5 6 17. Rajah 9 menunjukkan sebuah kuboid. Diagram 9 shows a cuboid. x cm 8 cm 15 cm Rajah/Diagram 9 Jika isi padu kuboid ialah 7.2 × 10–4 m3 , hitung nilai x. If the volume of the cuboid is 7.2 × 10–4 m3 , calculate the value of x. A 0.06 B 0.6 C 6 D 60 18. Robin mengambil suatu pinjaman peribadi sebanyak RM50 000 daripada bank yang mengenakan kadar faedah rata 3.5% setahun. Tempoh bayaran balik ialah 6 tahun. Hitung ansuran bulanannya. Robin takes a personal loan of RM50 000 from a bank which charges a flat interest rate of 3.5% per annum. The repayment period is 6 years. Calculate his monthly instalment. A RM760.25 B RM788.93 C RM825.16 D RM840.28 19. Rajah 10 menunjukkan C ialah titik tengah BD. Diagram 10 shows C is the midpoint of BD. A B C 7 cm D y x Rajah/Diagram 10 Diberi sin x = 7 25 , hitung nilai tan y. Given that sin x = 7 25 , calculate the value of tan y. A 7 24 B 7 12 C 24 25 D 12 7 20. Rajah 11 menunjukkan O ialah pusat bulatan. RS ialah tangen kepada bulatan pada titik R. Diagram 11 shows O is the centre of circle. RS is the tangent to the circle at point R. 62° Q P S R O x 46° Rajah/Diagram 11 Cari nilai x./Find the value of x. A 90° B 94° C 100° D 108° CONTOH
64 21. (a) Rajah 1 menunjukkan beberapa operasi melibatkan indeks. Diagram 1 shows a few operations involving indices. a24 × a2 (a4 ) 3 (a4 ) 8 a6 × a6 a–6 a6 a4 a–8 Rajah/Diagram 1 Berdasarkan contoh di bawah, isikan petak berikut dengan jawapan yang betul. Based on the example below, fill in the following boxes with correct answers. [2 markah/marks] Jawapan/Answer: a12 (i) (ii) a6 × a6 (b) (i) Bulatkan akaun yang membayar kadar faedah yang tertinggi. Circle the account which pays the highest interest rate. [1 markah/mark] Jawapan/Answer: Simpanan Savings Simpanan tetap Fixed deposit Semasa Current (ii) Bulatkan pelaburan dengan risiko tinggi. Circle the investment with the high risk. [1 markah/mark] Jawapan/Answer: Saham Shares Hartanah Properties Unit amanah Unit trust Bahagian B [20 markah/marks] Jawab semua soalan. Answer all questions. CONTOH
65 22. (a) Nyatakan sama ada digit yang bergaris itu bererti atau tidak bererti. Tandakan (✓) pada ruangan yang betul. State whether the underlined digit is significant or not significant. Mark (✓) at the correct space. [2 markah/marks] Jawapan/Answer: (i) Nombor Number Bererti Significant Tidak bererti Not significant 2 906 0.0473 (ii) (b) Padankan garis lurus yang berikut kepada persamaan yang sepadan. Match the following straight lines to the respective equations. [2 markah/marks] Jawapan/Answer: y = 3x + 4 y = 4x + 3 y = –4x – 3 y = –3x – 4 x y O 4 m = 3 x y O –3 m = –4 23. (a) X dan Y masing-masing adalah lokus bagi segi empat sama, ABCD dan segi empat tepat, PQRS. Lukis lokus X dan Y. X and Y are the loci for square, ABCD and rectangle, PQRS respectively. Draw loci for X and Y. [2 markah/marks] Jawapan/Answer: (i) AX = AB (ii) SY = RY A B D C P Q S R CONTOH
