AP Calculus AB Summer Review Packet 2015
This packet is a review of the prerequisite skills needed for AP Calculus AB. It is to be done NEATLY and on a SEPARATE sheet of
paper with appropriate work shown. All problems are non-calculator. The packet will be due at the end of the second week of school,
but it is highly recommended that you complete it before classes begin, and you will receive extra credit if you hand it in on the first
day of class. Complete solutions to the problems will be on my VISION page, my (Mrs. McConnell’s) CMS page, and in room 116. A
quiz on the summer assignment will be given at the end of the second week. Have a wonderful summer and I look forward to seeing
you in August!!
I.
1.
II.
Simplify. Show the work that leads to your answer.
x4
2
x  3x  4
x3  8
x2
2.
3.
5 x
x 2  25
2. cos 2x =_______________________________
______________________________
_______________________________
Pythagorean =______________________
______________________
______________________
3. sin 2x =_____________________________
1.
IV.
1.
V.
x 2  4 x  32
x 2  16
Trigonometric Identities
1.
III.
4.
Simplify each expression.
2
2
2. x
10
x5
1
1

xh x
1
1

3. x  3 3
x
4.
2x
1
8

 2
x  6x  9 x 1 x  2x  3
2
Solve for z.
2. y 2  3 yz  8 z  4 x  0
4 x  10 yz  0
Use f ( x) 
3,5 ,  2, 4 , 1,7  ,
g ( x)  x  3 ,
h( x)   3, 2 ,  4,3 , 1,6  ,
k ( x)  x 2  5
for the following questions.
1.
 f  h (1)
2.
6. k 1 ( x)
VI.
1.
 k  g  (5)
7.
1
f ( x)
3.
 f h (3)
8.
 kg  ( x)
4.
 g k  (7)
Follow the directions for each problem.
Evaluate
f ( x  h)  f ( x )
for f ( x)  x 2  2 x.
h
5


3. Simplify: x  x  x 2  x 2 


3
2
2. Expand: ( x  y )3
5. f 1 ( x)
VII.
Expand and simplify.
n3

n 0 2
4
1.
VIII.
1.
3
2.
n 1
x
x
11. 27
2
1
2
9. e 3ln x
10.
4 xy 2
1

12 x 3 y 5
3
 23  32 
12.  5a  4a 



 53  2
13.  4a 


14.
3(n  1)!
5n !
With slope -2, containing the point (3,4)
1.________________________________________
Containing the points (1,-3) and (-5,2)
2.________________________________________
With slope 0, containing the point (4,2)
3.________________________________________
Parallel to 2 x  3 y  7 and passes through (5,1) 4.________________________________________
Perpendicular to the line in prob #1, containing 5.________________________________________
the point (3,4)
Without a calculator, determine the exact value of each expression.
1.
sin 0
6.
cos
2. sin

7. tan
3


11. cos  sin 1
1.
8. ln
5. ln e 7
4. ln1
Using the point-slope form y  y1  m( x  x1 ) , write an equation for the line.
X.
XII.
7. log 1 8
2
3
IX.
1.
3. e (1 ln x )
2. eln 3
1
3
XI.
3
Simplify.
6. log 3  
1.
2.
3.
4.
5.
1
n
1

2

3. sin
2
7
4
8. tan


12. sin 1  sin
3
4

6
4. cos 
5. cos
2
3
10. tan
9. tan
7
6

2
7 

6 
For each function, determine its domain and range.
y  x4
2. y 
x2  4
3. y  4  x 2
4. y 
x2  4
Determine all points of intersection.
Parabola y  x 2  3x  4 and the line y  5 x  11
2. y  cos x and y  sin x in Quadrant I
XIII.
1.
Solve for x, where x is a real number. Show the work that leads to your solution.
x 2  3 x  4  14
2.
x4 1
0
x3
3. ( x  5)2  9
5. ( x  3)( x  3)  0
6. x 2  2 x  15  0
9. sin 2 x  sin x, 0  x  2
10. ( x  1)2 ( x  2)  ( x  1)( x  2) 2  0
12. log x  log( x  3)  1
13. e3 k  5
XIV.
1.
7. 12 x 2  3 x
4. 2 x 2  5 x  8
8. x  3  7
11. 27 2 x  9 x3
14. ln x  2t  3
Graph each function. Give its domain and range.
y  sin x
2. y  cos x
x4
x 1
5. y  x 2  6 x  1
6. y 
9. y 
10. y 
x
1
13. y 
x
3
x
 x2

14. y   x  2
4

3. y  tan x
7. y 
x2  4
x2
11. y  ln x
if x  0
if 0  x  3
if x  3
4. y  x3  2 x 2  3x
8. y  e x
12. y  x  3  2