Download MATH 1314 - College Algebra Review for Test 1

MATH 1314 - College Algebra
Review for Test 1
Section 1.1
1. Classify each of the following as one or more of the following: natural number, integer, rational
number, or irrational number.
2
(a) –5
(b) 7
(c)
(d) 3.97 (e) 0.257
3
−3 +17
2
2. Evaluate each of the following: (a) −42 − 2(3 + 5)
(b) −24 ÷ 3 × 2 +
−9 + 2
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3. Write each of the following in scientific notation: (a) 0.000395 (b) 54,300
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4. Write each of the following in standard notation: (a) 5.38 ×10−4
(
)(
(b) 9.24 ×10 4
)
5. Multiply and give your answer in scientific notation: 6 × 10−5 7 × 102
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6. Rachel’s weekly pay increased from $125 to $140. What was the percent change in her weekly
pay?
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Section 1.2
7. What is the mean of the set of numbers {72, 88, 96, 84}?
8. What is the median of the set of numbers {72, 88, 96, 84}?
9. Find the exact distance between the points (4,–5) and (–2,–1).
10. Find the midpoint of the line segment connecting the points (4,–5) and (–2,–1).
11. For the relation {( −3 ,4), (1,2), (5, −6 )}, (a) what is the domain and (b) what is the range?
12. Give the standard form of the equation of the circle
shown at the right.
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y
1
1
x
MATH 1314 - College Algebra - Review for Test 1 (Thomason) - p. 2 of 8
13. Give (a) the center and (b) the radius of the circle whose equation is ( x − 7)2 + ( y + 5)2 = 4 .
14. Give the standard form of the equation of the circle that has its center at (4,–3) with the point
(–1,9) on the circle.
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15. Give the standard form of the equation of the circle that has ends of a diameter at (–3,4) and (7,–6).
Section 1.3
16. (a) Is the set of ordered pairs {(1,3),(4,4), (3,1)} a function? Explain how you know.
y
(b) Is the relation whose graph is shown at the right a function?
Explain how you know.
1
x
1
(c) Is the relation given by the following table a function? Explain how you know.
X
1 3 4 3
Y
–5 3 0 2
17. Determine the domain of each of the following functions.
2
(a) f (x) = 2
(b) g(x) = x 2 + 2 (c) h( x) = 3x − 2
x − 25
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18. For f ( x) = −x 2 + 5, determine (a) f (−3) , (b) f (4) , and (c) f (a + 2) .
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19. (a) True or False: The graph of 4 y +12 = 0 is a vertical line that passes through –3 on the x-axis.
(b) True or False: The slope of the line 3x +12 = 0 is undefined.
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y
20. The graph of f is shown at the right.
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(a) What is the range of f?
(b) Determine f (−2) .
1
(c) Determine the value(s) of x for which f (x) = 2
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1
x
MATH 1314 - College Algebra - Review for Test 1 (Thomason) - p. 3 of 8
Section 1.4
21. The graph shown at the right shows the
price of x yards of carpeting.
(a) Find the slope of the graph.
(b) Interpret the slope as a rate of change.
y
70
56
42
28
14
1
2
3 4 5 6 7 8 9 10 x
Carpet (square yards)
Section 1.5
22. Express the following in interval notation: {x −3 ≤ x < 5}
23. Express the following in interval notation:
€
]
–5 –4 –3 –2 –1
(
0
1 2
3 4
5
y
24. Use the graph of f at the right to determine the
interval(s) in which (a) f is increasing and (b) f is
decreasing. Give your answers in interval notation.
1
x
1
25. For f ( x) = −x 2 − 2x + 3 , compute the average rate of change of f from x1 = −2 to x2 = 1.
26. For f (x) = 3x 2 − 5x + 4 , (a) determine f (x + h) and (b) determine the difference quotient
€ f (x + h) − f (x) and simplify.
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h
€ Section 2.1
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27. (a) Is the data in the table at the right linear? (b) If so,
determine the slope-intercept form of the equation of the
line passing through the data points?
x
y
0
2
3
6
6
10
9
14
MATH 1314 - College Algebra - Review for Test 1 (Thomason) - p. 4 of 8
y
28. Write a formula for the linear function f show in the
graph at the right.
