Download ALGEBRA 2 … SECOND SEMESTER FINAL EXAM … REVIEW

ALGEBRA 2 … SECOND SEMESTER FINAL EXAM … REVIEW
Chapter 1
1. Label the properties used to justify each step:
3
3
( x + 2 ) + ( − x )  = ( − x ) + ( x + 2 ) 
2
2
3
= ( − x + x ) + 2 
2
3
= [ 0 + 2]
2
3
= [ 2]
2
=3
Chapter 7
2. Write an equation that translates the parabola f ( x ) = −3x 2 left 5 units and up 2 units.
2
3. Describe the difference between the graphs of the parabolas f ( x ) = 2 ( x + 4 ) − 1 and
2
g ( x ) = 2 ( x + 4) + 3 .
4. Does f ( x ) = −2 x 2 − 8 x − 5 have a minimum or a maximum? State the domain and range.
5. Factor 3 x 2 + 5 x − 2 = 0 and determine the x-intercepts.
6. What is the factored form of the parabola shown in the graph:
y
3
2
1
x
-3
-2
-1
1
-1
-2
-3
7. Solve ( 5 x + 6 )
1
2
=x
2
3
4
Chapters 7 and 9
8. Graph g ( x ) = x 2 + 4 x + 5
Chapter 9
9. Identify the conic equation x 2 − 4 y 2 + 8 y − 4 = 16 .
2
10. Graph the conic x = 4 ( y + 3) − 2
Chapter 10
11. Simplify log 3 1 − log 3 27
12. Solve log 2 ( 4 x ) − log 2 ( x − 3) = 4 for x.
13. Solve 94 x −1 = 273 x for x.
14. Solve for x and leave in calculator ready form. 5 x = 29 .
15. Change from exponential to logarithmic form. Do not solve. 5 x = 125
16. Write as a single logarithm. log x − 3log y − 2 log z
17. Simplify e ln 3x
18. Simplify
( x )( x )
3
19. Simplify 16
3
4
i8
2
5
3
20. Graph y = 5 x and y = 10 x on the same coordinate plane. Label at least 2 points on each graph.
What point do these graphs share? Which graph increases faster?
21. Write log 5 625 = 4 in exponential form.
22. What is the inverse function of y =
2
x −5?
3
23. If f ( x ) = x 2 − 2 and g ( x ) = x + 7 , what is f ( g ( x ) ) ?
Chapter 11
24. Write an expression that represents the value of the nth term of each sequence below.
A) 7, 5, 3, 1,…..
B) 4, 2, 1,
1
, …..
2
3 3 3
25. Find the sum of the infinite geometric series, if it exists: 6 + + + + .....
2 8 32
Chapter 12
26. What is the reference angle for 300°? Use this reference angle to find the value of tan 300° .
27. What is the reference angle for θ = 230°
28. Use the unit circle to find the exact value of the trigonometric function sin 45° .
29. P ( 6, −8 ) is a point on the terminal side of θ in standard position. Find the exact value of the six
trigonometric functions for θ .
30. Write four different functions that can be used to find side x on ABC .
B
6
19°
C
31. If sin θ = −
x
A
3
and cos θ > 0 , in which quadrant is θ located?
5
Chapter 15
32. Fourteen horses recently competed in the Preakness race. In how many different ways could these
horses finish first, second, and third only?
33. Ten people are in the race to be the Republican candidate for the presidency in 2012. Determine
how many different combinations of 2 candidates are possible from a total of 10? Write in factorial
form and then simplify.
34. 12 actors, (4 males and 8 females) are auditioning for a show. The audition times are selected at
random. What is the probability that the first 3 actors selected to audition are female?
35. Find the probability of rolling a 1, 3, or an even number on a six-sided die.
36. Salvador has two 12-sided dice. Each is numbered 1 through 12 inclusive. If he tosses the dice,
what is the probability that the sum of the numbers will be a 20?
37. In a bucket, Sandra has 2 pennies, 4 nickels, 7 quarters, and 6 dimes. If she randomly picks a coin,
what is the probability that it is a nickel, given that it is valued at 10 cents or less?
4
38. What is the third term in the expansion of ( 3 x − 2 y ) ?
4
39. How many terms are in the expansion of ( x − 2 y ) ?