Document Sample

NAMA : _____________________ SULIT KELAS : _____________________ NO K.P : _____________________ 3472/2 A. GILIRAN : _________________- ADDITIONAL ____________________ MATHEMATICS PAPER 2 AUGUST 2008 2 ½HOURS JABATAN PELAJARAN NEGERI SABAH SIJIL PELAJARAN MALAYSIA TAHUN 2008 EXCEL 2 ___________________________________________________________________________ ADDITIONAL MATHEMATICS PAPER 2 (KERTAS 2) TWO HOURS THIRTY MINUTES (DUA JAM TIGA PULUH MINIT) ___________________________________________________________________________ JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. This question paper consists of three sections: Section A, Section B and Section C. 2. Answer all questions in Section A, four questions from Section B and two questions from Section C. 3. Give only one answer / solution for each question. 4. Show your working. It may help you to get marks. 5. The diagrams in the questions provided are not drawn to scale unless stated. 6. The marks allocated for each question and sub-part of a question are shown in brackets. 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 question paper consists of 13 printed pages. (Kertas soalan ini terdiri daripada 13 halaman bercetak.) [Turn over (Lihat sebelah) The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. 3472/2 CONFIDENTIAL 2 3472/2 ALGEBRA b b 2 4ac log c b 1. x 8. log a b 2a log c a 2. a m a n a m n 9. Tn a (n 1)d 3. a m a n a mn n 10. Sn [2a (n 1)d ] 2 4. (a m ) n a mn 11. Tn ar n1 5. loga mn loga m loga n a(r n 1) a(1 r n ) 12. Sn ,r 1 6. log a m log a m log a n r 1 1 r n a 7. log a m n loga m n 13. S , r 1 1 r CALCULUS dy dv du 4. Area under a curve 1. y uv, u v b dx dx dx = y dx or a b u dy v du u dv = x dy 2. y , dx 2 dx a v dx v 5. Volume generated b dy dy du = y 2 dx or 3. a dx du dx b = x 2 dy a STATISTICS 3472/2 CONFIDENTIAL CONFIDENTIAL 3 3472/2 1. x x W I i i N 7. I fx W i 2. x f n! 8. n P r n r ! 3. (x x ) 2 x 2 x 2 N N n! 9. n C n r !r ! r 4. f (x x ) 2 fx 2 x2 f f 10. P A B P A P B P A B 11. P X r nCr p r q nr , p q 1 1 2N F 12. Mean, μ = np 5. m L c fm 13. npq x 6. I Q1 100 14. Z Qo GEOMETRY 1. Distance 4. Area of triangle = x1 x2 y1 y2 1 2 2 = ( x1 y2 x2 y3 x3 y1 ) ( x2 y1 x3 y2 x1 y3 ) 2 2. Midpoint 5. r x2 y 2 x1 x2 y1 y2 x, y , xi yj 2 2 6. r ˆ x2 y 2 3. A point dividing a segment of a line nx mx2 ny1 my2 x, y 1 , mn mn TRIGONOMETRY 1. Arc length, s r 8. sin ( A B) sin A cos B cos A sin B 9. cos ( A B) cos Acos B sin A sin B 3472/2 CONFIDENTIAL CONFIDENTIAL 4 3472/2 1 2 tan A tan B 2. Area of sector, A r 10. tan ( A B) 2 1 tan A tan B 3. sin 2 A cos2 A 1 2 tan A 11. tan 2 A 4. sec2 A 1 tan 2 A 1 tan 2 A 5. cosec2 A 1 cot 2 A a b c 12. 6. sin 2 A 2sin A cos A sin A sin B sin C 7. cos 2 A cos2 A sin 2 A 13. a 2 b 2 c 2 2bc cos A 2 cos 2 A 1 1 2 sin 2 A 1 14. Area of triangle ab sin C 2 3472/2 CONFIDENTIAL CONFIDENTIAL 5 3472/2 Section A [40 marks] Answer all questions. 1 Solve the simultaneous equations 4 x y x 2 x y 3 . [5 marks] 2 Diagram 1 shows a straight line CD which meets a straight line AB at point D. The point C lies on the y-axis. Diagram 1 (a) State the equation of AB in the intercept form. [1 mark] (b) Given that 2AD = DB, find the coordinates of D. [3 marks] (c) Given that CD is perpendicular to AB, find the y-intercept of CD. [3 marks] 3 (a) Sketch the graph of y 3sin 2 x for 0 x 2 . [4 marks] (b) Hence, using the same axes, sketch a suitable straight line to find the number x of solutions for the equation 3sin 2 x =1 for 0 x 2 . State the number of solutions. [3 marks] 3472/2 CONFIDENTIAL CONFIDENTIAL 