Download Mid-Term B Review Problems

Honors Algebra 2B Mid-Term Review Problems
Name: ___________________
1. Which of these does NOT have the same value as the others?
A. log28
B. log39
C. log464
D. log5125
C. y = 2.5 (1.3)x
D. y = 2.5 (0.3)x
2. Which function represents exponential growth?
A. y = 2.5x1.3
B. y = -2.5x1.3
Sketch each graph. Label 3 points and the asymptote. Also name the domain & range.
x
3.
f ( x)  log3 x
domain:________________________
range:_________________________
1 x 1
2
2
domain:________________________
5. h( x)  
range:_________________________
1
4. g ( x)     1
3
domain:_______________________
range:_________________________
6. g ( x)  log3 ( x  3)  2
domain:_______________________
range:_________________________
Factor Completely
7.
27 x3  64
8.
375  24y3
 3 1
9. An angle drawn in standard position has a terminal side that passes through the point 
,   . What is
2
 2
the measure of the angle 3 ,5  ?
10. An angle of -585o is in standard position. What are the coordinates of the point at which the terminal side
intersects the unit circle?
11.
12.
2
?
3
Describe the translations from the parent function y  cos  to the new function: y  3cos  4  2  5
What is the exact value of sec
For problems #13-15, Graph 0, 2  :


13. y  3sin      1
3

14. f  x   tan  3 
15. f  x   csc  2  1
16.
Evaluate 5log9 3
17.
Use the equation of the exponential function whose graph passes through the points (2, 2) and (4, 50)
to find the value of y when x = -2.
18.
Use log x 2  0.4317 and log x 3  0.6846 to evaluate the value of log x 24 .
19.
Suppose you deposit $31000 in an account paying 3.7% annual interest compounded continuously.
How much do you have after 7 years, presuming no additional deposits or withdrawals.
20.
Solve ln( x  2)  3
You may only work ONE side of the Trigonometric Identities:
21.
sec2 x
 tan 3 x  tan x
cot x
22.
1  sin x 1  sin x

 4 tan x sec x
1  sin x 1  sin x
23.
1  sin x
 2sec 2 x  2sec x tan x  1
1  sin x
24.
sin   cos  tan  sin   sec  cos tan 
25.
tan 2 x  5 tan x  6 tan x  2

sec2 x  10
tan x  3
26.
1  sin x 
2
2
 cos4 x  4sin 2 x
27.
Sam and George are members of a surveying crew that is given the job of finding the height of Mt. Seaholm
(See the diagram below. Drawing not to scale. From a point on level ground, George measures the angle of
elevation to the top of the mountain at 22 . Sam is 710 meters closer to the mountain along the same line.
He measures the angle of elevation to the top of the mountain at 46 . How high is the mountain?
46
22
Sam
710m
George
28.
a) What is the value of all the angles?
5
12
b) Calculate the area of the triangle using Heron’s Formula
10
c) Calculate the area of the triangle using the Law of Sines
29. What is the value of x?
17
18
x
25
30. What is the value of  ?
5
12

10
31.
Suppose you deposit $215000 in an account paying 4.2% annual interest compounded quarterly.
How long until you triple your money? Answer MUST be in Years, Months, Days—No
DECIMALS.
7. Describe the asymptotes and holes for the graph of the rational functions.
x5
1
f ( x)  2
a) y  2
x  6x  5
x  4x  3
b)
8. Sketch the graph of the rational function. Label all of the important information:
3x 2  4 x  1
y 2
x  x6
9. Sketch the graph of the rational function. Label all of the important information:
2 x 2  2 x  24
y
x 2  16
10. Sketch the graph of the rational function. Label all of the important information:
x3  7 x  6
f  x  2
x  x2
Simplify and state any restrictions.
11.
2 x2  5x  2 2 x2  x 1
4 x2 1
x2  x  2
2
x3
15.
1
2
x3
12.
3
1

3 3
8 x y 4 xy
16.
5x
4
 2
x  x  6 x  4x  4
7
2
Solve each equation.
17.
4
5
 2
x 1 x  2x 1
18.
11 1 4
 
3x 3 x 2
19.
4
5
 2
0
x 1 x  2x 1
20.
11 1 4
 
0
3x 3 x 2
21.
3x
4
 2
0
x  7 x  18 x  10 x  16
22.
30
3

0.
m  25 m  5
2
2