66 (b) Berdasarkan pada Rajah 2, padankan sudut yang bersaiz sama. Based on Diagram 2, match the angles which are equal in size. [2 markah/marks] Jawapan/Answer: Rajah / Diagram 2 c b a f e d c d e f a b 24. (a) Rajah 3.1 menunjukkan trapezium P pada grid segi empat sama. Diagram 3.1 shows trapezium P on square grids. P D C A B Rajah/Diagram 3.1 Antara A, B, C dan D, yang manakah ialah lukisan berskala bagi P di bawah skala berikut? Among A, B, C and D, which one is the scale drawing of P under the following scales? [2 markah/marks] Jawapan/Answer: (i) 1 : 2 (ii) 1 : 1 2 CONTOH
67 (b) Rajah 3.2 menunjukkan beberapa indeks. Diagram 3.2 shows some indices. (m3 ) 4 m–3 m12 1 m3 m 4 3 3 √m4 Rajah/Diagram 3.2 Lengkapkan dua pasangan setara berdasarkan contoh yang diberi. Complete two equivalent pairs based on the given example. [2 markah/marks] Jawapan/Answer: 3 √ m 4 = m 4 3 (i) = (ii) = 25. (a) Bundarkan setiap nombor berikut kepada 3 angka bererti. Round off each of the following numbers to 3 significant figures. [2 markah/marks] Jawapan/Answer: (i) 648 501 : (ii) 0.023049 : (b) Rajah 4 menunjukkan satu heksagon. Lukis semula heksagon itu menggunakan skala 1 : 2. Diagram 4 shows a hexagon. Redraw the hexagon using a scale of 1 : 2. [2 markah/marks] Jawapan/Answer: Rajah/Diagram 4 CONTOH
68 Bahagian C 26. (a) (i) Hitung 1.5 × 104 – 3.6 × 102 dan berikan jawapan anda dalam bentuk piawai. Calculate 1.5 × 104 – 3.6 × 102 and give your answer in standard form. [2 markah/marks] Jawapan/Answer: (ii) Hitung 84.9 – 2.3 × 1.5 dan bundarkan jawapan anda betul kepada 1 angka bererti. Calculate 84.9 – 2.3 × 1.5 and round off your answer correct to 1 significant figure. [2 markah/marks] Jawapan/Answer: (b) Pada awal tahun, Janet telah membeli x unit saham Syarikat A yang bernilai RM1.25 seunit. Pada hujung tahun, syarikat tersebut memberi dividen sebanyak 6% dan Janet telah mendapat RM225. At the beginning of the year, Janet bought x units share of Company A which costed RM1.25 per unit. At the end of the year, the company gave 6% dividend and Janet received RM225. (i) Cari nilai x. Find the value of x. [2 markah/marks] Jawapan/Answer: (ii) Selepas itu, Janet menjual saham tersebut dengan RM3 600. Cari pulangan pelaburan tersebut. Then, Janet sold the shares with RM3 600. Find the return of investment. [2 markah/marks] Jawapan/Answer: [60 markah/marks] Jawab semua soalan. Answer all questions. CONTOH
69 (c) Hitung nilai / Calculate the value of: 32 7 5 . [2 markah / marks] Jawapan/Answer: 27. (a) Rajah 1.1 menunjukkan suatu prisma dengan keratan rentas seragam, JKBDFH. Diagram 1.1 shows a prism with the uniform cross section, JKBDFH. 8 cm 5 cm 6 cm 2.5 cm 2 cm A B K L F E C D I J G H 4 cm Rajah/Diagram 1.1 Lukis dengan skala penuh, pelan pepejal itu. Draw to full scale, the plan of the solid. [3 markah/marks] Jawapan/Answer: CONTOH
