Mr. Pisciotta's Favorite Classes
Directions: Using the equation below, complete the table of x- and y- values. Use this table to write the sets of ordered pair and to graph the points in the coordinate plane.
EQUATION: y = - 4x + 3
Table Ordered Pairs
|X |Y |
|-2 | |
|-1 | |
|0 | |
|2 | |
|3 | |
Graph
15Part Three Directions: Read the following scenario CAREFULLY.
A cell phone charges $60 a month for a plan that includes unlimited minutes and text messages.
The company then charges $2 for every megabyte of internet usage.
a) Equation - What is the total cost, C, of the monthly bill if you use m number of megabytes of internet usage? ______________________________________________________
b) Table – Using the equation in part A, complete the following chart:
|Megabytes (m) |Monthly Bill (C) |
|5 | |
|10 | |
|15 | |
|20 | |
|25 | |
c) Graph - Using the table in part B, construct a graph that compares internet usage to the monthly bill.
[pic]
| |2. |
|Directions: Write an equation for each sentence then solve the equation. |A number divided by 8 is 5. |
| |a/8 = 5 |
| |8(a/8) = 5(8) |
| |a = 40 |
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|3. |4. |
|32 plus a number is 57. |A number plus 33 is 62. |
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|5. |6. |
|58 minus a number is 47. |21 divided by a number is 3. |
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|7. |8. |
|Seven times a number is 35. |The difference between a number and 67 is 4. |
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|9. |10. |
|Eight times a number is 80. |The difference between a number and 56 is 37. |
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|11. |12. |
|A number divided by 9 is 10. |A number plus 18 is 51. |
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|13. |14. |
|72 minus a number is 12. |5 less than 2 times a number is 5. |
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|15. |16. |
|A number multiplied by 6 is 24. |55 plus a number is 96. |
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|17. |18. |
|A number divided by 11 is 2. |A number multiplied by 3 is 18. |
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|1. |2. |
|Write an algebraic expression for each verbal phrase |a number x divided into 25 |
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|3. |4. |
|7 times a number e |take away a number c from 16 |
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|5. |6. |
|difference of a number q and 24 |product of a number r and 41 |
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|7. |8. |
|13 more than a number j |a number a less 49 |
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|9. |10. |
|a number v decreased by 28 |a number b multiplied by 46 |
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|11. |12. |
|30 minus a number h |a number u divided by 36 |
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|13. |14. |
|quotient of 23 and a number e |8 less than a number y |
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|15. |16. |
|subtract a number m from 19 | |
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|17. |18. |
|sum of a number z and 34 |3 increased by a number p |
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|19. |20. |
|33 increased by a number u |add 6 to a number k |
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|21. |22. |
|take away a number f from 20 | |
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|23. |24. |
|sum of a number b and 35 |a number x times 44 |
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|25. |26. |
|a number w decreased by 12 |a number j minus 10 |
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|27. |28. |
|32 less a number t |48 multiplied by a number q |
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|29. |30. |
|4 divided by a number s |difference of a number c and 2 |
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Directions: Circle an answer for questions 1 through 5. Mark only one answer for each question. You may work problems on this sheet, but be sure to clearly mark an answer for each question. You may not use a calculator for this common assessment.
1. Which of the following situations could be represented by the equation
3b – 5 = 13?
A. Carl bought 3 books for b dollars each and had a $5 off coupon for a total of $13.
B. Carl bought 3 books for b dollars each and paid $5 tax for a total of $13.
C. Carl bought 5 books for b dollars each and had a $3 off coupon for a total of $13.
D. Carl bough 5 books for b dollars each and paid $3 tax for a total of $13.
2. To convert temperature from degrees Celsius to degrees Fahrenheit, you can multiply the Celsius temperature by 1.8 and add 32. Which equation
represents this situation?
A. F = 1.8C + 32
B. F = 32C + 1.8
C. F = 1.8C - 32
D. F = 32C - 1.8
3. Mr. Dover invested $1 dollar in 2003. His investment was worth $3 in 2004, $9 in 2005, $27 in 2006, and $81 in 2007. Which of the following equations represents this situation?
A. y = 3x
B. y = x3
C. y = 2x -1
D. y = 3x
4. Rich earned $2,500 more than 3 times the amount of money that Michael earned last year. Rich earned $125,500 last year. Which of the following equations can be used to find out much money Michael earned last year?
A. 3(2,500) + M = 125,500
B. 3(M) + 2,500 = 125,500
C. 125,500 – 3(M) = 2,500
D. 125,500 + 25,000(M) = 3
5. Tony bought a pair of shoes that cost $116. His shoes cost him $36 less than twice the price of Joe’s shoes. What did Joe’s shoes cost?
A. $40
B. $64
C. $76
D. $152
Directions: Circle an answer for questions 1 through 5. Mark only one answer for each question. You may work problems on this sheet, but be sure to clearly mark an answer for each question. You may use a calculator for this common assessment.
