Sumber Pendidikan
NAMA: ………………….………………………………………. TINGKATAN: ………………..
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PROGRAM PEMANTAPAN PRESTASI TINGKATAN 5
TAHUN 2017
MAJLIS PENGETUA SEKOLAH MALAYSIA (KEDAH)
|MODUL 2 |
|MATEMATIK |
|KERTAS 2 |
|(1449/2) |
|Dua jam tiga puluh minit |
|JANGAN BUKA MODUL INI SEHINGGA DIBERITAHU |
| | |Untuk Kegunaan Pemeriksa |
| | |Bahagian |Soalan |Markah Penuh |Markah diperoleh |
| | |A |1 |3 | |
|1 |Tulis nama dan tingkatan anda pada ruang yang | |2 |3 | |
| |disediakan. | | | | |
| | | |3 |4 | |
|2 |Modul ini adalah dalam dwibahasa. | |4 |4 | |
| | | |5 |4 | |
|3 |Soalan dalam bahasa Melayu mendahului soalan yang | |6 |5 | |
| |sepadan dalam bahasa Inggeris. | | | | |
| | | |7 |5 | |
| | | |8 |6 | |
|4 |Calon dibenarkan menjawab keseluruhan atau sebahagian | |9 |6 | |
| |soalan sama ada dalam bahasa Melayu atau bahasa | | | | |
| |Inggeris. | | | | |
| | | |10 |6 | |
| | | |11 |6 | |
| | |B |12 |12 | |
|5 |Calon dikehendaki membaca maklumat di halaman | |13 |12 | |
| |belakang modul ini. | | | | |
| | | |14 |12 | |
| | | |15 |12 | |
| |. | |16 |12 | |
| | |Jumlah | |
|Modul ini mengandungi 36 halaman bercetak. |
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RUMUS MATEMATIK
MATHEMATICAL FORMULAE
|Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan |
|The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. |
|PERKAITAN |
|RELATIONS |
|1 |am × an = am+n |10 |Teorem Pithagoras |
| | | |Pythagoras Theorem |
| | | |c2 = a2 + b2 |
|2 |am ÷ an = am – n | | |
|3 |(am) n = amn | | |
|4 |A-1 = [pic] |11 |[pic] |
|5 |Jarak / Distance =[pic] |12 |P(A( ) = 1 – P(A) |
|6 |Titik tengah / Midpoint | | |
| |[pic] | | |
| | |13 |[pic] |
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|7 |[pic] |14 |[pic] |
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| |[pic] | |[pic] |
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|8 |[pic] | | |
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|9 |[pic] |
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|BENTUK DAN RUANG |
|SHAPES AND SPACE |
|1 |[pic] |
| |[pic] |
|2 |Lilitan bulatan = πd = 2πj |
| |Circumference of circle = πd = 2πr |
|3 |Luas bulatan = πj2 |
| |Area of circle = πr2 |
|4 |Luas permukaan melengkung silinder = 2πjt |
| |Curved surface area of cylinder = 2πrh |
|5 |Luas permukaan sfera = 4πj2 |
| |Surface area of sphere = 4πr2 |
|6 |Isipadu prisma tegak = luas keratan rentas × panjang |
| |Volume of right prism = cross section × length |
|7 |Isipadu silinder = πj2t |
| |Volume of cylinder = πr2h |
|8 |Isipadu kom = [pic]πj2t |
| |Volume of cone = [pic]πr2h |
|9 |Isipadu sfera = [pic]πj3 |
| |Volume of sphere = [pic]πr3 |
| |Isipadu pyramid tegak = [pic]× luas tapak × tinggi |
|10 |Volume of right pyramid = [pic]× base area × height |
|11 |Hasil tambah sudut pedalaman polygon |
| |Sum of interior of a polygon |
| |= (n – 2 ) × 180( |
|12 |[pic] |
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|13 |[pic] |
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|14 |Faktor skala, k = [pic] |15. |Luas imej = k2 × luas objek |
| | | |Area of image = k2 × area of object |
| |Scale factor, k = [pic] | | |
|Untuk Kegunaan | |Bahagian A | |
|Pemeriksa | |Section A | |
| | |[52 markah / marks] | |
| | |Jawab semua soalan dalam bahagian ini. | |
| | |Answer all questions in this section. | |
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| |1 |Pada graf di ruang jawapan, lorek rantau yang memuaskan ketiga-tiga ketaksamaan y > 2x + 2, y > ˗ x ˗ 1 dan y ≤| |
| | |4. | |
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| | |On the graph in the answer space, shade the region which satisfies the three inequalities y > 2x + 2, y > ˗ x ˗| |
| | |1 and y ≤ 4. | |
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| | |[3 markah / marks] | |
| | |Jawapan / Answer: | |
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| |2 |Rajah 2 menunjukkan sebuah prisma tegak dengan tapak segi empat tepat ABCD di atas tapak mengufuk. Satah tegak ADE |Untuk Kegunaan |
| | |ialah keratan rentas seragam prisma itu. |Pemeriksa |
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| | |Diagram 2 shows a right prism with a rectangular base ABCD on a horizontal plane. The vertical plane ADE is the | |
| | |uniform cross-section of the prism. | |
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| | |(a) |Namakan sudut di antara satah ABF dengan tapak ABCD. | |
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| | | |Name the angle between the plane ABF and the base ABCD. | |
