Download alg. i second semester review w

Review for Second Semester Exam
Algebra I
Name_______________________
Simplify:
1.
6.
b7 x + 8gb4 x + 4g
c3x y hc− 6x yh
4
3
2
[6]
7. Write the polynomial as the product of two
binomials.
14 xp − 49 p − 4 xu + 14u
[1]
2.
c 4c d e h
4
6 5
2
[7]
[2]
Factor the polynomial completely.
3. Write the following without negative or zero
exponents.
20a 5b 4 c –5
4a 0b –5c 2
8. v 2 − 4vw + 4 w 2
[8]
[3]
9. 9 x 2 + 24 x + 16
4. Find the product by using the rules for special
products.
(5x + 7) 2
[9]
10. 16 x 2 − 81
[4]
Use the FOIL method to find the product.
5.
b7 x − 5gb5x − 7g
[5]
[10]
11. 3x 3 − 3x 2 − 6 x
[11]
Factor the polynomial completely.
Perform the indicated operation. Simplify and state
the restrictions on the variable.
12. 3x 3 − 6 x 2 − 9 x
18.
n2 − 4 n
⋅
n + 2 3n − 6
[12]
13. Solve by factoring: x 2 + 4 x = 21
[18]
19.
[13]
14. Solve by factoring: x 2 + 3x = 18
[14]
15. Solve by factoring: x 2 − 10 x = – 16
[15]
16. Solve by factoring: x 2 − 3x = – 2
x + 7 x 2 − 49
÷
x−7
7− x
[19]
20. Solve the rational equation by using the lowest
common denominator.
x
2
1
+
=
2
x −4 x−2 x+2
[20]
21. Solve the equation algebraically. Be sure to
check your solution(s).
2 x + 6 = 16
[16]
[21]
17. Simplify the expression. State any restrictions
on the variable.
8− x
2
x − 5x − 24
Find the sum or difference.
22.
c− x
[17]
[22]
2
h c
h
− 8 x − 5 − − 5x 2 − 8
Find the sum or difference.
23.
c− 7 x
2
h c
28. 7 3 − 27 + 4 3
h
+ 5x − 5 + − 2 x 2 − 3
[28]
29. Factor completely:
[23]
12 x 2 − 75
24. Use the Distributive Property to find each
product.
− 4 x 3 (5x 2 − 3x + 5)
[29]
30.
[24]
25. Use the FOIL method to find the product.
( x 2 + 2 )( x 2 − 4 )
50 − 2 2
[30]
31. Solve by factoring.
[25]
12 x 2 − 28 x = 5
26. Factor the polynomial completely.
x 2 + 2 x − 48
[31]
32. Simplify:
[26]
(
27. Express in simplest radical form.
48 x 7 y 5
)(2 x 4 y − 5)
8x 2 y3
16 x 5 y 4
[32]
[27]
33. − 3 5 − 3 25 − 45
[33]
34. Simplify. Then find the value of the result.
12
7
7
7
39. Write without negative exponents in simplest
form:
FG 3x IJ
Hx K
−2
3
[34]
35. Find the sum or difference.
3x 3 − 3x 4 + 9 − 3x 4 + 9 − 5x 3
c
h c
[39]
h
40. Solve the equation algebraically. Be sure to
check your solution(s).
2x − 4 = 9
[35]
36. Perform the indicated operation. Simplify and
find the restrictions on the variable.
9
8
–
2
x − 6 x − 16
x+2
[40]
41. For what value(s) of the variable is the
expression undefined?
–9
3
c − 9c 2 + 14c
[36]
37. Use the quadratic formula to solve the equation.
Give exact answers.
2 x 2 − x − 21 = 0
[37]
38. Which is the polynomial written as the product
of two binomials?
Complete the factorization.
b g b g
2x x + 3 + 7 x + 3
[41]
42. Perform the indicated operation. Simplify and
state the restrictions on the variable.
n 2 − 16
n
⋅
n + 4 5n − 20
[42]
43. Write the polynomial as the product of two
binomials.
15 pu − 25u − 9 px + 15x
[38]
[43]
44. Factor the polynomial completely.
x 2 + 4 x − 45
[44]
45. Solve by factoring: x 2 − 16 x + 63 = 0
[45]
49. M(–4, 1) is the midpoint of RS . If S has
coordinates (–1, 8), find the coordinates of R.
[49]
Perform the indicated operation. Simplify and find
the restrictions on the variable.
50.
6
4
–
x−7
x − 5x − 14
2
46. Solve the equation:
25x 2 = 49
[46]
47. Perform the indicated operation. Simplify and
find the restrictions on the variable.
6
5
+
x +8 x −8
[50]
51.
2
7
+
x+4 x−4
[51]
Solve the equation algebraically. Be sure to check
your solution(s).
52.
x+2 = x
[47]
48. Which are the coordinates of the midpoint of the
segment connecting (1, –13) and (8, –12)?
[52]
53.
[48]
[53]
x + 14 = x + 8
54. Astronomers measure large distances in lightyears. One light-year is the distance that light
can travel in one year, or approximately
5,880,000,000,000 miles. If a star is 11.0 lightyears from Earth, which expression in scientific
notation correctly represents how far the star is
from Earth?
57. The city commission wants to construct a new
street that connects Main Street and North
Boulevard as shown in the diagram below. The
construction cost has been estimated at $80 per
linear foot. If there are 5280 feet in 1 mile, find
the estimated cost for constructing the street.
Main Street is perpendicular to North
Boulevard.
North Blvd.
[54]
(new street)
4 mi
9 ×105
.
3×1010
Which is the answer in scientific notation?
55. Perform the following computation:
W
Main St. E
3 mi
S
[55]
56. Find the length of the missing side.
30
34
a
[57]
58. Which is the polynomial written as the product
of two binomials?
4x3 + 4x2 + x + 1
b gc h
[C] 4 x b x + 1g
[A] x + 4 4 x 2 − 1
2
b gc h
[D] xc4 x + x + 1h
[B] x + 1 4 x 2 + 1
2
[56]
[58]
59. A flower bed has a brick walkway surrounding
it. What is the area of the flower bed, including
the walkway?
x−3
2x − 4
[59]
Solve the equation algebraically. Be sure to check
your solution(s).
60.
x + 34 = x + 14
[60]
61.
[61]
x−2 = x−4