Download 3 π 7 sin 4 π 4 π 11 cos 6 π 3 tan 4 π 7 tan 6 π 5 tan 3 π arctan 1

NAME____________________________________________
Last Years Teacher :__________________________________
Grade in Pre Calculus:______________________
Section 1: Trigonometry
Determine the exact value of each without using a calculator:
1.
sin 0
4.
cos
7.
tan

4
3
4
3.
sin
7
4
cos3
6.
cos
11
6
7
6
9.
tan
5
3
2.
sin
5.
8.
tan

3
10.
 2
sin 1 

 2 
11.
 3
cos 1 

 2 
12.
arctan  1
13.

 2 
cos  sin 1 
 

 2 

14.

  
cos 1  tan   
 4 

15.

 3 
sin  arctan    
 4 

16. List the Pythagorean Trigonometric Identities:
_________________________
_________________________
_________________________
17. List the Double Angle Trigonometric Identities:
sin 2x  ____________________________
cos 2x  ____________________________
18. Find all the exact solutions to
19. Solve the equation:
2sin 2 ( x)  3sin( x)  2  0 on the interval  0, 2  .
2sin 2 ( x) cos( x)  cos( x) on the interval  0, 2  .
20. Use Trigonometric Identities to simplify:
21. Graph the following from
a.
y  sin 
 csc( x)  tan( x)  sin( x) cos( x)
0, 2 
b.
y  cos 
Section 2: Exponential Functions and Logarithms
Simplify:
1.
e3ln x
2.
eln 3
3.
e3ln x
4.
ln e3
5.
ln e2 x
6.
ln1
7.
log 1 8
8.
x13
x6
9.
x3
x
2
1
10.
27
2
3
5
x2
13.
x
2 3


11.  125x 3 


 x 
14. 

4 3
 x 
12.
6
15.
4
x5 x
e4 x
e3
Graph the following:
16.
y  2x
17.
y  log 4 x
Section 3: Algebra Review
Simplify the following:
2
1.
4.
4
1 1

x y
2.
xy
3
5
x3
x2  9
5.
1
x
x
3.
1
x
x
x 2  4 x  12
x 2  6 x  16
6.
x3  7 x 2  8 x
x3  8 x 2  2 x  16
For #’s 7-12, find the following for each function:
A. zero’s
7.
B. y-intercept
f  x   9  x2
C. domain (interval notation)
8.
f  x 
D. range
x4
x 2  16
E. graph
9.
11.
f  x   x3  5x 2  14 x
f  x  x  4
 x 2 , x  2
 3
2 x  2
10. f  x    x ,
2 x  1, x  2

12.
f  x 
1
x
For #’s 13-16, write the equation of a line in point-slope form:
13. A line containing
 2,5 and  3, 2 
14. A line containing
15. A horizontal line with a y-intercept at -3.
17. Quickly expand the binomial
19. Use sign analysis to solve:
20. Use the difference quotient,
 2 x  3
y  y1  m  x  x1 
4
 4, 1 and the origin.
16. A vertical line with a root at 5.
5

2
18. Simplify: x  x  x 2  x 


3
2
x4 4
 0
x3 x
f  x  h  f  x
2
, to find the slope of the secant line for: f  x   3x  1
h
21. Find the point(s) of intersection for:
f  x   x 2  4 x  32 and g  x   3x  5 , also state the domain
where g  x   f  x  and where f  x   g  x 