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1 NAMA : TINGKATAN : PEJABAT PELAJARAN DAERAH SEGAMAT, JOHOR PEPERIKSAAN AKHIR TAHUN SETARA /2 TINGKATAN 4 MATHEMATICS Kertas 2 Oktober 2½ jam Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. Tulis nama dan tingkatan anda pada ruangan yang disediakan. 2. Kertas soalan ini adalah dalam dwibahasa. 3. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam Bahasa Melayu. 4. Calon dibenarkan menjawab keseluruhan atau sebahagian soalan sama ada dalam bahasa Inggeris atau bahasa Melayu. 5. Calon dikehendaki membaca maklumat di halaman 2. Pemeriksa : Bahagian Soalan A B Jumlah Markah Penuh Markah Diperoleh Kertas soalan ini mengandungi 27 halaman bercetak.
2 2 INFORMATION FOR CANDIDATES MAKLUMAT UNTUK CALON 1. This question paper consists of two sections : Section A and Section B. Kertas soalan ini mengandungi dua bahagian : Bahagian A dan Bahagian B. 2. Answer all questions in Section A and in Section B. Jawab semua soalan dalam Bahagian A dan Bahagian B. 3. Write your answers in the spaces provided in the question paper. Tulis jawapan anda pada ruang yang disediakan dalam kertas soalan ini. 4. Show your working. It may help you to get marks. Tunjukkan kerja mengira anda. Ini boleh membantu anda untuk mendapatkan markah. 5. If you wish to change your answer, cross out the answer that you have done. Then write down the new answer. Jika and hendak menukar jawapan, batalkan jawapan yang telah dibuat. Kemudian tulis jawapan yang baru. 6. The diagrams in the questions provided are not drawn to scale unless stated. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan. 7. The marks allocated for each question and sub-part of a question are shown in brackets. Markah yang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan dalam kurungan. 8. A list of formulae is provided on pages 3 to 5. Satu senarai rumus disediakan di halaman 3 hingga A booklet of four-figure mathematical tables is provided. Sebuah buku sifir matematik empat angka disediakan. 10. You may use a non-programmable scientific calculator. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram. 11. Hand in this question paper to the invigilator at the end of the examination. Serahkan kertas soalan ini kepada pengawas peperiksaan pada akhir peperiksaan.
3 3 MATHEMATICAL FORMULAE RUMUS MATEMATIK The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan. RELATIONS PERKAITAN 1 a m x a n = a m+ n 2 a m a n = a m n 3 ( a m ) n = a mn 4 A -1 = 1 ad bc 5 Distance / Jarak d c b a = x x y y 6 Midpoint / Titik tengah x1 x2 y1 y2 ( x, y ) =, Average speed = distance travelled time taken jarak yang dilalui Purata laju = masa yang diambil 10 Pythagoras Theorem Teorem Pithagoras c 2 = a 2 + b 2 11 P ( A ) = n( A) n( S) 12 P ( A ) = 1 P(A) 13 m = 14 m = y x 2 2 y x pint asan y m pint asan x 1 1 y-intercept x-intercept 8 Mean = Min sum of data number of data hasil tambah nilai data bilangan data 9 Mean = sum of (class mark frequency) sum of frequencies hasil tambah( nilai titik tengah kekerapan ) Min hasil tambah kekerapan