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| | |(b) |Hitung sudut di antara satah ABF dengan tapak ABCD. | |
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| | | |Calculate the angle between the plane ABF and the base ABCD. | |
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| | | |[3 markah / marks] | |
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| | |Jawapan / Answer : | |
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|Untuk Kegunaan |3 |Rajah 3 menunjukkan suatu gabungan pepejal yang terdiri daripada cantuman sebuah separuh silinder dengan sebuah | |
|Pemeriksa | |prisma tegak. ABKJ ialah keratan rentas prisma tegak itu. MK ialah diameter separuh silinder itu. | |
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| | |Diagram 3 shows a composite solid, formed by joining a half-cylinder with a right prism. ABKJ is the cross-section | |
| | |of the right prism. MK is the diameter of the half-cylinder. | |
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| | |[pic] | |
| | |Rajah / Diagram 3 | |
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| | |Diberi BK = 28 cm, AJ = 14 cm dan AE = 20 cm. | |
| | |Isi padu gabungan pepejal itu ialah 17 000 cm3. | |
| | |Menggunakan [pic], hitung nilai h. | |
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| | |Given BK = 28 cm, AJ = 14 cm and AE = 20 cm, | |
| | |The volume of the composite solid is 17 000 cm3. | |
| | |Using [pic], calculate the value of h. | |
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| | | |[4 markah / marks] | |
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| | |Jawapan / Answer: |Untuk Kegunaan |
| | | |Pemeriksa |
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|Untuk Kegunaan |4 |Menggunakan pemfaktoran, selesaikan persamaan berikut: | |
|Pemeriksa | | | |
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| | |Using factorisation, solve the following quadratic equation: | |
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| | |3x (x – 2) = 7x + 10 | |
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| | |[4 markah / marks] | |
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| | |Jawapan / Answer: | |
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| |5 |Menggunakan kaedah penghapusan atau kaedah penggantian, hitung nilai x dan nilai y yang memuaskan persamaan | |
| | |linear serentak berikut: | |
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| | |Using elimination or substitution method, calculate the value of x and of y that satisfy the following| |
| | |simultaneous linear equation: | |
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| | |[pic] | |
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| | |[4 markah / marks] | |
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| | |Jawapan / Answer: | |
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| |6 |(a) |(i) |Nyatakan sama ada yang berikut adalah pernyataan atau bukan pernyataan: |Untuk Kegunaan |
| | | | | |Pemeriksa |
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| | | | |State whether the following is a statement or not a statement: | |
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| | | | |– 5 + 3 < – 4 | |
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| | | |(ii) |Tuliskan implikasi berdasarkan maklumat berikut: | |
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| | | | |Write down implication base on the following information: | |
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| | | | |Antejadian |: |x ialah gandaan 4. | |
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| | | | |Antecedent |: |x is a multiple of 4. | |
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| | | | |Akibat |: |x ialah nombor genap. | |
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| | | | |Consequence |: |x is an even number. | |
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| | |(b) |Tulis dua implikasi berdasarkan pernyataan majmuk berikut: | |
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| | | |Write two implications based on the following compound statements: | |
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| | | |[pic] jika dan hanya jika [pic]. | |
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| | | |[pic] if and only if [pic]. | |
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| | |(c) |Tuliskan Premis 2 untuk melengkapkan hujah berikut: | |
