Download Exam Review: Algebra B

Algebra B
Name ____________________________
Final Exam Review
CHAPTER 7
Use the graph to the right to determine the number of solutions
each system has. (L 7-1)
1.
y  x4
2.
2x  2 y  2
y  x  1
x  y  4
Use substitution to solve the system of equations. (L7-2)
3.
y  3x  1
4.
x  2 y  1
y  x  3
x  y  1

Use elimination to solve the system of equations. (L7-3, L7-4)
5.

2x  3y  19
6.
3x  3y  1

5s  t  6
7.
5s  2t  3

6x  4 y  20
8.
4x  2y  4

2x  y  2
3x  5y  6
9. Ann is 5 years less than twice the age of Jill. If their ages total 28, how old is Ann?
10. The sum of two numbers is 41. Their difference is 5. What are the numbers?
CHAPTER 8
Simplify. Assume that no denominator is equal to zero.
1. (3a4b2c)(ab2c 4 ) (L8-1)
2. (5x 2 y 3 ) 3 (L8-1)


a12
3. 4 (L8-2)
a

6n 3 y
5.
2n 1 y 3
n5
4. 3 (L8-2)
n

5x 4
6.  3  (L8-2)
x 
(L8-2)


7. Find the degree of the polynomial. (L8-4)
2x 3 y  4 xy2  9x 3 y 2

8. Arrange the terms of the polynomial so that the “powers of x” are in descending order. (L8-4)
8x 2 y 3  x 5 y  5x 3 y 3  y 7
Find the sum or difference. (L8-5)
9. (n 2  3n)  (2n 2  n)


10. (9t 2  4t  6)  (t 2  2t  4)


11. 3b2 (4b  7)  2b(b2  5b  3)
Solve the equation. (L8-6)
12. 4(2x 1) 12x  2(8x 12)
13. 2(6x  4)  2  4(x  4)


Find the product. (L8-6, L8-7)
14. 3x 3 (5x 25x  3)
15. 4a(2a3  7a2  3a 11)


16. (x  2)(x  4)

17. (x  4)(x  8)
18. (3x  2)(4 x 2  2x  7)

Chapter 9: Factoring

Factor the polynomial, if possible. If the polynomial cannot be factored using integers, write prime.
1. 3ab 3 c  9b 2 c  12b 5
2. 6 x 2  4 x  3 x  2
3. z 2  11z  30
4. 3 x 2  7 x  2
5. 2h 2  9h  5
6. 16h 2  64
Solve the equation.
7. 64 w 2  9
9. c 2  4c  45
8. 5 g 2  22 g  8  0
10. 6 x 2  7 x  3  0
Chapter 10; Part A
x
11. Write the equation for the axis of symmetry for the graph of y  2 x 2  4 x  2 .
b
2a
12. What are the coordinates of the vertex of the graph? ____________
y
Use the graph to the right to answer questions 13-16.
5
4
13. How many real roots does it have? _________________
3
2
14. What are the solution(s)? ___________________
15. Does the parabola open up or down? _________________
1
–5
–4
–3
–2
–1
–1
1
–2
16. Is the vertex a minimum or maximum? ____________________
–3
–4
–5
Solve the equation by using the Quadratic Formula. Round to the nearest tenth if necessary.
x
17. 2 x 2  5 x  7  0
18.
 b  b 2  4ac
2a
x2 – 6x – 9 = 0
19. 3x 2  7 x  6  0
2
3
4
5
m
20. Given the equation y  4( x  2) 2  1 , what is the vertex of its graph? ____________________
21. Given the equation y  ( x  6) 2 , what is the vertex of its graph? ____________________
Chapter 10; Part B
Assume y varies inversely as x.
22. If y  124 when x  12 , find y when x  24 .
23. If y  54 when x  4 , find x when y  27 .
24. Which equation models exponential growth?
a.
y  3x
b.
y6
x
1
y 
4
x
c.
1
y 
4
x
c.
d. y  2(0.5) x
25. Which equation displays exponential decay?
a.
y  3x
b.
y  6x
d. y  2(0.5) x
FORMULAS
General Growth: __________________________
Exponential Growth: ________________________
key words: _________________________________
key words: __________________________________
Exponential Decay: ________________________
Half-Life: _________________________________
key words: _________________________________
key word: __________________________________
Compound Interest: ________________________
key words: __________________________________
26. Computer use around the world has risen 18% annually since 1980. If 17.9 million computers were in use
in 1985, write an equation for the number of computers in use for t years after 1985.
Equation: ______________________________
27. If the number of rabbits in a cage double every two years, how many will be in the cage after 6 years if you
start out with 2?
Equation: __________________________
Answer: ____________
28. Tim bought an SUV for 43,500 in 2006. What is the value of the SUV in 2008 if it depreciates at 14% each
year?
Equation: __________________________
Answer: ____________
29. Carbon-10 has a half-life of 1,620 years. If you begin with 4 grams of Carbon-10, how much will remain after
3 half life periods?
Equation: __________________________
Answer: ____________
30. The Johnson family purchased a new home in 2003 for $225,000. The value has appreciated 7.5% each year.
What will the home be worth in 2012?
Equation: __________________________
Answer: _____________
31. If you invest $1,000 compounded monthly at a rate of 5%, how much will be in the account after 10 years?
Equation: ___________________________
Answer: ______________
Chapter 10: Graphing
32. Graph y  x 2  2 x  6
x
y
35. Graph y  13 
33. Graph y  4(2 x )
x
x
y
x
-2
-1
-2
-1
.
0
0
1
1
2
2
34. Graph y 
24
x
x
y
y
Chapter 11: Radical Expressions
Simplify.
36.
40
35.
38. 8 54  4 6
41.
4
5  60
39. 4 3  2 12

42. 2 3  4 5
81
8
37.

40.
6
6
64


43. 4  3 4  3
2
2
5
44. 27 3
45. 64 3
46. 8 3
4
7
47. Write the expression x in root notation. ___________________
58. Write the expression 4 18 3 in exponent notation. ______________
Solve the equation. Then check your solution.
59. 2c  1  5
60.  4  4 x  4  0
61.
g 6  3

Capstone – Family Functions.
62.
y  2x 2  2x  1
63.
y  3 x  1  2
64. y 
x  4 1
65. y  4(2.93) x
66. y 
x4
x 1
67. y  2 x 3  5 x 2  2 x  3
Match each equation to its graph.
A.
B.
C.
D.
E.
F.
68. y  2 x  1
G.