1
x
1
3
29. For f (x) = − x + 6 , (a) give the slope, (b) give the x-intercept, (c) give the y2
intercept, and (d) draw the graph.
30. For −4 x + 5y = 20 , (a) give the slope, (b) give the x-intercept, (c) give the y-intercept,
€ and (d) draw the graph.
31. For 3y = −12 , (a) give the slope, (b) give the x-intercept, (c) give the y-intercept, and
€ (d) draw the graph.
32. For 2x −10 = 0 , (a) give the slope, (b) give the x-intercept, (c) give the y-intercept, and
€ (d) draw the graph.
⎧ 4
if x ≤ 2
€ 33. For the piecewise function f is defined by f (x) = ⎨
, determine
⎩−x + 3 if x > 2
(a) f (−3) and (b) f (3) . (c) Graph f .
Section 2.2
€
y
€
€ is riding a bicycle along a straight highway. The graph
34. A person
at the right shows the rider’s distance y in miles from a First Aid
Station after x hours.
(a) Find the slope-intercept form of the equation of the line.
(b) How fast is the bicyclist traveling?
(c) How far from the First Aid Station was the bicyclist initially?
(d) How far from the First Aid Station was the bicyclist after 2 hours?
35
30
(4,31)
25
20
15
10
5
0
(1,13)
1
2
3 4
35. Determine the slope-intercept form of the equation of the line that is perpendicular to
2
y = x −12 and that passes through the point (6,–1)
3
€
5 6
x
MATH 1314 - College Algebra - Review for Test 1 (Thomason) - p. 5 of 8
36. Determine the slope-intercept form of the equation of the line that is parallel to 3x + 4 y = 12 and
that passes through the point (12,–5).
37. In 2005, the number of homes in the U.S. with flat screen televisions was 17.5 million. Since
€ increasing at a constant
then, the number of homes in the U.S. with flat screen televisions has been
rate of 8.2 million homes per year. Let t represent the number of years since 2005 and write a
formula for the linear function N that models this situation.
38. In 2000 there were 7.6 million automobiles produced in the United States and in 2004 there were
6.4 million. The formula V (t) = −0.3t + 7.6 models these data exactly, where t = 0 corresponds to
2000, t = 1 to 2001, and so on. Use V (t) to estimate the number of automobiles manufactured in the
U. S. in 2009.
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39. In 1998 the value
of a house was $150,000 and in 2006 the value of the house was $182,000.
€
€ approximates the value of the house in year x.
Find a linear function V that
40. Suppose y is direction proportional to x and that y = 12 when x = 7 . Find y if x = 10 .
41. The cost of tuition is directly proportional to the number of credit hours taken. If 12 credit hours
cost $528, what would be the cost of 15 credit hours. €
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Section 2.3
42. Solve the equation: −2(3x − 4) − 5 = 6 − (x −1)
2
3 5
7
43. Solve the equation: x − = x +
3
4 6
12
€
44. Solve for b: 3a − 5b = 8
45. Jelly Beans€sell for $2 a pound and Gummy Bears sell for $3 a pound. How many pounds of
each kind of candy must be used to produce a 10 pound mixture worth a total of $27.50?
€
46. Suppose Joe, working alone, can rake a certain lawn in 4 hours and that John, working alone, can
rake the same lawn in 8 hours. How long would it take Joe and John working together to rake the
same lawn?
47. A rectangular window has a length that is 8 inches more than its width. The perimeter of the
window is 100 inches. Find the length and width of the window.
48. A car went 301 miles in 5 hours, traveling part of the time at 55 miles per hour and part of the
time at 65 miles per hour. For what length of time did the car travel at each speed?