70 (b) Rajah 1.2 menunjukkan persamaan garis lurus SU ialah 5y = –4x + 40. Diagram 1.2 shows the equation of straight line SU is 5y = – 4x + 40. y O S T U(m, 0) x Rajah/Diagram 1.2 (i) Cari nilai m. Find the value of m. [2 markah/marks] (ii) Jika T terletak 4 unit dari paksi-y, cari persamaan ST. If T lies 4 units from y-axis, find the equation of ST. [2 markah/marks] Jawapan/Answer: (i) (ii) (c) Rajah 1.3 menunjukkan sebuah blok keluli dalam bentuk kuboid. Diagram 1.3 shows a steel block in the shape of a cuboid. 8 m 3 m 2 m Rajah/Diagram 1.3 Blok keluli itu dileburkan untuk membuat galas bebola. Jisim setiap galas bebola ialah 2.4 g. Jika ketumpatan keluli ialah 7 850 kg/m3 , cari bilangan galas bebola yang dihasilkan. Beri jawapan anda dalam bentuk piawai. The steel block is melted to make ball bearings. The mass of a ball bearing is 2.4 g. If the density of steel is 7 850 kg/m3 , find the number of ball bearing produced. Give your answer in standard form. [3 markah/marks] Jawapan/Answer: CONTOH
71 28. (a) Rajah 2.1 menunjukkan sebuah kuboid. Diagram 2.1 shows a cuboid. D A 9 cm B C E H F 4 cm 13 cm G Rajah/Diagram 2.1 Hitung/Calculate (i) panjang, dalam cm, AC. the length, in cm, of AC. [2 markah / marks] Jawapan/Answer: (ii) sudut di antara garis AC dan garis AH. the angle between the line AC and line AH. [2 markah/marks] Jawapan/Answer: (b) Luas sebuah padang yang berbentuk segi empat sama dalam lukisan ialah 25 cm2 . Diberi bahawa luas sebenar padang tersebut ialah 100 m2 . Cari skala yang digunakan. The area of a square field in picture is 25 cm2 . Given the actual area of the field is 100 m2 . Find the scale used. [2 markah/marks] Jawapan/Answer: CONTOH
72 (c) Rajah 2.2 menunjukkan suatu gabungan dua segi empat sama yang sama, PQTU dan QRST, yang dilukis pada grid segi empat sama. Diagram 2.2 shows a combination of two identical squares, PQTU and QRST, drawn on a square grid. Rajah/Diagram 2.2 P Q R U T S (i) X ialah titik yang bergerak dengan keadaan jaraknya sentiasa sama dari titik P dan titik R. Dengan menggunakan huruf, nyatakan lokus bagi X. X is a point which moves such that it is equidistant from point P and point R. By using the letter, state the locus of X. [1 markah/mark] Jawapan/Answer: (ii) Pada Rajah 2.2, lukis / On Diagram 2.2, draw (a) lokus bagi titik Y dengan keadaan PY = PU. the locus of point Y such that PY = PU. (b) lokus bagi titik Z dengan keadaan jaraknya sentiasa sama dari garis PQR dan garis UTS. the locus of point Z such that it is equidistant from line PQR and line UTS. [2 markah/marks] (iii) Seterusnya, tandakan persilangan di antara lokus Y dan lokus Z menggunakan simbol ⊗. Hence, mark the intersection between locus Y and locus Z using the symbol ⊗. [1 markah/mark] CONTOH
