Math 72, Nelson
Final Exam Review
Fall 2002
In any word problem on this test, be sure you define any variable you use and give the equation
or inequality. Then solve the equation or inequality. You will not receive full credit without
giving the equation/inequality and the definition of the variable. Don't forget units in your
answer.
1. The parking garage at the Oakland Convention Center costs $3.00 for the first 2 hours and
$1.25 for each additional hour. Give an expression for the total cost of parking C, in terms of
x, the number of hours you park.
2.
How many hours was I parked there this weekend if my parking charge was $9.25? Give the
equation and then solve it symbolically (algebraically). No credit will be given for the answer
without the equation and work.
3. Use unit analysis to convert $ 80,000 per year to an hourly wage (dollars per hour). Assume
that you work 50 weeks in a year and 40 hours each week. Show your work.
4. A cylindrical can has a height of 4 inches and a radius of 2 inches. What is the volume of the
can in cubic inches?
5. How much paper (in square inches) would be required to make a label for the above can?
6. How many times bigger (in area) is a 16” pizza than an 8” pizza? (Assume that the pizza
goes all the way to the edge, so you lose nothing to crust) Show your work.
7. Write each of these in interval notation, inequality notation, and line graph form.
Inequality notation
Interval notation
Line Graph Form
a._______________
(-, 3]
______________
b.  2  x  4
______________
______________
c. _______________
______________
______________
3
8. My refrigerator has a “spill-proof” tray that is 14 inches long by 15 inches wide. It has a lip,
which is 1/16 of an inch in height. If a 12-ounce can empties, will the spill be small enough
to be held in the spill-proof tray?
9. Lois wants to make 10 liters of 29% sugar syrup by mixing syrup containing 50% sugar with
syrup containing 20% sugar. How much of each should she use?
10. West Coast electric charges a $5.00 basic fee and $0.03715 per kilowatt-hour used. Consider
the total cost in terms of kilowatt-hours used. Which of the two numbers is the slope? How
do you know?
11. MCI offered me 5 cents a minute for all calls with a $1.95 service charge per month. Sprint
offered me 10 cents a minute with no service charge. I chose Sprint. What does that tell you
1
about the number of minutes of calls that I make per month? To get full credit you must
define a variable, give an inequality, solve the inequality, and give the answer in proper
English.
12. Three consecutive integers have a sum of 87. Find them.
13. The width of a rectangle is three meters less than its length. The perimeter of the rectangle is
72 meters. Find the dimensions of the rectangle.
14. Nguyen wishes to mix 30 pounds of nuts worth $4 a pound with nuts worth $2 a pound in
order to make a mixture worth $3.50 a pound. How many pounds of the $2 nuts should he
use?
15. A 180 foot rope is cut into three pieces so that the second piece is twice as long as the first,
and the third piece is three times as long as the second. How long is each piece?
16. The perimeter of a rectangle is 310 meters. The length is 25 meters more than the width.
Find the width and length of the rectangle.
17. The sum of two consecutive odd integers is 48. What are the integers?
18. A shirt marked 5% off is selling for $19.99. What was the original price?
19. A tennis court for singles is 24 feet longer than twice its width. The perimeter is 210 feet.
Find its dimensions.
20. The sum of two numbers is 18. The larger equals 5 times the smaller. Find the numbers.
21. One angle of a triangle is four times as large as another angle in the triangle. The third angle
is 60 larger than the smaller of the first two. What is the measure of each angle?
22. The sum of three consecutive integers is 108. What are the integers?
23. If a car that normally sells for $9750 is marked down by 17.5%, what is the new price?
24. If an airplane is found to have used 36% of its fuel after 2.16 hours of flight, how much time
does the pilot have to find a refueling stop?
25. A used car is on sale for $3599.00. A down payment of 15% is required. How much will the
down payment be?
26. On a map, 1 inch represents 3/5 of a mile. How many miles are represented by 3.2 inches?
27. The temperature at 5 A.M. was -10 degrees. If the temperature rose 2 degrees per hour, what
was the temperature at noon?
