Matematik soalan kertas 1

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Matematik soalan kertas 1

  1. 1. 1449/1MatematikKertas 1Oktober20061 ¼ jam SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN AKHIR TAHUN TINGKATAN 4 2006 MATEMATIK Kertas 1 Satu jam lima belas minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU1. Kertas soalan ini mengandungi 40 soalan.2. Jawab semua soalan.3. Jawab dengan menghitamkan ruangan yang betul pada kertas jawapan.4. Bagi setiap soalan hitamkan satu ruangan sahaja.5. Sekiranya anda hendak menukarkan jawapan, padamkan tanda yang telah dibuat. Kemudian hitamkan jawapan yang baru.6. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan.7. Satu senarai rumus disediakan di halaman 2 hingga halaman 3.8. Buku sifir matematik empat angka boleh digunakan.9. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram. Kertas soalan ini mengandungi 16 halaman bercetak [Lihat sebelah
  2. 2. SULIT 2 1449/1 MATHEMATICAL FORMULAEThe following formulae may be helpful in answering the questions. The symbolsgiven are the ones commonly used. RELATIONS1. am  an = am + n2. am  an = am - n3. (am)n = am n ( x 2  x1 ) 2   y 2  y1  24. Distance =5. Midpoint  x  x 2 y1  y 2  (x, y) =  1 ,   2 2  distance traveled6. Average speed = time taken sum of data7. Mean = number of data8. Pythagoras Theorem c2 = a2 + b2 y 2  y19. m x 2  x11449/1 © 2006 Hak Cipta Sektor SBP SULIT
  3. 3. SULIT 3 1449/1 SHAPE AND SPACE 11 Area of trapezium =  sum of parallel sides  height 22 Circumference of circle = d = 2r3 Area of circle = r24 Curved surface area of cylinder = 2rh5 Surface area of sphere = 4r26 Volume of right prism = cross sectional area  length7 Volume of cuboid = length  width  length8 Volume of cylinder = r2h 1 29 Volume of cone = r h 3 4 310 Volume of sphere = r 3 111 Volume of right pyramid =  base  height 312 Sum of interior angles of a polygon = (n – 2)  180°13 arc length angle subtended at centre = circumference of circle 360° area of sector angle subtended at centre14 = area of circle 360° PA15 Scale factor, k = PA16 Area of image = k2  area of object. [Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP SULIT
  4. 4. SULIT 4 1449/1 Answer all questions1 Round off 0.0608 correct to two significant figures. A 0.060 B 0.061 C 0.0610 D 0.06002 The side of a cube is 4.3 cm. The volume, in cm³, of the cube correct to three significant figures is A 80.0 B 79.5 C 79.50 D 79.5003 Express 0.0007023  108 as a number in standard form. A 0.7023  1011 B 7.023  1012 C 7.023  104 D 7023  101 6054 0.0368   50000 A 4.89  10–2 B 4.89  10–3 C 4.89  10–4 D 4.89  10–55 In Diagram 1, AB is a tangent to the circle at point P and ASR is a straight line. R Q y° S B 87° 62° P DIAGRAM 1 A Find the value of y. A 25 B 31 C 48 D 531449/1 © 2006 Hak Cipta Sektor SBP SULIT
  5. 5. SULIT 5 1449/16 The area of a rectangular nursery plot is 1.08 km². Its width is 1 200 m. The length of the nursery plot, in m, is A 9  10–1 B 9  10–2 C 9  102 D 9  1047 In Diagram 2, O is the centre of the circle. AB and CB are tangents to the circle at A and C respectively. A 40° B E 80° O y° D C DIAGRAM 2 Find the value of y. A 110 B 115 C 120 D 1258 In Diagram 3, PQRST is a pentagon. STU is a straight line. T S U 32° y° P x° R Q DIAGRAM 3 Find the value of x + y. A 212 B 362 C 384 D 392 [Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP SULIT
  6. 6. SULIT 6 1449/19 In Diagram 4, PQRSTU and PVWXQ are regular hexagon and pentagon respectively. R X Q S W T P m° V U DIAGRAM 4 The value of m is A 24 B 32 C 48 D 5010 Diagram 5 shows the graphs of y = sin x and y = cos x. y 1 O 360° –1 P DIAGRAM 5 The x-coordinate of point P is A 270° B 225° C 215° D 180°11 It is given that cos  = –0.454 where 180° ≤  ≤ 270°, find the value of . A 117° B 207° C 243° D 297°1449/1 © 2006 Hak Cipta Sektor SBP SULIT
  7. 7. SULIT 7 1449/112 In Diagram 6, KLMN is a straight line and JK = KM. J x° K N 12 cm L 3 cm M DIAGRAM 6 The value of tan x is 1 A  4 1 B  3 C –3 D –413 Simplify p  (2p–1)3 ÷ 2p –4. A 3p B 3p2 C 4p D 4p214 Diagram 7 shows a triangle KLM and a shaded triangle, drawn on square grids. M D C A L B K DIAGRAM 7 Triangle KLM is the image of the shaded triangle under an enlargement. Which of the points, A, B, C or D, is the centre of the enlargement? [Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP SULIT
  8. 8. SULIT 8 1449/1 2u  1 2  w15 Express  as a single fraction in its simplest form. uw w 1  uw A uw uw  1 B uw 2u  uw  1 C uw 2u  1 D uw 1 316 32  18 2  2 2  = A 36 B 54 C 108 D 162 3 1 4  (5 ) 4 2 217  4 A 2 B 5 C 37.5 D 5018 8pq – (3p + q)2 = A 3p2 + q2 + 5pq B 3p2 – q2 + 3pq C –9p2 – q2 + 2pq D –9p2 – q2 + 10pq1449/1 © 2006 Hak Cipta Sektor SBP SULIT
