Download Honors Algebra 2B final exam Review June 2013

Honors Algebra 2B Trimester Review
NOTE: This is intended to assist you in your final exam review preparations and not be the only tool you use in
studying. This may or may not be complete and comprehensive on every topic covered in the course.
Label the indicated angles by their degree measure, radian measure and coordinates on the Unit Circle.
180
0
1. Which angle is NOT co-terminal with the others?
A.
5
6
B.
19
6
C. 510o
D.
7
6
 1
 2

2. An angle drawn in standard position has a terminal side that passes through the point   , 
3
.
2 
What is one possible measure of the angle?
3. An angle of -120o is in standard position. What are the coordinates of the point at which the terminal side intersects the
unit circle?
 5 
?
 4 
4. What is the exact value of cos  
5. What is the exact value of tan
2
?
3
 
 6
6. Find the exact value of tan 

.

Find the Exact Value of each function:

7.
cos120  cos
8.
1   cos 210
9.
1
5  
5 

If sec  
, then what is:  sec
   tan
 ?
cos 
6  
6 

10.
If cot  

3
2
2
2
cos 
17
, then what is: cot
?
6
sin 
11. Which angle, in standard position, is NOT coterminal with the others?
A. -190o
B. 170o
C. 190o
D. 550o
 2
2
,

.
 2
2 

12. An angle drawn in standard position has a terminal side that passes through the point 
What are TWO possible measures of the angle, in standard position?
13. Given that cos  0 , find the other five trigonometric ratios for  .
sin   
1
3
csc 
cos 
sec 
tan 
cot  
Verify. You may only work one side of the equation.
a) sin   cos  
b)
 sec   tan  
Graph from 0
to 2 .
14. y = 2sin( ½  )
 

2 
15. y = tan 
16. y = -cos 2 
2
cot   1
csc 

1  sin 
1  sin 
Verify the identity. Work only with the left side of the identity.
17. csc x  csc x  sin x  
19.
sin x  cos x
 cot x  csc 2 x
sin x
sec2 x
 tan 3 x  tan x
cot x
18.
1  sin x
 2sec 2 x  2sec x tan x  1
1  sin x
20.
sec x  cos x
 sin x
tan x
21. Find all of the exact solutions on the interval: 0, 2  .
a)
c)




sin  x    sin  x    1
4
4


b) 2  sin 2 x  2 cos 2
x
2
sin5x  sin x  0
22. Calculate the EXACT values of :
a)
cos

12
b)
cos 52.5
23. A vertical pole is at the side of a straight road that makes an angle of 15 with the horizontal. When the angle of
elevation of the sun is 57, the pole casts a shadow 75 feet long directly down the road, as shown in the figure.
Approximate the length of the pole.
57
15
24. a)
What is the value of all the angles?
5
12
b) Calculate the area of the triangle using the Law of Sines
10
c) Calculate the area of the triangle using Heron’s Formula
25. Find:
z1
z2
Z1= 24(cos
5
5
+ i sin
)
3
3
26. Express in complex trigonometric form:
27. Express in standard complex form: 4(cos
28.
Z2 = 8(cos 75 + i sin 75 )
z= -3 + 4i
11
11
+ i sin
)
6
6
Use DeMoivre’s Theorem to find (Use Radians):
 1  i 3 
12
29. Solve the following system of equations using matrices.
2 x  3 y  4 z  2
x 
y  5 z  11
4y 
z  7
True or False:
30. The product of a 4  3 matrix multiplied by another 4  3 matrix is yet another 4  3 matrix.
31. The sum of a 4  3 matrix added to another 4  3 matrix is yet another 4  3 matrix.
32. Find the equation of the parabola:
1,1 ,  2,10 , and 3, 23 .
y = ax2 + bx + c,
that passes through the following three points:
 2 3 
1 3 
 3 2 




33. Let A= 1 2 and B= 1 2 and C= 
 . Be certain that your answers are in proper format.




 4 1
5 4 
6 5 




a) Solve:
B+A
c)
AxC
b) Solve:
3Ax2B
d)
(BxC)+A
34. Write the first 5 terms of each sequence.
a.
a1  5
b) an 
ak 1  3(2  ak )
(n  1)!
2n
35. Use the Binomial Theorem to expand and simplify ( x 2  3)5 .
36. Seaholm decides to run its own lottery to help students pay for their college education. A player must match all
five numbers from a choice of 1 through 30. Mrs. Lancaster asks you to figure out how many different
combinations of five numbers are possible.
37. Find the 15th term of the sequence where a18  48 and r =
38. Find S12 for the series -7 + 35 - 175 + ….
39. Evaluate the infinite geometric series 3  2 
50
40. Find the sum:
 3n .
n 1
4 8
  ... .
3 9
1
.
2