4 SHAPES AND SPACE BENTUK DAN RUANG 1 Area of trapezium = 2 1 sum of parallel sides height Luas trapezium = 2 1 hasil tambah dua sisi selari tinggi 2 Circumference of circle = d = 2 r Lilitan bulatan = d = 2 j 3 Area of circle = r 2 Luas bulatan = j 2 4 Curved surface area of cylinder = 2 rh Luas permukaan melengkung silinder = 2 jt 5 Surface area of sphere = 4 r 2 Luas permukaaan sfera = 4 j 2 6 Volume of right prism = cross sectional area length Isipadu prisma tegak = luas keratan rentas panjang 7 Volume of cylinder = r 2 h Isipadu silinder = j 2 t 8 Volume of cone = 3 1 r 2 h Isipadu kon = 3 1 j 2 t 9 Volume of sphere = 3 4 r 3 Isipadu sfera = 3 4 j 3 10 Volume of right pyramid = 3 1 base area height Isipadu piramid tegak = 3 1 luas tapak tinggi 11 Sum of interior angles of a polygon = ( n 2) 180 Hasil tambah sudut pedalaman poligon = ( n 2) 180
5 12 arc length circumference of panjang lengkuk lilitan bulatan 5 angle subtended at centre circle 360 sudut pusat area of sector area of circle luas sektor luas bulatan angle subtended at centre 360 sudut pusat o Scale factor, k = Faktor skala, k = PA' PA PA' PA 15 Area of image = k 2 area of object Luas imej = k 2 luas objek
6 6 Section A Bahagian A [ 52 marks ] [ 52 markah] Answer all questions in this section. Jawab semua soalan dalam bahagian ini. 1. The Venn diagram in the answer space shows set P,Q and R such that the universal set, Gambar rajah Venn di ruang jawapan menunjukkan set P,Q dan R dengan keadaan set semesta, = P Q R On the diagrams in the answer space, shade Pada rajah di ruang jawapan, lorekkan (a) Set P Q Set ( P Q ) R [4 marks / 4 markah] Answer / Jawapan : (a) P R P R Q Q
7 2. Calculate the value of x and of y that satisfy the following simultaneous linear equation: Hitungkan nilai x dan y yang memuaskan persamaan linear serentak berikut : x + 2y = x y 7 [4 marks / 4 markah] 2 Answer / Jawapan : 3. Solve the quadratic equation Selesaikan persamaan kuadratik 3x (x 1) 2 x 6 [4 marks / 4 markah] Answer / Jawapan :
8 4. Diagram 4 shows a solid cone with a hemisphere removed from the cone. The diameter of the hemisphere is 21 cm and the radius of the cone is 12 cm. The volume of the remaining solid is cm 3. ` Rajah 4 menunjukkan sebuah pepejal berbentuk kon dengan sebuah hemisfera yang telah dikeluarkan daripada kon tersebut. Diameter hemisfera itu ialah 21 cm dan jejari kon ialah 12 cm. Isipadu pepejal yang tinggal ialah cm 3. 8 Using π = 22, calculate 7 Dengan menggunakan π = 22, hitungkan 7 (a) the volume, in cm³, of the hemisphere. isipadu, dalam cm³, hemisfera itu. Diagram 4 / Rajah 4 the height, in cm, of the cone. tinggi, dalam cm, kon tersebut. [ 5 marks / 5 markah ] Answer / Jawapan : (a)
9 9 5. (a) State whether the following compound statement is true or false. Nyatakan sama ada pernyataan berikut adalah benar atau palsu and dan Write down two implication based on the following statement : Tulis dua implikasi berdasarkan pernyataan berikut : 2x 3 6 if and only if x > 5 2x 3 6 jika dan hanya jika x > 5 (c) Given a pattern of a numerical sequence as follow : Diberi satu siri jujukan nombor adalah seperti berikut : 2 = 3 ( 1 ) = 3 ( 2 ) = 3 ( 3 ) = 3 ( 4 ) The 9 th term in the sequence is.... Sebutan ke -9 dalam siri jujukan itu ialah... [ 5 marks / 5 markah ] Answer / Jawapan : a).. b) Implication 1 / Implikasi 1 Implication 2 / Implikasi 2 :.. :.. c) The 9 th term in the sequence is / Sebutan ke 9 dalam siri jujukan itu ialah...