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| | | |Write down Premise 2 to complete the following argument: | |
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| | | |Premis 1 |: |Semua gandaan 8 adalah gandaan 4. | |
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| | | |Premise 1 |: |All multiples of 8 are multiples of 4. | |
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| | | |Premis / Premise 2 |: |………………………………………………….. | |
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| | | |Kesimpulan: |: |64 adalah gandaan 4. | |
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| | | |Conclusion |: |64 is a multiple of 4. | |
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| | | |[5 markah / marks] | |
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| | |Jawapan / Answer: | |
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| | |(a) |(i) |…………………………………………………………………………… | |
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| | | |(ii) |Implikasi / Implication: |………………………………………………. | |
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| | | | | |………………………………………………. | |
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| | |(b) |Implikasi / Implication 1: |………………………………………………….... | |
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| | | |Implikasi / Implication 2: |…………………………………………………… | |
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| | |(c) |Premis / Premise 2 |: |…………………………………………………….. | |
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|Untuk Kegunaan |7 |Rajah 7 menunjukkan PQRT ialah sebuah trapezium. Garis lurus PT adalah selari dengan garis lurus QR. Garis lurus RT | |
|Pemeriksa | |adalah selari dengan paksi-y. | |
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| | |Diagram 7 shows PQRT is a trapezium. The straight line PT is parallel to the straight line QR. The straight line RT | |
| | |is parallel to the y-axis. | |
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| | |Cari | |
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| | |Find | |
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| | |(a) |persamaan garis lurus PT. | |
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| | | |the equation of the straight line PT. | |
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| | |(b) |pintasan-x bagi garis lurus PT. | |
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| | | |the x-intercept of the straight line PT. | |
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| | | |[5 markah / marks] | |
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| | |Jawapan / Answer: | |
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| | | |Diberi bahawa [pic], dengan keadaan M ialah matriks [pic]. |Untuk Kegunaan |
| |8 |(a) | |Pemeriksa |
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| | | |Cari matriks M. | |
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| | | |It is given that [pic], where M is [pic] matrix. | |
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| | | |Find the matrix of M. | |
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| | |(b) |Tulis persamaan linear serentak berikut dalam bentuk matriks: | |
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| | | |Write the following simultaneous linear equations as a matrix equation: | |
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| | | |[pic] | |
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| | | |Seterusnya, menggunakan kaedah matriks, hitung nilai x dan nilai y. | |
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| | | |Hence, by using matrix method, calculate the value of x and of y. | |
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| | | |[6 markah / marks] | |
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| | |Jawapan / Answer: | |
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|Untuk Kegunaan |9 |Rajah 9 menunjukkan sektor OPQR berpusat O. OQR ialah sebuah segi tiga sama kaki. Diberi bahawa (POR = 150(. | |
|Pemeriksa | | | |
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| | |Diagram 9 shows sector OPQR with centre O. OQR is an isoceles triangle. It is given that| |
| | |(POR = 150(. | |
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| | |[pic] | |
| | |Rajah / Diagram 9 | |
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| | |Menggunakan [pic], hitung | |
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| | |Using [pic], calculate | |
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| | |(a) |perimeter, dalam cm, seluruh rajah itu, | |
