Download AP Calculus AB Chapter 1 Review Packet Name Test on Chapter 1

AP Calculus AB
Chapter 1 Review Packet
Name ______________________
Test on Chapter 1: _____________________
Suggested Review Problems from each section (for extra practice): Answers will be posted online.
Underlined problems should be completed without a calculator.
1.1 p. 9 9, 13, 17, 21-27 odd, 32, 35, 37, 41, 44
1.2 p. 19 5, 6, 7, 9, 11, 14, 16, 20, 22, 25, 27, 31, 34, 37, 46, 51, 53
1.3 p. 26
3, 6, 7, 9, 13-18, 22, 23, 32, 34-38
1.5 p. 44
3, 4, 7, 8, 12, 14, 16, 24, 33, 34, 38, 41
1.6 p. 52 6, 9, 10, 17-22, 27, 28, 32, 34, 38, 39
Chapter 1 Review Exercises: #1 – 12 Due: _______________ #13 – 22 Due: __________________
Write an equation of the specified line in point-slope form (NO Calc):
1. through (1, -6) with slope 3
2. through (4, -12) and parallel to 4x + 3y = 12
3. through (-2, -3) and perpendicular to 3x – 5y = 1
Determine if the function is even, odd, or neither (NO Calc):
4. y  x2  2 x  1
6. y 
x4  1
x3  2 x
5. y  x 2  1
Find the domain and range and graph the function (NO Calc):
7. y  x  2
8. y  16  x 2
9. y  ln( x  3)  1
Write a piecewise formula for the functions (NO Calc):
10.
11.
Find a)  f g  1
12. f ( x) 
1
x
g ( x) 
b)  g f  2
1
x2
c)  f
f  x 
d)
g
g  x 
(NO Calc):
Write a formula for f g and g f and find the domain and range of each (NO Calc):
13. f ( x)  2  x 2
14. f ( x)  x
g ( x)  x  2
g ( x)  1  x
For f(x), a) find f 1 and show that  f
f 1  ( x)   f 1 f  ( x)  x and b) Graph f and f 1 in the same
viewing window (NO Calc):
15. f ( x)  ( x  2)2 , x  2
Find the six trigonometric values of  . Give exact answers (NO Calc):
3
16.   cos 1  
7
Solve the equation over the interval 0  x  2 .
17. sin x  0.2
(Calc OK)
18. cos x 
2
(NO Calc)
2
19. cot x   3 (NO Calc)
Solve for x (Calc OK):
20. e 0.2 x  4
21. A drug is administered intravenously for pain. The function f ( x)  90  52 ln(1  t ), 0  t  4 gives the
number of units of the drug in the body after t hours. (Calc OK)
a) What was the initial number of units of the drug administered?
b) How much is present after 2 hours?
22. The number of guppies in Susan’s aquarium doubles every day. There are four guppies initially.(Calc OK)
a) Write the number of guppies as a function of time t.
b) How many guppies were present after 4 days? After 1 week?
c) When will there be 2000 guppies?
d) Give reasons why this might not be a good model for the growth of Susan’s guppy population.