73 29. (a) Rajah 3.1 menunjukkan MNO dan MPQ ialah segi tiga bersudut tegak dan MPO ialah satu garis lurus. Diagram 3.1 shows MNO and MPQ are right-angled triangles and MPO is a straight line. Diberi bahawa OP = 12 cm dan tan y = 5 12 , cari Given OP = 12 cm and tan y = 5 12 , find (i) nilai bagi sin y. the value of sin y. [2 markah / marks] Jawapan/Answer: (ii) panjang, dalam cm, PM. the length, in cm, of PM. [2 markah / marks] Jawapan/Answer: (b) Rajah 3.2 menunjukkan kadar faedah mudah bagi Bank P dan Bank Q. Diagram 3.2 shows the simple interest rate of Bank P and Bank Q. Bank P Faedah bulanan Monthly interest 0.35% Bank Q Kadar faedah Interest rate 3.2% setahun 3.2% per annum Rajah/Diagram 3.2 Norhayati menyimpan RM12 000 dalam setiap bank itu masing-masing. Hitung perbezaan bagi faedah yang didapati daripada dua bank selepas satu tahun. Norhayati saves RM12 000 each in Bank P and Bank Q respectively. Calculate the difference in interest earned between the two banks after one year. [3 markah / marks] Jawapan/Answer: O Q y M N P 24 cm Rajah/Diagram 3.1 CONTOH
74 (c) Rajah 3.3 menunjukkan sebuah bulatan, ABCD. ATC dan BTD adalah garis lurus. Diagram 3.3 shows a circle, ABCD. ATC and BTD are straight lines. T 75° A B C D 42° Rajah/Diagram 3.3 Cari nilai bagi Find the value of (i) ∠BAD [1 markah/mark] Jawapan/Answer: (ii) ∠ACB [1 markah/mark] Jawapan/Answer: (iii) Diberi ∠ATB = 80°, cari nilai bagi ∠DBC. Given ∠ATB = 80°, find the value of ∠DBC. [1 markah/mark] Jawapan / Answer: CONTOH
75 30. (a) Rajah 4.1 menunjukkan maklumat mengenai jualan komputer riba. Diagram 4.1 shows the information on the sales of laptop. Pelan pembayaran ansuran bulanan: Monthly instalment payment plan: • Tiada wang pendahuluan No down payment • Kadar faedah rata 4.2% setahun Flat interest rate 4.2% per annum • Tempoh pinjaman: 2 tahun Loan tenure: 2 years RM4 200 Diskaun/Discount: 10% Rajah/Diagram 4.1 Hitung ansuran bulanan yang perlu dibayar oleh pembeli. Calculate the monthly instalment payable by the buyer. [3 markah/marks] Jawapan/Answer: (b) Rajah 4.2 menunjukkan sebuah trapezium, PQST. QRS ialah suatu garis lurus. Diagram 4.2 shows a trapezium, PQST. QRS is a straight line. x y P T Q R S 15 cm Rajah/Diagram 4.2 Diberi PR = RS, kos x = 3 5 dan tan y = 6 5 . Hitung Given that PR = RS, cos x = 3 5 and tan y = 6 5 . Calculate (i) panjang, dalam cm, RS. the length, in cm, RS. [1 markah/mark] Jawapan/Answer: CONTOH
76 (ii) luas, dalam cm2 , PQST. the area, in cm2 , PQST. [3 markah/marks] Jawapan/Answer: (c) Rajah 4.3 menunjukkan sebuah prisma dengan tapak berbentuk segi empat tepat, ABCD. ABIJKL ialah keratan rentas seragamnya. Diagram 4.3 shows a prism with a rectangular base, ABCD. ABIJKL is the uniform cross section. K F E D A L B 7 cm 5 cm 3 cm 3 cm 2 cm 6 cm I H C G J Y Rajah/Diagram 4.3 Lukiskan dengan skala penuh, dongakan pepejal itu pada satah mencancang yang selari dengan BC sebagaimana dilihat dari Y. Draw to full scale, the elevation of the solid on a vertical plane parallel to BC as viewed from Y. [3 markah/marks] Jawapan/Answer: CONTOH
