Add Math P1 Trial Spm Sbp 2007

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Add Math P1 Trial Spm Sbp 2007

  1. 1. 3472/1 Matematik Tambahan Name : ………………..…………… Kertas 1 Ogos 2007 Form : ………………………..…… 2 Jam SEKTOR SEKOLAH BERASRAMA PENUH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERCUBAAN SPM 2007 MATEMATIK TAMBAHAN For examiner’s use only Kertas 1 Marks Dua jam Question Total Marks Obtained JANGAN BUKA KERTAS SOALAN INI 1 3 SEHINGGA DIBERITAHU 2 3 3 3 1 This question paper consists of 25 questions. 4 3 2. Answer all questions. 5 3 6 3 3. Give only one answer for each question. 7 3 4. Write your answers clearly in the spaces provided in 8 3 the question paper. 9 4 10 3 5. Show your working. It may help you to get marks. 11 4 6. If you wish to change your answer, cross out the work 12 4 that you have done. Then write down the new 13 4 answer. 14 3 7. The diagrams in the questions provided are not 15 2 drawn to scale unless stated. 16 3 17 4 8. The marks allocated for each question and sub-part of a question are shown in brackets. 18 3 19 3 9. A list of formulae is provided on pages 2 to 3. 20 3 21 3 10. A booklet of four-figure mathematical tables is provided. 22 3 . 23 3 11 You may use a non-programmable scientific 24 4 calculator. 25 3 12 This question paper must be handed in at the end of TOTAL 80 the examination . Kertas soalan ini mengandungi 13 halaman bercetak 3472/2 2007 Hak Cipta SBP [Lihat sebelah SULIT
  2. 2. SULIT 2 3472/1 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. ALGEBRA −b ± b 2 − 4ac log c b 1 x= 8 logab = 2a log c a 2 am × an = a m + n 9 Tn = a + (n-1)d 3 am ÷ an = a m - n n 10 Sn = [2a + ( n − 1) d ] 2 4 (am) n = a nm 11 Tn = ar n-1 5 loga mn = log am + loga n a (r n − 1) a (1 − r n ) 12 Sn = = , (r ≠ 1) m r −1 1− r 6 loga = log am - loga n a n 13 S∞ = , r <1 7 log a mn = n log a m 1− r CALCULUS dy dv du 1 y = uv , =u +v 4 Area under a curve dx dx dx b du dv = ∫y dx or u v −u a 2 y= , dx , = dx 2 dx b v dy v = ∫ x dy a dy dy du 5 Volume generated 3 = × b dx du dx ∫ = πy dx or 2 a b ∫ πx 2 = dy a GEOMETRY 1 Distance = ( x1 − x 2 ) 2 + ( y1 − y 2 ) 2 5 A point dividing a segment of a line  nx1 + mx 2 ny1 + my 2  ( x,y) =  ,  2 Midpoint  m+n m+n   x1 + x 2 y1 + y 2  (x , y) =  ,   2 2  6 Area of triangle = 1 3 r = x2 + y2 ( x1 y 2 + x 2 y 3 + x3 y11 ) − ( x 2 y1 + x3 y 2 + x1 y 3 ) 2 xi + yj 4 r= ˆ x2 + y 2 3472/1 2007 Hak Cipta SBP [ Lihat sebelah SULIT
  3. 3. SULIT 3 3472/1 STATISTIC 1 x = ∑x ∑ w1 I1 N 7 I= ∑ w1 n! ∑ fx Pr = n 8 2 x = (n − r )! ∑f n! 9 n Cr = 3 σ = ∑(x − x ) 2 = ∑x 2 −x _2 (n − r )!r! N N 10 P(A ∪ B) = P(A)+P(B)- P(A ∩ B) 4 σ= ∑ f ( x − x) 2 = ∑ fx 2 −x 2 11 P (X = r) = nCr p r q n − r , p + q = 1 ∑f ∑f 12 Mean µ = np 1  2N−F 5 m = L+ C 13 σ = npq  fm      x−µ 14 z= σ Q1 6 I= × 100 Q0 TRIGONOMETRY 1 Arc length, s = r θ 9 sin (A ± B) = sinA cosB ± cosA sinB 1 2 10 cos (A ± B) = cosA cosB  sinA sinB 2 Area of sector , L = rθ 2 3 sin 2A + cos 2A = 1 tan A ± tan B 11 tan (A ± B) = 1  tan A tan B 4 sec2A = 1 + tan2A a b c 2 2 12 = = 5 cosec A = 1 + cot A sin A sin B sin C 6 sin 2A = 2 sinA cosA 13 a2 = b2 + c2 - 2bc cosA 2 2 7 cos 2A = cos A – sin A = 2 cos2A - 1 1 = 1 - 2 sin2A 14 Area of triangle = absin C 2 2 tan A 8 tan 2A = 1 − tan 2 A 3472/1 2007 Hak Cipta SBP [ Lihat sebelah SULIT
