Pre calculus mathematics marking guide january 2009

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Pre-Calculus Mathematics: Marking Guide (January 2009) Exemplar Mark: 1½ out of 4 Note(s): gave 1 mark for consistent factors gave ½ mark for evaluating combination
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22 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 7 G5 The probability that Alex wears his boots is 0.35. When he wears his boots, the probability that he jumps in a puddle is 0.6. When he does not wear his boots, the probability that he jumps in a puddle is 0.3. Given that Alex jumps in a puddle, what is the probability that he is wearing his boots? Express your answer correct to 3 decimal places. Solution Note(s): deduct ½ mark if answer is not expressed as a single fraction or decimal ( )( ) ( )( ) ( )( ) P(boots and jump) P(boots jump) P(jump) 0.35 0.6 0.35 0.6 0.65 0.3 0.21 0.21 0.195 0.21 0.405 0.518 519 14 0.519 27 = = + = + = = = or ½ mark for P(boots and jump) ½ mark for complement of P(boots) [0.65] ½ mark for P(no boots and jump) 1 mark for conditional probability ratio (including addition) ½ mark for simplification 3 marks
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Pre-Calculus Mathematics: Marking Guide (January 2009) 23 Exemplar Mark: 1½ out of 3 Note(s): gave ½ mark for P(boots and jump) gave ½ mark for complement of P(boots) [0.65] gave ½ mark for P(no boots and jump)
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24 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 8 G2 A mathematics class dropped a paper cup 500 times. The results of this experiment are shown in the table. A student plays a game where he drops a cup 3 times. He wins the game if the cup lands in the same position all 3 times. Using the data in the table above, determine the probability of winning this game. Express your answer correct to 3 decimal places. Solution Position of the cup Frequency open end up 50 open end down 115 on its side 335 ( ) 3 3 3 50 115 335 P 3 same 500 500 500 up down side 0.001 0.012 167 0.300 763 0.313 93 0.314 = + + = + + = = 2 marks for P(3 same) (1 mark for probabilities, 1 mark for raising to the power of 3) 1 mark for adding cases 3 marks
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Pre-Calculus Mathematics: Marking Guide (January 2009) 25 Exemplar Mark: 2 out of 3 Note(s): gave 1 mark for probabilities gave 1 mark for adding cases
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26 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 9 E3 Solve for n algebraically: 2 36 n C = Solution Method 1 Method 2 ( ) ( ) ( ) 1 36 2! 1 72 two consecutive positive numbers 72 9 8 72 9 n n n n n = = = = = Note(s): give 1 mark for correct answer using trial and error 1 mark for set-up ½ mark for correctly expanding numerator ½ mark for simplification ½ mark for both values of n ½ mark for rejecting extraneous root ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) 2 2 ! 36 2! 2 ! ! 72 2 ! 1 2 ! 72 2 ! 1 72 72 72 0 8 9 0 8 n n n n n n n n n n n n n n n n n = = = = = = + = = − 9 n = 1 mark for set-up ½ mark for simplifying 1 mark for explanation ½ mark for the value of n 3 marks 3 marks
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Pre-Calculus Mathematics: Marking Guide (January 2009) 27 Exemplar Mark: 1 out of 3 Note(s): gave 1 mark for trial and error
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28 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 10 a) B6 b) B4 The graph of ( ) y f x = is shown below.
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