AP Calculus AB Questions and Free Response Questions

FREE RESPONSE QUESTIONS (RUBRIC ATTACHED IN A SEPARATE FILE):

1. A box is to be constructed from a sheet of cardboard that is 20 cm by 60 cm, by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum volume this box could have?

2. Find the amplitude and period of y = –3cos(2x + 3).  Use your calculator to graph the function and state its symmetry. Find the first positive x-intercept using your calculator’s zero function. 

3. Find two functions f(x) and g(x) such that f[g(x)] = x but g[f(x)] does not equal x. 

4. State the vertical, horizontal asymptotes and zeros of the rational function, f(x) = ${x^2+3x+2}/{x^2+5x+4}$. Why is there no zero at x = –1? 

5. Give an example and explain why a polynomial can have fewer x-intercepts than its number of roots.