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| | | |the perimeter, in cm, of the whole diagram, | |
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| | |(b) |luas, dalam cm2, kawasan yang berlorek. | |
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| | | |the area, in cm2, of the shaded region. | |
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| | | | [6 markah /marks] | |
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| | |Jawapan / Answer: |Untuk Kegunaan |
| | | |Pemeriksa |
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| Untuk Kegunaan|10 |Rajah 10 menunjukkan graf laju-masa bagi suatu zarah dalam tempoh 37 saat. | |
|Pemeriksa | | | |
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| | |Diagram 10 shows a speed-time graph of a particle for a period of 37 seconds. | |
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| | |(a) |Nyatakan laju seragam, dalam ms(1, zarah itu. | |
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| | | |State the uniform speed, in ms(1, of the particle. | |
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| | |(b) |Hitung purata laju, dalam ms(1, perjalanan zarah itu dalam tempoh 12 saat yang terakhir. | |
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| | | |Calculate the average speed, in ms(1, of the particle for the last 12 seconds. | |
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| | |(c) |Hitung nilai t, jika jumlah jarak yang dilalui oleh zarah itu dalam 15 saat yang pertama ialah 165 m. | |
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| | | |Calculate the value of t, if the total distance travelled by the particle in the first 15 seconds is 165 m. | |
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| | | |[6 markah / marks] | |
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| | |Jawapan / Answer : |Untuk Kegunaan |
| | | |Pemeriksa |
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|Untuk Kegunaan |11 |Rajah 11 menunjukkan lapan kad yang berlabel dengan huruf dan nombor di dalam kotak Y dan kotak Z. | |
|Pemeriksa | | | |
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| | |Diagram 11 shows eight labelled cards with letter and number in box Y and box Z. | |
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| | |Sekeping kad dipilih secara rawak daripada kotak Y dan kemudian sekeping kad lagi dipilih secara rawak daripada kotak| |
| | |Z. | |
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| | |A card is picked at random from box Y and then another card is picked at random from box Z. | |
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| | |(a) |Senaraikan ruang sampel. | |
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| | | |List the sample space. | |
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| | |(b) |Dengan menyenaraikan semua kesudahan yang mungkin bagi peristiwa itu, cari kebarangkalian bahawa | |
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| | | |By listing down all the possible outcomes of the event, find the probability that | |
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| | | |(i) |kedua-dua kad dilabel dengan huruf, | |
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| | | | |both card are labelled with a letter, | |
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| | | |(ii) |sekeping kad dilabel dengan huruf dan sekeping kad lagi dilabel dengan nombor. | |
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| | | | |one card is labelled with a letter and the other card is labelled with a number. | |
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| | | |[6 markah / marks] | |
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| | |Jawapan / Answer: |Untuk Kegunaan |
| | | |Pemeriksa |
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| | |(b) |(i) | | |
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| | | |(ii) | | |
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| | |Bahagian/Section B | |
| | |[48 markah/marks] | |
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| | |Jawab mana-mana empat soalan dalam bahagian ini. | |
| | |Answer any four questions from this section. | |
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| |12 |(a) |Lengkapkan Jadual 12 di ruang jawapan pada halaman 20 bagi persamaan [pic] dengan menulis | |
| | | |nilai-nilai y apabila x = – 2 dan x = 2·5. | |
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| | | |Complete Table 12 in the answer space on page 20 for the equation [pic] by writing down the values | |
