SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 2008

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1 SULIT 47/ Matematik Tambahan Kertas Sept 008 Jam Name :.. Form :.. SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 008 MATEMATIK TAMBAHAN Kertas Dua jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU This question paper consists of 5 questions.. Answer all questions.. Give only one answer for each question. 4. Write your answers clearly in the spaces provided in the question paper. 5. Show your working. It may help you to get marks. 6. If you wish to change your answer, cross out the work that you have done. Then write down the new answer. 7. The diagrams in the questions provided are not drawn to scale unless stated. 8. The marks allocated for each question and sub-part of a question are shown in brackets. 9. A list of formulae is provided on pages to. 0. A booklet of four-figure mathematical tables is provided.. You may use a non-programmable scientific calculator. This question paper must be handed in at the end of the examination. Question For examiner s use only Total Marks TOTAL 80 Marks Obtained Kertas soalan ini mengandungi 5 halaman bercetak 47/ 008 Hak Cipta Zon A Kuching [Lihat Sebelah Sarawak Zon A Trial SPM 008 SULIT

2 SULIT 47/ The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. b x = b 4ac a ALGEBRA 8 log a b = log log c c b a a m a n = a m + n a m a n = a m n 4 (a m ) n = a nm 5 log a mn = log a m + log a n m 6 log a = log a m log a n n 7 log a m n = n log a m 9 T n = a + (n )d n 0 S n = [a ( n ) d] T n = ar n n n a( r ) a( r ) S n = r r a S, r < r, (r ) dy dv du y = uv, u v dx dx dx du dv v u u dy y, dx dx, v dx v dy dx dy du du dx CALCULUS 4 Area under a curve b = y dx or a b = x dy a 5 Volume generated b = y dx or a b = x dy a GEOM ETRY Distance = Midpoint x (x, y) = x ( x x ) ( y y ) y, y 5 A point dividing a segment of a line nx mx ny my (x, y) =, m n m n 6. Area of triangle = r x y ( ) ( ) x y x y x y x y x y x y x i yj 4 r x y 47/ Sarawak Zon A Trial SPM Hak Cipta Zon A Kuching SULIT

3 SULIT 47/ STATISTICS x = N x = = 4 = x fx f ( x x) = N f ( x x) f = x N x fx f x wi i 7 I i wi 8 9 n P r n C r n! ( n r)! n! ( n r)! r! 0 P(A B) = P(A) + P(B) P(A B) P(X = r) = r C p q n r n r, p + q = N F 5 m = L C fm P 6 I 00 P 0 Mean, = np npq x 4 z = TRIGONOMETRY Arc length, s = r Area of sector, A = sin A + cos A = 4 sec A = + tan A 5 cosec A = + cot A 6 sin A = sinacosa r 7 cos A = cos A sin A = cos A = sin A 8 tana = tan A tan A 9 sin (A B) = sinacosb cosasinb 0 cos (A B) = cos AcosB sinasinb tan (A B) = a sin A b sin B tan A tan B tan Atan B c sinc a = b +c bc cosa 4 Area of triangle = absin C 47/ 008 Hak Cipta Zon A Kuching Lihat sebelah Sarawak Zon A Trial SPM 008 SULIT

4 SULIT 4 47/ Answer all questions. For examiner s use only Diagram shows the linear function f. x f f(x) n 4 DIAGRAM (a) State the value of n. (b) Using the function notation, express f in terms of x. [ marks ] Answer : (a)... Two functions are defined by f : x x and gf : x x ax b, find the value of a and of b. (b)... g : x x x. Given that [ marks ] Answer :... Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT

5 For examiner s use only SULIT 5 47/ x The function of p is defined as p(x), x h. x Find (a) the value of h, (b) p ( x ). [ marks ] Answer : (a).. (b)... 4 Find the range of values of t if the following quadratic equation has no roots (t + ) x + 6x + = 0. [ marks ] 4 Answer :... 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [ Lihat sebelah SULIT

6 SULIT 6 47/ 5 Given that and are the roots of the quadratic equation x x 7. Form the quadratic equation whose roots are and. For examiner s use only [ marks ] 5 Answer :... 6 Diagram shows the graph of a curve y = a(x + p)² + q that passes through the point (0, 5) and has the minimum point (, ). Find the values of a, p and q. y [ marks ] (0, 5) O (, ) DIAGRAM x Answer : p =... q =... 6 a =... Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT

