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Semester 2 Final Test Review
1. Simplify:
2. Simplify:
5𝑥 2 𝑦
3𝑎𝑏
5
𝑥−4
÷
+
10𝑥 3 𝑦
9𝑎2 𝑏3
2
𝑥−5
2
2
x  18
3. Simplify: x 27 x  18  x  11
2
x  81
x 4
4. Solve for x:
3
2

4 x  5 x  10
5. Solve for x:
1 x 18
 
2 6 x
6. Find the vertical asymptotes(s) of the function: y 
7. Describe the translation and sketch a graph:
𝑦=
x2  4
x 2  7 x  12
1
+2
𝑥−3
8. A graph of the following equation would create which of the conic shapes?
3𝑥 2 − 4𝑦 2 = 36
9. Write the standard form of the equation of the circle with a radius of 3 and its center at (2, 1).
10. Write an equation of an ellipse with co-vertices at (–3, 0) and (3, 0), and vertices at (0, –5) and (0, 5).
11. Graph:
4x2 + 25y2 = 100
12. A 4 person committee is chosen at random from a group of 10 people. How many different
committees are possible?
13. Find the mean, median, and mode for the following set of data {5, 4, 7, 5, 6, 6, 8, 9, 1, 4, 6, 5, 3, 5}
14. 12 people entered a race. If there are no ties, in how many ways can the first three places come out?
15. A bag contains 6 white marbles and 8 red marbles. One marble is drawn at random and not replaced.
Then a second marble is drawn. What is the probability that the first marble is red and the second one is
white?
16. Solve for x: 8  4 x 1
17. Evaluate: log 3 27
18. Use the change of base formula to evaluate the expression log 3 15 .
19. Condense the expression:
2 log 5 x  3 log 5 b
20. Expand: log a
5x 3
ba 3
21. Solve for x: 52𝑥 = 15
22. Solve for x: ln(3x  2)  0
23. Rewrite in to exponential form: log 4 16 = 2
t
 1  200
24. The rate of decay of a particular sample can be modeled by the equation: y  200  , where y
2
represents the units existing after a specified amount of time, t. How many units will be left after 200
days?
25. If there are initially 400 bacteria in a culture, and the number of bacteria increase by 12% each hour,
how many bacteria will be present after 6 hours?
26. Write an exponential function to model the following situation. A population of 1200 zebras
decreases at an annual rate of 10%. How many zebras will there be after 7 years?
27. Find the sum of the first 15 terms of the series:
–4 + 0 + 4 + 8 . . .
28. Find the rule for the nth term of the arithmetic sequence.
3, 7, 11, 15, 19, . . .
29. Find the 21st term of the sequence:
-6, 3, 12, 21, ……
30. Find the sum of the infinite series:
1 1 1 1
    ......
3 9 27 81
31. For the series 3, -6, 12, -24, …. find the sum of the first 20 terms?
4
32. Evaluate:
 2(3)
n 1
n 1
33. Write the first five terms of the sequence defined by
a1  3 and d = 3
34. Write the first five terms of the sequence defined by
a1  3 and r = 3
35. What is the coefficient of the x4y6 term in the expansion of (x + y)10?
36. Expand (3x  2) 6
37. Find the exact value of the sin 300º.
5
38. Find the exact value of the cos 
radians.
3
39. Convert 210º to radians
4
radians to degrees
3
41. Find the measure of an angle between 0 and 360 that is coterminal with  180
40. Convert
42. Find the period and amplitude and graph the following equation: 𝑦 = 3 sin 2𝜃