Section 2.4
49. Solve for x and give the solution in interval notation: −2(3x − 5) + 4 > 2x − 6
50. Solve for x and give the solution in interval notation: −7 < −2x + 5 ≤ 11
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MATH 1314 - College Algebra - Review for Test 1 (Thomason) - p. 6 of 8
51. Solve and give your solution in interval notation: −1 ≤
3x − 5
<7
4
52. The total cost y of producing x copies of a CD is given by y = 2500 + 5x . For what number of
CDs will the total cost be between $3,175 and $3,900?
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Section 2.5
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53. Graph y = 3x − 6 .
54. Solve: 4 x − 5 = 7
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55. Solve: 2x − 3 = −4
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56. Solve: 3x − 4 = 5x + 9
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57. Solve and give the solution in interval notation: 5x − 8 < 2
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58. Solve and give the solution in interval notation: 2x − 5 ≥1
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Answers
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1. (a) integer, rational number (b) irrational number (c) rational number (d) rational number
3. (a) 3.95 × 10−4 (b) 5.43 × 10 4
2. (a) –144 (b) –18
5. 4.2 × 10−2
6. 12%
€
7. 85
11. (a) {−3,1,5} (b) {4,2, −6}
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2
2
14. ( x − 4) + ( y + 3) = 169
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12. ( x +1)2 + ( y +1)2 = 9
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2
10. (1, −3)
13. (a) (7, −5) (b) 2
2
15. ( x − 2) + ( y +1) = 50
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16. (a) Yes, because no first number in the ordered pairs is repeated as a first number.
(b) No, because the graph fails the Vertical Line Test.
€ as a first number in the ordered pairs.
(c) No, because 3 is repeated
{
}
17. (a) x x ≠ −5,5
{
{
}
20. (a) x 0 ≤ x ≤ 3
€
}
(b) x x is a real number
18. (a) –4 (b) –11 (c) −a 2 − 4a +1
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9. 2 13
8. 86
4. (a) 0.000538 (b) 92,400
⎧
2 ⎫
(c) ⎨ x x ≥ ⎬
3 ⎭
⎩
19. (a) F (b) T
€
(b) 3 (c) –3, –1, 3
21. (a) 7 (b) Carpet cost $7 per sq yd.
MATH 1314 - College Algebra - Review for Test 1 (Thomason) - p. 7 of 8
22. [−3,5)
23. (−∞, −1](2, ∞)
24. (a) (−∞, −1][3,4] (b) [−1,3][4, ∞)
26. (a) 3x 2 + 6hx + 3h 2 − 5x − 5h + 4 (b) 6x + 3h − 5
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27. (a) Yes
3
29. (a) −
(b) (4,0) (c) (0,6)
2
€
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4
(b) y = x + 2
3
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2
28. y = − x + 2
3
30. (a)
€
25. –1
4
(b) (−5,0) (c) (0,4)
5
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31. (a) 0 (b) none (c) (0, −4)
32. (a) undefined (b) (5,0) (c) none
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33. (a) 4 (b) 0
34. (a) y = 6x + 7 (b) 6 mph (c) 7 mi (d) 19 mi
3
35. y = − x + 8
2
€
(c)
€
3
36. y = − x + 4
4
37. N (t ) = 8.2t +17.5
38. 4.9 million
€
39. V (t ) = 4000x − 7,842,000
40.
41. $660
42. −
€
€
€
43. –8
€
€
120
7
4
5
3a − 8
44.
5
MATH 1314 - College Algebra - Review for Test 1 (Thomason) - p. 8 of 8
45. 2.5 lb of Jelly Beans, 7.5 lb of Gummy Bears
46. 2
2
hr
3
47. Length: 29 in., Width: 21 in.
48. 2.4 hr at 55 mph, 2.6 hr at 65 mph
€
⎛
5 ⎞
49. ⎜ −∞, ⎟
2 ⎠
⎝
50. [−3,6)
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€
⎡ 1 ⎞
51. ⎢ ,11⎟
⎣ 3 ⎠
52. Between 135 and 280 CDs.
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1
54. − ,3
2
55. No solution
5 13
56. − , −
8 2
⎛ 6 ⎞
57. ⎜ ,2⎟
⎝ 5 ⎠
58. ( −∞,2] [3, ∞ )
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