7 For examiner s use only SULIT 7 47/ 7 Find the range of values of x for which x(x ) 5. [ marks] 7 Answer :... x 8 Solve 7 x 9 [ marks ] 8 Answer :... 9 Given that lg 0 and lg7, find, without using scientific calculator or mathematical tables, find the value of log 4. [ marks ] 9 Answer :... 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [ Lihat sebelah SULIT

8 SULIT 8 47/ th 0 The n term of an arithmetic progression is given by T n 5n. Find For examiner s use only (a) the first term and the common difference, (b) the sum of the first 5 terms of the progression. [4 marks] Answer : (a). (b) The first three terms of a geometric progression are 968, 656, 87,.... Find the three consecutive terms whose product is [ marks ] Answer :... Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT

9 For examiner s use only SULIT 9 47/ Diagram shows the straight line obtained by plotting log 0 y against log 0 x. log 0 y (4, h ) (0, 6) 0 DIAGRAM log 0 x 4 The variables x and y are related by the equation y kx, where k is a constant. Find the value of (a) k, (b) h. [ 4 marks ] Answer : (a) (b)... The coordinates of the vertices of a triangle PQR are P(, h), Q(, 0) and R(5, h). If the area of the PQR is 9 units, find the values of h. [ marks ] Answer : h =. 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [ Lihat sebelah SULIT

10 SULIT 0 47/ x y 4 If the straight line is perpendicular to the straight line 5 p 0x y 0, find the value of p. [ marks ] For examiner s use only 4 Answer :. 5 Given the vectors a i mj, b 8 i j and c 5 i j. If vector a b vector c, find the value of the constant m. ~ is parallel to [ marks ] 5 Answer :.. Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT

11 For examiner s use only SULIT 47/ 6 The diagram 4 shows a parallelogram ABCD drawn on a Cartesian plane. y B A O x C D It is given that AB i j and BC 4 i j. Find DIAGRAM 4 (a) BD, (b) AC. [ 4 marks ] 6 Answer : (a) (b).. 7 Solve the equation sin 5cos cos for [ marks ] 7 Answer : / Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [ Lihat sebelah SULIT

12 SULIT 47/ 8 Given that sin x = 5 and 90 < x < 70, find the value of sec x. [ marks ] For examiner s use only Answer : The diagram 5 shows a semicircle of centre O and radius r cm. C A O B DIAGRAM 5 The length of the arc AC is 7 cm and the angle of COB is 69 radians. Calculate (a) the value of r, (b) the area of the shaded region. [Use π =.4] [ 4 marks ] Answer : (a).. (b).. Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT

13 For examiner s use only SULIT 47/ 0 Find the coordinates of the turning points of the curve y = x + x. [4 marks] 0 Answer : Given that y = m and m = x +. Find dy (a) in terms of x, dx (b) the small change in y when x increases from to 0. [ 4 marks ] Answer : (a).. 4 (b).. Find x dx [ marks ] Answer :.. 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [Lihat Sebelah SULIT

14 SULIT 4 47/ Ben and Shafiq are taking driving test. The probability that Ben and Shafiq pass the test are 5 and respectively. For examiner s use only Calculate the probability that at least one person passes the test. [ marks ] Answer :.. 4 A committee of 5 members is to be selected from 6 boys and 4 girls. Find the number of ways in which this can be done if (a) the committee has no girls, (b) the committee has exactly boys. [ marks ] 4 Answer : (a).. (b).. 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 SULIT

15 For examiner s use only SULIT 5 47/ 5 A random variable X has a normal distribution with mean 50 and variance. Given that P[X > 5] = 088, find the value of. [ marks ] 5 Answer : END OF QUESTION PAPER 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [Lihat Sebelah SULIT SULIT