| | | |of y when x = – 2 and x = 2·5. | |
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| | | |[2 markah / marks] | |
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| | |(b) |Untuk ceraian soalan ini, gunakan kertas graf yang disediakan pada halaman 21. Anda boleh menggunakan | |
| | | |pembaris fleksibel. | |
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| | | |Menggunakan skala 2 cm kepada 1 unit pada paksi-x dan 2 cm kepada 5 unit pada paksi-y, lukis graf[pic] | |
| | | |untuk –3 ≤ x ≤ 5. | |
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| | | |For this part of the question, use the graph paper provided on page 21. You may use a flexible curve rule. | |
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| | | |Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph [pic] for | |
| | | |–3 ≤ x ≤ 5. | |
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| | | |[4 markah / marks] | |
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| | |(c) |Daripada graf di 12(b), cari | |
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| | | |From the graph in 12(b), find | |
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| | | |(i) |nilai y apabila x = 0·5 | |
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| | | | |the value of y when x = 0·5. | |
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| | | |(ii) |nilai x apabila y = (10. | |
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| | | | |the value of x when y = (10. | |
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| | | | |[2 markah / marks] | |
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| | |(d) |Lukis satu garis lurus yang sesuai pada graf di 12(b) untuk mencari nilai-nilai x yang memuaskan persamaan | |
| | | |[pic] untuk –3 ≤ x ≤ 5. | |
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| | | |Nyatakan nilai-nilai x ini. | |
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| | | |Draw a suitable straight line on the graph in 12(b) to find the values of x which satisfy the equation | |
| | | |[pic] for –3 ≤ x ≤ 5. | |
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| | | |State these values of x. | |
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| | | |[4 markah / marks] | |
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|Untuk Kegunaan | |Jawapan / Answer: | |
|Pemeriksa | | | |
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| | |(a) |[pic] | |
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| | | |x | |
| | | |–3 | |
| | | |–2 | |
| | | |–1 | |
| | | |0 | |
| | | |1 | |
| | | |2(5 | |
| | | |3 | |
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| | | |y | |
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| | | |13 | |
| | | |10 | |
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| | | |–11 | |
| | | |–22 | |
| | | |–35 | |
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| | | |Jadual / Table 12 | |
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| | |(b) |Rujuk graf pada halaman 21. | |
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| | | |Refer graph on page 21. | |
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| | |(c) |(i) |[pic] | |
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| | | |(ii) |[pic] | |
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| | |(d) | | | |
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| | | |[pic], [pic] | |
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| |[pic] |Untuk Kegunaan |
| | |Pemeriksa |
| |13 |(a) |Rajah 13(1 menunjukkan titik (2, 4) dan garis lurus y = 1 dilukis pada satah Cartes. | |
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| | | |Diagram 13(1 shows the point (2, 4) and the straight line y = 1 drawn on a Cartesian plane. | |
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| | | |Penjelmaan T ialah satu translasi [pic] | |
| | | |Penjelmaan P ialah satu pantulan pada garis lurus y = 1 | |
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| | | |Nyatakan koordinat imej bagi titik (2, 4) di bawah penjelmaan berikut: | |
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| | | |Transformation T is a translation [pic] | |
| | | |Transformation P is a reflection in the straight line y = 1 | |
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| | | |State the coordinate of the image of point (2, 4) under the following transformations: | |
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| | | |(i) |T, | |
