Name__________________________ PRE-CALCULUS SPRING 2017 EXAM REVIEW

This is not an exhaustive list of practice problems. Old homework and their answers are posted
on my website. Study 2nd semester TPAs as well.
Simplify the following completely.
1.
csc cot 
sec
Given that cos A 
2.cos   cos  sin 2 
3.
sin  cos 

cos  sin 
4. sec2   sin 2 
1
1
, with A in quadrant I, and sin B   , with B in quadrant IV, find the following:
3
2
5. sin  A  B 
Given that sin A  
6. cos  A  B 
7. tan  A  B 
5
7
4
with A in quadrant IV, tan B 
with B in quadrant III, and cos C  
with C
13
24
5
in quadrant II, find the exact value of the following:
8. sin 2A
9. tan 2A
10. cos 2C
Solve the following for 0    2
11. 1  sin2   1  cos2 
12. sin  tan sin  0
13. The USS Aardvark sailed 120 miles from Port Possum on a bearing of 325° to Port Hyena, then
sailed 100 miles from Port Hyena on a bearing of 75° to Port Honey Badger. What bearing would the
Aardvark have to sail to return directly to Port Possum?
14. Butch hiked 6 miles on a bearing of 135°, then turned and went 7 miles on a bearing of 148°. How far
is his final destination from his starting point?
15. Given triangle side lengths a  7, b  11, c  12 , find the measure of the smallest angle.
16. Find the value of each expression. Leave answers exact.
3
2
c. Cos 1 (
a. Tan 1 1
b. Sin 1
e. Sin 1 0
f. sin(Cos 1 )
3
5
3
)
2
d. Tan 1 3
5
)
12
h. cos(Sin 1 1)
g. sec(Tan 1
17. Evaluate the following.
a. cos(Arctan 3)
1
2
b. sin(Sin 1 )
c. Arcsin(sin
3
)
4
1
2
d. csc(Tan 1 ( ))
18. Let f1  1, f 2  1, f 3  2, f4  3,... be the terms of the Fibonacci sequence. Find
 f7    f8 
2
2
.
19. What is the sum of the coefficients of the 3rd and 5th terms of  4x  y  ?
4
20. What is the sum of the first 8 terms of the sequence 1225, 245, 49, 9.8, …?
21. How many distinct arrangements are possible using all of the letters in the words STATE MEDALS?
22. The Bear Wallow high school volleyball team has 5 setters, 6 blockers and 3 roamers. How many 6member teams can be formed if each team needs 2 setters, 3 blockers and 1 roamer?
23. An infinite geometric sequence has a common ratio of ¼ and a sum of 44. What is the first term of
the sequence?
24. Set S  1, 2, 3,4,5,6,7 . How many 5-element subsets of set S are there?
25. If
A
B
17 x  21
, find the partial fraction decomposition.


x  8 3 x  1 3 x 2  25 x  8
26. Convert to polar coordinates:
 6,  6 3 
28. Convert to a rectangular equation: r  3cos
29. Convert to a polar equation: x  15


27. Convert to rectangular coordinates:  4,
5 
6 
Sketch the graph.
30. r  2cos
31. r  4sin 2
33. Expand using the Binomial Theorem:
 3 x2  4 y 
34. Find the sixth term of
a  3
32. r  2  4cos 
5
10
.
35. Find the next four terms of the recursive sequence given by a1  3, an  an1  5.
36. Find the 102nd term of 5, 13, 21, 29, 37, …
37. In an arithmetic sequence a5  24 and a9  40. Find an explicit formula.
38. Find the ninth term of 4, 20, 100, 500, …
39. Find the indicated partial sum:
(a) S10 for

  3n  1 
(b) S6 for
n 1

3
 4k
k 1
40. Find the sum of the infinite series.

2 1
(a)    
2
k 1 3
k 1
41. If v   5, 12  , then

 3
(b)  3   
n 2  4 
v ?

42. If J  3, 7  and K  12, 10  , find the component form of KJ
n
43. If u  3, 7 and v  9,1 , find the following:
(a) the dot product u  v
(b) the angle between the two vectors
44. Write the parametric equations for:
 x  3
4
2

 y  1
9
2
1
Simplify to a single term or single number.
45. sin x  csc x  sin x   _________________________
46.
tan x cot x
 _________________________
cos x
47. In 1978, Lars deposited 1000 Deutschmarks into an account that earns 4.75% interest compounded
quarterly. How long (in years) did it take for the account to be worth 1800 Deutschmarks?
(Deutschmarks was the former standard monetary unit in Germany until the introduction of the Euro)
Additional Topic List:
1. Polar graphing (be able to write equations from given information)
2. Recursive formulas/Explicit formulas for arithmetic/geometric