10 6. Diagram 6 shows the straight line PQ is parallel to straight line RS. The equation of the straight line QR is 2y = 3x Rajah 6 menunjukkan satu garis lurus PQ yang selari dengan garis lurus RS. Persamaan garis lurus QR ialah 2y = 3x + 6. Diagram 6 / Rajah 6 Find / Carikan a) the gradient of the straight line RS, kecerunan garis lurus RS, b) the equation of the straight line PQ, persamaan garis lurus PQ, c) the x-intercept of the straight line PQ. pintasan-x bagi garis lurus PQ. [ 5 marks / 5 markah ] Answer / Jawapan : (a) (c)
11 7. Diagram 7 shows two sectors OVW and OXY with the same centre O. Rajah 7 menunjukkan dua sektor OVW dan OXY yang mempunyai pusat yang sama O. 11 Diagram 7 /Rajah 7 It is given that VOW = 30 o. Using π = 7 22, calculate Diberi bahawa VOW = 30 o. Dengan menggunakan π = 7 22, hitungkan (a) the perimeter, in cm, of the whole diagram, perimeter, dalam cm, seluruh rajah itu, the area, in cm 2, of the shaded region. luas, dalam cm 2, kawasan yang berlorek. Answer / Jawapan : [6 marks / 6 markah ] (a)
12 12 8 (a) Express in standard form. Ungkapkan dalam bentuk piawai Calculate the value of and give your answer in standard form Kirakan nilai nyatakan jawapan anda dalam bentuk piawai (c) Find the value of x 4.5 and state your answer correct to two significant figures. Cari nilai bagi x 4.5 dan nyatakan jawapan anda betul kepada dua angka bererti. [ 4 marks / 4 markah ] Answer / Jawapan : (a) (c)
13 13 9. In Diagram 9, USR and VQTS are straight lines. Dalam Rajah 9, USR dan VQTS ialah garis lurus. U x o S P T Diagram 9 / Rajah 9 V y o Q R It is given that TS = 29 cm, PQ = 13 cm, QR = 16 cm and sin x o = Diberi bahawa TS = 29 cm, PQ = 13 cm, QR = 16 cm dan sin x o = Answer / Jawapan: 8. Find the value of tan y o Cari nilai bagi tan y o. 17 [ 5 marks / 5 markah ]
14 A class consisting 30 boys and k girls. If a student is chosen at random from the class, the probability of 2 choosing a girl is. 7 Sebuah kelas mempunyai 30 orang murid lelaki dan k orang murid perempuan. Jika seorang murid dipilih 2 secara rawak daripada kelas itu, kebarangkalian murid yang dipilih itu seorang murid perempuan ialah. 7 (a) If a student is chosen at random from the class, state the probability that a boy will be chosen. Jika seorang murid kelas itu dipilih secara rawak, nyatakan kebarangkalian bahawa murid yang dipilih itu adalah seorang murid lelaki. Calculate the value of k. Hitungkan nilai k. (c) In the middle of the year, another 8 girls joined the class. Find the probability of choosing a girl now. Pada pertengahan tahun, 8 orang pelajar perempuan baru telah mendaftar masuk ke kelas tersebut. Cari kebarangkalain seorang pelajar perempuan dipilih sekarang. Answer / Jawapan : [ 5 marks ] [ 5 markah ] (a) (c)
15 11. Diagram 11 shows a cuboid with horizontal rectangle base HJKL. Rajah 11 menunjukkan sebuah kuboid dengan tapak segiempat tepat HJKL. 15 Diagram 11 / Rajah 11 (a) Name the angle between the plane DEH and the plane DEKJ, Namakan sudut di antara satah DEH dan satah DEKJ, Name the angle between the line EH and the plane HJKL, Namakan sudut di antara garis HE dan satah HJKL, (c) Calculate the angle between the line EH and the plane HJKL. Kira sudut di antara garis EH dan satah HJKL. Answer / Jawapan : [ 5 marks ] [ 5 markah ] (a) (c)