2
28. On 3 consecutive plays, the San Francisco 49ers football team gained 8 yards, lost 5 yards,
and gained 12 yards. Did they gain enough to get the 10 yards needed for the First Down?
29. The temperature at 9 pm was -2 degrees Fahrenheit. If the temperature dropped 3 degrees
Fahrenheit per hour, what was the temperature at midnight.
30. A parking meter contains 112 dimes and quarters. If it has x dimes, give:
a) an expression for the number of quarters.
b) an expression for the monetary value of those quarters.
31. The sales price of a car plus the 6 percent tax came to $15,741. How much did the car cost
before the tax was figured in?
32. My February 1999 Puget Sound Energy bill was for $80.18. This represents a $5.36 Basic
Charge and an average kilowatt-hour (KWH) price of $.058 per KWH. (Note: This averages
all the KWHs and the residential/farm exchange into one price.) Give the equation to solve
for x, the number of KWHs I used. As always, to get full credit you will have to give the
equation, not just the answer.
33. Convert 26 miles into meters. (Remember you must show work, not just an answer.)
34. Which is a better buy: an 18-inch pizza for $16 or two 12-inch pizzas for a price of $16 for
the pair? Assume that the pizza goes all the way to the edge, so you lose nothing to crust.
The size of a pizza is its diameter. Show your work.
35. One year after it was purchased, a farm tractor depreciated in value 8 percent, to $29,440.
How much was the purchase price?
36. A film processor charges $2.50 for developing and $.20 per print for a roll of 24 negatives.
Steven dropped of a 24-exposure roll and the bill came to $6.90. How many negatives were
not printable?
37. You have $14.00 with you when you enter a restaurant. The tax rate in King County is 8.2%.
You plan to tip 15% of the total check (not just the menu price). What is the maximum menu
price before tax and tip that you can afford? Round to the nearest penny if necessary. What
percent on the menu price are you actually tipping?
38. Adam's Pizza Parlor increases the radius of its special pizza by 2 inches. This gives their
pizza an extra 28 square inches of pizza. What was the size of the pizza before the
increase? (The “size” of a pizza is its diameter.) Please note that the picture is not drawn to
scale. Also note that this looks like a quadratic equation rather than a linear equation, but it is
not.
3
2
x
2
39. Give an expression for the unshaded portion of the big square in terms of x, the side of the
smaller shaded square. Show your work.
4
x
40. Give an expression for the perimeter of a rectangle with length 4x and width 3x – 1, where x
is measured in feet. Simplify your answer, and give units.
41. A person is driving at 88 feet per second. If the speed limit is 55 miles per hour, is she
driving above or below the speed limit? By how much? Should the police pull her over?
42. If the price of gasoline in Canada is $0.50 (Canadian) per liter, how much USA money do
you need to buy a gallon of gas? Assume that 1 dollar US currency is worth 1.28 dollars
Canadian.
43. Give an expression for the area of a rectangle with length 4x and width 3x - 1, where x is
measured in feet. Simplify your answer, and give units.
44. A tree casts a 12-foot shadow at the same time a yardstick casts a 24-inch shadow. Find the
height of the tree.
45. The picture below was scanned from a 4-inch by 6-inch
print. Assume the process used similar rectangles as
described in the text and in your homework. If the image
here is 49 millimeters wide, how tall is it in millimeters?
You must give an equation for this problem and then solve it
to get credit.
4
46. Arlington is 5 miles due north of Coulterville and Baker Beach is 12 miles due west of
Coulterville. To drive directly from Arlington to Baker Beach, you must drive a back road
with a speed limit of 40 mph. If you drive from Arlington to Baker Beach by way of
Coulterville then you can drive a highway and the speed limit is 55 mph. Which way is
faster if you obey the speed limit?
47. A recipe calls for 2 cups of water to one-third cup of dry oats. Maintaining that ratio, how
many cups of oats would be used with 3 cups of water.
48. The cost of producing a pickleball paddle is $14. In addition, there are fixed costs of
$200,000. The manufacturer sells the paddles for $28. To make a profit, how many paddles
must be sold? Be sure to give your answer as a range of values.
