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Solutions to exam review

  1. 1. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions
  2. 2. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions2.
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  35. 35. SolutionSolutions to Exam Review Pre-Calculus 40s Old Exam Questions Method 1 1 + sin q + 1 - sin q LHS = 1 mark for common denominator (1 - sin q )(1 + sin q ) 2 = 1 mark for identity cos 2 q = 2sec 2 q 1 mark for identity ( = 2 tan 2 q + 1 ) 1 mark for identity = 2 tan 2 q + 2 = RHS 4 marks Method 2 2sin 2 q 1 1 RHS = +2 ½ mark LHS = + cos 2 q 1 - sin q 1 + sin q 2sin 2 q 2 cos 2 q ½ mark = + 1 + sin q + 1 - sin q 1 mark for common cos 2 q cos 2 q = 1 - sin q 2 denominator 2sin 2 q + 2 cos 2 q = cos 2 q ( ) 2 2 sin 2 q + cos 2 q = 1 mark for identity = ½ mark for cos 2 q cos 2 q factoring LHS = RHS 2 ½ mark for = cos q 2 simplifying 4 marks Page 54 Marking Guide—Pre-Calculus Mathematics (40S)—January 2005
  36. 36. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions 78. 79.
  37. 37. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions 80. 81. 82.
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  53. 53. 3x + 4 = 7 2 x +1Solutions to Exam Review Pre-Calculus 40s Old Exam Questions Solution log 3x + 4 = log 72 x +1 ½ mark for taking the log of both sides ( x + 4 ) log 3 = ( 2 x + 1) log 7 ½ mark for log theorem x log 3 + 4 log 3 = 2 x log 7 + log 7 ½ mark for distributing x log 3 - 2 x log 7 = log 7 - 4 log 3 ½ mark for isolating and factoring x x ( log 3 - 2 log 7 ) = log 7 - 4 log 3 log 7 - 4 log 3 x= ½ mark for solving for x log 3 - 2 log 7 x = 0.877 ½ mark for consistent answer 3 marks 113. Note(s): · log 3 = 0.477 121 ln 3 = 1.098 612 log 7 = 0.845 098 ln 7 = 1.945 910 · if brackets are omitted in the second step, but assumed to be there, deduct ½ mark · the final answer must be correct to at least 3 decimal places Page 18 Marking Guide—Pre-Calculus Mathematics (40S)—January 2005 114.
  54. 54. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions Question No. 35 Outcome: D1, B3 State the range of the function f ( x ) = 2- x . 115. 116. Answer ( 0, ¥ ) OR y > 0 1 mark
  55. 55. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions 117.118.119.
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  67. 67. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions 150. 151. Question No. 31 Outcome: B1 The graph of y = x 2 - 4 x - 5 crosses the x-axis at -1 and 5. Where does the graph of y = ( x + 10 ) - 4 ( x + 10 ) - 5 cross the x-axis? 2 Answer 152. -11, - 5 ½ mark for each correct answer 1 mark 153.
  68. 68. The graph of the function f ( x ) = 5sin x + p touches the x-axis once in the interval [ 0, 2p] .Solutions possibleReview of p. State a to Exam value Pre-Calculus 40s Old Exam Questions Answer 154. 5 or –5 1 mark 155. Marking Guide—Pre-Calculus Mathematics (40S)—January 2005 Page 43
  69. 69. Question No. 49Solutions to Exam Review Pre-Calculus 40s Old Exam Questions Outcome: B1, B5 Solution 156. a) y = f ( x + 3) b) y = f ( x) - 2 y y (-2, 3) (1, 3) (1, 1) (4, 1) (-4, 0) x x (-7, -2) (-2, -2) 1 mark 1 mark for absolute value 2 marks 1 mark for vertical shift 1 mark 2 marks Note(s): · in a) deduct ½ mark for one incorrect point · in b) deduct 1 mark if they are done in the wrong order Marking Guide—Pre-Calculus Mathematics (40S)—January 2005 Page 67
  70. 70. b) y = f ( 2x) c) y = - f ( x) -3 3 xSolutions to Exam )Review d) y = f ( - x Pre-Calculus 40s Old Exam Questions 157. Solution a) y b) y 4 2 x x -3 3 -1.5 1.5 c) d) y y 2 x x -3 3 -3 3 -2 4 marks Page 64 Marking Guide—Pre-Calculus Mathematics (40S)—January 2005

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