1. Which means “3 more than 6 times a number?
A. 6x – 3
B. (6/x) + 3
C. 6x + 3
D. (6/x) – 3
2. This month, Ari ran 5 more miles than 3 times the number of miles she ran last month. She ran 41 miles this month. How many miles did he run last month?
A. 8
B. 12
C. 15.3
D. 108
3. What number is 3.5 less than 3.1 times 17?
A. 23.6
B. 41.85
C. 49.2
D. 63.55
4. Martha used a piece of rope 16.25 feet long to stake trees. She cut the rope into pieces that were 3.5 feet long. How many pieces of rope did she use to stake trees?
A. 1
B. 2
C. 3
D. 4
5. The product of a number and 7 is decreased by 15. If the result is 20, what is the number?
A. 4
B. 5
C. 6
D. 7
1. Three friends went to dinner and paid d dollars each, including tax and tip. They had a $15 coupon and paid less than $120 all together. Which of the following represents this situation?
A. 3d + 15 > 120
B. 3d – 15 > 120
C. 3d + 15 < 120
D. 3d – 15 < 120
2. Which ordered pair is not part of the solution of 2x + 4y = 16?
A. (0, 4)
B. (2, 3)
C. (3, 2)
D. (10, -1)
3. What function is represented by the graph below?
A. y = x + 1
B. y = 3x + 2
C. y = -5x + 6
D. y = -5x – 6
4. Which number makes this number line the solution set?
2x + 2 _?_ 6
A. ≥
B. >
C. <
D. =
5. What is the solution set to the following inequality?
0.4 t – 2.6 < 4.8
A. t < 4.4
B. t < 5.5
C. t < 14.8
D. t < 18.5
1. What is the rule of this function?
|x |y |
|-3 |-11 |
|-1 |-7 |
|2 |-1 |
|5 |5 |
|7 |9 |
A. y = x + 2
B. y = 2x – 5
C. y = 3x – 2
D. y = 4x – 2
2. Given the following linear equation, what is the value of x if y= 10?
4x – 2y = 8
A. 8
B. 7
C. 6
D. 5
3. Given the equation y = 6x – 2, what numbers complete this x/y table?
|x |-1 |0 |1 |
|y | | | |
A. {-8, -2, -4}
B. {-8, 2, 4}
C. {4, -2, 4}
D. {-8, -2, 4}
4. Which situation can be represented by the equation 5x – 10 = 72?
A. Rachel bought 5 sweaters for x dollars each. There was a $10 discount, so she spent $72 all together.
B. Rachel bought 5 sweaters for x dollars each. She paid $10 in tax for a total of $72 all together.
C. Rachel bought x sweaters for $10 each. She paid $5 in tax for a total of $72 all together.
D. Rachel bought 10 sweaters for x dollars each. She paid $5 in tax for total of $72 all together.
5. Which equation represents the pattern in the following graph?
A. y = 2x
B. y = 4x
C. y = 2x + 1
D. y = 2x + 5
1. Use the equation y = 2x +1 to find the missing y values in the table below.
|x |-2 |-1 |0 |1 |2 |
|y | | | | | |
A. {-3, -1, 1, 3, 5}
B. {-3, -2, 0, 3, 5}
C. (-3, -1, 1, 2, 5}
D. (-3, -2, 1, 3, 5}
2. The following table shows the x/y values for an equation. Which equation matches those values?
|x |-2 |-1 |0 |1 |2 |
|y |-11 |-8 |-5 |-2 |1 |
A. y = 3x – 5
B. y = 3x + 5
C. y = -3x – 5
D. y = -3 x + 5
3. Which of the following the graph of y = [pic]x[pic]?
A.
B.
C.
Writing Equations
Directions: Read and analyze each scenario. Write an equation (or variable expression) that represents the scenario. Solve the equation.
1. The sum of three times a number plus 25 is 175. Write an equation to model this scenario and find the value of the number.
2. The sum of three consecutive integers is 90. What are the values of the integers?
3. The sum of two consecutive numbers divided by three is 71. What are the values of the numbers?
4. You are purchasing CDs from a music club. You pay $4 for shipping on any n number of CDs, $17 for each CD. Write an equation for the cost, C, of n CDs. Then find the cost of six CDs
5. At the movies, popcorn costs $2.75 and drinks cost $1.25. Write an expression to find the total cost, C, of p popcorns and d drinks. Find the total cost for snacks if 3 people buy popcorn and 4 people buy drinks.
6. BONUS: You sell 14 items for a school fundraiser and make a total of $142. A T-shirt costs $11 and a hat costs $9. How many T-shirts did you sell? How many hats did you sell? (Directions: An equation is not needed, just determine an answer for this question.)
Part One Directions: Read each question carefully. Write and solve a proportion that can be modeled by the real-world scenario.
1. Damian is making brownies to serve at the family picnic. If the recipe calls for 2 ½ cups of cocoa to serve 4 people, how many cups will he need if there will be 60 people at the picnic?
