# Matematik Soalan Kertas 2 Ting 4 2006

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1449/2MatematikKertas 2Okt20062 jamSEKTOR SEKOLAH BERASRAMA PENUHBAHAGIAN SEKOLAHKEMENTERIAN PELAJARAN MALAYSIAPEPERIKSAAN AKHIR TAHUNTINGKATAN 4 2006Kertas soalan ini mengandungi 22 halaman bercetak1449/2 @ 2006 Hak Cipta SBPMATEMATIKKertas 2Dua jam tiga puluh minitJANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHUPemeriksaBahagian Soalan MarkahPenuhMarkahDiperoleh1 42 43 44 55 56 47 78 59 310 5A11 612 1213 1214 1215 12B16 121. Kertas soalan ini mengandungi duabahagian : Bahagian A dan BahagianB.2. Jawab semua soalan Bahagian A danempat soalan daripada Bahagian B.3. Jawapan hendaklah ditulis dengan jelasdalam ruang yang disediakan dalamkertas soalan.4. Tunjukkan langkah-langkah pentingdalam kerja mengira anda. Ini bolehmembantu anda untuk mendapatkanmarkah.5. Rajah yang mengiringi soalan tidakdilukis mengikut skala kecualidinyatakan.6. Satu senarai rumus disediakan dihalaman 2 dan 3.7. Anda dibenarkan menggunakankalkulator saintifik yang tidak bolehdiprogram.JumlahNAMA : TINGKATAN : SULIT 1449/21449/2 SULIT2The 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 n4 A-1=||.|

\| a cb dbc ad15 P(A) = ( )( ) S nA n6 P(A) = 1 P(A)7 Distance = ( )21 221 2 ) ( y y x x + 8 Midpoint(x, y) = |.|