  4. 4. For examiner’s use only Answer all questions. 1. Given set A = {9, 36, 49, 64} and set B = {-8, -6, 3, 4, 6, 7, 8}. The relation from set A to set B is "the square root of ", state (a) the range of the relation, (b) the object of 8, (c) the image of 49. [ 3 marks ] Answer : (a) …………………….. 1 (b) ……………………... (c).................................... 3 −3 2. Given the function f(x) = , x ≠ 0 and the composite function gf(x) = 4x. Find x (a) g(x), (b) the value of x when gf(x) = 8. [ 3 marks ] 2 Answer : (a) …………………….. 3 (b) ……………………... 3472/1 2007 Hak Cipta SBP [Lihat sebelah SULIT
  5. 5. SULIT 5 3472/1 For examiner’s use only 3 Diagram 1 shows a function f : x → ax 2 + bx . x f ax 2 + bx 3 5 1 3 DIAGRAM 1 Find the value of a and of b. [ 3 marks ] 3 3 Answer : .........………………… 4 Solve the quadratic equation 2 x ( x − 5) = ( 2 − x )( x + 3) . Give your answer correct to four significant figures. [ 3 marks ] 4 3 Answer : .........………………… 3472/1 2007 Hak Cipta SBP [ Lihat sebelah SULIT
  6. 6. For examiner’s use only 5 Given the roots of the quadratic equation of 4ax 2 + bx + 8 = 0 are equal. Express a in terms of b. [ 3 marks ] 5 Answer : ................................. 3 ___________________________________________________________________________ 6 Diagram 2 shows the graph of a quadratic function f(x) = 3(x + p)2 + 2, where p is a constant. The curve y = f(x) has the minimum point (4, q), where q is a constant. State (a) the value of p, (b) the value of q, (c) the equation of the axis of symmetry. [ 3 marks ] ( 4, q ) DIAGRAM 2 3472/1 2007 Hak Cipta SBP [Lihat sebelah SULIT
  7. 7. SULIT 7 3472/1 Answer : (a) ……........................ 6 (b) ……........................ For examiner’s (c).................................. 3 use only 7 Find the range of values of x for which x( x − 6) ≤ 27 . [ 3 marks ] 7 3 Answer : .................................. 8. Solve the equation 81x +1 − 27 2 x −3 = 0 . [ 3 marks ] 8 3 Answer : ................................... 9. Given log7 2 = h and log7 5 = k. Express log7 2.8 in terms of h and k. [ 4 marks ] 9 3472/1 2007 Hak Cipta SBP [ Lihat sebelah 4 SULIT
  8. 8. Answer : ...................................... For examiner’s use only 10. Solve the equation log 3 (3t + 9) − log 3 2t = 1 . [ 3 marks] 10 3 Answer : ....……………...……….. 11. The first three terms of an arithmetic progression are 6, p − 2, 14,...…. Find (a) the value of p , (b) the sum of the first tenth term . [ 4 marks ] 8 11 Answer: a)…...…………..…....... 3 b) .................................... 4 3472/1 2007 Hak Cipta SBP [Lihat sebelah SULIT
  9. 9. SULIT 9 3472/1 For examiner’s use only 12. The sum of the first n terms of the geometric progression 64, 32, 16, ….. is 126. Find (a) the value of n, (b) the sum to infinity of the geometric progression. [ 4 marks ] 12 Answer: a)…...….………..…....... 4 b) .................................... ___________________________________________________________________________ 1 13. Diagram 3 shows a linear graph of against x 2 . y 1 y ●(4,6) x2 ● ( 0 , -2 ) DIAGRAM 3 p The variables x and y are related by the equation = 2x 2 + q , y where p and q are constants. a) determine the values of p and q , b) express y in terms of x . [ 4 marks ] 3472/1 2007 Hak Cipta SBP [ Lihat sebelah SULIT