77 31. (a) Rajah 5.1 menunjukkan PQR ialah tangen kepada bulatan yang berpusat O di titik Q. RSOU ialah suatu garis lurus. Diagram 5.1 shows PQR is a tangent to the circle with centre O at point Q. RSOU is a straight line. O z U x Q T P R y 121° 66° S Rajah/Diagram 5.1 Diberi ∠QSU = 66° dan ∠RST = 121°, hitung nilai Given that ∠QSU = 66° and ∠RST = 121°, calculate the value of (i) x (ii) y (iii) z [3 markah/marks] Jawapan/Answer: (b) Rajah 5.2 menunjukkan sebuah segi empat selari, OPQR. Diagram 5.2 shows a parallelogram, OPQR. P(8, 4) O y Q x R(–5, 3) Rajah/Diagram 5.2 (i) Cari persamaan bagi garis lurus QR. Find the equation of the straight line QR. [3 markah/marks] Jawapan/Answer: CONTOH
78 (ii) Tentukan pintasan-x bagi garis lurus QR. Determine the x-intercept of the straight line QR. [1 markah/mark] Jawapan/Answer: (c) Rajah 5.3 menunjukkan suatu segi empat tepat, JKLM yang dilukis pada grid segi empat sama. Diagram 5.3 shows a rectangle, JKLM drawn on square grids. Pada rajah, lukis On the diagram, draw (i) lokus bagi titik X yang bergerak dengan keadaan KX = KL. the locus of point X which moves such that KX = KL. (ii) lokus bagi titik Y yang bergerak dengan keadaan Y sentiasa berjarak sama dari garis JK dan garis ML. the locus of point Y which moves such that it is always equidistant from the line JK and line ML. (iii) Seterusnya, tandakan dengan simbol ⊗ pada titik persilangan bagi lokus X dan lokus Y. Hence, mark with symbol ⊗ on the intersection of locus X and locus Y. [3 markah/marks] Jawapan/Answer: J K M L Rajah/Diagram 5.3 CONTOH
J1J1 Jawapan CONTOH
CONTOH
J3 PRAKTIS 1 Bahagian A 1. A 2. C 3. A 4. C 5. D 6. B 7. B 8. D 9. D 10. B 11. A 12. C 13. B 14. D 15. C 16. A 17. D 18. B 19. A 20. C Bahagian B 1. (a) (i) ( 4 √5) 3 (ii) 0 (b) (i) (m4 ) 2 (ii) m–4 2. (a) a14 a4 ; a4 ÷ a–6 (b) (i) 125 (ii) 1 125 3. (a) (i) x12 (ii) x 9 2 (b) p 5 7 = 7√p5 , p10 = (p2 ) 5 atau/or 1 p4 = p–4 4. (a) (i) 5 (ii) 4 (b) (i) 65 (ii) 63 Bahagian C 1. (a) (i) m9 (ii) k6 (iii) p–6 (b) (i) 0.01 (ii) x = 1 (c) y = 3 4 2. (a) (i) g–7 (ii) 50 (b) p = 2, q = 8 (c) x 1 2 y2 cm 3. (a) n = 3 (b) x = 5, y = √5 (c) x = 12y + 5 10 4. (a) 8q4 p7 (b) 2 (c) x = –1 PRAKTIS 2 Bahagian A 1. B 2. C 3. B 4. D 5. C 6. A 7. D 8. B 9. D 10. A 11. C 12. A 13. B 14. D 15. C 16. A 17. D 18. B Bahagian B 1. (a) (i) 2 (ii) 4 (b) (i) –3 (ii) 9 2. (a) (i) 3 (ii) 5 (b) (i) 8.04 × 105 (ii) 3.7 × 10–6 3. (a) (ii) 0.0004307 → 0.000431 (iv) 0.002004 → 0.00200 (b) (i) 0.000275 (ii) 670 000 Bahagian C 1. (a) (i) 28 500 (ii) 1.02 (iii) 0.0700 (b) (i) 1.512 × 106 cm (ii) 3.266 × 1010 cm2 (c) 6.696 × 106 2. (a) (i) 9.25 × 10–3 (ii) 3.47 × 100 (iii) 5.401 × 106 (b) 1.6294 × 10–25 kg (c) 1.007 × 105 3. (a) (i) 0.000258 (ii) 734 000 (iii) 9 600 000 (b) 3.854 × 10–26 kg (c) 1.74 × 10–3 m3 4. (a) 31.5 (b) (i) 1.26 × 10–2 m3 (ii) 7 135 kgm–3 (c) 3.24 × 104 PRAKTIS 3 Bahagian A 1. D 2. B 3. A 4. C 5. C 6. A 7. B 8. A 9. D 10. C 11. C 12. B 13. A 14. B 15. C 16. D Bahagian B 1. (a) Saham/Shares Amanah saham/Unit trusts (b) (i) ✓ (ii) ✗ 2. (a) (i) ✓ (ii) ✓ (iii) ✓ (iv) ✓ (b) (i) Saham syarikat/Company shares (ii) Hartanah/Real estate CONTOH
