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NSS MATHEMATICS IN ACTION HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION do by PAPER MATHEMATICS Compulsory Part musical composition 2 Time allowed 1 hour 15 minutes 1. Read c befully the instructions on the Answer Sheet and insert the information mandatory in the spaces provided. 2. there ar 45 questions in this book. All questions carry equal attach. 3. Answer solely Questions. You argon advised to use an HB pencil to mark all the dissolvents on the Answer Sheet. disparage marks essential be completely erased with a clean rubber. 4. You should mark alone ONE answer for each question. If you mark more than one answer, you will receive NO MARKS for that question. . No marks will be deducted for wrong answers. Pearson Education Asia Limited NSS MIA 2012 gibe Paper (Compulsory Part) Paper 2 There are 30 questions in Section A and 15 questions in Section B. The diagrams in this paper are not necessarily drawn to scale. Choose the best answer for each question. Sectio n A 1. If n is an integer, then 33 n = 9 n ? 1 6. Which of the following statements round the equality 3( x ? 2) 2 ? 6 x ? 2 is true? A. It has distinct, rational existent roots. B. It has distinct, irrational real roots. C. It has equal real roots. D. It has no real roots. 7. It is known that a polynomial g(x) is ivisible by 2x + 3. Which of the following mustiness be a factor of g(4x 3)? 2 n ? 1 A. B. C. D. 2. x 2 ? y 2 ? 2 xy ? 4 ? A. B. C. D. 3. A. B. C. D. 8. 1. 5. 8049. 8053. a = 3, b = ? 2 . a = 3, b = ? 3 . a = ? 2, b = ? 2 . a = ? 2, b = ? 3 . B. C. D. 9. Let p be a constant. Solve the equating ( x ? p )( x ? p ? 1) ? x ? p . A. B. C. D. Pearson Education Asia Limited NSS MIA 2012 Mock Paper (Compulsory Part) Paper 2 2 1. 1 . 6 1. 2. ? Peter sold a vase to Mary at a profit of 15 %. Later, Mary sold the vase to David for $ 6400 and gained $ 420. What was the cost price of the vase for Peter? A. B. C. D. x ? ?p x ? p ? 1 ? ? p or x ? p ? 1 x ? ? p or x ? p 2x ? 3 4x ? 3 8x ? 3 8x ? 9 If x is an integer square 4x ? 1 , then the 2(1 ? x) ? 6 x and x ? ?2 greatest value of x is A. If 5a ? 2b ? a ? 4b ? 11 , then A. B. C. D. 5. ( x ? y ? 2)( x ? y ? 2) ( x ? y ? 2)( x ? y ? 2) ( x ? y ? 2)( x ? y ? 2) ( x ? y ? 2)( x ? y ? 2) If f ( x) ? x 2012 ? 2012 x ? 2012 , then 2 f (? 1) ? 3 = A. B. C. D. 4. ?1? . ?3? 3n ? 1 . 3n ? 2 . 35 n ? 2 . $ 5200 $ 5970 $ 6877 $ 7780 10. The scale of a map is 1 250. If the area of a playground on the map is 20 cm2, what is the actual area of the playground? A. B. C. D. 11. 5000 cm2 125 m2 625 m2 5000 m2 A.B. C. D. Let an be the nth boundary of a sequence. If a1 ? ?2 , a2 ? 1 and a n ? 2 ? 4a n ? 1 ? a n for any positive integer n, then a5 = A. B. C. D. 14. The circumference of a dress circle is measured to be 10 cm, good to the nearest 0. 5 cm. Which of the following is a possible area of the circle? 15. 86. 66. 46. 26. In the condition, CDE and BDF are straight lines. If DF = DE and AB // CE, rein ?ABD. 12. It is effrontery that s varies jointly as t2 and u. If t is increased by 15% and u is decreased by 20%, then s A. B. C. D. is decreased by 8 %. is decreased by 5. 8 %. is increased by 5. 8 %. is increased by 8 %. 13. If z ? y and y 2 ? 4. 2 cm2 8. 55 cm2 8. 14 cm2 7. 11 cm2 A. B. C. D. 76? 104? 116? 128? 16. In the understand, a = 1 , which of the x following is true? cardinal. z2 ? y2 1 x? y 2 3xz is a non-zero constant. A. B. C. D. I and II only I and common chord only II and leash only I, II and ternion I. II. Pearson Education Asia Limited NSS MIA 2012 Mock Paper (Compulsory Part) Paper 2 A. B. C. D. 3 40?. 45?. 50?. 55?. 17. In the figure, ABCD is a rhombus and FBC is a triangle. If FA = 2 cm and BC = 3 cm, find ED. 19. In the figure, a circular cone is cut into two parts A and B by a plane parallel to the house. 4 that of the 9 original cone, find the ratio of the olumes of A and B. If the base area of A is A. B. C. D. A. B. C. D. 1 cm 1. 2 cm 1. 5 cm 1. 8 cm 18. The figur e shows a right pyramid with a square base and a slant leap of length 17 cm. If the total length of the edges of the pyramid is 132 cm, find the total surface area of the pyramid. 23 8 19 8 27 19 27 20. Through which of the following transformations, would figure A be transformed to figure B? I. Translation II. Rotation III. Reflection A. B. C. D. A. B. C. D. 544 cm2 608 cm2 736 cm2 800 cm2 II III I and III only II and III only 21. If the point P(7, 1) is rotated clockwise just about the origin through 90? o Q, what is the distance between P and Q? A. B. C. D. Pearson Education Asia Limited NSS MIA 2012 Mock Paper (Compulsory Part) Paper 2 4 5 units 72 units 10 units 128 units 22. If a 0, b 0 and c 0, which of the following may represent the graph of the straight line ax ? by ? c ? 