Download ExamView - math 2 review1 fall 2013.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
Math 2 review 1 Fall 2013 Mr. Dowler
Short Answer
Find the opposite and the reciprocal of the number.
1. 500
2. 3
3. –1.74
4. 4 − π
Name the property of real numbers illustrated by the equation.
5. −2(x + 11) = −2x − 22
Ê
6. 2 ⋅ ÁÁÁ
Ë
ˆ
Ê
8 ⋅ 7 ˜˜˜ = ÁÁÁ 2 ⋅
¯
Ë
ˆ
8 ˜˜˜ ⋅ 7
¯
7. π ⋅ 6 = 6 ⋅ π
8. –6 + 6 = 0
9. –2.5 + 0 = –2.5
10. Find the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5).
Find the slope of the line.
1
11. y = − x − 4
2
12. 3x + 5y = −15
13.
1
3
x+
1
2
y = 6
14. Simplify |−12 + 5| .
Evaluate the expression for the given value of the variable(s).
15. −5a + 5b ; a = 5, b = −6
1
Name: ________________________
16.
2(3h + 6)
−6 + h
ID: A
; h = −3
17. |3b + 8| + || 1 − b 2 || − 2b 3 ; b = –2
18. x 2 − 9x − 4; x = –4
19. −x 3 + 3x 2 + 2x + 4; x = –1
20. 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.
21. −2c + 3d + 4c + 2d
22. −(3y + 2) − 8y
Solve the equation.
23. 5y − 11 = −17 + 4y
24. 2y + 9 = −5(y − 4)
25. 6(x − 0.8) − 0.2 (5x − 4) = −2
26. |x + 4| = 16
27. 2 |2x − 3| + 8 = 14
Solve the equation or formula for the indicated variable.
28. S = 4r 2 t , for t
29. T =
2U
, for U
E
30. 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.
Solve the inequality. Graph the solution set.
31. 6 + 4k ≤ 22
2
Name: ________________________
ID: A
32. 3r – 10 ≤ –6
33. –4k – 8 ≤ –12
34.
2(4y – 2) > –68
35. 5(2m + 5) – 9 < –34
36. 2(4b + 5) < 9 + 8b
37. 17 + 9b ≥ 3(3b – 1)
Solve the problem by writing an inequality.
38. 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.
Solve the compound inequality. Graph the solution set.
39. 8x + 8 ≥ 16 and 9x – 14 ≤ 31
40. 9x – 3 < –57 or 3x + 3 > 6
41. −12 ≤ 2x − 4 < 2
42. 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.
43. 4 |4 − 3x| = 4x + 6
44. |2x − 5| = 10 + x
Solve the inequality. Graph the solution.
45. | 3x + 6 | ≥ 12
46. | 2x + 7 | < 15
|
1|
47. 3 | x + | < 2
|
2|
3
Name: ________________________
ID: A
48. Make a mapping diagram for the relation.
{(–1, 0), (0, –1), (1, –3), (5, –4)}
49. For f (x ) = 3x + 2 , find f (−1) .
50. Suppose f (x ) = 4x − 2 and g (x ) = −2x + 1 .
f (0)
Find the value of
.
g (−1)
51. Graph the equation 4x + 4y = 10 by finding the intercepts.
52. Graph the equation 4x + 2y = 8.
Graph the inequality.
53. 4x – 2y ≤ 4
54. Write an inequality for the graph.
55. Is the relation {(–1, 5), (–2, 4), (–1, 4), (2, –2), (1, 1)} a function? Explain.
56. Is the relation {(1, 2), (–3, –5), (4, 1), (–1, –2), (0, 1)} a function? Explain.
9
57. Graph the equation y = − x − 3 .
5
Essay
58. 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.
4
ID: A
Math 2 review 1 Fall 2013 Mr. Dowler
Answer Section
SHORT ANSWER
1. –500,
2. −3,
1
500
1
3
50
87
1
π − 4,
4−π
Distributive Property
Associative Property of Multiplication
Commutative Property of Multiplication
Inverse Property of Addition
Identity Property of Addition
1
y + 4 = − (x + 6)
8
1
−
2
3
−
5
2
−
3
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
3. 1.74, −
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
1
ID: A
TE
2
30. 7.5 cm by 22.5 cm
31. k ≤ 4
29. U =
32. r ≤ 1
1
3
33. k ≥ 1
34. y > –8
35. m < –5
36. no solutions
37. all real numbers
38. 12x − (8x + 20) ≥ 100; x ≥ 30
39. x ≥ 1 and x ≤ 5
40. x < –6 or x > 1
41. −4 ≤ x < 3
42. 7 ≤ x ≤ 13.5
5
11
43. x =
or x =
8
4
44. x = 15
2
ID: A
45. x ≤ −6 or x ≥ 2
46. –11 < x < 4
1
1
47. −1 < x <
6
6
48.
49. –1
2
50. −
3
51.
3
ID: A
52.
53.
54. 5x – 4y < –20
55. No; a domain value corresponds to two or more range values.
56. Yes; for each element in the domain there is exactly one element in the range.
57.
4
ID: A
ESSAY
58.
[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
5