16 16 Section B Bahagian B [ 48 marks ] [ 48 markah ] Answer any four questions from this section. Jawab mana-mana empat soalan daripada bahagian ini. 12 The data below shows the donations, in RM, collected by a welfare home. Data di bawah menunjukkan sumbangan, dalam RM, yang diterima oleh sebuah rumah kebajikan (a) Based on the data, complete Table 12 in the answer space. Berdasarkan data itu, lengkapkan Jadual 12 di ruang jawapan. [4 marks] [4 markah] Based on table 12 in 12(a), calculate the estimated mean of the donation collected and give the answer correct to 2 decimal places. [3 marks ] Berdasarkan Jadual 12 di 12(a), hitung min anggaran sumbangan yang dipungut dan berikan jawapan betul kepada 2 tempat perpuluhan. [3 markah] (c) For this part of the question, use the graph paper provided. Untuk ceraian soalan ini, guna kertas graf yang disediakan. By using scale of 2 cm to RM 5 on the horizontal axis and 2 cm to 1 donater on the vertical axis, draw a frequency polygon for the data. [4 marks] Dengan menggunakan skala 2 cm kepada RM 5 pada paksi mengufuk dan 2 cm kepada 1 penderma pada paksi mencancang, lukis satu poligon kekerapan bagi data tersebut. [4 markah] (d) Based on the frequency polygon in (c), state the number of donater who donate less than RM 36. Berdasarkan poligon kekerapan dalam (c), nyatakan bilangan penderma yang menderma kurang daripada RM 36 [ ] [ah ]
17 17 Answer / Jawapan: (a) Class interval / Selang Kelas Midpoint / Titik tengah Frequency / Kekerapan Table 12 Jadual 12 (c) Refer graph on page 18. Rujuk graf pada halaman 18. (d)
18 18 Graph for Question 12 Graf untuk Soalan 12
19 (a) Given that Diberi bahawa ξ = { x : 12 x 30, x is an integer } ξ = { x : 12 x 30, x adalah nombor bulat } A = { x : x is a multiple of 3 } A = { x : x ialah nombor gandaan 3 } B = { x : x is a number with 7 as a digit } B = { x : x ialah nombor yang mempunyai digit 7 } C = { x : x is number with sum of digits less then 5 } C = { x : x ialah nombor dimana hasil tambah digit-digitnya kurang dari 5 } (i) List all the elements of set B and set C. Senaraikan semua element bagi set B dan set C. (ii) Find n( A B ). Cari n( A B ). (iii) Find n( A U C ). Cari n( A U C ). [ 6 marks ] [ 6 markah ]
20 20 (i) Complete the following statement using the quantifier all or some, to make it a true statement. Lengkapkan pernyataan berikut dengan menggunakan pengkuantiti semua atau sebilangan, untuk membentuk suatu pernyataan benar... quadratic equation have two different roots... persamaan kuadratik mempunyai dua punca yang berbeza. (ii) Complete the premise in the following argument : Lengkapkan premis dalam hujah berikut : Premise 1 Premis 1 Premise 2 / Premis 2 : : All pentagons have 5 sides : Semua pentagon mempunyai 5 sisi... Conclusion Kesimpulan : ABCDE has 5 sides : ABCDE mempunyai 5 sisi (iii) Make a general conclusion by induction for the sequence of numbers 0, 5, 18, 39, which follows the following pattern. Buat satu kesimpulan umum secara aruhan bagi urutan nombor 0, 5, 18, 39, yang mengikut pola berikut. 0 = 4 (0) = 4 (1) = 4 (2) = 4 (3) (iv) Write down the converse of the following implication. Hence, state whether the converse is true or false. Tulis akas untuk implikasi berikut. Seterusnya, nyatakan sama ada akas tersebut adalah benar atau palsu. If p < 4, then p < 8. Jika p < 4, maka p < 8. [ 6 marks / 6 markah ]
