Name:________________
Block:___________
Pre-Calculus Quarter 2 Test Review
Evaluating & Graphing Logs/Exponential Functions (Chapter 4)
1. log 4 16(  x  2)
2. e x  e3 x (
2
1
)
e2
Solve/Simplify.
3. 492 x  7 x
2
 45
 1 
4. log 5  
 25 
Graph.
5. f ( x)  1  3(2 x )
Domain:_______________ Range:____________ Asymptote:_____________
Increasing/Decreasing_____________
6. g ( x)  3  log( x  2)
Domain:_______________ Range:____________ Asymptote:_____________
Increasing/Decreasing_____________
7. Find the inverse of f(x) =
2x  3
x4
and prove they are inverses of each other.
Trigonometric Functions (Chapter 5)
Evaluate.
11
to degrees.
6
9. Convert 210° to radians.
10. What is the exact value of
tan 120°?
11. What is the exact value of
5
sec
?
3
12. In which quadrant is θ if
csc θ > 0 and tan θ < 0?
13. What is the exact value of cos
θ if θ is in quadrant II and
24
sin  
?
25
1
and tan   0
5
what is the exact value of sin  ?
15. What is the value of tan θ if
(-8, 3) is on the terminal side of θ
in standard position?
16. Find a negative angle
measures that is coterminal with
130°.
8. Convert
14. If cos   
17. What is the reference angle
of 245° in standard position?
18. What is the reference angle
4
of
in standard position?
3
19. What is the period and phase
shift of f(x) = sin(3x – π)?
Period:___________________
Phase Shift:_______________
Graph the functions below.
20. y = -2 sin(2x + π)
22. y  csc
1
x
4
21. y = 3 cos(2x + π)
23. y  cot(3x)
24. y = 3 tan x
25. Write a function for the graph below.
-5π -
5π
Analytic Trigonometry (Chapter 6)
Find values to answer the following questions.
3
3
   2 , what is the
25. If cos   and
5
2
value of sin  ?
26. When P(2, -5) is on the terminal side of θ in
standard position, what is the value of
cos θ?
27. What is the solution of sec θ = 1.8492 to the
nearest hundredth of a radian?
28. What is the solution of sin θ = 0.8704 to the
nearest hundredth of a degree?
29. Use calculator to solve sin   0.5 on interval
[0, 2 )
30. Use calculator to solve tan  
[0, 2 )
3
on interval
3
Prove the following identities.
tan 
 sec   cos 
31.
csc 
33.
tan   sec   1
 tan   sec 
tan   sec   1
32.
sin  cos 

 sin   cos 
tan  cot 
34.
sin 2   tan 
 tan 2 
2
cos   cot 
Use reference triangles to find the exact value of each of the following expressions.
 2 

 5 
36. cos 1 sin
35. sec sin 1   
3 

 6 

37. If the terminal side of θ intersects the unit circle 38. If the terminal side of θ intersects the unit circle
 20 21 
 2 77 
at P ,  , what are the values of the six
at P  ,
 , what are the values of the six
 29 29 
9 
 9
trigonometric functions?
trigonometric functions?
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
39. Find the exact value of the expression below.
40. Find the exact value of the expression below.
4
3
sin[sin 1 ( )  tan 1 ( )]
5
4

5
 4
tan  sin 1     cos 1 
13 
 5
