Download AP Calculus Summer Packet for school year 2012/2013 (email me if

AP Calculus Summer Packet for school year 2012/2013
(email me if you have questions [email protected])
No calculator is allowed for these questions.
Show all work neatly on separate paper. Due the
first day of school. I will schedule review sessions in August - I will post the date on my Web
Page. You can also email me if you want to get a group of people together to review these
problems
1. Find the slope of 2x + 4y = 5
2. Find the equation of the line parallel to x - 2y = 12 and passing through (2,-5). Write your
answer in the following forms:
a. Point – slope
b. Slope intercept
3. Find the equation of the line perpendicular to 3x +4y = -8 and passing through (0,-2). Write your
answer in the following forms:
a. Point – slope
b. Slope intercept
4. Find all vertical and horizontal asymptotes of the following graphs – express asymptotes as an
equation:
a.
y
x2
x2  4
b. y= e-x +1
c. y = ln (x-3)
5. Find the domain and range of:
a. e-2x +1
b. y = ln (x+2)
c. tan -1 x
d. cos x
e. sin (arctan x)
f. ln (cos x)
6. Describe the end behaviors of the following graphs:
a. f(x) = x4 + 3x3 – 6x
b. f(x) = -3x3 + x2
7. Find the following values:
5
)
3
7
b. cos( 
)=
6
a. sin(
c. arccos -1 =
d. tan (arccos ( 
3
))=
2
8. Find csc θ given cosθ =
12
and tan θ < 0
13
9. The point (27,7) is on the terminal side of an angle in standard position. Determine the
values of all six trig functions.
10. Find the smallest positive value x for which f(x) = sin(
x
) – 1 is a maximum.
3
11. Given triangle ABC , mC  90 , mB  60 , and AC = 23, find AB. (sketch triangle –
remember, no calculator)
12. Find the reference angle of  = 136degrees.
13. Determine two solutions on [0, 2  ) such that sec  
14. Solve the following equations in the interval [0, 2  ):
a. 4sin2x -1 =0
b. tan2x + tanx = 0
c. sin 2x = .5
d. sec x -2 = 0
e. 2sin2x + sin x = 1
2 3
3
4 5
and sec(θ) = 6, find tan (θ).
9
15. Given sin(θ) =
16. Sketch the angles in standard position and state the value of all 6 trig functions
4
3
7
b.  
6

c.  
3
a.

17. Rewrite the angle in degree measure and find two positive co-terminal angles in radian
measure:  
7
6
12 5
, ), find the value of cos  .
13 13
19. Sketch triangle ABC and solve given: a  13, b  18, c  26 (calculator allowed)
18. Given a terminal point of a ray (
20. Find the x-intercepts of f(x) = x3 -2x2-x +2
21. Find the inverse ,f-1(x), of the following functions:
a. f(x) = 2 x
b. f(x) = 2e-x
22. If the point (5,-2) is on the graph of a function, then what point must be on the graph of its
inverse, f-1(x)?
23. Given f(x) = lnx and g(x) = 4-x2, find f(g(x)) and identify the domain and range of the composite
function.
24. Given f(x) = 2x2 – 3x, find
f (2  h)  f (2)
and simplify.
h
25. Solve and or simplify without a calculator:
a.
b.
c.
d.
e.
Log3(x-4) = 0
ln x4 = 10
e2x- ex = 6
ln(6x – 6) = 2
log42 + log48 = ?
1 3
) =?
125
b
g. logb(3b) = , b=?
2
2
2x ( x -15)
h. e =e
f.
log3(
26. Identify the x and y intercepts of f(x)= 4ln(x-2)
27. Expand the following expression as a sum, difference, and/or constant multiple of logarithms
using the log rules:
ln
x2
x3  1
28. Condense the following expression as a single term :
2(log5x + log57) –
1
(log5y)
3
29. Find the domain of the function: f(x) = ln(
x3
)
x2
30. Find all values of x such that f(x) = g(x) given:
f(x) = x2 +19x +73
g(x) = 2x +1
31. Find the roots of f(x) =
8x2  1
7
32. Determine if the following functions are odd, even , or neither:
a. y = x3 +2
b. y = x3 +2x
c. y = x  2
2
d. y = e x - 1
33. Use long division to divide:
x 4  3x 2  4
x2  x  3
34. Use synthetic division to divide:
x3  27 x  54
x 3
35. Find the following limits
a.
b.
lim
x4
lim
x 0
x4
x  x  12
2
x3  3
x
36. Know these graphs by heart: ex , lnx, sinx, cosx, tanx,
x , x2, x3, (x-h)2+(y-k)2=r2