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Soalan Setara Matematik SPM Kertas 1 Sabah 2012

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  • 1. SULIT 1449/1 JABATAN PELAJARAN DAERAH PAPARPEPERIKSAAN SETARA PERINGKAT DAERAH PAPARSIJIL PELAJARAN MALAYSIA 1449/1MATHEMATICSPaper 120121 Hour 15 Minutes One hour and fifteen minutes JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU1. This question paper consists of 40 questions.2. Answer all questions.3. Answer each question by blackening the correct space on the answer sheet.4. Blacken only one space for each question.5. If you wish to change your answer, erase the blackened mark that you have done. Then blacken the space for the new answer.6. The diagram in the questions provided are not drawn to scale unless stated.7. A list of formulae is provided on pages 2 to 4.8. A booklet of four-figure mathematical tables is provided.9. You may use a non-programmable scientific calculator. This paper consists of 21 printed pages1449/1 [Lihat sebelah SULIT
  • 2. SULIT 2 1449/1 MATHEMATICAL FORMULAE RUMUS MATEMATIKThe following formulae may be helpful in answering the questions. The symbols given are the onescommonly used. Rumus-rumus berikut boloeh membantu anda menjawab soalan. Simbol-simbol yang diberi adalahyang biasa digunaan. 1 a m × a n = a m+n 10 Pythagoras Theorem / Teorem Pithagoras 2 a m ÷ a n = a m −n c2 = a2 + b2 3 ( a m ) n = a mn 11 1 d −b  4 A −1 =   ad − bc  − c  a  12 P ( A ) =1 − P ( A) y 2 − y1 5 Distance/ jarak 13 m= x 2 − x1 = ( x1 − x 2 ) 2 + ( y1 − y 2 ) 2 y − int ercept 14 m =− x − int ercept 6 Midpoint/ Titik tengah  x + x 2 y1 + y 2  ( x, y ) =  1 ,   2 2  7 sum of data 8 Mean = number of data sum of ( class mark × frequency) 9 Mean = sum of frequencies1449/1 [Lihat sebelahSULIT
  • 3. SULIT 3 1449/1 SHAPES AND SPACE 11 Area of trapezium = × sum of parallel sides × height 2 Luas trapezium =2 Circumference of circle = π d = 2πr Lilitan bulatan = πd = 2πj3 Area of circle =π 2 r Luas bulatan = πj 24 Curved surface area of cylinder = 2π rh Luas permukaan melengkung silinder = 2πjt5 Surface area of sphere = 4πr 2 Luas permuaan sfera = 4πj26 Volume of right prism = cross sectional area × length Isipadu prisma tegak = luas keratan rentas × panjang7 Volume of cylinder = πr 2 h Isipadu silinder = πj2t 1 28 Volume of cone = πr h 3 Isipadu kon = 49 Volume of sphere = π3 r 3 4 Isipadu sfera = πr3 3 110 Volume of right pyramid = × luas tapak × tinggi 3 Isipadu piramid tegak =11 Sum of interior angles of a polygon Hasil tambah sudut pedalaman poligon = (n −2) ×180 1449/1 [Lihat sebelahSULIT
  • 4. SULIT 4 1449/1 arc length angle subtended at centre12 = circumference of circle 360  area of sector angle subtended at centre13 = area of circle 360  PA14 Scale factor, k = PA Faktor skala, k =15 Area of image = k2 × area of object Luas imej = k2 × luas objek1449/1 [Lihat sebelahSULIT
  • 5. SULIT 5 1449/1 Answer all question.1 Round off 0.05264 correct to three significant figures. Bundarkan 0.05264 betul kepada tiga angka bererti. A 0.05 B 0.053 C 0.0526 D 0.05272 Express 593000 in standard form. Ungkapkan 593000 dalam bentuk piawai. A 5.93 × 103 B 5.93 × 105 C 5.93 × 10 -3 D 5.93 × 10 -53 0.0079 − 7.5 ×10 −4 = A 4.00 ×10 −4 B 4.00 ×10 −3 C 7.15 ×10 −4 D 7.15 ×10 −34 The net weight of a small packet of instant coffee is 2.0 ×10-2 kg. A box contains 30 kg of instant coffee powder. Estimate the number of packets of instant coffee that can be packed from the box of instant coffee powder. Berat bersih sebungkus kopi segera ialah 2.0 × 10-2 kg. Satu kotak mengandungi 30 kg serbuk kopi segera.. Anggarkan bilangan bungkusan kopi segera yang dapat dibungkus daripada serbuk kopi segera dalam kotak itu. A 1.5 × 10 4 B 1.5 × 10 3 C 6.0 × 10 4 D 6.0 × 10 35 State the value of digit 6 in the number 26348 , in base ten.1449/1 [Lihat sebelahSULIT
