Briefly explain your calculations solution method 1

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repetitions of digits and the second digit is even? Briefly explain your calculations. Solution Method 1 Method 2 3 marks 1 mark for Case 1 ½ mark for Case 2 1 mark for addition of cases ½ mark for explanation of cases ½ mark for Case 1 ½ mark for Case 2 1 mark for addition of cases ½ mark for explanation of cases ½ mark for Case 3 3 marks 8 4 8 Case 1: 256 not 0 2,4,6,8 9 1 8 Case 2: 72 0 Total : 256 72 328 = = + = 8 4 1 Case 1: 32 2,4,6,8 0 9 1 8 Case 2: 72 0 8 4 7 Case 3: 224 2,4,6,8 Total: 32 72 224 328 = = = + + =
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Marking Guide—Pre-Calculus Mathematics (40S)—January 2007 Page 25 EXEMPLAR Mark: 3 out of 3
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Page 26 Marking Guide—Pre-Calculus Mathematics (40S)—January 2007 Question No. 8 Outcome: G2 A jar contains 7 yellow marbles and 3 green marbles. When a marble of one colour is removed, it is replaced by 2 marbles of the other colour. Two marbles are chosen randomly. Find the probability that both marbles are the same colour. State your answer as an exact value or correct to 3 decimal places. Solution 4 marks ( ) ( ) ( ) 7 6 Case 1: P 2 yellow 10 11 42 110 3 2 Case 2: P 2 green 10 11 6 110 42 6 48 Total: P 2 same colour 110 110 110 24 55 0.436 ⎞⎛ = ⎟⎜ ⎠⎝ = ⎞⎛ = ⎟⎜ ⎠⎝ = = + = or or ½ mark for 7 10 ½ mark for 6 11 ½ mark for product ½ mark for 3 10 ½ mark for 2 11 ½ mark for product 1 mark for addition of cases
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Marking Guide—Pre-Calculus Mathematics (40S)—January 2007 Page 27 EXEMPLAR Mark: 3½ out of 4 Note(s): deducted ½ mark for P(G|G) 2 9 =
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Page 28 Marking Guide—Pre-Calculus Mathematics (40S)—January 2007 Question No. 9 Outcome: H2 The third term of a geometric sequence is 24 and the sixth term is 1536. a) Find the value of the common ratio. b) Find the value of the first term. Solution a) Method 1 Method 2 3 marks 2 5 3 1 6 1 2 5 1 1 1 1 2 5 2 5 5 2 3 24 1536 24 1536 24 1536 24 1536 64 4 t t r t t r t r t r t t r r r r r r r r = = = = = = = = = = 1 mark (½ mark for each term) 1 mark for equating the fractions 1 mark 1 4 3 3 24 1536 , , , , , new sequence: 24 1536 1536 24 64 4 t t r r r = = = = = 1 mark for labelling the 6th term as 4 t in the new sequence 1 mark ½ mark ½ mark 3 marks
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Marking Guide—Pre-Calculus Mathematics (40S)—January 2007 Page 29 Question No. 9 Outcome: H2 b) or 1 mark 1 24 3 16 2 t = = 1 1536 1024 3 2 t = =
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Page 30 Marking Guide—Pre-Calculus Mathematics (40S)—January 2007 Mark: 2½ out of 3 Note(s): deducted ½ mark for writing 3 3 64 r = (notation error) EXEMPLARS a) b) Mark: ½ out of 1 Note(s): deducted ½ mark for substitution error on line 2
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Marking Guide—Pre-Calculus Mathematics (40S)—January 2007 Page 31
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