49. Late one evening, a 6-foot person is standing 5 feet from a streetlight that is the only source
of light. The streetlight gives off light that causes the person to have a 3-foot shadow. How
tall is the streetlight?
50. St. Paul Island in Alaska has 12 fur seal rookeries (breeding places). In order to estimate the
fur seal pup population in the Gorbath rookery, 4963 fur seal pups were tagged in early
August. In late August, a sample of 900 pups was examined and 218 of these were found to
be tagged and 682 were not tagged. Estimate the total number of fur seal pups in this
rookery.
51. Reliable Rentals will rent a car for $35 per day plus $.10 per mile whereas Wonderful
Wheels rents a car for $30 per day plus $.12 per mile. I need a car for 5 days. For what
range of mileage will I be ahead financially by renting from Wonderful Wheels?
52. Longview State College’s football stadium, which seats 4500 people, always sells out for
home games. Ticket prices are $5 in advance or $8 at the gate. How many tickets should be
reserved until game day at the gate, if the school budget says that at least $24,000 must be
grossed per game? (Your answer should be a range.)
53. Given that x = 5 and y = -3, evaluate
x2  y2
y2  x
54. Given that x = 3 and y = -2, evaluate 3x - 2y(x + y2)
55. Given that a = -4.5, what is the value of -a?
56. An investment of $10,500 increases 6 percent per year. To find its value after 15 years,
evaluate 10500(1 + .06)15
57. Identify the terms in 4 - 5y - 6y2 .
58. Combine like terms: 3x3 + 4x + 6x3.
59. Combine like terms: 5 + 4x - x.
x
3x
60. Find the perimeter of the given figure.
x
5
2x
61. Simplify: 3(6x - 5) - 3(5 - 6x).
62. Simplify: 3y2 - 5(2y + 32).
63. Classify each of the following as:
a. Identity
b. Conditional equation
c. Equation with no solutions
3x - 5 = 2x + 1
_____________
x+1=x+2
_____________
5x = 4x + x
_____________
64. The length of a rectangle is 6 times the width. Find a simple formula for the perimeter. Use x
for the width.
65. For g(x) = x2 – 3x + 2, find g(3), g(0), and g(-3).
Perform the operations indicated, and simplify your answers. If your answer is a fraction, make
sure it is in lowest terms. Do not leave negative exponents in your answer.
66. -(5 + (3 + 2 (1 - 7)) + 1)
67. 7 - (3 - 7)
68. 5 + 3(6 + 2) - 42
69. (2+4)(42 - 24 + 22)
70. 2 + 3(4 + 5(6 - 2))
-3
71. (-3)
72. –2-2
3
-2
-1
0
73. (-3) - 2 + (-5) + 3
74. (x3y1z5)2
75. (x3y2)3
76. (55y4z2)3
77. (3x5)2
0
78. (3x )(-2x-5)
x 2 y 3
79.
x 3 y 2
4 x y 
 xy 
2
80.
2 2
1 3
81. (-5a2 + 2a - 3) + (6a2 - 2a + 3)
82. (2x2 - 5x3 - x) - (-4x2 -6x3 + 8x)
83. (5x4 - 3x2 + 2) - (4x2 + 3x4 - 5)
84. (4c - 5) (3c - 2)
85. (x2 + 3x + 2) (x2 + 6x + 8)
86. (y3 + 1) (y3 - 1)
87. 4x (5x3 – 2x2 + 7x - 3)
6
88. (3x4 – 5x3 + 2x + 1) – (2x4 + 2x3 – x2 + 4)
89. (4x - 1)(2 + 3x)
90. (x - 3)2
91. 2y(y + 2)2
92. (9x - 1)2
93. (7x2 - 1)2
94. (13x3y + 3x2y - 5y) + (x3y + 4x2y - 3xy + 3y)
95. (-5x - x2 - 3) - (-3x2 + 2x - 10)
96. (a-b) (a2 + ab + b2)
97. -2 (3x - y)2 + (2x2 + y2)
98. 3a (2a + v) - 7(a + v)2
99. x2 + 3x(x -4)
100. (x2)2 + 6x + 6(x4 + 1)
101. (x + 2)2
102. (x - 3)3
103. (3x - 2)(x - 4)
104. (x - 3)2 + 2x2 - (7x + 4)
105. (x - 1)(x + 2) + (x + 2)(x + 4)
106. x2yz2 + x(xy) + y(xz)2 + xy2
107. (-2)2
108. x2(y + x) + x(2x2 + xy)
109. (x - 2)(x + 3)(x - 1)
110.
