Download Alg 2 review 1 Fall 2013 Mr. Dowler

Name: ________________________ Class: ___________________ Date: __________
ID: A
Alg 2 review 1 Fall 2013 Mr. Dowler
Short Answer
Insert <, >, or = to make the sentence true.
1. − |9|
|2|
2. |−10 − 9|
|4 − 14|
3. Simplify |−12 + 5| .
Evaluate the expression for the given value of the variable(s).
4. −5a + 5b ; a = 5, b = −6
5.
2(3h + 6)
−6 + h
; h = −3
6. |3b + 8| + || 1 − b 2 || − 2b 3 ; b = –2
7. x 2 − 9x − 4; x = –4
8. −x 3 + 3x 2 + 2x + 4; x = –1
9. The expression −16t 2 + 1500 models the height of an object t seconds after it has been dropped from a height
of 1500 feet. Find the height of an object after falling for 2.8 seconds.
Simplify by combining like terms.
10. −2c + 3d + 4c + 2d
11. −(3y + 2) − 8y
Solve the equation.
12. 5y − 11 = −17 + 4y
13. 2y + 9 = −5(y − 4)
14. 6(x − 0.8) − 0.2 (5x − 4) = −2
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Name: ________________________
ID: A
15. |x + 4| = 16
16. 2 |2x − 3| + 8 = 14
Solve the equation or formula for the indicated variable.
17. S = 4r 2 t , for t
18. T =
2U
, for U
E
Solve for x. State any restrictions on the variables.
19. ax + bx + 6 = 9
20. a(bx − 9) = cx − 3
21. A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the dimensions of the rectangle.
Round to the nearest tenth if necessary.
22. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle
is 54 cm?
Solve the inequality. Graph the solution set.
23. 6 + 4k ≤ 22
24. 3r – 10 ≤ –6
25. –4k – 8 ≤ –12
26.
2(4y – 2) > –68
27. 5(2m + 5) – 9 < –34
28. 2(4b + 5) < 9 + 8b
29. 17 + 9b ≥ 3(3b – 1)
Solve the problem by writing an inequality.
30. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts.
Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at
least $100.
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Name: ________________________
ID: A
Solve the compound inequality. Graph the solution set.
31. 8x + 8 ≥ 16 and 9x – 14 ≤ 31
32. 9x – 3 < –57 or 3x + 3 > 6
33. −12 ≤ 2x − 4 < 2
34. The perimeter of a square garden is to be at least 28 feet but not more than 54 feet. Find all possible values
for the length of its sides.
Solve the equation. Check for extraneous solutions.
35. 4 |4 − 3x| = 4x + 6
36. |2x − 5| = 10 + x
Solve the inequality. Graph the solution.
37. | 3x + 6 | ≥ 12
38. | 2x + 7 | < 15
|
1|
39. 3 | x + | < 2
|
2|
40. Make a mapping diagram for the relation.
{(–1, 0), (0, –1), (1, –3), (5, –4)}
41. For f (x ) = 3x + 2 , find f (−1) .
42. Suppose f (x ) = 4x − 2 and g (x ) = −2x + 1 .
f (0)
Find the value of
.
g (−1)
43. Graph the equation 4x + 4y = 10 by finding the intercepts.
44. Graph the equation 4x + 2y = 8.
Graph the inequality.
45. 4x – 2y ≤ 4
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Name: ________________________
ID: A
46. Write an inequality for the graph.
47. Is the relation {(–1, 5), (–2, 4), (–1, 4), (2, –2), (1, 1)} a function? Explain.
48. Is the relation {(1, 2), (–3, –5), (4, 1), (–1, –2), (0, 1)} a function? Explain.
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49. Graph the equation y = − x − 3 .
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Essay
50. A manufacturing company’s profits are modeled by the equation y = −45, 000 + 1.2x , where y dollars is the
total profit and x is the number of items manufactured. Graph the equation and explain what the x- and
y-intercepts represent.
Other
51. What is the maximum number of 3.5-to-5-min songs that can fill a 120-min CD? What is the minimum
number? Write your answer as a compound inequality. Explain your reasoning.
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ID: A
Alg 2 review 1 Fall 2013 Mr. Dowler
Answer Section
SHORT ANSWER
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
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20.
21.
22.
23.
<
>
7
–55
2
3
21
48
6
1374.56 ft
2c + 5d
−11y − 2
−6
4
1
7
0.4
x = 12 or x = −20
x = 3 or x = 0
S
t =
4r 2
TE
U =
2
3
x =
; a ≠ −b
a+b
−3 + 9a
x =
; ab ≠ c
ab − c
7.5 cm by 22.5 cm
13.5 cm, 18 cm, and 22.5 cm
k≤4
24. r ≤ 1
1
3
25. k ≥ 1
1
ID: A
26. y > –8
27. m < –5
28. no solutions
29. all real numbers
30. 12x − (8x + 20) ≥ 100; x ≥ 30
31. x ≥ 1 and x ≤ 5
32. x < –6 or x > 1
33. −4 ≤ x < 3
34. 7 ≤ x ≤ 13.5
5
11
35. x =
or x =
8
4
36. x = 15
37. x ≤ −6 or x ≥ 2
38. –11 < x < 4
1
1
39. −1 < x <
6
6
2
ID: A
40.
41. –1
2
42. −
3
43.
44.
3
ID: A
45.
46. 5x – 4y < –20
47. No; a domain value corresponds to two or more range values.
48. Yes; for each element in the domain there is exactly one element in the range.
49.
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ID: A
ESSAY
50.
[4]
The y-intercept represents the set-up costs and the x-intercept represents the least
number of items for which the company does not lose money, or a break-even point.
[3] minor errors in graph or explanation
[2] correct graph with incorrect explanation or incorrect graph with correct explanation
[1] no graph and errors in explanation or no explanation and errors in graph
OTHER
51. 24 ≤ x ≤ 34; if all of the songs on the CD are the maximum length, 5 minutes long, then the minimum
number of songs will fit on the CD. 120 divided by 5 is 24, so the CD can contain a minimum of 24 songs.
The shortest possible song is 3.5 minutes. Since 120 divided by 3.5 is approximately 34.29, the CD can
contain at most 34 complete songs.
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