6 3472/2 4 Given that the gradient of the tangent to the curve y 2 x3 6 x 2 9 x 1 at point P is 3, find (a) the coordinates of P, [2 marks] (b) the equation of the tangent and normal to the curve at P. [4 marks] 5 Table 1 shows the distribution of the ages of 100 teachers in a secondary school. Age <30 <35 <40 <45 <50 <55 <60 (years) Number of 8 22 42 68 88 98 100 teachers Table 1 (a) Based on Table 1, copy and complete Table 2. Age 25 - 29 (years) Frequency Table 2 [2 marks] (b) Without drawing an ogive, calculate the interquartile range of the distribution. [5 marks] 6 The first three terms of a geometric progression are also the first, ninth and eleventh terms, respectively of an arithmetic progression. (a) Given that all the term of the geometric progressions are different, find the common ratio. [4 marks] (b) If the sum to infinity of the geometric progression is 8, find (i) the first term, (ii) the common difference of the arithmetic progression. [4 marks] 3472/2 CONFIDENTIAL CONFIDENTIAL 7 3472/2 Section B [40 marks] Answer four questions. 7 Use graph paper to answer this question. Table 3 shows the values of two variables, x and y, obtained from an experiment. Variables x and y are related by the equation y ab x , where a and b are constants. x 1 2 3 4 5 6 y 41.7 34.7 28.9 27.5 20.1 16.7 Table 3 (a) Plot log10 y against x by using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 0.2 unit on the log10 y -axis. Hence, draw the line of best fit. [4 marks] (b) Use your graph from (a) to find (i) the value of y which was wrongly recorded, and estimate a more accurate value of it, (ii) the value of a and of b, (iii) the value of y when x = 3.5. [6 marks] 8 Diagram 2 shows a trapezium PQRS. U is the midpoint of PQ and PU 2SV . PV and TU are two straight lines intersecting at W where TW : WU = 1 : 3 and PW = WV. S V R T W P U Q Diagram 2 It is given that PQ 12a, PS 18b and QR 18b 5a . (a) Express in terms of a and/or b , 3472/2 CONFIDENTIAL CONFIDENTIAL 8 3472/2 (i) SR , (ii) PV , (iii) PW . [5 marks] (b) Using PT : TS = h : 1, where h is a constant, express PW in terms of h, a and/or b and find the value of h. [5 marks] 9 Diagram 3 shows a circle with centre C and of radius r cm inscribed in a sector OAB of a circle with centre O and of radius 42 cm. [Use = 3.142] Diagram 3 Given that AOB rad , find 3 (a) the value of r, [2 marks] (b) the perimeter, in cm, of the shaded region, [4 marks] (c) the area, in cm2, of the shaded region. [4 marks] 3472/2 CONFIDENTIAL CONFIDENTIAL 9 3472/2 10 Diagram 4 shows part of the curve y x 1 . y A y x 1 y=k R S x O Diagram 4 The curve intersects the straight line y = k at point A, where k is a constant. The 1 gradient of the curve at the point A is . 4 (a) Find the value of k. [3 marks] (b) Hence, calculate (i) area of the shaded region R : area of the shaded region S. (ii) the volume generated, in terms of π, when the region R which is bounded by the curve, the x-axis and the y-axis, is revolved through 360o about the y-axis. [7 marks] 11 (a) A committee of three people is to be chosen from four married couples. Find how many ways this committee can be chosen (i) if the committee must consist of one woman and two men, (ii) if all are equally eligible except that a husband and wife cannot both serve on the committee. [5 marks] (b) The mass of mango fruits from a farm is normally distributed with a mean of 820 g and standard deviation of 100 g. (i) Find the probability that a mango fruit chosen randomly has a minimum mass of 700 g. (ii) Find the expected number of mango fruits from a basket containing 200 fruits that have a mass of less than 700 g. [5 marks] Section C 3472/2 CONFIDENTIAL CONFIDENTIAL 10 3472/2 [20 marks] Answer two questions. 