Algebra 2
Name: _________________________
End of Course Review
Date: _____________ Period: _____
1. What is the end behavior of y  x 4  2 x3  x  1 ?
__________ & __________
2. What is the end behavior of y   x5  6 ?
__________ & __________
3. Write the third degree polynomial with zeros at 1, 2, and 3.
_______________
4. Write the third degree polynomial with zeros at 1, –1, and –4.
_______________
5. Give a cubic equation in factored form for the function.
____________________
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
6. Give a quartic equation in factored form for the function.
____________________
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
7. Simplify: ( x  2)( x 2  2 x  7) .
Algebra 2 Final Exam Review
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8. Simplify: ( x  1)( x 2  2 x  3) .
_______________
9. Find all the rational zeros of 2 x 4  7 x 2  4 .
__________
10. Find all the rational zeros of x 4  4 x 2  12 .
__________
11. Divide ( x3  12 x 2  39 x  28)  ( x  7) .
_______________
12. Divide (2 x 2  3x  1)  ( x  4) .
_______________
13. Find the rational root of x3  5 x 2  2 x  10  0 .
__________
14. Find all the rational roots of x3  2 x 2  5 x  6  0 .
__________
15. One root of 2 x3  3x 2  8 x  12  0 is 2. What are the other 2 roots?
__________
16. One root of 3 x3  2 x 2  19 x  6  0 is 3. What are the other 2 roots?
__________
17. Simplify: (4a 2b)3 (ab 4 ) 2 . No negative exponents in the answer.
__________
18. Simplify:
19. Simplify:
x 2 y 3 z
. No negative exponents in the answer.
xy 4 z 5
75a4b7 .
__________
__________
20. Simplify: 2 x 49 xy 2 .
__________
21. Simplify: 5 3 2 xy 6  3 8 y 3 .
__________
Algebra 2 Final Exam Review
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22. Simplify: 2 5 64 x 2 y 3  4 5 4 x3 y 8 .
__________
23. Simplify by rationalizing the denominator:
24. Simplify by rationalizing the denominator:
2
.
__________
1 2
.
3 2
__________
3 5
4
25. Simplify (27) 3 .

__________
2
26. Simplify 8 3 .
__________
1
27. Solve: (4 x  1) 4  4  1 .
__________
4
3
28. Solve: 2( x  1)  4  36 .
__________
29. Consider the functions f ( x)  x3 and g ( x)  2 x  1 . Find ( f g )(1) .
__________
x
. Find ( g f )(4) .
2
__________
30. Consider the functions f ( x)  2 x 2  1 and g ( x) 
31. What is the inverse for y  5 x  1 ?
__________
32. What is the inverse for y  4 x  3 ?
__________
33. Write a function to model the value of a laptop that costs $1200
and depreciates 30% each year.
Algebra 2 Final Exam Review
Mitchell
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34. Write a function to model the value of a diamond that costs
$2700 and appreciates $15% each year.
_______________
35. A savings account has an initial balance of $2500. It earns 2.72%
annual interest, compounded continuously. How much is in the
account after 10 years?
__________
36. You have purchased a $500 CD (certificate of deposit) paying
3.6% annual interest, compounded continuously. How much is
it worth after 5 years?
__________
37. What is the value of log3 27 ?
__________
38. What is the value of log 0.01?
__________
39. Expand log 7 (5 x) .
_______________
40. Write as a single log: 2 log x  log y .
__________
41. If x varies directly with y & x = 1.7 when y = 10, what is the value
of x when y = 14?
__________
42. If x varies directly with y & x = 2.5 when y = 7, what is the value
of y when x = 9?
__________
43. Graph
y
3
.
x
Algebra 2 Final Exam Review
1
44. Graph y   .
x
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45. y varies directly with the cube of x and inversely with z. Write an
equation to describe this situation.
__________
46. a varies jointly with b and c and inversely with the square of d.
Write an equation to describe this situation.
__________
47. Simplify:
x  3 x 2  2 x  15
.

x2  9 x2  2 x  1
__________
48. Simplify:
5 y  20 7 y  35
.

3 y  15 10 y  40
__________
16  x 2
x4
 2
49. Simplify: 2
.
x  2x  3 x  4x  3
__________
50. Simplify:
x 2  10 x  16
x 8
 2
.
2
x  6 x  16 x  64
__________
51. Simplify:
x
7x  6
 2
.
x3 x  x6
__________
52. Simplify:
x 1
x

.
x  2x  8 4x  8
__________
2
53. Solve:
4
5

.
x  2 2x  3
__________
54. Solve:
1 3 7
  .
4x 4 x
__________
Algebra 2 Final Exam Review
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2
2
55. Graph ( x  1)  ( y  2)  4 .
Algebra 2 Final Exam Review
2
2
56. Graph ( x  3)  ( y  1)  25 .
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Answers
1. up & up
20. 14xy x
2. up & down
21. 10 y 3 3 2 x
3. x3  6 x 2  11x  6
22. 16 xy 2 5 8 y
4. x3  4 x 2  x  4
5. y  x( x  3)( x  2)
23.
3 2  10
4
24.
54 2
7
6. y  ( x  3)( x  1)( x  1)( x  4)
7. x3  3x  14
25. 81
8. x3  x 2  x  3
1
4
9. ±2
26.
10. no rational roots
27. 20
11. x 2  5 x  4
28. {–7, 9}
12. 2x – 5 R 19
29. –27
13. 5
30.
33
2
14. {–2, 1, 3}
3

15.  ,  2 
2

1

16. 2,  
3

31. y 
1
1
x
5
5
32. y 
x2  3
4
17. 64a4b11
33. y = 1200(0.7)x
y7
18. 3 4
xz
34. y = 2700(1.15)x
35. $3281.47
19. 5a 2b3 3b
Algebra 2 Final Exam Review
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36. $598.61
47.
x5
( x  1) 2
48.
7( y  4)
6( y  4)
49.
( x  4)( x  1)
x 1
37. 3
38. –2
39. log75 + log7x
x2
y
40. log
50. x + 8
41. 2.38
51.
x2
x2
52.
( x  2)
4( x  4)
42. 25.2
43.
y
4
3
53. 
2
1
–4
–3
–2
–1
–1
1
2
3
x
4
2
3
54. –9
–2
55.
–3
y
–4
4
3
y
44.
4
2
3
1
2
–4
1
–3
–2
–1
–1
1
2
2
4
3
4
x
–2
–4
–3
–2
–1
–1
1
2
3
4
x
–3
–4
–2
–3
56.
–4
y
8
6
45. y 
4
kx3
z
2
–8
46. a 
kbc
d2
–6
–4
–2
–2
6
8 x
–4
–6
–8
Algebra 2 Final Exam Review
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