J4 Bahagian C 1. (a) (i) RM17 104.29 (ii) RM2 104.29 (b) Jumlah faedah/Total interest = RM46 170 x = 3.8 (c) 2.7% 2. (a) (i) RM1 080 (ii) RM1 230 ∴ Perbezaan/Difference RM1 230 – RM1 080 = RM150 (b) (i) RM290 (ii) RM5 550.76 (iii) RM5 901.33 3. (a) RM1.58 (b) RM971.58 (c) RM1.74 4. (a) RM45 000 (b) RM405 000 (c) 3.47% PRAKTIS 4 Bahagian A 1. A 2. C 3. D 4. A 5. B 6. D 7. C 8. D 9. B 10. A 11. C 12. D 13. B 14. D 15. A Bahagian B 1. (a) (i) 1 : 3 (ii) 1 : 1 (b) (i) C (ii) 1 : 2 3 2. (a) (i) 1 : 3 (ii) 1 : 3 5 (b) Bahagian C 1. (a) (i) 18 m (ii) 9 cm (b) (i) BC = 25 cm (ii) 760 cm (c) 625 cm2 2. (a) P (b) (i) 1 : 1 4 (ii) x = 4.8 cm, 15.36 cm2 (c) (i) 1 : 400 000 (ii) 212 km 3. (a) 2 880 cm2 (b) (i) (ii) PRAKTIS 5 Bahagian A 1. C 2. B 3. D 4. A 5. B 6. A 7. A 8. B 9. C 10. D 11. C 12. C 13. B 14. A 15. B Bahagian B 1. (a) (i) m p (ii) m n (b) (i) , (ii) . 2. (a) (i) Sisi bersebelahan/Adjacent side (ii) Sisi bertentangan/Opposite side (b) (i) ✗ (ii) ✗ (iii) ✓ Bahagian C 1. (a) (i) sin x = 12 13 CONTOH
J5 (ii) kos/cos x = 5 13 (iii) tan x = 12 5 (b) (i) 6.401 m (ii) 13.614 m (c) (i) sin x = 24 25 (ii) QR = 16 cm, tan y = 4 3 2. (a) 291° 48ʹ (b) 97° 9ʹ (c) (i) 5 cm (ii) kos/cos y = 7 25 3. (a) (i) tan x = 5 12 (ii) PT = 10 cm, sin y = 15 17 (b) (i) 4.607 m (ii) 28° 45ʹ (c) x = 9.238 cm, Luas/Area = 36.952 cm2 PRAKTIS 6 Bahagian A 1. B 2. D 3. C 4. A 5. D 6. C 7. A 8. B 9. A 10. C 11. B 12. D 13. A 14. B 15. A Bahagian B 1. (a) (i) ✓ (ii) ✗ (iii) ✗ (b) (i) BENAR/TRUE (ii) BENAR/TRUE 2. (a) (i) ✓ (ii) ✗ (b) (i) ✗ (ii) ✓ Bahagian C 1. (a) x = 80°, y = 55°, z = 25° (b) (i) x = 90° (ii) y = 96° (iii) z = 108° (c) (i) x = 64° (ii) y = 107° (iii) z = 43° 2. (a) (i) x = 56° (ii) y = 62° (iii) z = 28° (b) 31.66 cm (c) (i) x = 35° (ii) y = 22° (iii) z = 33° 3. (a) (i) x = 63° (ii) y = 27° (iii) z = 73° (b) (i) 12 cm (ii) 20 cm (iii) 24 cm (c) (i) 180° – 4x (ii) 45° – x PRAKTIS 7 Bahagian A 1. C 2. D 3. A 4. B 5. C 6. B 7. D 8. A Bahagian B 1. (a) ✗ (b) ✓ (c) ✓ (d) ✗ 2. (a) (b) 3. (a) (b) Bahagian C 1. (a) E/D F G/C K/A 3 cm J 3 cm H/B 4 cm CONTOH
J6 (b) (i) 2 cm 4 cm 4 cm 2 cm K/E J/F B/C M L H/G A/D 2 cm N 3 cm 4 cm (ii) H K J B/A C/N/D G E F 2 cm 1 cm 1 cm 4 cm 2 cm 6 cm L/M 2. (a) 2 cm 2 cm 3 cm 5 cm 6 cm 5 cm (b) 102.5 cm3 (c) 738 g PRAKTIS 8 Bahagian A 1. B 2. C 3. A 4. D 5. B 6. D 7. C 8. A 9. A 10. D 11. C 12. C 13. B 14. B Bahagian B 1. (a) (i) ✓ (ii) ✓ (b) (i) Pembahagi sudut/Angle bisectors (ii) Garis selari/Parallel lines 2. (a) (i) HF (ii) DB (b) F Bahagian C 1. (a) P Q S R (b) (i) SR (ii) P Q S R (c) P R Q S T 2. (a) S P R Q O (b) (i) KM (ii) M L J K PRAKTIS 9 Bahagian A 1. B 2. D 3. A 4. C 5. B 6. A 7. D 8. B 9. A 10. C 11. B 12. B 13. D 14. A 15. C Bahagian B 1. (a) (i) m = –2, c = 8 (ii) m = – 1 4 , c = 3 (b) (i) 5 (ii) –7 2. (a) (–2, 13); (5, –1) (b) (i) PALSU/FALSE (ii) BENAR/TRUE 3. (a) (i) 3x + 4y = 12 (ii) y = 3 4 x – 3 8 CONTOH
