Analisis Mata Pelajaran

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99 SPM 2008 [ 756/1 ] [ 756/2 ] Additional Mathematic Analisis Mata Pelajaran Analsis of Additional Mathematic ( 2004-2007 ) NO TOPICS PAPER 1 PAPER 2 2004 2005 2006 2007 2004 2005 2006 2007 1

7,8 - - - - 6 Coordinate Geometr 14,15 14 12 1,14 2 9 9 2 7 Statistics - 2 24 22 4 4 6 5 8 Circular Measure 19 18 16 18 9 10 10 9 9 Differentiation 20,21 19,20 17,18, 19,20 5b,10a 2a,8a - 4(a),(b) 19

1 99 SPM 2008 [ 756/1 ] [ 756/2 ] Additional Mathematic Analisis Mata Pelajaran Analsis of Additional Mathematic ( ) NO TOPICS PAPER 1 PAPER Functions 1,2, 1,2, 1,2 1,2, Quadratic Equations 4 4, Quadratic Functions 5,6 6 4,5 5, Simultaneous Equations Indices and Logarithms 7,8 7,8,9 6,7,8 7, Coordinate Geometr 14, , Statistics Circular Measure Differentiation 20,21 19,20 17,18, 19,20 5b,10a 2a,8a - 4(a),(b) Solution of Triangles Inde Number Progressions 9,10, 11,12 10,11, 12 9,10 9,10, Linear Law Integration , a,10b 2b,8b, 8c 8 4(c),10 15 Vectors 16,17 15,16 1,14 15, Trigonometric Functions Permutations and Combinations Probabilit Probabilit Distributions Motion Along A straight Line Linear Programming TOTAL

2 100 TIMES HIGHER EDUCATION ADDITIONAL MATHEMATICS Paper 1 Nov./Dis 2 hour 1. Answer all the questions DO NOT OPEN UNTILL INTSRUCTED TO 2. Think thoroughl before answering an of the questions. If ou need to change our answer, erase the answer properl and thoroughl before remarking the question sheet. This question paper contains 5 printed pages and 0 non printed pages 472/1

3 101 Answer all question ( 80 marks ) 1. Diagram 1 shows a graph that represents the relation between and. State (a) the tpe of relation between and (b) whether the relation is a function. [ marks ] 0 DIAGRAM 1 2. Given an arithmetic progression 20, 5, - 10, - 25,.., Find the number of terms of the progression. [ 2 marks ]. The ninth term and the sith term of a geometric progression are 1792 and 224 respectivel. If all the terms are positive, find (a) the common ratio. (b) the first term [ marks ] 4. The equations of two straight lines are + = 2 and =k + 7k. Given that the two lines are perpendicular to each other, find the value of k. [ 2 marks ] 5. The graph of a function = (+h) (-k) intersect the - ais at = -4 and = 6 where h and k are positive constants. a) state the values of h and k b) find the equation of the ais of smmetr [ marks ] 6. Given that cos = and is an obtuse angle, find the value of sin ( 90º ) [ 2 marks ] = 7. Find the values of p given the quadratic equation has two real and equal roots. [ marks ] 2 p 8. The roots of a quadratic equation are -5 and, form the equation in the form a² + b + c = 0, where a, b and c are constants. 4 [ 2 marks ] 9. There are 4 red marbles, 7 blue marbles and 5 ellow marbles in a bo. Two marbles are drawn at random from the bo, one after the other, without replacement. Calculate the probabilit that (a) both balls are of the same colour (b) both balls are not blue [ 4 marks ] 472/1

4 Diagram 2 shows the sectors of two circles OPQ and ORS with centres at O. Given that OP = PR and POQ = 0.8 radian, find the perimeter of the shaded region. 2 cm P R O θ DIAGRAM 2 Q S [ marks ] 11. A curve passes through point ( -1,1 ) and has a gradient function ² ( ² - 1 ) + 1 Find the equation of the curve. [ marks ] 12. Solve the equation [ marks ] log 5 + 2log = log (2 + ) k k k 1 1. Solve the equation + ( ) [ marks ] = Colour Yellow 1 Green Number of pens Orange 16 Table 1 Table 1 shows the number of pens in a bo. The probabilit of picking a green pen at random is. Calculate the total number of pens in the bo. 11 [ marks ] 15. Diagram shows seven cards. J E N A R I S DIAGRAM How man different arrangements can be obtained if the arrangement must begin with a vowel? [ marks ] 16. A committee of 8 members has to be formed from 10 teachers and 4 students. Calculate the number of was this can be done if (a) 5 teachers are committee members (b) not more than 2 students are committe [ 4 marks ] 472/1

5 Given that f ( ) d = 8. Find the value of k if f ( ) + k d = 16 [ marks ] Given P ( -,4) and Q (6,-7). Find (a) PQ (b) the unit vector for PQ [ marks ] 19. Find the equation of the normal to the curve = ² at the point (1,2). [ 4 marks ] 20. Given that sin 0 º = h and cos 40 º = k, epress cos 70 º in terms of h and k. [ 4 marks ] Given the function f ( ) =, 0 and the composite function f g() = 4. Find (a) g() (b) the value of when gf() = 6 [ 4 marks ] 472/2

6 Seven numbers, k, 4, 5, 7, 2k, 12 and 12 have a mean of h. When the number 9 is added to the set of data, the new mean is 29 h. Find the value of k and of h. [ 4 marks ] X is a random variable of a normal distribution with a mean of 6.4 and a standard deviation of 1.4. Find (a) the Z score if X = 8.5 (b) P ( 6.4 X 8.5 ) [ 4 marks ] Diagram 4 shows a straight line graph of against ². m 2 Given where m and n are constants. Calculate the value of m and of n. = 2 + n (-1,0) 1 DIAGRAM 4 (2,6) ² 25. Solve the equation cos² + sin - 1 = 0 for 0º 60º [ 4 marks ] END OF QUESTION PAPER 472/2

NATIONAL QUALIFICATIONS

Mathematics Higher Prelim Eamination 04/05 Paper Assessing Units & + Vectors NATIONAL QUALIFICATIONS Time allowed - hour 0 minutes Read carefully Calculators may NOT be used in this paper. Section A -