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| | | |(ii) |TP. | |
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| | | | |[3 markah / marks] | |
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| | |Jawapan / Answer: |Untuk Kegunaan |
| | | |Pemeriksa |
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| | |(b) |Rajah 13(2 menunjukkan sisi empat ABCD, EFGH dan JKLM, dilukis pada satah Cartes. | |
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| | | |Diagram 13(2 shows quadrilaterals ABCD, EFGH and JKLM, drawn on a Cartesian plane. | |
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| | | |(i) |JKLM ialah imej bagi ABCD di bawah gabungan penjelmaan VW. | |
| | | | |Huraikan selengkapnya penjelmaan: | |
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| | | | |JKLM is the image of ABCD under the combined transformation VW. | |
| | | | |Describe in full, the transformation: | |
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| | | | |(a) |W. | |
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| | | | |(b) |V. | |
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| | | |(ii) |Diberi bahawa sisi empat ABCD mewakili suatu kawasan yang mempunyai luas 225 cm2. | |
| | | | |Hitung luas, dalam cm2, kawasan yang berlorek. | |
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| | | | |It is given that quadrilateral ABCD represents a region of area 225 cm2. | |
| | | | |Calculate the area, in cm2, of the shaded region. | |
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| | | |[9 markah / marks] | |
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| | |Jawapan / Answer: |Untuk Kegunaan |
| | | |Pemeriksa |
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| | |(b) |(i) |(a) |W |: |………………………………………………|
| | | | | | | |…………. |
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| | | |(ii) | | | | |
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| |14 |Data dalam Rajah 14 menunjukkan markah Matematik bagi 30 orang murid dalam suatu peperiksaan percubaan. | |
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| | |The data in Diagram 14 shows the marks of Mathematics for 30 pupils in a trial examination. | |
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| | |33 | |
| | |37 | |
| | |27 | |
| | |55 | |
| | |75 | |
| | |48 | |
| | |68 | |
| | |30 | |
| | |57 | |
| | |48 | |
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| | |54 | |
| | |45 | |
| | |35 | |
| | |78 | |
| | |62 | |
| | |70 | |
| | |52 | |
| | |68 | |
| | |36 | |
| | |58 | |
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| | |56 | |
| | |85 | |
| | |48 | |
| | |51 | |
| | |85 | |
| | |44 | |
| | |42 | |
| | |53 | |
| | |63 | |
| | |64 | |
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| | |Rajah / Diagram 14 | |
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| | |(a) |Berdasarkan data itu, lengkapkan Jadual 14 di ruang jawapan yang disediakan pada halaman 28. | |
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| | | |Based on the data, complete Table 14 in the answer space provided on page 28. | |
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| | | | [4 markah / marks] | |
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| | |(b) |(i) |Nyatakan kelas mod. | |
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| | | | | State the modal class. | |
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| | | |(ii) |Berdasarkan Jadual 14 di ruang jawapan, hitung min anggaran markah bagi seorang murid. | |
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| | | | | Based on Table 14 in the answer space, calculate the estimated mean of the mark for a pupil. | |
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| | | |[4 markah / marks] | |
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| | |(c) |Untuk ceraian soalan ini, gunakan kertas graf yang disediakan pada halaman 28. | |
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| | | |Dengan menggunakan skala 2 cm kepada 10 markah pada paksi mengufuk dan 2 cm kepada 1 murid pada paksi mencancang, | |
| | | |lukis satu histogram berdasarkan Jadual 14. | |
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| | | |For this part of the question, use the graph paper provided on page 28. | |
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| | | |By using the scale of 2 cm to 10 marks on the horizontal axis and 2 cm to 1 pupil on the | |
| | | |vertical axis, draw a histogram based on Table 14. | |
