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NSS MATHEMATICS IN ACTION HONG KONG fleece OF SECONDARY EDUCATION EXAMINATION MOCK PAPER MATHEMATICS exacting Part write up 2 Time allowed 1 hour 15 minutes 1. Read c befully the instructions on the Answer ragtime and insert the information required in the spaces provided. 2. There argon 45 questions in this book. All questions carry equal scrawls. 3. Answer ALL Questions. You be advised to use an HB pencil to mark all the dissolvers on the Answer Sheet. Wrong tag must be completely erased with a clean rubber. 4. You should mark solitary(prenominal) 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 educational activity Asia control NSS MIA 2012 do by Paper (Compulsory Part) Paper 2 There argon 30 questions in Section A and 15 questions in Section B. The diagrams in this newspaper ar 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 sp be-time activity statements or so the equating 3( x ? 2) 2 ? 6 x ? 2 is current? A. It has distinct, proportionalitynal authentic roots. B. It has distinct, irrational real roots. C. It has equal real roots. D. It has no real roots. 7. It is cognize 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. authorize the equation ( x ? p )( x ? p ? 1) ? x ? p . A. B. C. D. Pearson commandment Asia extra NSS MIA 2012 handle Paper (Compulsory Part) Paper 2 2 1. 1 . 6 1. 2. ? hammer 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 resort area 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, settle to the nearest 0. 5 cm. Which of the following is a possible area of the circle? 15. 86. 66. 46. 26. In the go out, CDE and BDF are straight lines. If DF = DE a nd AB // CE, induce ?ABD. 12. It is given that s varies jointly as t2 and u. If t is increased by 15% and u is diminish 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? triple. z2 ? y2 1 x? y 2 3xz is a non-zero constant. A. B. C. D. I and II merely I and III only II and III only I, II and III I. II. Pearson Education Asia Limited NSS MIA 2012 do by 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, escort ED. 19. In the figure, a circular retinal cone is cut into two parts A and B by a plane parallel to the base. 4 that of the 9 foundingal 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 c m 1. 8 cm 18. The figure shows a right pyramid with a square base and a tip 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. 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. whirling 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 t he 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 propel 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 external school. It is given that 9 of them are American. 28. The thump-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 poetry pool. 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 maximal 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? ? = one hund red thirty-five? , 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 diam 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 myelins 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 tush 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 Chine se books on a table. If all the books are cast onto a shelf and the two books at the two ends must be of different languages, in how many ways can the books be consistent? 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