  • 6. SULIT 6 1449/1 Nyatakan nilai digit 6 bagi nombor 26348 , dalam asas sepuluh. A 48 B 64 C 384 D 6006 101012 – 1102 = A 10012 B 11012 C 11112 D 1101127 In the Diagram 1 shows a hexagon PQRSTU. Dalam Rajah 1 menunjukkan heksagon PQRSTU. Diagram 1 Rajah 1 Find the value of x + y. Cari nilai x + y. A 132 B 257 C 334 D 5148 In Diagram 2, PTU is an equilateral triangle and STU is a straight line. Dalam Rajah 2, PTU ialah segi tiga sama sisi dan STU ialah garis lurus. R S x° 1150 T 80° Q 130° y°1449/1 [Lihat sebelah USULIT P Diagram 2 Rajah 2
  • 7. SULIT 7 1449/1 Calculate the value of x + y Hitung nilai bagi x + y A 175 B 260 C 320 D 5459 In Diagram 3, PQR is a tangent to the circle centre O at Q and TSR is a straight line. Dalam Rajah 3 PQR ialah tangen kepada bulatan berpusat O di Q dan TSR ialah garis lurus. Diagram 3 Rajah 3 Find the value of x. Cari nilai x. A 35 B 40 C 55 D 701 Diagram 4 shows S’ is an image of S under a rotation.0 Rajah 4 menunjukkan S’ ialah imej bagi S di bawah satu putaran.1449/1 [Lihat sebelahSULIT
  • 8. SULIT 8 1449/1 Diagram 4 Rajah 4 Which statement represent the rotation above? Kenyataan yang manakah mewakili putaran di atas? A Rotation 90°clockwise at centre R Putaran 90°ikut arah jam pada R B Rotation 90°anti-lockwise at centre Q Putaran 90°ikut arah lawan jam pada Q C Rotation 180°at centre R Putaran 180° pada R D Rotation 180° at centre Q Putaran 180° pada Q1449/1 [Lihat sebelahSULIT
  • 9. SULIT 9 1449/11 Diagram 5 shows two Squares ABCD and PQRS drawn on a square grid.1 Rajah 5 menunjukkan dua segiempat sama ABCD dan PQRS, dilukis pada grid segiempat sama. A P B D S O Q R Diagram 5 C Rajah 5 PQRS is the image of ABCD under an enlargement. Find the centre and scale factor of the enlargement. PQRS ialah imej bagi ABCD dibawah suatu pembesaran. Cari pusat dan faktor skala pembesaran itu. Centre of enlargement Scale factor Pusat pembesaran Faktor skala A Titik O 3 B Titik O C Titik A D Titik A12 Which of the following graphs represents y = cos 2x° for 0°≤ x ≤ 360°? Antara graf yang berikut, manakah mewakili y = cos 2x° untuk 0 ≤ x ≤ 360°?1449/1 [Lihat sebelahSULIT
  • 10. SULIT 10 1449/1 A B C D13 In Diagram 6, O is a centre of a unit circle. Dalam rajah 6, O ialah pusat bulatan unit.1449/1 [Lihat sebelahSULIT
  • 11. SULIT 11 1449/1 Diagram 6 Rajah 6 Find the value of cos mo Cari nilai kos mo A 0.6 B -0.8 C -0.75 D -1.3314 Diagram 7 shows a cuboid with a horizontal base KLMN. Rajah 7 menunjukkan sebuah kuboid dengan tapak mengufuk KLMN. Diagram 7 Rajah 7 Name the angle between line LS and the plane LMRQ. Nanamakan sudut di antara garis LS dan satah LMRQ A ∠SLR B ∠SLM C ∠SML D ∠SRL1449/1 [Lihat sebelahSULIT
  • 12. SULIT 12 1449/115 In Diagram 8, A and B are two points on the horizontal ground. BCD is a building. Given that the angle of elevation of C from A is 38° and the angle of elevation of D from A is 55°. Dalam Rajah 8, A dan B ialah dua titik pada permukaan mengufuk. BCD ialah sebuah bangunan. Diberi sudut dongakan C dari A ialah 38° dan sudut dongakan D dari A ialah 55°. Diagram 8 Rajah 8 Calculate the distance, in m, of CD Kira jarak, dalam m, bagi CD. A 8.14 B 8.58 C 25.87 D 28.2616 Diagram 9 shows two vertical poles, PQ and RS, on a horizontal plane. The angle of depression of vertex R from vertex P is 35o and PQ = 2RS. Rajah 9 menunjukkan dua batang tiang tegak, PQ dan RS, yang terletak pada permukaan mengufuk. Sudut tunduk puncak R dari puncak P ialah 35o dan PQ = 2RS. Diagram 9 Rajah 91449/1 [Lihat sebelahSULIT