16 SULIT 47/ 47/ Matematik Tambahan Kertas ½ jam Sept 008 SEKOLAH-SEKOLAH ZON A KUCHING LEMBAGA PEPERIKSAAN SEKOLAH ZON A PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 008 MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. This question paper consists of three sections : Section A, Section B and Section C.. Answer all question in Section A, four questions from Section B and two questions from Section C.. Give only one answer / solution to each question.. 4. Show your working. It may help you to get marks. 5. The diagram 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 to. 8. A booklet of four-figure mathematical tables is provided. 9. You may use a non-programmable scientific calculator. Kertas soalan ini mengandungi halaman bercetak 47/ 008 Hak Cipta Zon A Kuching [Lihat sebelah Sarawak Zon A Trial SPM 008 SULIT

17 SULIT 47/ The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. b x = b 4ac a ALGEBRA 8 log a b = log log c c b a a m a n = a m + n a m a n = a m n 4 (a m ) n = a nm 5 log a mn = log a m + log a n m 6 log a = log a m log a n n 7 log a m n = n log a m 9 T n = a + (n )d n 0 S n = [a ( n ) d] T n = ar n n n a( r ) a( r ) S n = r r a S, r < r, (r ) dy dv du y = uv, u v dx dx dx du dv v u u dy y, dx dx, v dx v dy dx dy du du dx CALCULUS 4 Area under a curve b = y dx or a b = x dy a 5 Volume generated b = y dx or a b = x dy a GEOM ETRY Distance = Midpoint x (x, y) = x ( x x ) ( y y ) y, y 5 A point dividing a segment of a line nx mx ny my (x, y) =, m n m n 6. Area of triangle = r x y ( ) ( ) x y x y x y x y x y x y x i yj 4 r x y 47/ Sarawak Zon A Trial SPM Hak Cipta Zon A Kuching SULIT

18 SULIT 47/ STATISTICS x = N x = = 4 = x fx f ( x x) = N f ( x x) f = x N x fx f x wi i 7 I i wi 8 9 n P r n C r n! ( n r)! n! ( n r)! r! 0 P(A B) = P(A) + P(B) P(A B) P(X = r) = r C p q n r n r, p + q = N F 5 m = L C fm P 6 I 00 P 0 Mean, = np npq x 4 z = TRIGONOMETRY Arc length, s = r Area of sector, A = sin A + cos A = 4 sec A = + tan A 5 cosec A = + cot A 6 sin A = sinacosa r 7 cos A = cos A sin A = cos A = sin A 8 tana = tan A tan A 9 sin (A B) = sinacosb cosasinb 0 cos (A B) = cos AcosB sinasinb tan (A B) = a sin A b sin B tan A tan B tan Atan B c sin C a = b +c bc cosa 4 Area of triangle = absin C 47/ 008 Hak Cipta Zon A Kuching [Lihat sebelah Sarawak Zon A Trial SPM 008 SULIT

19 SULIT 4 47/ SECTION A [40 marks] Answer all questions in this section. Solve the simultaneous equations p m and p m pm 8. Give your answers correct to three decimal places. [5 marks] (a) Given that the surface area, S cm, of a sphere with radius r is 4 r. Find ds dr. Hence, determine the rate of increase of the surface area of the sphere if the radius is increasing at the rate of 0 cm s when r =. [ marks] (b) Given that y = x d y x +, find the values of x if dx + dy + 4x = y. dx [4 marks] Table shows the distribution of scores obtained by a group of students in a competition. Score 4 5 Number of students TABLE (a) Calculate the standard deviation of the distribution. [ marks] (b) If each score of the distribution is multiplied by and then subtracted by c, the mean of the new distribution of scores is 8, calculate (i) the value of c, (ii) the standard deviation of the new distribution of scores. [ marks] 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT

20 SULIT 5 47/ 4 Diagram shows a sector AOB with centre O and a radius of cm. C A O DIAGRAM B Point C lies on OA such that OC : OA = : 4 and OCB = 90. [Use π =.4] Find (a) the value of COB, in radian, (b) the perimeter of the shaded region, (c) the area of the shaded region. [ marks] [ marks] [ marks] 5 Diagram shows a square with side of length a cm was cut into four equal squares and then every square was cut into another four equal squares for the subsequent stages. a cm a cm Stage Stage Stage DIAGRAM Given that the sum of the perimeters of the squares in every stage form a geometric progression. (a) If the sum of the perimeters of the squares cut in stage 0 is 0 40 cm, find the value of a. [ marks] (b) Calculate the number of squares cut from stage 5 until stage 0. [4 marks] 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT

21 SULIT 6 47/ 6 In Diagram, ABC is a triangle. The point P lies on AC and the point Q lies on BC. The straight lines BP and AQ intersect at R. C P A R Q DIAGRAM B It is given that AB 4x, AC 6y, AP PC and BC BQ. (a) Express in terms of x and y (i) BP, (ii) CQ. (b) Given that BR ( x y) and RP mbr. 4 [ marks] (i) State BR in terms of m, x and y. (ii) Hence, find the value of m. [5 marks] Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT

22 SULIT 7 47/ 7 Use graph paper to answer this question. SECTION B [40 marks] Answer four questions from this section. Table shows the values of two variables, x and y, obtained from an experiment. c The variables x and y are related by the equation y where c and d are x d constants. (a) Plot xy against y, by using a scale of cm to 0.4 unit on the x-axis and cm to unit on the y-axis. Hence, draw the line of best fit. [ 5 marks ] (b) Use your graph from 7(a) to find the value of (i) c, (ii) d, x 4 5 y TABLE (iii) x when y = 5 x. [ 5 marks ] 8 (a) Prove that cosec x tan x cot x. (b) (i) Sketch the graph of y sin x for 0 x. [4 marks] [ marks] (ii) Hence, sketch a suitable straight line on the same axes, and state the number of solutions to the equation sin x x for 0 x. [ marks] 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT

23 SULIT 8 47/ 9 (a) The results of a study shows that 0% of the residents of a village are farmers. If residents from the village are chosen at random, find the probability that (i) exactly 5 of them are farmers, (ii) less than of them are farmers. [5 marks] (b) The age of a group of teachers in a town follows a normal distribution with a mean of 40 years and a standard deviation of 5 years. Find (i) the probability that a teacher chosen randomly from the town is more than 4 years old. (ii) the value of m if 5% of the teachers in the town is more than m years old. [5 marks] 0 Solutions by scale drawing will not be accepted. Diagram 4 shows a straight line AD meets a straight line BC at point D. y C 8 A(7, 7) D B(, ) O x Given DIAGRAM 4 ADB = 90 and point C lies on the y-axis. (a) Find the equation of the straight line AD. [ marks ] (b) Find the coordinates of point D. [ marks ] (c) The straight line AD is extended to a point E such that AD : DE = :. Find the coordinates of the point E. [ marks ] (d) A point P moves such that its distance from point B is always 5 units. Find the equation of the locus of P. [ marks ] Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT

24 SULIT 9 47/ (a) Diagram 5 shows a curve y = x 4x and a straight line y = x. y y x 4x y x 0 x Find the volume of the solid generated when the shaded region is rotated through 60 about the x-axis. [6 marks] (b) The gradient of the curve y = px qx at the point (, ) is 5. Find (i) the value of p and of q. DIAGRAM 5 (ii) the equation of the normal to the curve at the point (, ). [4 marks] 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT

25 SULIT 0 47/ SECTION C [0 marks] Answer two questions from this section. A particle starts moving in a straight line from a fixed point O. Its velocity V ms is given by V 4t 8t, where t is the time in seconds after leaving O. (Assume motion to the right is positive) Find (a) the initial velocity of the particle. (b) the values of t when it is momentarily at rest. (c) the distance between the two positions where it is momentarily at rest. (d) the velocity when its acceleration is 6 m s. [ mark] [ marks] [ marks] [4 marks] In the diagram, ABC and EDC are straight lines. E cm D 0 cm 7 cm 6 cm A B 5 cm C Given that AE = 0 cm, BD = 7 cm, BC = 5 cm, CD = 6 cm and DE = cm. Calculate (a) BCD, (b) AEC, (c) AC, (d) the area of triangle BDE. [ marks] [ marks] [ marks] [ marks] Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT

