64 pre calculus mathematics marking guide january

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64 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 51 F3 Sketch a clearly labelled graph of the following: ( ) 2 2 3 1 16 9 x y + + = Solution Note(s): give a maximum of 1 mark for correct graph of ( ) ( ) 2 2 2 2 3 3 1 or 1 16 9 9 16 x x y y + + = = ½ mark for ellipse ½ mark for centre ½ mark for consistent endpoints of major axis ½ mark for consistent endpoints of minor axis -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 i i i i i y x -7 7 -7 7 2 marks x y 1 1
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Pre-Calculus Mathematics: Marking Guide (January 2009) 65 Exemplar Mark: ½ out of 2 Note(s): gave ½ mark for ellipse
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66 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 52 H3 Evaluate: 1 3 k k = Solution Note(s): deduct ½ mark if answer is not expressed as a single fraction 2 3 1 1 1 1 1 3 3 3 3 1 3 1 3 1 3 1 1 3 1 3 2 3 1 2 k k t r S = = + + + = = = = = 1 mark for 1 t 1 mark for r 1 mark for substitution into correct formula 3 marks
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Pre-Calculus Mathematics: Marking Guide (January 2009) 67 Exemplar Mark: 1½ out of 3 Note(s): gave 1 mark for 1 t gave 1 mark for substitution into correct formula deducted ½ mark for arithmetic error
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Pre-Calculus Mathematics: Marking Guide (January 2009) 69 Appendices
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70 Pre-Calculus Mathematics: Marking Guide (January 2009)
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Pre-Calculus Mathematics: Marking Guide (January 2009) 71 MARKING GUIDELINES Arithmetic error, deduct ½ mark Concept error, deduct 1 mark Final probability answer greater than 1, deduct ½ mark Intercept stated as an ordered pair, deduct ½ mark Expression changed to an equation or vice versa, deduct ½ mark Units of measure missing or incorrect, deduct ½ mark Degree symbol in angle measure missing, deduct ½ mark Correct answer stated in degrees instead of radians or vice versa, deduct 1 mark Variable introduced without being defined, deduct ½ mark Example: (Note: Student can write “ k ∈Ι ” or “ k is an integer”.) LHS and RHS equated throughout the proof of an identity, deduct 1 mark Variable omitted more than once in a trig identity or equation, deduct ½ mark Variable changed without being redefined, in either an equation or an identity, deduct ½ mark for poor notation Example: 2 sin x ” written instead of “ 2 sin x ”, deduct ½ mark Incorrect precision or rounding, deduct ½ mark 2 2 2sin 1 cos 1 1 sin 1 2 , 1 6 6 x x x x θ θ = = = = π = = ± or [ ] 2 sin 1 1 sin 2 5 , 0, 2 5 2 2 6 x x x x k k = = π π = π 6 6 π π = + π + π, 6 over or k ” not defined, deduct ½ mark Appendix A
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72 Pre-Calculus Mathematics: Marking Guide (January 2009) In a binomial theorem expansion, answer given as an entire term when only the numerical coefficient is requested, deduct ½ mark Parentheses omitted when using the log of a power theorem such as: Unsimplified fractions such as 1 1 2 3 2 + , deduct ½ mark (Note: Unreduced fractions such as 6 8 or unrationalized fractions such as 3 2 1 are acceptable.) Error made while simplifying fractions, deduct ½ mark Cases in permutations, combinations, or probability problems not briefly described, deduct ½ mark Brackets in a fraction omitted but assumed, deduct ½ mark Example: 2 2 4 3 9 =
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  • Spring '12
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  • Trigonometry, Logarithm, New Testament chapters, pre-calculus mathematics

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