21 Answer / Jawapan : a) (i) (ii) (iii) b) (i)... (ii) Premise 2 / Premis 2 :... (iii)... (iv)......
22 Diagram 14 Rajah 14 The data in Diagram 14 shows the marks scored by 30 students in a monthly mathematics test. Data dalam Rajah 14 menunjukkan markah yang diperolehi oleh 30 pelajar dalam ujian bulanan matematik. (a) Based on the data in Diagram 14 and by using a class interval of 5, complete Table 14 in the answer space. [ 4 marks ] Berdasarkan data dalam Rajah 14 dan dengan menggunakan saiz selang kelas 5, lengkapkan Jadual 14 pada ruang jawapan. [ 4 markah ] Based on table 14, Berdasarkan Jadual 14, (i) state the modal class nyatakan kelas mod (ii) calculate the mean marks for the monthly mathematics test. hitungkan min markah ujian bulanan matematik. [ 4 marks ] [ 4 markah ] (c) By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 student on the vertical axis, draw a histogram for the data. [ 4 marks ] Menggunakan skala 2 cm kepada 5 markah pada paksi mengufuk dan 2 cm kepada 1 murid pada paksi mencancang, lukis satu histogram bagi data tersebut. [ 4 markah ]
23 23 Answer / Jawapan: (a) Class interval Selang kelas Midpoint Titik tengah Frequency Kekerapan Table 14 Jadual 14 (i) (ii) (c) Refer graph on page 24. Rujuk graf di halaman 24.
24 24 Graph for Question 14 Graf untuk soalan 14
25 25 15 (a) y P (0,8) R S 0 T (3,0) Q (8,0) x Diagram 15 Rajah 15 Diagram 15 shows two straight lines drawn on a Cartesian plane. R is the midpoint of PQ and S is the midpoint of RQ. Rajah 15 menunjukkan dua garis lurus dilukis padah suatu satah Cartesan. R adalah titik tengah PQ dan S adalah titik tengah RQ. Find Carikan (i) (ii) the gradient of straight line PQ, kecerunan garis lurus PQ, the coordinate of point S koordinat bagi titik S (iii) the equation of straight line ST. persamaan garis lurus ST. [ 6 marks ] [ 6 markah ]
26 15 26 M U R A H H A T I The cards shown above are put into a box. Kad-kad yang ditunjukkan di atas dimasukkan ke dalam sebuah kotak. (i) A card is picked at random from the box. Sekeping kad dikeluarkan secara rawak daripada kotak itu. (a) Find the probability of picking a card with alphabet H. Cari kebarangkalian bahawa kad yang dikeluarkan itu berhuruf H. Find the probability of picking a card with vowels. Cari kebarangkalian bahawa kad yang dikeluarkan itu berhuruf vokal. (ii) A few cards with alphabet Y are added into the box. If a card is picked at random from the box, the probability to pick a card with consonant is 7 5. Find the number of cards with alphabet Y. Hence, find the probability of picking a card with alphabet Y. Beberapa kad yang berhuruf Y ditambah ke dalam kotak itu. Jika sekeping kad dikeluarkan secara rawak dari kotak itu, kebarangkalian bahawa kad yang dikeluarkan berhuruf konsonan ialah 7 5. Cari bilangan kad berhuruf Y. Seterusnya, cari kebarangkalian mengeluarkan kad yang berhuruf Y. [ 6 marks ] [ 6 markah ]
27 Answer / Jawapan : 27 (a) (i) (ii) (iii) (i) (ii) (iii) END OF QUESTION PAPER KERTAS SOALAN TAMAT
28 PEJABAT PELAJARAN DAERAH SEGAMAT PEPERIKSAAN AKHIR TAHUN SETARA 2010 SKEMA PEMARKAHAN MATEMATIK TINGKATAN 4 KERTAS 2 No Solutions Marks 1(a) 2 marks Note : Give 2 marks Note : Give Total : 4 marks