26 SULIT 47/ 4 Use the graph paper provided to answer this question. Mr. Simon has RM 600 to buy x scientific calculators and y reference books. The total number of scientific calculators and reference books is not less than 60. The number of reference books is at least half the number of scientific calculators. The price of a scientific calculator is RM 40 and the price of a reference book is RM 0. (a) Write three inequalities other than x 0 and y 0 that satisfy the conditions above. [ marks] (b) By using a scale of cm to 0 units on both axes, construct and shade the region R that satisfies all the conditions above. [ marks] (c) If Mr. Simon buys 50 reference books, what is the maximum balance of money after the purchase? [4 marks] 5 Table shows the monthly expenditure and weightage of Mohd Amirul for the year 005 and 007. Item Expenditure (RM) Year 005 Year 007 Price Index Weightage Food Rental p 5 Transport q 50 5 Others 60 r 5 4 TABLE (a) Find the values of p, q and r. (b) Find the composite index for the year 007 based on the year 005. [ marks] [ marks] (c) Given the composite index for the year 008 based on the year 007 is 8, calculate the monthly expenditure of Mohd Amirul for the year 008. [4 marks] END OF QUESTION PAPER 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT SULIT

27 SULIT 47/ Additional Mathematics Paper Sept 008 SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM TINGKATAN ADDITIONAL MATHEMATICS Paper MARKING SCHEME This marking scheme consists of 6 printed pages Sarawak Zon A Trial SPM 008

28 PAPER MARKING SCHEME 47/ Number Solution and marking scheme Sub Marks Full Marks (a) (b) 0 x 5 or f : x x 5 or f(x) = x 5 a = and b = gf(x) = x + x (x ) + (x ) + B B (a) (b) x, x x y = x x B 4 t > t < or equivalent (6) (t +)() < 0 B B 5 x + x + 4 = 0 () = 4 and + = 7 and = B B Sarawak Zon A Trial SPM 008

29 Number Solution and marking scheme Sub Marks Full Marks 6 a = a( )² + = 5 p = and q = B B 7 x 5 (x 5)(x + ) 0 x² x 5 0 B B 8 x 4 x x or equivalent x x or x x B B 9 5 lg lg7 lg lg4 lg B B 0 (a) d 5 T = 4 or T = 9 B (b) 585 8, 54, 6 n = or 54 or 8 or equivalent (Solving) a = 968 and r = B B Sarawak Zon A Trial SPM 008

30 4 Number (a) Solution and marking scheme k Sub Marks Full Marks (b) log 0 y 4log 0 x + log 0 k h B 4 h B h 4 p h h h h h h h h B B p or equivalent B p 5 5 m = m or m 5 5 m 5 6 B B 6 (a) a b 5i m j BD i 5 j BD BA AD or BA BC B B 4 (b) 50 AC 7i j B Sarawak Zon A Trial SPM 008

31 5 Number Solution and marking scheme , 9.58 Sub Marks Full Marks cos 5 5cos or equivalent 5 cos x B B B B 9 (a) r = 6 (b) AOC = 0.45 or 7. = r (0.45) or 458 or 46 (6) ( 69) B B 4 0 (, ) and (0, ) x = 0, 4 B 4 dy = 0 or x(x + ) = 0 dx B dy = x + 6x dx B Sarawak Zon A Trial SPM 008

32 6 Number (a) dy dx Solution and marking scheme 4x 6 or equivalent Sub Marks Full Marks dy dm 6m and dm dx B 4 (b) 08 y [4() 6] 0 0 B ( x) c ( x) c B ( x) or B 5 4 or equivalent 5 B 4 (a) 6 4 or 5 B (b) C C B B B Sarawak Zon A Trial SPM 008

33 47/ Matematik Tambahan Kertas ½ jam Sept 008 SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 008 MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU MARKING SCHEME Skema Pemarkahan ini mengandungi 5 halaman bercetak Sarawak Zon A Trial SPM 008

34 QUESTION NO. ADDITIONAL MATHEMATICS MARKING SCHEME TRIAL ZON A KUCHING 007 PAPER SOLUTION MARKS p m p P 5 * m m * m m p p p p * * 8 m.8, p.7, p.67 Eliminate p or m Solve the quadratic equation by using quadratic completing the square p OR p.7, m.8, m.67 Note : OW- if the working of solving quadratic equation is not shown. 5 (a) ds ds ds dr = 8 r or = dr dt dr dt 8 () Sarawak Zon A Trial SPM 008