2. A piglet can gain 3 pounds in 36 hours. If this rate continues, how long will it take the pig to reach 18 pounds?
3. Denise’s rabbit can eat 70 pounds of food in 80 days. How long will it take the rabbit to eat 87.5 pounds?
4. Jessica drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles?
5. If 6 pounds of apples cost $9, then how much would 21 pounds of apples cost?
6. If $24 worth of fertilizer covers 5,000 square feet, then how much would it cost to cover 30,000 square feet?
7. If a chain link fence costs $180 for 20 feet installed, how much would it cost to install 300 feet?
8. The scale on a map is 1 inch equals 5 feet. What is the distance between two points on the map that are 8 1/2 inches apart on the map?
9. A $4 sales tax is charged for a $50 purchase. At this rate, what is the sales tax for a $1200 purchase?
10. A store makes a profit of $15,000 for every 300 coats that they sell. If they make a profit of $25,000, how many coats did they sell?
Part Two Directions: Read each question carefully. Write and solve an equation that can be modeled by the real-world scenario.
11. The difference between the product of seven and a number and twelve is 16. What is the value of the number?
12. Five divided by a number plus four equal five. What is the value of the number?
13. You order two pair of Polo boots from Dillard’s Online. The website charges 14.95 for shipping and handling. Your total comes to 312.95. If each pair of boots is the same price, what is the value of one pair of boots?
14. You order four Kevin Hart DVDs from . You are charged $9 for shipping and handling. If your total order comes to $59, what did you pay for one DVD?
1. Which statement is true?
a) 3.18 < -4
b) 3.05 = 3½
c) -4.23 > -4.2
d) 10.949 < 10[pic]
2. Which number line displays the fractions in correct order?
a) 0 2/3 ½ ¼ 1
b) 0 ½ 2/3 ¼ 1
c) 0 ½ ¼ 2/3 1
d) 0 ¼ ½ 2/3 1
Using the information in the table below, answer questions 3 and 4.
3. Which lists shows the lakes in order from highest elevation to the lowest depth?
a) Craigs, Jones, Silver, Gieselmann, Seneca
b) Gieselmann, Jones, Craigs, Silver, Seneca
c) Seneca, Silver, Craigs, Jones, Gieselmann
d) Seneca, Gieselmann, Silver, Jones, Craigs
4. Which of the following lakes has the lowest elevation?
a) Craigs Pond
b) Jones Lake
c) Silver Lake
d) Seneca
5. Consider points H, I, J, and K on the following number line.
K J I H
-3 -2 ¼ 0 ¾ 1½
Which point is the second smallest?
| Name |Elevation |
|Jones Lake |-30 |
|Silver Lake |90 |
|Gieselmann Lake |-162 |
|Seneca Lake |445 |
|Craigs Pond |0 |
a) H
b) I
c) J
d) K
1. How is fifty-five million, seventy thousand written in scientific notation?
e) 5.507 · 107
f) 5.570 · 107
g) 5.507 · 1010
h) 5.570 · 1010
2. Louisiana has 8.277 × 103 square miles of water. How is 8.277 × 103 square miles expressed in standard form?
a) 8.277000 square miles
b) 8,277 square miles
c) 8,277,000 square miles
d) 827.7square miles
3. The average distance from Earth to the Sun is 93,000,000 miles. How is 93,000,000 written in scientific notation?
e) 93 · 106
f) 9.3 · 107
g) 93 · 108
h) 9.3 · 108
4. In the year 2009, Louisiana had a population of 4.492076 × 106 residents.
How is this number represented in standard form?
a) 4,492.076 residents
b) 4,000,000 residents
c) 449,207.6 residents
d) 4,492,076 residents
5. The number of people around the world who speak Chinese is estimated at 874,000,000. How is this number written in scientific notation?
a) 8. 74 × 107
b) 8.74 × 108
c) 87.4 × 107
d) 874 × 106
6. The speed of light is approximately 300,000,000 meters per second. How is 300,000,000 written in scientific notation?
a) 3 · 108
b) 300 · 106
c) 30 · 107
d) 30 · 108
1. The sports teams at Acadian Middle School are writing thank you notes to donors that contributed to the new sports complex. The basketball team wrote 350 notes in 2.5 hours. How many thank you notes did they write per hour?
i) 140
j) 325
k) 600
l) 875
2. Peaches are on sale for 2 for $1.00. Kayla wants to buy 9 peaches. How much will she spend on peaches?
i) $2.00
j) $4.50
k) $9.00
l) $18.00
3. A case of bottled water contains 24 bottles and costs $13.00. What is the approximate unit cost of a bottle of water?
a) $0.54
b) $0.56
c) $1.05
d) $1.85
4. Melinda was paid $58 for 8 hours of work. What was her hourly wage?
a) $7.25
b) $8.00
c) $50.00
d) $66.00
5. Rachel runs 1600 meters in 5 minutes, 30 seconds. Approximately, how far does Rachel run in one minute?
a) 275 meters
b) 291 meters
c) 302 meters
d) 320 meters
6. New Jersey’s population in 2000 was about 8,414,000 people. New Jersey’s area is 7417 square miles. What was the population per square mile in this city in the year 2000?
a) 1,134
b) 2,000
c) 3,708
d) 4,207
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