  • 13. SULIT 13 1449/1 Find the distance of QS, in cm correct to one decimal places. Cari panjang QS, dalam cm betul kepada satu tempat perpuluhan. A 1.2 B 1.4 C 1.6 D 2.017 Diagram 10 shows three points, P, Q and R, on horizontal plane. Q is due east of P. Rajah 10 menunjukkan tiga titik P, Q dan R, yang terlentak pada suatu satah mengufuk. Q berada di timur P. Diagram 10 Rajah 10 Given bearing R from Q is 230o. Find the bearing R from P. Diberi bearing R dari Q ialah 230o . Cari bearing R dari P. A 017o B 107o C 1970 D 214018 P(25°N, 10°E) and Q are two points on the earth’s surface. Q is due south of P. The. distance between P and Q is 2400 nautical miles. The latitude of Q is P(25°N, 10°E) dan Q ialah titik pada permukaan bumi. Q terletak ke selatan P. Jarak antara P dan Q ialah 2400 batu nautika. Latitud bagi Q ialah A 15o N B 65o N C 65o S D 15o S1449/1 [Lihat sebelahSULIT
  • 14. SULIT 14 1449/1 19 2(m – 3)2 + 3 – 2m2 = A 21 – 12m B 11m - 2 C 12m - 2 D 21 – 8m20. 20 Express as a single fraction in its simplest form. Ungkapkan sebagai satu pecahan tunggal dalam bentuk termudah. A p +1 8p2 −8p B p ( p + 1) 4p2 − 4p C p3 ( p −1)( p + 1) D 1 8( p −1) 1− n 21 Given that = p , express n in terms of p 1 + 2n 1− n Diberi = p , nyatakan n dalam sebutan p 1 + 2n A 1− p n= 2 p +1 B p −1 n= 2+ p C 1− p n= 3 D p −1 n= 2 1449/1 [Lihat sebelah SULIT
  • 15. SULIT 15 1449/1 Given that 7 − p = 4(1− 2p) , calculate the value of p.22 Diberi bahawa 7 − p = 4(1− 2p) , hitung nilai p. A 8 7 B 3 7 3 C − 7 8 D − 723 4 19 3 = 3  1 4   A 19  4  1 3   B 19  3 C 19 4 4 D 19 324 Simplify: y −6 × 2 y 4 Ringkaskan: y −6 × 2 y 4 A 2y−2 B 2 y −1 C 2y9 D 2 y 1025 List all the integers values of x that satisfy both simultaneous linear inequalities 4x - 5 ˂ 7 and 5 - x ≤ 6 Senaraikan semua nilai integer bagi x yang memenuhi kedua-dua ketaksamaan linear 4x - 5 ˂ 7 dan 5 - x ≤ 6 A -1,0,1,2,3 B -1,0,1,2 1449/1 [Lihat sebelah SULIT
  • 16. SULIT 16 1449/1 C 0,1,2,3 D -1,1,226 Diagram 11 is a bar chart showing the number of coconuts sold by Ahmad in five days. Rajah 11 ialah carta palang yang menunjukkan bilangan kelapa yang dijual oleh Ahmad dalam tempoh lima hari. Number 250 of coconuts Bilangan 200 kelapa 150 100 50 0 Mon Tues Wed Thur Fri Isnin Selasa Rabu Khamis Jummat Diagram 11 Rajah 11 Find the mean number of coconuts sold per day. Cari min kelapa yang dijual sehari. A 150 B 200 C 250 D 30027 Table 1 is a frequency table which shows the mass of fish caught by 20 fishermen. Jadual 1 ialah jadual kekerapan yang menunjukkan jisim ikan yang ditangkap oleh 20 orang nelayan. 1449/1 [Lihat sebelah SULIT
  • 17. SULIT 17 1449/1 Table 1 Jadual 1 Given that the mean mass of fish caught by the fisherman is 17.1 kg, find the value of x. Diberi min jisim ikan yang ditangkap oleh nelayan adalah 17.1 kg, cari nilai x. A 2 B 3 C 4 D 5 2928 Diagram 12 shows universal set,a function. ≤ x ≤ 21, x is an integer} and set R = It is given that the the graph of ξ = {x : 10 Rajah 12 a number such that the satu fungsi. digits is an odd number}. { x : x is menunjukan graf bagi sum of two Find set R’ . Diberi bahawa set semesta ξ = {x : 10 ≤ x ≤ 21, x ialah integer}, dan set R = { x : x ialah nombor dengan keadaan hasil tambah dua digitnya ialah nombor ganjil}. Carikan set R’ A {10,12,14,16,18,20} B { 11, 13, 15, 17, 19, 21} C {10, 11, 13, 15, 17, 19,} D { 11, 13, 15,17,19,20} Diagram 12 Rajah 12 A y = x2 +3 B y = ( x + 3) 2 C y = x 2 −3 D y = ( x − 3) 2 1449/1 [Lihat sebelah SULIT