111.
112.
113.
Express in normal notation: 5.3 * 10-7
Calculate and give the answer in scientific notation: 400,000,000,000 / 10- 4
Express in scientific notation: .00000043
Express in normal notation: 7.033 *106
114. Avogadro's number is 6.02 * 1023 and is the number of molecules in a mole of a
substance. If we have 2,000,000,000 moles of a substance, how many molecules do we
have? Put your answer in scientific notation. (Hint: you should just multiply the two
numbers.)
115.
116.
Answer the following questions for the polynomial 5x2 + 4x3 - 1 + 10x
a) How many terms does it have? What is the coefficient of the first term?
Give an example of an expression with one variable that is not a polynomial.
How many terms are there in the following?
117. 3x - 2xy2 + 7t ________________________
118. 4(y - 3) - 7x ________________________
119. 2y(x - 4) + 5(x + 4) ________________________
120. 4xy + 3y2 - 3x ________________________
121. 3(x + 2) + 7x ________________________
122. 4x(y + 3) + 2(x + 1) ________________________
7
123.
If the following are in in factored form, give the number of factors, and what they are. If
they are not in factored form, state that.
a)4x(x - 7)
b) 3(x + 2) - 4(x + 2)
c) 5x2y3
Evaluate the following expressions, given the values indicated for the variables.
124.
125.
126.
127.
128.
-y2; y = 3
2x2 - y; x = 4, y = -2
(5x + 3y + 1)/(2x) ; x = -1, y = 2
x0 + (x - y)2 - y3 + x2; x = 2, y = 1
(y + 2x)x3 - y0 + x2; x = 3; y = 4
Find all solutions, if there are any, to the following equations and inequalities.
129.
130.
131.
132.
133.
134.
135.
136.
137.
17 - x = -5
3(2 - 3x) = 2(x + 2)
-3(x + 2) < 5(7 + 2x)
5(x - 3) = (1/3)(15x -12)
4(3x + 3) = 6 - 2(4x + 1)
5(3 - 2x) + 5 = -2(6x - 2) + 15
6d - 4 >3d + 5
x + 3(x +2) = 2(2x + 3)
4(x + 1) > (3x – 6)/3
138.
6(x - 4) = 7 - 2(x + 3)
1
1 1
 x     x  1
2
3 3
x
5

8 20
x2 x5

4
7
3(2x - 1) = 6x + 3
5x + 4 > 3x + 18
4  3 – 2x
5x + 4x = 9x
x+2=x-2
x-4=5
y + 3 > 8.9
x + 2x = 3x
6x - 6 = 6x
x/2 = 7
–y + 2 = 67
2 - y = -5
(1/2)(x + 3) = (1/3)(x - 1)
(1/7)x + 2 = (1/2) x + 3
(1/7)(x + 1) = (2/3)(x - 1) + 3(x - 2)
139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
149.
150.
151.
152.
153.
154.
155.
156.
8
157.
158.
159.
160.
161.
162.
163.
(1/3)(x + 6) = 8
(5/7) x - 30 = (5/3) x
3(2x - 1) = 6x + 3
x + 3(x +2) = 2(2x + 3)
2x - 2[3x - 2(1 - x)] = -12
5x - 3 = 12x + 2
5
2

3x  4 x  4
164.
2
3

x x  10
165.
What is the area of a circle with radius 4 inches? (Be sure to give units.)
166.
Give an example of an irrational number.
If the following are in factored form, give the number of factors. If they are not in factored form
give the number of terms. In either case, circle the appropriate word.
167.
168.
169.
