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NSS MATHEMATICS IN ACTION HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION MOCK PAPER MATHEMATICS Compulsory Part Paper 2 Time allowed: 1 hour 15 minutes 1. Read carefully the instructions on the Answer Sheet and insert the information required in the spaces provided. 2. There are 45 questions in this book. All questions carry equal marks. 3. Answer ALL Questions. You are advised to use an HB pencil to mark all the answers on the Answer Sheet. Wrong marks must be completely erased with a clean rubber. 4. You should mark only 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 Mock 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. Section A 1. If n is an integer, then 33 n = 9 n ? 1 6. Which of the following statements about the equation 3( x ? 2) 2 ? 6 x ? 2 is true? A. It has distinct, rational real 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 must 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 equation ( 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 satisfying 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 term 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 circle is measured to be 10 cm, correct to the nearest 0. 5 cm. Which of the following is a possible area of the circle? 15. 86. 66. 46. 26. In the figure, CDE and BDF are straight lines. If DF = DE and AB // CE, find ?ABD. 12. It is given 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 figure, a = 1 , which of the x following is true? III. z2 ? y2 1 x? y 2 3xz is a non-zero constant. A. B. C. D. I and II only I and III only II and III only I, II and III 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 base. 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 figure shows a right pyramid with a square base and a slant edge 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. 2:3 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 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. Find 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 figure, O is the centre 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 below 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 grou p 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 mode 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 log 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 geometric sequence. Which of the following must be true? I. x3, y3, z3 are in geometric 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 centre 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 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 books 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–