  9. 9. SULIT 9 1449/119 Diagram 8 shows a right prism with rectangular base KLMN. P Q 5 cm N M K 6 cm 8 cm L DIAGRAM 8 Calculate the angle between the line PL and the base KLMN. A 20° 18  B 24° 16  C 24° 22  D 26° 34 20 The angle of elevation of the peak of pole P from the peak of pole Q is 60°. The two poles are vertically planted in a horizontal ground. Which diagram below represents the situation described? P Q A C 30° 60° P Q Q B D P 60° 30° P Q [Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP SULIT
  10. 10. SULIT 10 1449/121 Diagram 9 shows a pole, PR on a horizontal plane. P 160° R Q DIAGRAM 9 Calculate the angle of depression of Q from vertex P. A 70° B 60° C 30° D 20° h22 Given that v   , then h = t vt A  vt B 2 v2 C  2t v 2t D 223 There are two helicopters X and Y at height 300 m and 340 m above sea level respectively. If the angle of elevation of helicopter Y from helicopter X is 41°, calculate the horizontal distance, in m, between the two helicopters. A 26.2 B 30.2 C 34.2 D 46.01449/1 © 2006 Hak Cipta Sektor SBP SULIT
  11. 11. SULIT 11 1449/1 w24 Given that y  , express w in terms of y. 1 w y A w 1 y y B w 1 y 1 y C w y 1 y D w y25 In Diagram 10, Q is the image of P under a reflection. P K L N M H Q DIAGRAM 10 The axis of reflection is the straight line that joins H and A K B L C M D N m 1 2m26 Express  as a single fraction in its simplest form. n 3n 3m  1 A 4n 3m  1 B 3n 2 m 1 C 3n 5m  1 D 3n [Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP SULIT
  12. 12. SULIT 12 1449/1 k27 The solution for 1   k  3 is 2 A k≥4 8 B k≥ 3 5 C k≥ 2 5 D k≥ 328 The solution for simultaneous linear inequalities 3n + 1 > –11 and 20 ≤ 8 – 4n is A 3<n ≤4 B –4 < n ≤3 C –3 < n <4 D –4 < n ≤ –329 Diagram 11 is a pie chart showing the colours of t-shirts chosen by a number of students. Red Yellow 60° 190° Blue DIAGRAM 11 If 18 students chose yellow t-shirts, find the number of students who chose red t-shirts. A 108 B 72 C 36 D 331449/1 © 2006 Hak Cipta Sektor SBP SULIT
  13. 13. SULIT 13 1449/130 Table 1 shows the frequency distribution of the scores obtained by a group of pupils in a competition. Time (min) 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35 Frequency 4 10 12 9 5 TABLE 1 Calculate the mean of the distribution. A 21.375 B 22.875 C 23.125 D 25.25031 Diagram 12 is a bar chart showing the number of candidates who obtained scores 1 to 5 in a Mathematics test. Number of Candidates 20 15 10 5 1 2 3 4 5 Score DIAGRAM 12 If the passing score is the mean score, calculate the percentage of students who pass the test. A 90 B 70 C 60 D 50 [Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP SULIT
  14. 14. SULIT 14 1449/132 It is given that the universal set  = {x : 1  x  20, x is an integer}, set P = {2, 3, 6, 7, 9, 11, 13, 17}, set Q = {x : x is a prime number} and set R = {x : x multiple of 3}. Find n[(P  R)’  Q]. A 5 B 6 C 7 D 933 Diagram 13 is a Venn diagram showing the sets P, Q and R such that the universal set  = P  Q  R. P Q R DIAGRAM 13 The shaded region represents the set A P’  (Q  R) B P  (Q  R)’ C P  (Q  R)’ D P’  (Q  R)34 Diagram 14 is an incomplete Venn diagram showing the elements in sets P, Q and R. P R Q .s .c .y .m .w .g .q .k DIAGRAM 14 It is given that the universal set,  = P  Q R, n(Q) = 6 and n(PR) = 3. Find n(P’ Q  R). A 8 B 10 C 11 D 121449/1 © 2006 Hak Cipta Sektor SBP SULIT
  15. 15. SULIT 15 1449/1 2x 5y35 Find y-intercept of the straight line   3. 3 6 18 A  5 4 B  5 18 C 5 4 D 536 The straight line PQ has gradient –2 and passes through the point (3, –5). It is parallel to the straight line y + mx – 4 = 0. Find the value of m. A –3 B –2 C 2 D 337 Diagram 15 shows two straight lines, OR and QR, on a Cartesian plane. y Q R(1, 8) P O x DIAGRAM 15 The distance and the x-intercept of PQ is 15 units and –9 respectively. Find the gradient of QR. A –1 B –4 C –7 D –8 [Lihat sebelah1449/1 © 2006 Hak Cipta Sektor SBP SULIT
  16. 16. SULIT 16 1449/138 Table 2 shows the distribution of a group of students playing a game. Form One Form Two Girls x 12 Boys 8 6 TABLE 2 A student is chosen at random from the group to start the game. The probability 2 that a girl from Form One will be chosen is . Find the value of x. 15 A 2 B 4 C 6 D 839 A box contains a number of yellow marbles and 10 red marbles. A marble is chosen at random from the box. The probability of choosing a yellow marble is 3 . Then, a number of red marbles is put in the box. If a marble is now selected 5 1 at random from the box, the probability that a red marble chosen is . How 2 many red marbles are there in the box? A 15 B 20 C 25 D 3040 A dice is rolled twice and the sum of the number shown is noted. Find the probability that the sum of the numbers being 7. 1 A 6 1 B 4 1 C 3 1 D 2 END OF QUESTION PAPER1449/1 © 2006 Hak Cipta Sektor SBP SULIT

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