  • 18. SULIT 18 1449/130 Diagram 13 is a Venn diagram showing the elements of the universal set, ξ, set M and set N. Rajah 13 ialah gambar rajah Venn yang menunjukkan unsur-unsur set semesta, ξ , set M dan set N. Diagram 13 Rajah 13 List all the elements of set (M ∩ N). Senaraikan semua unsur bagi set (M ∩ N) . A {4} B { 1, 5 } C { 2, 3 } D { 1, 2, 3, 5 } 1449/1 [Lihat sebelah SULIT
  • 19. SULIT 19 1449/13231 Determine the subsets of set Q =straight line 3x + 2y + 12 = 0 List all the x-intercept of the {2, 3, 5} Tentukan pintasan-x bagi garis lurus 3x + 2y + 12 = 0 A {2}, {3}, {5} A B -6 {2}, {3}, {5}, { } B C -4 {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}, {2, 3, 5} C D 4 {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}, {2, 3, 5}, { } D 633 3 In Diagram 10, the gradient of straight line PQ is 4 3 Dalam Rajah 10, kecerunan garis lurus PQ ialah 4 Diagram 14 Rajah 14 Determine the x-intercept of the straight line PQ. Carikan pintasan x bagi garis lurus PQ A - 16 B -6 C -12 D -18 The straight line 3y = px - 6 is parallel to the straight line 4x - 2y = 9 .34 Find the value of p. Garis lurus 3y = px - 6 ialah selari dengan garis lurus 4x - 2y = 9 . Hitung nilai p. A -6 B 2 C 4 D 6 1449/1 [Lihat sebelah SULIT
  • 20. SULIT 20 1449/135 1 3 Given that the probability of team P to win in a first match and second match are and 5 5 respectively. Find the probability of team P to lose in both matches. Diberi kebarangkalian pasukan P memenangi pertandingan pertama dan kedua masing- 1 3 masing ialah dan . 5 5 Cari kebarangkalian pasukan P kalah dalam kedua-dua pertandingan itu. A 22 25 B 8 25 C 6 25 D 3 2536 In a group of 100 college students, 80 are boys. In the second intake 20 more girls join the college. If a student is chosen at random from the college, state the probability that the student chosen is a girl. Dalam satu kumpulan 100 orang pelajar kolej, 80 orang daripadanya adalah lelaki. Dalam pengambilan kedua 20 orang pelajar perempuan lagi mendaftar di kolej itu. Jika seorang pelajar dipilih secara rawak daripada kolej itu, nyatakan kebarangkalian bahawa pelajar yang dipilih adalah perempuan. A 1 6 B 1 5 C 1 3 D 5 637 It is given that K varies directly as the cube root of x. Find the relation between K and x. Diberi bahawa K berubah secara langsung dengan kuasa tiga x. Cari hubungan antara K dan x. A K ∝3 x 1 B K∝3 x C K ∝x 3 1 D K∝ 3 x 1449/1 [Lihat sebelah SULIT
  • 21. SULIT 21 1449/138 Table 3 shows the relation between three variables, r, s and t. Jadual 3 menunjukkan hubungan antara tiga pembolehubah, r, s dan t. r 4 16 s 2 8 t 2 m Table 2 Jadual 2 Given that s varies directly as cube of t and inversely as square root of r. Calculate the value of m. Diberi bahawa s berubah secara langsung dengan kuasa tiga t dan berubah secara songsang dengan punca kuasa dua r. Hitung nilai m. A 4 B 8 C 16 D 64 5 3  2 139  2  =  1  − 3  0  A 7 6  −1   1  B  1 5  − 7   2  C 1 5  1   2  D  10 3  − 6   0  1449/1 [Lihat sebelah SULIT
  • 22. SULIT 22 1449/1 3 2  2   x   4 40 Given     −   =   , find the value of x, 4 4  1   3   9         3 2  2   x   4  Diberi   4 4  1  −  3  =  9  , cari nilai x              A -2 B 2 C 4 D 6 END OF QUESTION PAPER SOALAN TAMAT 1449/1 [Lihat sebelah SULIT

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