4x(x - 7) _____________ terms/factors
3(x + 2) - 4(x + 2) _____________ terms/factors
5x2y3 _____________ terms/factors
170.
A bouncing ball bounces one-third the previous height with each bounce. What is the
height of the 4th bounce if the ball starts from 2187 inches. Give an input-output table for
this problem.
171.
Give an expression for the sum of 3 consecutive integers, assuming that x is the first.
172.
a) Sketch a graph of y = -x2 + 2x - 3 on your calculator, and carefully transfer as much of
it as will fit on to the grid below.
b) Use zooming or the table function to give the largest input x that gives an output of 0.
Do this to the nearest tenth.
173.
a) Sketch a graph of y = x3 – 4x on your calculator, and carefully transfer as much of it as
will fit on to the grid below.
b) Use zooming or the table function to give the largest input x that gives an output of 2.
Do this to the nearest tenth.
174.
1
x  2 (on your calculator if you wish), and carefully transfer
3
as much of it as will fit on to the grid below.
a)Sketch a graph of y =
b) Use zooming or the table function to give the largest input x that gives an output of
3.25. Do this to the nearest tenth.
9
175.
Give an input-output table for the following situation, using the integers between 0 and 5
as the inputs. The output is the square of the input if the input is odd and the output is the
sum of -2 and the input if the input is even.
176.
Fill in the following input-output table based on the entries shown
Input
1
2
3
4
5
n
220
Output
-3
2
7
12
177.
You have rectangular tables that seat 2 people along each length and 1 person along each
width. Give an input-ouput table for the number of people that can be seated (when putting the
tables end to end) based on the input of how many tables you use. You have a total of 5 tables
now. If you add 12 tables, what is the total number of people that can be seated in one long line.
178.
Give an input-output table for the following situation, using the integers between 0 and 5
as the inputs. The output is the product of the input and 5.
Input
Output
0
1
2
3
4
5
Solve the following formulas for the indicated variable.
179.
180.
181.
182.
183.
184.
185.
186.
187.
188.
189.
190.
C = 2r for r
y = mx + b for x
P = 2l + 2w for w
6x + 3y = 10 for y
y = mx + b for b
C1V1 = C2V2 for C2
A =(½) (b1 + b2)h for b1
y = mx + b for m
P = 2l + 2w for l
A = (½)(b1 + b2)h for b2
A= ab for a
y = mx + b for x
10
191.
192.
193.
s = (½)gt2 + vot +so for vo
yx(r + s) = q + 1 for r
A line parallel to the line y = 2x - 3 would have a slope of ________. A line
perpendicular to the line y = 2x - 3 would have a slope of _______.
194.
For g(x) = 2x + 1, find g(3) and g(-2)
195.
For f(x) = 5x – 2x2, find f(2) and f(-1).
196.
For the following table fill in the blanks in a way that will make y not be a function of x.
x
5
3
(Show work.)
(Show work.)
y
9
2
8
4
197.
For the following table fill in the blanks in a way that will make y be a function of x, and
will allow you to find f(2). f(2) = ________.
x
5
3
y
9
2
8
4
198.
Find the equation of the line with the given point (4,1) and the slope = 2/3.
199.
For each graph, tell whether it does or does not represent a function.
200.
Determine whether the table represents a linear relationship. If it is linear, state the slope of
the line, using the proper units. If it is not linear, explain why.
Time (in seconds) Distance (in feet)
2
64
11
3
4
5
96
128
160
201.
What is the equation of the line which is parallel to the line 4x + 2y = 8 and goes through
the point (-4, 2) ?
202.
What is the equation of the line which is perpendicular to the line 4x + 2y = 8 and goes
through the point (-2, 5) ?
203.
Use the graph (or an algebraic method) to find the solution set of x + 1 > 3x – 7:
204.
The cost in dollars of producing 100 computer desks is $ 8500. To produce 200 desks is
$16500. Assume that the total cost is a linear function of the number of desks.
205.
a)
Find the slope of this linear relationship, including units.
b)
c)
Find the y-intercept.
What does the y-intercept represent in the context of this production setup?
d)
Give the equation that describes this relationship. Predict the cost if 1000 desks
are produced.
