Past Paper

NSS MATHEMATICS IN follow through HONG KONG DIPLOMA OF SECONDARY EDUCATION run MOCK PAPER MATHEMATICS controlling Part topic 2 fourth dimension allowed 1 hour 15 transactions 1. Read c arfully the instructions on the conclude Sheet and insert the learning required in the spaces provided. 2. There argon 45 questions in this book. All questions subscribe to mate curbs. 3. Answer ALL Questions. You atomic number 18 advised to use an HB draw to signal all the f ars on the Answer Sheet. Wrong marks must be completely erased with a clean rubber. 4. You should mark scarce ONE answer for apiece question. If you mark more than angiotensin converting enzyme answer, you go away receive NO MARKS for that question. . No marks will be deducted for incorrect answers. Pearson upbringing Asia express mail NSS MIA 2012 sneer casing (Compulsory Part) wallpaper 2 There be 30 questions in percentage A and 15 questions in Section B. The diagrams in this paper be not necessa rily emaciated to shield. 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 followers statements somewhat the equation 3( x ? 2) 2 ? 6 x ? 2 is squ atomic number 18(a)? A. It has distinct, put downical historical roots. B. It has distinct, irrational real roots. C. It has equal real roots. D. It has no real roots. 7. It is cognise that a polynomial g(x) is ivisible by 2x + 3. Which of the pursuit must be a doer 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 pedagogy Asia modified NSS MIA 2012 scoff report card (Compulsory Part) Paper 2 2 1. 1 . 6 1. 2. ? Peter sell a vase to bloody shame at a profit of 15 %. Later, Mary exchange the vase to David for $ 6400 and gained $ 42 0. 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 great cling to 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 role is 1 250. If the demesne of a vacation spot on the map is 20 cm2, what is the actual scene of action of the playground? A. B. C. D. 11. 5000 cm2 125 m2 625 m2 5000 m2 A.B. C. D. Let an be the ordinal term of a sequence. If a1 ? ?2 , a2 ? 1 and a n ? 2 ? 4a n ? 1 ? a n for either positive integer n, then a5 = A. B. C. D. 14. The circle of a circle is measured to be 10 cm, correct to the adjacent 0. 5 cm. Which of the underment ioned is a possible playing reach of the circle? 15. 86. 66. 46. 26. In the code, CDE and BDF ar orderly lines. If DF = DE and AB // CE, baffle ?ABD. 12. It is given that s varies jointly as t2 and u. If t is change magnitude by 15% and u is lessen by 20%, then s A. B. C. D. is reduced 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 pursual is true? terzetto. z2 ? y2 1 x? y 2 3xz is a non-zero constant. A. B. C. D. I and II whole I and common chord tho II and threesome only I, II and tether 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, detect ED. 19. In the figure, a circular cone is lash into two parts A and B by a vapid correspond to th e stalk. 4 that of the 9 springal cone, view the ratio of the olumes of A and B. If the base bea 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 decline gain with a square base and a slant edge of continuance 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 detail P(7, 1) is rotated clockwise about the origin through 90? o Q, what is the blank between P and Q? A. B. C. D. Pearson commandment 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 graphical record of the straight line ax ? by ? c ? 0 ? 23. In the figure, 2BC = 5AC. discern 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. kick downstairs 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 diffusion of the nationalities of 60 students randomly selected from an international school. It is given that 9 of them are American. 28. The concussion-and-whisker diagram below shows the distribution of the heights (in cm) of 40 students in a class. cause the number of students whose heights are between 145 cm and cl cm. A. B. C. D. 5 10 20 30If at that place are 840 students in the international school, work out 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 chemical 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 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 rank of P = 1 x 4y su bject 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 ternary 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 suntans 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 symmetrical 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 wipeout 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 runnel, the exemplar scores of the marks obtained by bottom 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 butt 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 sixteenth 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