35 QUESTION NO. SOLUTION MARKS (b) dy d y x and dx dx P 4 + (x ) + 4x = x x + (x )( x + ) = 0 x =, 7 (a) x.9 or fx 9 P 9 (.9) 0 Use the formula 58 Or equivalent (b) (i) (.9) c.8 c = (ii).58* = 76* 6 Sarawak Zon A Trial SPM 008

36 4 QUESTION NO. SOLUTION MARKS 4 (a) cos or = 45 4 P 077 rad (b) 797 or (077) or (077) (c) () () (a) 4a() 9 = a = 5 (b) a =, r = 4(both correct) or Sarawak Zon A Trial SPM 008

37 5 QUESTION NO. SOLUTION MARKS 6 (a) (i) BP y 4x P (ii) CQ CB or Equivalent 8 CQ x 4y (b) (i) BR BP m P 5 BR 4x y m P 4x y m = ( x y) 4 4 m m = 5 8 Sarawak Zon A Trial SPM 008

38 6 QUESTION NO. 7 (a) SOLUTION y xy MARKS 0 All values of xy correct (accept correct to decimal places) xy dy c P Refer to the graph. Plot xy against y 6 points mark correctly Line of best fit (b)(i) m = c (ii) p = 5 0 d = 0 (iii) y = Sarawak Zon A Trial SPM 008

39 7 QUESTION NO. SOLUTION MARKS 8 (a) sin x cos x cosx sin x sin x cos x sin x sin x cos x sin x cos x sin x or cosec x (b) (i) & (ii) y 6 x Shape of sine curve Amplitude of and period P P Translation x y 0 P Draw the straight line correctly Number of solutions = Sarawak Zon A Trial SPM 008 0

40 8 QUESTION NO. 9 (a) (i) 0 p 0. q SOLUTION P MARKS 5 P[ X 5] C (0.) (0.7) (ii) P[X = 0] + P[X = ] + P[X = ] = (07) + 0 C (0.) (0.7) + C (0.) (0.7) = 058 (b)(i) PZ (ii) m 0.5 P X m m Sarawak Zon A Trial SPM 008

41 9 QUESTION NO. SOLUTION MARKS 0 (a) m BC = or m AD = or m AD = y 7 = (x 7) or 7 = (7) + c y = x 7 (b) y = x + 8 P x 7 = x + 8 or equivalent D(6, 5) (c) x 7() = 6 or y 7() = 5 E(4, ) (d) ( x) ( y ) 5 x² + y² 4x 4y + = 0 0 Sarawak Zon A Trial SPM 008

42 0 QUESTION NO. (a) x = 0, 5 SOLUTION MARKS (5) (5) x 4 x dx 4 5 x 4 x x (5) (5) (4) (4) (b) (i) dy = px q or 5 = p equivalent or = p q dx 4 p =, q = (ii) Gradient of normal = 5 5y + x = or equivalent Sarawak Zon A Trial SPM 008 0

43 QUESTION NO. (a) SOLUTION MARKS V P o (b) 4t 8t 0 Use v = 0 (t )(t) 0 t,, (c) 4 [ t 4t t] Integrate v dt 4 [ ( ) 4( ) 4 ( )] [ ( ) 4( ) ( )] m (d) a 8t 8 4 t s V 4() 8() 5ms Sarawak Zon A Trial SPM 008 0

44 QUESTION NO. (a) cos BCD (5)(6) SOLUTION MARKS BCD = 788 (b) sin CAE sin * CAE = 57 * AEC 499 (c) AC 0 8 (0)(8)cos 49 9 AC = 7805 (d) Area of BDE = 5 6sin 7846 = Use of the formula ab sin C 0 Sarawak Zon A Trial SPM 008

45 Answer for question 4 y (a) I. x y 60 II. y x III. 4xy 60 (b) Refer to the graph, or straight lines correct st. lines correct Correct shaded area 90 (c) (i) (0, 50) 80 Max balance after purchase = RM[ ] = RM (0) (0, 50) Sarawak Zon A Trial SPM x

46 4 5 (a) Q Use of formula I 00 Q0 5 p = 09. q = 00 N,, 0 r = 486 (b) I = = 4.5 (c) Monthly expenditure for Year 007 = 986 x RM Sarawak Zon A Trial SPM 008

47 Answer for question 7 xy (a) 5 y xy Sarawak Zon A Trial SPM y

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