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| | | |[4 markah / marks] | |
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|Untuk Kegunaan | |Jawapan / Answer: | |
|Pemeriksa | | | |
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| | |(a) |Markah | |
| | | |Marks | |
| | | |Kekerapan | |
| | | |Frequency | |
| | | |Titik tengah | |
| | | |Midpoint | |
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| | | |20 – 29 | |
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| | | |24(5 | |
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| | | |Jadual / Table 14 | |
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| | |(b) |(i) | | |
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| | |(c) |Rujuk graf di halaman 29. | |
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| | | |Refer graph on page 29. | |
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|[pic] |Untuk Kegunaan |
| |Pemeriksa |
| |15 |(a) |Rajah 15(1 menunjukkan sebuah pepejal berbentuk prisma tegak dengan tapak segi empat sama ABCD terletak di atas | |
| | | |satah mengufuk. Permukaan ABKJGF ialah keratan rentas seragam prisma itu. Segi empat tepat GJMH ialah satah | |
| | | |condong. Segi empat tepat FGHE dan JKLM ialah satah mengufuk. Tepi AF dan CL adalah tegak. | |
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| | | |Diagram 15(1 shows a solid right prism with square base ABCD on a horizontal plane. The surface ABKJGF is the | |
| | | |uniform cross section of the prism. Rectangle GJMH is an inclined plane. Rectangles FGHE and JKLM is a | |
| | | |horizontal plane. Edges AF and CL are vertical. | |
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| | | |Lukis dengan skala penuh, pelan pepejal itu. | |
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| | | |Draw to full scale, the plan of the solid. | |
| | | |[3 markah / marks] | |
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| | | |Jawapan / Answer: |Untuk Kegunaan|
| | | | |Pemeriksa |
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| | | |(a) | |
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| | |(b) |Sebuah pepejal lain berbentuk prisma tegak dengan tapak segi empat tepat PQRT dicantumkan kepada prisma dalam | |
| | | |Rajah 15(1 pada satah mencancang TCLMH. PQVU ialah keratan rentas seragam prisma dan segi empat tepat HUVW ialah| |
| | | |satah condong prisma itu. Gabungan pepejal adalah seperti yang ditunjukkan dalam Rajah 15(2. Tapak ABCPQRTD | |
| | | |terletak di atas satah mengufuk. | |
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| | | |Another solid right prism with rectangular base PQRT is joined to the prism in Diagram 15(1 at the vertical plane| |
| | | |TCLMH. PQVU is a uniform cross section and rectangle HUVW is an inclined plane of that prism. The composite solid| |
| | | |is as shown in Diagram 15(2. The base ABCPQRTD lies on a horizontal plane. | |
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| | | |Lukis dengan skala penuh, | |
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| | | |Draw to full scale, | |
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| | | |(i) |dongakan gabungan pepejal itu pada satah mencancang yang selari dengan BC, sebagaimana dilihat dari X, | |
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| | | | |the elevation of the composite solid on a vertical plane parallel to BC, as viewed from X, | |
| | | | [4 markah / | |
| | | |marks] | |
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| | | |(ii) |dongakan gabungan pepejal itu pada satah mencancang yang selari dengan AB, sebagaimana dilihat dari Y. |Untuk Kegunaan |
| | | | | |Pemeriksa |
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| | | | |the elevation of the composite solid on a vertical plane parallel to AB, as viewed from Y. | |
| | | | |[5 markah / marks] | |
| | |Jawapan / Answer: | |
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| | |(b) |(i), (ii) | |
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| |16 |Rajah 16 menunjukkan empat titik H, J, K dan X pada permukaan bumi. HK ialah diameter bumi. | |
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| | |Diagram 16 shows four points H, J, K and X on the surface of the earth. HK is the diameter of the earth. | |
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| | |(a) |Cari kedudukan H. | |
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| | | |Find the position of H. | |
| | | |[3 markah / marks] | |