J7 (b) (i) RS (ii) PQ 4. (a) (i) x = 5 (ii) y = –3 (b) (i) 8x + 2y = 13 (iv) x 2 + y 8 = 1 Bahagian C 1. (a) y = –2x + 6 (b) (i) y = – 1 2 x + 8 (ii) 16 (iii) x = 8, (8, 4) 2. (a) (i) k = 6 (ii) y = –2x + 6 (iii) 9 unit2 /units2 (b) (i) 9 km (ii) 4y = –3x + 15 3. (a) (i) 2y = x + 5 (ii) 5 2 (b) (i) y = –3 (ii) 2y + 5x = 34 (iii) k = 6.8 UJIAN AKHIR SESI AKADEMIK (UASA) Bahagian A 1. B 2. C 3. D 4. B 5. A 6. B 7. D 8. A 9. B 10. C 11. D 12. B 13. A 14. A 15. B 16. A 17. C 18. D 19. B 20. C Bahagian B 21. (a) (i) (a4 ) 3 (ii) a4 a–8 (b) (i) Simpanan tetap/Fixed deposit (ii) Saham/Shares 22. (a) (i) Bererti/Significant (ii) Tidak bererti/Not significant (b) 23. (a) (i) A D B C Lokus X Locus of X (ii) P S Q R Lokus Y/Locus of Y (b) 24. (a) (i) A (ii) D (b) (i) (m3 ) 4 = m12 (ii) m–3 = 1 m3 25. (a) (i) 649 000 (ii) 0.0230 (b) Bahagian C 26. (a) (i) 1.5 × 104 – 0.036 × 104 = 1.464 × 104 (ii) 81.45 = 80 (b) (i) x × 1.25 × 0.06 = 225 x = 3 000 (ii) ROI = 3 600 + 225 – (3 000 × 1.25) 3 000 × 1.25 × 100% = 2% (c) (5√32)7 = 27 = 128 27. (a) A/L 2 cm 4 cm 5 cm C/E G/I B/K D/F H/J (b) (i) 5(0) = –4(m) + 40 m = 10 (ii) Koordinat S ialah (0, 8). Coordinate of S is (0, 8). m = – 8 4 = –2 ∴ Persamaan ST/Equation of ST y = –2x + 8 (c) 7 850 × 48 × 1 000 2.4 = 157 000 000 = 1.57 × 108 28. (a) (i) 15.81 cm (ii) ∠CAH = 14°12ʹ (b) 5 1 000 = 1 200 = 1 : 200 (c) (i) QT CONTOH
Berdasarkan kehendak Dokumen Standard Kurikulum dan Pentaksiran (DSKP) Memenuhi format, standard dan keperluan kertas UASA terkini Disusun mengikut topik-topik dalam buku teks Menggabung jalinkan elemen Kemahiran Berfikir Aras Tinggi (KBAT) dan i-Think Jawapan lengkap disediakan Judul-judul dalam siri ini: Subjek Tingkatan Bahasa Melayu Reka Bentuk & Teknologi Geografi Sejarah Pendidikan Islam Matematik (Dwibahasa) Sains (Dwibahasa) English 1 2 3 Demi Pentaksiran KSSM Dicetak oleh: Swan Printing Sdn. Bhd. (274710-X) Lot 5249, Jalan BS7/1, Kawasan Perindustrian Bukit Serdang, 43300 Seri Kembangan, Sel. D.E. Lot 1 & 2, Jalan BS 7/1A, Taman Bukit Serdang, Seksyen 7, 43300 Seri Kembangan, Selangor Darul Ehsan. • Bhg. Penjualan: 03 – 8959 2001/ 3001/ 4003 • Faks: 03 – 8957 3611 • Bhg. Editorial: 03 – 6150 3009 • Faks: 03 – 6150 1007 • E-mel: [email protected] • Laman Web: www.pep-publications.com tak oleh: Swan Printing Sdn. Bhd. (274710-X) 5249, Jalan BS7/1, Kawasan Perindustrian Bukit Serdang, 43300 Seri Kembangan, Sel. D.E. & 2, Jalan BS 7/1A, Taman Bukit Serdang, Seksyen 7, 00 Seri Kembangan, Selangor Darul Ehsan. g. Penjualan: 03 – 8959 2001/ 3001/ 4003 • Faks: 03 – 8957 3611 g. Editorial: 03 – 6150 3009 • Faks: 03 – 6150 1007 mel: [email protected] man Web: www.pep-publications.com Sem. M’sia: RM6.90 Sabah/ S’wak: RM7.50 KSSM Pentaksiran TOPIK Demi TOPIK MATEMATIK (Dwibahasa) 3 9 786294 831872 ISBN 978-629-483-187-2 CONTOH