  10. 10. Answer : a) p = ………………..……. 13 q = ……………….....…... For examiner’s 4 b) y = ….………………..... use only 14. Given that the point P ( − 2,3) divides the line segment A( −4, t ) and B (r,8) in the ratio AP : PB = 1 : 4 , find the value of r and of t. [ 3 marks ] 14 3 Answer : .………………… 15 Given that x = 9 i − 8 j and y = 3i , find y − x . [ 2 marks ] % % % % % % % 15 2 Answer : .…………………. 3472/1 2007 Hak Cipta SBP [Lihat sebelah SULIT
  11. 11. 16 SULIT 11 3472/1 4 For examiner’s use only 16 Diagram 4 shows the points P ( −5,−4) and Q (3,−2) . y 0 x Q (3,− 2) P DIAGRAM 4 Find uuu r a) PQ in terms of unit vector i and j , % % uuur b) unit vector in the direction PQ . [ 3 marks ] 16 uuu r Answer: a) PQ = …….…………... 3 b) ……………………….. ___________________________________________________________________________ 17. Solve the equation 3 sin 2 θ + 5 cos θ = 1 for 0 0 ≤ θ ≤ 360 0 . [ 4 marks ] 17 3472/1 2007 Hak Cipta SBP [ Lihat sebelah SULIT 4
  12. 12. Answer: …...…………..…....... For examiner’s use only 18. The diagram 5 shows a circle PAQ with centre O, of radius 8 cm. SR is an arc of a circle with center O. The reflex angle POQ is 1.6π radians. [ 3 marks ] S P 8 cm A 1.6 rad O Q R DIAGRAM 5 Given that P and Q are midpoints of OS and OR respectively, find the area of shaded region, giving your answer in terms of π . 18 Answer:……………………… 3 cm 2 ___________________________________________________________________________ 19. The radius of circle decreases at the rate of 0.5cms −1 . Find the rate of change of the area when the radius is 4 cm. [ 3 marks ] 19 3472/1 2007 Hak Cipta SBP [Lihat sebelah SULIT 3
  13. 13. SULIT 13 3472/1 For examiner’s use only Answer:……………………… 3x + 4 20. Given that f ( x ) = , find f ′(3) . [3 marks] 3 − x2 20 3 Answer: …...…………..…....... ___________________________________________________________________________ 21. A set of numbers x1 , x2 , x3 , x4 ,..., xn has a median of 5 and a standard deviation of 2. Find the median and the variance for the set of numbers 6 x1 + 1,6 x2 + 1,6 x3 + 1,.......,6 xn + 1 . [ 3 marks ] 21 Answer: median = …………………….. 3 variance =.……………..……… 22. A box contains 6 black balls and p white balls. If a ball is taken out randomly from 4 the box, the probability to get a white ball is . Find the value of p. 7 [ 3 marks ] 3472/1 2007 Hak Cipta SBP [ Lihat sebelah SULIT
  14. 14. 22 3 For examiner’s Answer: p = …………………….. use only 23. 5% of the thermos flasks produced by a company are defective. If a sample of n thermos flasks is chosen at random, variance of the number of thermos flasks that are defective is 0.2375. Find the value of n. [ 3 marks ] 23 3 Answer: …...…………..…....... ___________________________________________________________________________ 24. Given that the number of ways of selecting 2 objects from n different objects is 10, find the value of n. [ 4 marks ] 24 Answer: …………………………… 4 3472/1 2007 Hak Cipta SBP [Lihat sebelah SULIT
  15. 15. SULIT 15 3472/1 For examiner’s use only 25. A the random variable X has a normal distribution with mean 50 and variance, σ 2 . Given that P ( X > 51 ) = 0.288, find the value of σ . [3 marks] 25 3 Answer: …...…………..…....... END OF QUESTION PAPER 3472/1 2007 Hak Cipta SBP [ Lihat sebelah SULIT
  16. 16. 3472/1 2007 Hak Cipta SBP [Lihat sebelah SULIT

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