AP CALCULUS summer2009 workshopI

# AP CALCULUS summer2009 workshopI - AP CALCULUS SUMMER...

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AP CALCULUS SUMMER WORKSHOP I Problems : 1) Consider the points () A 23 , , B 56 , , C , and ( ) Dk ,2 . Find the value of k so that a) AB is parallel to CD b) AC is perpendicular to BD 2) Find the perimeter of the triangle formed by the coordinate axes and the line 77 36 2772 xy + = . 3) A lattice point is a point whose coordinates are integers . How many lattice points are there on the line 34 5 9 + = that lie in the first quadrant? 4) Two lines are drawn in the first quadrant with the first line having x and y intercepts of 4 and 6 while the second line has x and y intercepts of 6 and 4. These two lines together with the x and y axes carve out a quadrilateral. Find the area of the quadrilateral. 5) ( New South Wales Department of Education Leaving Certificate Examination 1965, Mathematics I ) If xy c = 2 , prove that 11 1 cx cy c + + + = . By using this result, or otherwise, find the numerical values of a) 1 65 5 1 5 +− + ++ b) 2 72 7 1 72 + + + log log ab ba 6) ( New South Wales Department of Education Leaving Certificate Examination 1965, General Mathematics ) ABC

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AP CALCULUS summer2009 workshopI - AP CALCULUS SUMMER...

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