Does the following table give y as a function of x? If not, why not? If so, give the
domain of the function.
x y
2 6
4 6
5 9
7 2
Completely factor the following. If the expression cannot be factored, please state that.
206.
207.
208.
209.
x2 + 10x + 21
x2 - 7x - 30
4r2 + r - 3
3x2 + 10x + 7
12
210.
211.
212.
213.
214.
215.
216.
217.
218.
219.
220.
221.
222.
223.
224.
225.
226.
227.
228.
229.
230.
231.
232.
233.
234.
235.
3r2 + r - 10
6x2 + x - 1
x2 - x – 6
3x2 + 10x + 4
4x2 - 4x + 1
2x2 + 5x - 3
15x2 + 17x - 4
16x2 - 1
4x2 - 9
5x2 - 23x + 6
a3b - b3a
x2 + 2x - 5
63x2 - 28
(x + y)2 - 9z2
3x2 + 4x - 4
2x2 - x - 3
x2 +3x - 28
x2 - 81
x2 - 16x
5x2 - 35x +60
12x2 -13x - 4
x2+ 10x + 11
28x2 + 20x +3
x2y3 + y2x3
x2 + y2
3x2 + 4x + 41
Make tables (if necessary) and graph the following equations.
236. y = 2x - 4
237. y = 3x - 3
238. 3y +4x = 24
239. x + 4 = 0
240. y = -3
Find the slope of the following lines.
y = 3x - 5
241. 3x - 2y = 8
242. The line joining (2,-3) and (4,6)
243. The line joining (4,-2) and (-1,-4)
244. A line parallel to y = 2x + 9
245. A line perpendicular to the line through (-1,-2) and (3,5)
246. A line parallel to the line through (-1,-2) and (3,5)
247. A line perpendicular to 4x - 2y = 16
248.
249.
Give an example of a 3rd degree monomial.
Give an example of a 4th degree binomial
13
250.
Give the numerical value of the slope in the following picture, and interpret it in terms of
the units given in the graph:
200
miles
100
4
251.
252.
8
hours
Give the equation of the line above if we use m for miles and h for hours.
How many terms are there in the following expressions ( Do not simplify them first.):
a) 3x - 5y2 + .25
___________ b) 4(x + y - 4) + 7(2x -5)
Use the following graph to answer the questions after it.
y
A
x
B
253.
254.
255.
256.
C
Give the approximate slopes of the three lines.
Give the approximate y-intercepts of the three lines.
When x = 4 in graph C, give the value of y.
When x = -8 in graph B, give the value of y.
Solve the following systems of equations. Give answers as ordered pairs for those that have a
unique solution. If there is not a unique solution, state whether the system represents parallel
lines or coincident lines, and justify your answer.
257.
3x – 2y = 7
14
2x + y = 7
258.
y = 2x – 5
y = 2(x – 2.5)
259.
4x – 3y = 21
3x + 2y = 3
260.
3y = 2x – 5
y = 2(x + 2.5)
261.
-3x + y = -2
6x – 2y = 6
262.
3x + y = 7
x + 3y = 5
263.
Make up and give me a system of two linear equations in two unknowns x and y such that
the system has no solutions.
264.
Make up and give me a system of two linear equations in two unknowns x and y such that
the system has an infinite number of solutions.
265.
Identify the coordinates of the points labeled A and B in the following picture assuming
the points labeled are correct. The x and y axes are not shown, and the picture
(0,0)
is not necessarily to scale. Show your work.
(-4,-5)
A
B
(0,-7.5)
266.
Also find the distance from the origin to point B and from point B to the point (-4, -5)
267.
Find the coordinates of A and B.
(0, 0)
A
(5, -4)
(0, -6)
B
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268.
A manufacturing plant uses water that ends up getting too warm to release directly into
the river near the plant, since the hotter water would change the ecosystem. Water/waste
water guidelines require the water released to be only 40 degrees Fahrenheit. To comply
with the guidelines, the company has built a 10,000-gallon mixing tank where they mix
their heated water with their regular water source, which has a temperature of 37 degrees
Fahrenheit. On a given day the water they want to release has a temperature of 45
degrees Fahrenheit. How much of this water must they mix with how much of the 37
degree water to fill the tank with 10,000 gallons of water that meets the 40 degree
requirement?