29 No Solutions Marks 2 3x 2y = - 14 or equivqlent 4x = - 8 or equivqlent x = -2 y = 4 Total : 4 marks 3 3x 2 5x 12 = 0 ( 3x + 4 ) ( x 3 ) = 0 x = 4 3 x = 3 Total : 4 marks 4 (a) 2 22 x x ( 10.5 ) cm x x x h 1 22 x x x h = h = 28 Total : 5 marks
30 No Solutions Marks 5 (a) False Implication 1 : If 2x 3 6 then x > 5 Implication 2 : If x > 5 then 2x 3 6 1mark (c ) 3 ( 9 ) Total : 5 marks 6 (a) m RS = 3 or 9 1 or or equivalent 12 = 1 ( 6 ) + c 3 y = 1 x ( c ) 0 = x = 42 1 x Note : Accept answer without working for 2 marks. Total : 5 marks
31 No Solutions Marks 7((a) x 2 x x 7 or x 2 x x x 2 x x x 2 x x or equivalent 42 2 or or x x 7 or x x x x 14 1 x 7 x x x or or Total : 6 marks 8 (a) x x 10 7 (c) ( 2 s.f ) Total : 4 marks
32 No Solutions Marks 9 QS = 34 cm QT = 5 cm PT = 12 cm tan y o 12 = 5 2 marks Total : 5 marks 10 (a) 5 7 n( S ) = 42 k = 12 (c) or Total : 5 marks 11 (a) HDJ or JDH EHK or KHE (c) or 13 Tan EHK = or Total : 5 marks
33 No Solutions Marks 12 (a) Class interval / Selang Kelas Midpoint / Titik tengah Frequency / Kekerapan Class interval all correct Midpoint - all correct Frequency - all correct 2 marks Note : Allow one mistake in frequency for. 23(5) 28(4) 33(6) 38(10) 43(7) 48(4) marks (c) Frequency polygon Axes drawn in correct direction with uniform scales. *6 point plotted correctly using correct midpoint. Note : *5 points correctly ploted, give. Straight line passes through all the 6 points,(18,0) and (53, 0) correctly. s 2 marks (d) 15 Total : 12 marks
34 Graph For Question Frequency Donation
35 No Solutions Marks 13(a) (i) B = { 17, 27 } C = { 12, 13, 20, 21, 22, 30 } (ii) A B = { 12, 15, 18, 21, 24, 30 } n (A B ) = 6 (iii) ( A U C ) = { 14, 16, 17, 19, 23, 25, 26, 28, 29 } n( A U C ) = 9 Total : 6 marks 13 (i) (ii) (iii) (iv) Some ABCDE is a pentagon / ABCDE ialah sebuah pentagon 4n 2 + n n = 0, 1, 2, If p < 8, then p < 4. / Jika p < 8, maka p < 4. False / Palsu Total : 6 marks
36 No Solutions Marks 14 (a) Class interval Selang kelas Midpoint Titik tengah Frequency Kekerapan Class interval all correct Midpoint - all correct Frequency - all correct 2 marks Note : Allow one mistake in frequency for. (i) (ii) 42(2) 47(4) 52(3) 57(9) 62(7) 67(5) marks (c) Histogram Axes drawn in correct direction with uniform scales. *6 bars drawn correctly using class interval or midpoint or upper boundary. 2 marks Note : *5 bars drawn correctly, give. Correct histogram using the given scales. Total : 12 marks
37 Graph For Question Frequency Marks
38 No Solutions Marks 15 (a) (i) (ii) m PQ = -1 coordinates of R = ( 4,4 ) coordinates of S = ( 6,2 ) (iii) m ST = = ( 2 3 )(3) + c y = 2 3 x 2 Total : 6 marks 15 (i) (a) (ii) x 5 x or equivalent 2 marks x = 5 p( Y) = 5 14 Total : 6 marks
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Please check the relevant boxes. Undergraduate Malaysian Postgraduate International Student name: Student Application Form Instructions: 1. Please fill out this form in pen or apply online at www.monash.edu.my/advancement/future/index.html
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Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 2F Centre Number Monday 12 January 2015 Afternoon Time: 2 hours Candidate Number
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