AP CALCULUS summer2009 workshopIII

# AP CALCULUS summer2009 workshopIII - AP CALCULUS SUMMER...

This preview shows pages 1–3. Sign up to view the full content.

AP CALCULUS SUMMER WORKSHOP III Problems : 1) ( 2004 Nova Scotia Math League , Game 2 : Team Question ) The parabola y x = 2 meets the parabola y x x = − + 2 6 4 at two points, P and Q . Find the equation of the line passing through P and Q . 2) ( 2004 Nova Scotia Math League , Game 4 : Team Question ) The integers b and c are chosen so that: i) The quadratic equation 5 0 2 x bx c + + = has two roots, one of which is 2. ii) The quadratic equation 5 0 2 x cx b + + = has two roots, one of which is 3. Determine the values of b and c . 3) ( 2004 Nova Scotia Math League , Game 2 : Team Question ) In Δ ABC , sides AB and AC are 10 units long. Determine the maximum possible area of Δ ABC . 4) Let S = + + + + + 1 2 3 4 5 6 2009 2009 2009 2009 2009 2009 . Determine the last digit of S . Hint : Look for a pattern in each of the addends (i.e. 1 2 3 4 5 2009 2009 2009 2009 2009 , , , , and 6 2009 ). 5) Consider the function ( ) f x x x = 2 2 2 . a) Find the domain of ( ) f x . b) If x 1 , then find the equation of the inverse function, ( ) f x 1 . c) Find the range of ( ) f x . 6) Find the domain of the following functions: a) ( ) f x x x = + 4 b) ( ) f x x x = + 1 3 c) ( ) ( ) f x x = ln 4 2 d) ( ) f x x x x = + + 2 7 10 1 7) What is the range of ( ) f x x = 1 2 2 sin ? Hint : Start with the inequality − ≤ 1 2 1 sin x and perform some algebraic manipulations on it. 8) Data was collected during an experiment in which an enzyme with its substrate was subjected to a medium with a varying pH. The result of the effects of pH on the action of the enzyme on its substrate is shown in the graph

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document