\| + +2,22 1 2 1 y y x x9 Average speed =10 Mean =11 Mean =12 Pythagoras Theoremc2= a2+ b2131 21 2x xy ym=14ercept int xercept int ym=distance traveledtime takensum of datanumber of dataSum of (midpoint of interval frequency)Sum of frequenciesSULIT 1449/21449/2 SULIT3SHAPE AND SPACE1 Area of trapezium =21 sum of parallel sides height2 Circumference of circle = td = 2tr3 Area of circle = tr24 Curved surface area of cylinder = 2trh5 Surface area of sphere = 4tr26 Volume of right prism = cross sectional area length7 Volume of cylinder = tr2h8 Volume of cone =31tr2h9 Volume of sphere =34tr310 Volume of right pyramid =31 base area height11 Sum of interior angles of a polygon = (n 2) 180121314 Scale factor, k =PAPA'15 Area of image = k2 area of object.arc length angle subtended at centrecircumference of circle 360area of sector angle subtended at centrearea of circle 360==SULIT 1449/21449/2 SULIT4Section A[52 marks]Answer all questions in this section.1 Solve the quadratic equation2135 2 2=pp.[4 marks]Answer:2 Calculate the value of p and of q that satisfy the following simultaneous linearequations:3p 4q = 213 221= + q p[4 marks]Answer:ForExaminersUseSULIT 1449/21449/2 SULIT53 Diagram 1 shows a right prism. Right angled triangle PQR is the uniform cross-section of the prism.DIAGRAM 1(a) Name the angle between the plane STP and the plane STQR,(b) Calculate the angle between the plane STP and the plane STQR.[4 marks]Answer:(a)(b)ForExaminersUse[Lihat sebelahPQ RSTU9 cm18 cm12 cmSULIT 1449/21449/2 SULIT64 A straight line ST is parallel to line y = 2x + 5 and passes through point (4, 2).Find(a) the gradient of the straight line ST,(b) the equation of the straight line ST and hence, state its y-intercept.. [5 marks]Answer:(a)(b)5 A bag contains 50 pens. 15 of them are blue and the rest are red and green.A pen is chosen at random from the bag.(a) Find the probability that a blue pen is chosen.(b) The probability of choosing a green pen is51. How many green pensare there in the bag?(c) Another 10 green pens are put into the bag. Find the probability that agreen pen is chosen from the bag.[5 marks]Answer:(a)(b)(c)SULIT 1449/21449/2 SULIT76 Diagram 2(a) shows a container in the form of a right pyramid fully filled withwater. Diagram 2(b) shows an empty cylindrical container. The height of thepyramid is 15 cm.DIAGRAM 2(a) DIAGRAM 2(b)All the water from the right pyramid container is poured into the cylindricalcontainer.By using t =722, calculate the height, in cm, of the water level in the cylinder.[4 marks]Answer:ForExaminersUse[Lihat sebelah14 cmA BCDE12 cm8 cmSULIT 1449/21449/2 SULIT87 In Diagram 3, OPQS is a quadrant with the centre O and OSQR is a semicirclewith the centre S.DIAGRAM 3Given that OP = 14 cm. Using =722, calculate(a) the area, in cm2, of the shaded region,(b) the perimeter, in cm, of the whole diagram.[6 marks]Answer:(a)(b)O PQRS60TForExaminersUseSULIT 1449/21449/2 SULIT98 (a) Determine whether the following is a statement or not. Give a reason toyour answer.(b) Rewrite the following statement by inserting the word not into theoriginal statement. State the truth value of your new statement.(c) Construct a true statement using a suitable quantifier for the given objectand the property.[5 marks]Answer:(a) ..(b) ..(c) .ForExaminersUse[Lihat sebelah64 = 423 is the factor of 15Object : TrianglesProperty : Have a right angleSULIT 1449/21449/2 SULIT109 The Venn diagram in the answer space shows set P, set Q and set R with theuniversal set = P Q R.On the diagrams provided in the answer space, shade(a) the set Q (P R),(b) the set Q R P.. [3 marks]Answer:(a) (b)10 In Diagram 4 , AE is a tangent to the circle centre O, at A. CDE is a straight line.DIAGRAM 4Find the value of(a) x(b) y(c) z[5 marks]Answer:(a)(b)(c)ForExaminersUsePRQA20BC D70zxy O EPRQSULIT 1449/21449/2 SULIT1111 (a) Diagram 5 shows a unit circle.DIAGRAM 5Find the value of(i) sin v(ii) cos v + sin 270[3 marks](b) Diagram 6 shows a rhombus PQRS.DIAGRAM 6It is given that TSQ is a straight line and tan x =125 .Find(i) the length of RP(ii) sin x[3 marks]Answer:(a) (i)(ii)(b) (i)(ii)ForExaminersUse[Lihat sebelah1 111yxv( 0.42, 0.91)OPQRSTx 26 cmSULIT 1449/21449/2 SULIT12Section B[48 marks]Answer four questions in this section.12 (a) In Diagram 7, a straight line RS is parallel to the straight line PQ. Theequation of PQ is 2y = x 4.DIAGRAM 7Find(i) the y-intercept of PQ,(ii) the value of m,(iii) the equation of RS.[6 marks]Answer:(a) (i)(ii)(iii)ForExaminersUseyx OR Q(8, m)PS(4, 5)SULIT 1449/21449/2 SULIT13(b) In Diagram 8, EFGH is a parallelogram and O is the origin. The gradientof EF is 2.DIAGRAM 8Find(i) the equation of line EF,(ii) the coordinates of H,(iii) the gradient of HF.[6 marks]Answer:(b) (i)(ii)(iii)[Lihat sebelahForExaminersUseHx O GEF(4, 10)y12SULIT 1449/21449/2 SULIT1413 (a) Diagram 9 shows a right prism with a horizontal rectangular base PQRS.DIAGRAM 9Given that E and F are midpoints of WV and SR respectively.(i) Find the length of PF,(ii) Calculate the angle between the line PE and the plane PQRS,(iii) Name the angle between the plane PQVE and the plane PQUT.[6 marks]Answer:(a) (i)(ii)(iii)ForExaminersUse8 cm5 cm7 cm12 cmPQ RUWTEFSVSULIT 1449/21449/2 SULIT15(b) In Diagram 10, MP and LQ are two vertical flagpoles standing onhorizontal ground KLM .DIAGRAM 10Given that the angle of depression of P from Q is 38, MP = 5 m,LQ = h m and KM = 10 m.Calculate(i) the angle of elevation of P from K,(ii) the value of h.[6 marks]Answer:(b) (i)(ii)ForExaminersUse4005 mP70 MQh mKL13[Lihat sebelahSULIT 1449/21449/2 SULIT1614 (a) (i) Fill the blanks with and or or in order to form a true statement.(a) sin 30 =21cos 30 =21(b) All the multiples of 3 are multiples of 6 all multiplesof 6 are multiples of 3.(ii) Complete the argument below.Premise 1 : If a e A, then a e A B.Premise 2 : __________________________________Conclusion : 5 e A(iii) Make a general conclusion by induction for the sequence13, 28, 49, 76, which follows the following pattern:13 = 3 (2)2+ 128 = 3 (3)2+ 149 = 3 (4)2+ 176 = 3 (5)2+ 1[6 marks]Answer:(a) (i) (a) .(b) .(ii) ..........................................................................................................(iii) ..........................................................................................................ForExaminersUseSULIT 1449/21449/2 SULIT17(b) Diagram 11 is an incomplete Venn diagram. A group of 45 studentsinvolved in their favourite games.DIAGRAM 11Given that = B S T and the number of students who involve inbadminton only is the same as the students who involve in tennis only.Find the number of students who involve in(i) all the three games,(ii) neither badminton nor tennis,(iii) two games only.(iv) tennis only.[6 marks]Answer:(b) (i)(ii)(iii)(iv)ForExaminersUse[Lihat sebelahB = Badminton253611T = TennisS = Squasy14SULIT 1449/21449/2 SULIT1815 The daily distances, in km, travelled in 40 days by a salesman are shown inDiagram 12.DIAGRAM 12(a) Using data in Diagram 12 and a class interval of 10 km, complete Table 1in the answer space.[4 marks]Answer:(a)TABLE 1(b) Determine the range of the given data. [1 mark](c) Based on your table in (a), calculate the estimated mean distancetravelled.[3 marks]Answer:(b)(c) (i)(ii)(d) For this part of the question, use the graph paper on page 19.By using a scale of 2 cm to 10 km on the x-axis and a scale of 2 cm to1 day on the y-axis, draw a frequency polygon for the data above.[4 marks]Answer:(d) Refer graph on page 19.42 62 51 37 70 14 12 9353 45 54 27 70 76 91 7268 58 57 65 21 18 22 8764 63 57 59 70 19 41 5536 56 50 57 73 75 13 39Distance (km) Midpoint Frequency11 2021 3031 40ForExaminersUseSULIT 1449/21449/2 SULIT19Graph for Question 15(d)SULIT 1449/21449/2 SULIT2016 The histogram in Diagram 13 shows the marks achieved in a test by a group ofstudents in a particular school.DIAGRAM 13(a) Find the total number of students who sat for the test. [1 mark](b) Find the modal class. [1 mark](c) Based on the h

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