Fiesta 1: Ap Calculus Ab

AP CALCULUS AB | 2008 | Shubleka | Fiesta # 1 

     Name________________________ 

Please write your answers neatly on a separate sheet. No calculators are permissible on this assessment. 1. If f ( x) = e x and g ( x) = x 2 , find the following: •

f ( g (1))

•

g ( f (1))

•

f ( g ( x))

•

g ( f ( x))

•

g ( g ( x))

•

f (t ) g (t )

2. Find the inverse of the functions f ( x) = 2 x + 3 , h( x) = x 2 + 2 x − 1 ( x > 0) , and

g ( x) = 5xx+−21 . Show the work leading to your answer. 3. Express x in terms of the other variables in the picture:

4. According to Car and Driver, an Alfa Romeo going at 70 mph requires 177 feet to stop. Assuming that the stopping distance is proportional to the square of velocity, find the stopping distances required by an Alfa Romeo going at 35 mph and at 140 mph (its top speed). 5. a) If f ( x) = ax 2 + bx + c , what can you say about the values of a, b, and c if: i)  

(1, 1) is on the graph?

 

AP CALCULUS AB | 2008 | Shubleka | Fiesta # 1 

ii)

(1, 1) is on the vertex?

iii)

The y-intercept is (0, 6)?

     Name________________________ 

b) Find the quadratic function satisfying all three conditions. 6. Find the period and amplitude of f ( x) = 0.1sin(π x) + 2 . 7. On the graph of f ( x) = sin x , points P and Q are at consecutive highest and lowest points. Find the slope of the segment connecting P and Q. 8. Find the half-life of a radioactive substance that is reduced by 30% in 20 hours. 9. If the size of a bacteria colony doubles in 5 hours, how long will it take for the number of bacteria to triple? 10. Solve for x : 7 x + 2 = e17 x .