269.
An oil spill of 13,000 gallons happens on a lake of 670,000 square feet. If the oil spreads
over the whole area of the lake, how deep will the oil be? It doesn't matter what shape
the lake is. If you want to think of it as rectangular to make the problem easier to
visualize, feel free to do that. Give your answer to the nearest hundredth of an inch.
Recall that 231 cubic inches are equal to 1 gallon.
270.
Bob buys 3 pounds of grapes at $0.98 per pound, 5 pounds of potatoes at $0.49 per
pound, and 2 pounds of broccoli at $0.89 per pound. What is the total cost of his
purchase?
271.
A safe ladder position for reaching 9 feet up a wall is 2.25 feet from the base of the ladder
to the wall. How long a ladder is needed?
272.
What is the safe ladder position for reaching 14 feet up a wall (4:1 ratio)? How long a
ladder is needed?
273.
A Boeing 747 holds 279 more people than a Boeing 707. If the two planes together carry
721 people, how many does each plane carry? (The total number of people includes
crew.)
274.
An English muffin and two fried eggs contain 330 calories. Three English muffins and
one egg contain 515 calories. How many calories are in each item?
275.
Suppose 5 grams of carbohydrate and 2 grams of fat contain 38 calories. Furthermore, 2
grams of carbohydrate and 6 grams of fat contain 62 calories. How many calories are in
1 gram of carbohydrate? In 1 gram of fat?
276.
Mr. McFadden has a farm where he raises cows and ducks. There are 20 total heads
among the animals and 64 total feet. How many cows and how many ducks are there?
State your assumptions.
277.
Georgia purchases 200 shares of Boeing stock at $54 per share. How many shares of
Nike stock can she purchase at $71 per share if she has a total of $25,000 to invest?
278.
How many gallons of cold water (summer temperature 60) would need to be added to a
bathtub containing 12 gallons of hot water at 140 to lower the temperature to 103?
16
279.
Find the missing sides of each right triangle below.
12
15
11
18
280.
The following triangles are similar. Find the length of the side marked x. Note that
the picture is not to scale. Show your work.
52
x
13
5
281.
282.
283.
Find the third side of each of the above triangles.
Find the distance between (-2,-2) and (5,7)
Find the equation of the line joining each of the above pairs of points.
284.
Determine if the following graph represents a function and EXPLAIN your answer.
y
x
285.
286.
287.
288.
Convert 75 feet per second into miles per hour.
Convert 45 feet per second into miles per hour.
Convert 75 miles per hour into feet per second.
Convert 1.62 Canadian dollars per liter into United States dollars per gallon, if a U.S.
dollar is worth 1.29 Canadian dollars.
289.
Find the perimeter and area of the trapezoid shown in this picture which is not perfectly
drawn to scale. The distance between the parallel sides is 2 inches.
6 in
y
290.
Find the equation of the line graphed to the right.
3 in
3 in
4 in
x
17
291.
Convert 26.2 miles into yards.
292.
Convert 10 kilometers into inches.
293.
Convert 200 ounces into gallons.
294.
Convert 15 square feet into square inches.
295.
Convert 27 ounces into cubic inches.
296.
My kitchen drawers are 12 inches wide and go back 21 inches under the counter. If I
pour a 2 liter bottle of Diet Pepsi into the drawer, how deep will the liquid be in the
drawer, to the nearest tenth of an inch. Show all your work.
297.
Give the domain and range of the following functions. Assume that where each part of a
graph ends, there is an arrow to show that it continues.
298.
In the late afternoon a 6-minute long distance call to the Azores Islands cost a total of
$6.21. That same afternoon a 9-minute call cost $8.94. Both of these costs include a
connection fee, in addition to the cost for the minutes talked. Assume the cost of such a
call is linear. Find the linear equation that gives cost in terms of the length of the call.
What is the cost per minute of a call? What is the connection fee?