12 A particle moves along a straight line and passes through a fixed point O. Its velocity, v m s–1, is given by v pt 2 qt 16 , where t is the time, in seconds, after passing through O, p and q are constants. The particle stops momentarily at a point 64 m to the left of O when t = 4. [Assume motion to the right is positive.] Find (a) the initial velocity of the particle, [1 mark] (b) the value of p and of q, [4 marks] (c) the acceleration of the particle when it stops momentarily, [2 marks] (d) the total distance traveled in the third second. [3 marks] 3472/2 CONFIDENTIAL CONFIDENTIAL 11 3472/2 13 Table 4 shows the prices of four types of book in a bookstore for three successive years. Price in year (RM) Price index in Price index in Book 2001 2002 Weightage 2000 2001 2002 based on 2000 based on 2000 P w 20 30 150 225 6 Q 50 x 65 115 130 5 R 40 50 56 125 140 3 S 80 z 150 y y 2 Table 4 (a) Find the values of w, x, y and z. [4 marks] (b) Calculate the composite index for the year 2002 based on the year 2001. [4 marks] (c) A school spent RM4, 865 to buy books for the library in the year 2002. Find the expected total expenditure of the books in the year 2003 if the composite index for the year 2003 based on the year 2002 is the same as for the year 2002 based on the year 2001. [2 marks] 3472/2 CONFIDENTIAL CONFIDENTIAL 12 3472/2 14 Use graph paper to answer this question. A farmer wants to plant x-acres of vegetables and y-acres of tapioca on his farm. Table 5 shows the cost of planting one acre and the number of days needed to plant one acre of vegetable and one acre of tapioca. Vegetables Tapioca Cost of planting RM100 RM 90 per acre Number of days 4 2 needed per acre Table 5 The planting of the vegetables and tapioca is based on the following constraints: I The farmer has a capital of RM1800. II The total number of days available for planting is 60. III The area of his farm is 20 acres. (a) Write down three inequalities, other than x 0 and y 0 , which satisfy all the above constraints. [3 marks] (b) By using a scale of 2 cm to 4 acres on both axes, construct and shade the region R that satisfies all the above constraints. [3 marks] (c) By using your graph from (b), find (i) the maximum area of tapioca planted if the area of vegetables planted is 10 acres, (ii) the maximum profit that the farmer can get if the profit for one acre of vegetables and one acre of tapioca planted are RM60 and RM20 respectively. [4 marks] 3472/2 CONFIDENTIAL CONFIDENTIAL 13 3472/2 15 Diagram 5 shows a quadrilateral ABCD such that ABC is acute. Diagram 5 (a) Calculate (i) ABC , (ii) ADC , (iii) the area, in cm2, of quadrilateral ABCD. [8 marks] (b) A triangle AB’C has the same measurement as triangle ABC, that is, AC = 15 cm, CB’ = 9 cm and B ' AC 30 , but is different in shape to triangle ABC. (i) Sketch the triangle ABC . (ii) State the size of AB 'C . [2 marks] END OF QUESTION PAPER 3472/2 CONFIDENTIAL

DOCUMENT INFO

Shared By:

Categories:

Tags:
pada tahun, jabatan pelajaran negeri, hari ini, negeri sabah, sijil pelajaran malaysia, pejabat pelajaran daerah, johor bahru, jabatan pelajaran, keputusan spm, keputusan peperiksaan, sekolah menengah, mata pelajaran, sekolah rendah, pada hari ini, utusan malaysia

Stats:

views: | 643 |

posted: | 3/31/2010 |

language: | Malay |

pages: | 13 |

OTHER DOCS BY cit19873

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.