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| | |(b) |Hitung jarak terpendek, dalam batu nautika, dari K ke Kutub Utara diukur sepanjang permukaan bumi. | |
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| | | |Calculate the shortest distance, in nautical miles, from K to the North Pole measured along the surface of the | |
| | | |earth. | |
| | | |[2 markah / marks] | |
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| | |(c) |Hitung jarak, dalam batu nautika, dari J ke timur ke K mengikut selarian latitud sepunya. | |
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| | | |Calculate the distance, in nautical miles, from J due east to K measured along the common parallel of latitude. | |
| | | |[3 markah / marks] | |
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| | |(d) |Sebuah kapal terbang berlepas dari K arah ke barat ke J mengikut selarian latitud sepunya dan kemudian terbang | |
| | | |arah selatan ke X. Purata laju bagi keseluruhan penerbangan itu ialah 600 knot. | |
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| | | |Hitung jumlah masa, dalam jam, yang diambil bagi seluruh penerbangan itu. | |
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| | | |An aeroplane took off from K flew due west to J along the common parallel of latitude and then flew due south to | |
| | | |X. The average speed for the whole flight was 600 knots. | |
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| | | |Calculate the total time, in hours, taken for the whole flight. | |
| | | |[4 markah / marks] | |
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| | |Jawapan / Answer: |Untuk Kegunaan |
| | | |Pemeriksa |
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| | |(a) | | |
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| | |(b) | | |
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| | |(c) | | |
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| | |(d) | | |
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|MAKLUMAT UNTUK CALON |
|INFORMATION FOR CANDIDATES |
|1 |Kertas soalan ini mengandungi dua bahagian: Bahagian A dan Bahagian B. |
| | |
| |This question paper consist of two sections: Section A and Section B. |
| | |
|2 |Jawab semua soalan dalam Bahagian A dan mana-mana empat soalan daripada Bahagian B. |
| | |
| |Answer all questions in Section A and any four questions from Section B. |
| | |
|3 |Tulis jawapan anda pada ruang yang disediakan dalam kertas soalan ini. |
| | |
| |Write your answers in the spaces provided in the question paper. |
| | |
|4 |Tunjukkan kerja mengira anda. Ini boleh membantu anda untuk mendapatkan markah. |
| | |
| |Show your working. It may help you to get marks. |
| | |
|5 |Jika anda hendak menukar jawapan, batalkan jawapan yang telah dibuat. Kemudian tulis jawapan yang baru. |
| | |
| |If you wish to change your answer, cross out the answer that you have done. Then write down the new answer. |
| | |
|6 |Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan. |
| | |
| |The diagrams in the questions provided are not drawn to scale unless stated. |
| | |
|7 |Markah diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan dalam kurungan. |
| | |
| |The marks allocated for each question and sub-part of a question are shown in brackets. |
| | |
|8 |Satu senarai rumus disediakan di halaman 2 dan 3 |
| | |
| |A list of formulae is provided on pages 2 and 3. |
| | |
|9 |Anda dibenarkan menggunakan kalkulator saintifik. |
| | |
| |You may use a scientific calculator. |
| | |
|10 |Serahkan kertas soalan ini kepada pengawas peperiksaan pada akhir peperiksaan. |
| | |
| |Hand in this question paper to the invigilator at the end of the examination. |
[pic]
-----------------------
[pic]
[pic]
x
2
4
(4
8
y
O
(2
2
4
6
(2
(4
(6
E
F
D
C
A
B
12 cm
10 cm
5 cm
Rajah / Diagram 2
P
Q ((4, (4)
R
T ( 8, 5)
x
y
O
Rajah / Diagram 7
Rajah / Diagram10
O
12
25
18
15
37
t
Laju / Speed (ms(1)
Masa / Time (s)
Rajah / Diagram 11
8
5
4
N
M
R
Q
J
Kotak / Box Y
Kotak / Box Z
Graf untuk Soalan 12
Graph for Question 12
2
4
6
2
4
(2
(4
(
(2, 4)
Rajah / Diagram 13(1
x
O
y
8
10
y = 1
(2
(4
B
C
D
L
J
H
K
G
F
A
E
M
2
2
4
6
8
4
6
8
10
Rajah / Diagram 13(2
O
y
x
10
12
14
Graf untuk Soalan 14
Graph for Question 14
A
B
D
C
E
K
F
J
G
H
8 cm
7 cm
7 cm
3 cm
4 cm
Rajah / Diagram 15(1
L
M
2 cm
X
Y
A
B
D
C
E
K
F
J
G
H
8 cm
7 cm
7 cm
3 cm
4 cm
Rajah / Diagram 15(2
L
M
2 cm
T
V
P
U
R
Q
W
2 cm
2 cm
6 cm
9 cm
42˚
S
O
K (150˚T/ E)
J
H
X
N/ U
58˚
Rajah / Diagram 16
KERTAS SOALAN TAMAT
END OF QUESTION PAPER
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