0 ? 23. In the figure, 2BC = 5AC. materialize sin ? . A. 2 29 A. B. C. B. D. 24. 29 2 cos(180? ? ? ) 1 ? ? sin(180? ? ? ) tan(90? ? ? ) A. B. C. D. C. 2 5 5 2 tan 2 ? tan ? 1 1 25. In the figur e, O is the perfume of the circle ABCD. Find x. D. A. B. C. D. 36? 40? 42? 45? 26. What is the area of the circle x2 + y2 + 12x ? y + 9 = 0? A. B. C. D. Pearson Education Asia Limited NSS MIA 2012 Mock Paper (Compulsory Part) Paper 2 5 9? 43? 52? 61? 27. Two fair dice are thrown once. What is the probability of getting a sum of 4 or 6? A. B. C. D. 1 6 2 9 5 9 5 36 30. The pie chart to a lower place shows the distribution of the nationalities of 60 students randomly selected from an international school. It is given that 9 of them are American. 28. The box-and-whisker diagram below shows the distribution of the heights (in cm) of 40 students in a class. Find the number of students whose heights are between 145 cm and 150 cm. A. B. C. D. 5 10 20 30If there are 840 students in the international school, estimate the number of Australian students in the school. A. 196 B. 208 C. 216 D. 224 Section B 31. 29. a , a, a + d, a + 3d and a + 6d is a group of numbers. Which of the following must be true? A. B. I. The mean of the group of numbers is a + 2d. II. The median of the group of numbers is a + d. III. The modal value of the group of numbers is 2. A. B. C. D. C. D. I and II only I and III only II and III only I, II and III Pearson Education Asia Limited NSS MIA 2012 Mock Paper (Compulsory Part) Paper 2 1? 6 ab b ? ? 2 a ? b b? a 2 1 a2 a2 ? b2 b2 a2 ? b2 a 2 ? 2ab ? b 2 a2 ? b2 32. Which of the following best represent the graph of y ? 2 record 3 x ? x 2 x ? 1 34. Solve 16 ? 2 ? A. A. B. C. D. B. 15 ? 0. 2 5 2 5 or 3 2 5 log 8 log 5 ? log 2 log 4 35. If a and k are real numbers and a ? 11i ? (2 ? 3i )(3 ? ki) , then A. B. C. D. C. D. NSS MIA 2012 Mock Paper (Compulsory Part) Paper 2 ? ? 1 . ? 1. ? ? 1 . ? 1. 36. Find the maximum value of P = 1 x 4y subject to the following constraints. 1 ? x ? 3 2 ? y ? 4 ? ? ?2 y ? x ? 2 ? x ? 2 ? ?2 y ? 33. If ? and ? are the roots of the quadratic equation 4 x 2 ? 5 x ? 3 ? 0 , find the value 1 1 + . of 2? 2? 3 A. ? 5 2 B. ? 5 5 C. 8 5D. 6 Pearson Education Asia Limited a ? 3, k a ? 3, k a ? 9, k a ? 9, k A. B. C. D. 7 3 4 6 7 37. It is given that three positive numbers x, y and z are in nonrepresentational sequence. Which of the following must be true? I. x3, y3, z3 are in nonrepresentational sequence. II. 3x, 3y, 3z are in geometric sequence. III. log x2, log y2, log z2 are in arithmetic sequence. A. B. C. D. 40. The figure shows a circle with oculus O. BC and BA are the tangents to the circle at C and D respectively. If ? BAC = 42? , find ? BOC. I and II only I and III only II and III only I, II and III 38. Find x in the figure, correct to the nearest integer. A. B.C. D. 66? 72? 84? 90? 41. The figure shows a triangular prism ABCDEF, where both ? ABF and ?DCE are right-angled isosceles A. B. C. D. 12 13 14 15 triangles. If AB = 10 and BC = 5, find the angle between the line AE and the plane ABCD, correct to the nearest degree. 39. Solve 1 + sin? cos ? = 3sin2? for 0? ? ? ? 360?. A. B. C. D. ? = 45? or 225? ? = 135? , 207? or 225? ? = 45? , 153? , 225? or 333? ? = 135? , 153? , 315? or 333? Pearson Education Asia Limited NSS MIA 2012 Mock Paper (Compulsory Part) Paper 2 A. B. C. D. 8 14? 17? 22? 45? 42. The figure shows a circle which is symmetrical about the y-axis. A(4, 1) nd B are two end points of a diameter of the circle. If the equation of the tangent to the circle at B is 4 x ? 3 y ? 31 ? 0 , find the coordinates of the centre of the circle. A. B. C. D. 3 (0, ) 2 (0, 2) 5 (0, ) 2 1 ( ? , 2) 2 44. A box contains 50 bulbs and 8 of them are defective. Two bulbs are drawn at random from the box without replacement. Given that at least(prenominal) one bulb drawn is defective, find the probability that exactly one bulb drawn is defective. 4 A. 13 3 B. 5 4 C. 5 12 D. 13 45. In a Chinese test, the standard scores of the marks obtained by John and Mary are 1. 05 and 0. 8 respectively. Which of the following are true? I.II. III. 43. There are 2 different English boo ks and 4 different Chinese books on a table. If all the books are put onto a shelf and the two books at the two ends must be of different languages, in how many ways can the books be arranged? A. B. C. D. A. B. C. D. 32 40 192 384 Pearson Education Asia Limited NSS MIA 2012 Mock Paper (Compulsory Part) Paper 2 Mary performs better than John in the test. Compared with John, the mark obtained by Mary is closer to the mean mark of the test. The mark obtained by John is below the 16th percentile of the marks in the test. I and II only I and III only II and III only I, II and III End of test 9