299.
A pressure washer costs $60 for the first 5 hours, and $9 for each additional hour. What
is the total number of hours rented, if the total cost is $123? To get full credit you must
define a variable, give an equation, solve the equation, and give the answer in proper
English.
300.
Pink Cab Company costs $2.00 to “get into the cab” and then costs $0.75 per mile. Blue
Cab costs $3.25 to get into the cab and then $0.50 per mile. What range of miles must I
be driving if I pick Blue Cab to save money? To get full credit you must define a
variable, give an inequality, solve the inequality, and give the answer in proper English.
301.
A cab ride of 8 miles has a total cost of $6.00. A ride of 12 miles cost $7.00. In both
cases the cost is made up f a fixed charge to get into the cab and a per mile charge. a) Give
a formula for y, the total cost, as a linear function of x, the number of miles driven in the
cab. b) How much would a trip of 16 miles cost?
18
302.
A wedding reception caterer charges a basic fee to use their facilities and a charge per
person. A wedding reception for 150 people costs a total of $3900. If you go up to 186
people, the total cost becomes $4800. How much would it cost for 300 people? (Be sure
that you give the equation. Let x be the number of people and y be the total cost.)
303.
Find the last leg of a right triangle that has a hypotenuse of 34 and a leg of 10.
304.
Recall that D = rt is the relationship between distance, rate, and time. Build an inputoutput table showing the distances traveled in 4 hours at speeds of 0, 30, 60 and 90 miles
per hour.
305. Consider the function f ( x)  x 2 4 x  1 . Find f(2) and f(-2).
306. Consider the function f ( x)  6 x  9 . Find f(3) and f(-4).
307. Consider the function f ( x)  2 x 3  3x  5 . Find f(-3) and f(4).
308. Consider the function f ( x)   x 2  x  2 . Find f(-1) and f(3).
In the following series of questions, answer “not possible” if it can’t be done.
309.
310.
311.
312.
313.
314.
Give a number which is a rational number, but is not an integer.
Give a number which is a natural number, but is not an integer.
Give a number which is an integer, but not a whole number.
Give a number which is real, but is not rational.
Give a number which is real, but is also rational.
Give a number which is an integer, but is not real.
__________
__________
__________
__________
__________
__________
Give a mathematical expression for the following, using n or x as the input number. Be careful
of the slight differences.
315. The quotient of a number and 4, decreased by 3.
316. The product of 7 and a number, decreased by 4.
317. The product of 7 and a number decreased by 4.
__________
__________
__________
318. Using only the Commutative Property of Addition, rewrite the following expression:
4(x + 3) = ______________
319. Using only the Commutative Property of Multiplication, rewrite the following expression:
4(x + 3) = ______________
320. Using only the Distributive Property, rewrite the following expression:
4(x + 3) = ______________
321. Find the difference in elevation between the highest point in North America, Mt.
McKinley (Denali), and the lowest point, Death Valley. Their elevations (relative to sea
level) are 20,320 feet and –282 feet, respectively.
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322.
323.
324.
325.
326.
327.
328.
329.
330.
331.
332.
333.
334.
335.
336.
337.
338.
339.
340.
341.
342.
What do we mean by the square root of a number?
What do we mean by the square of a number?
What does the Pythagorean Theorem say?
What is the sum of the angles of a triangle?
What is the perimeter of a geometric figure? How do you find it?
How do you find the area of a square? a rectangle? A triangle? A circle?
What is the circumference of a circle?
What do we mean by the absolute value of a number?
What does x-1 mean?
What are the five main properties of exponents (the nice laws)?
What is x0?
What is the difference between -22 and (-2)2? Why is this?
What is a polynomial?
What is a linear equation?
Explain how to plot points on the Cartesian Coordinate System.
Explain how to graph Ax + By = C on the Cartesian Coordinate System.
What are x- and y-intercepts and how do you find them?
What does the slope of a line represent?
What is the slope of a horizontal line? a vertical line?
What do you know about the slopes of parallel lines?
What do you know about the slopes of perpendicular lines?
Hope it was fun!
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