Name Period Revised 8/2014

Transcription

1 Name Period Revised 8/2014

2 TABLE OF CONTENTS Keystone Algebra 1 Exam Eligible Content.. 2 Operations with Rational Numbers CC Standards: A , A , A Coordinate Plane.. 12 CC Standards: A , A Matrices CC Standards: A Properties CC Standards: A Algebraic Expressions CC Standards: A Distributive Property CC Standards: A Solve Equations.. 21 CC Standards: A , A , Word Problems and Applications.. 25 CC Standards: A A Pythagorean Theorem CC Standards: A A Models 1 to 8 Word Problem Review CC Standards: A A Function Tables & Graphs CC Standards: A , A , A , A , A! , A , A , A , A Scatterplots & Line of Best-Fit 38 CC Standards: A , A , A , A PA Keystone Algebra 1 Formula Sheet.. 39 Vocabulary and Verbal Models SPECIAL NOTE This workbook is designed for 8 th grade math students at Log College Middle School. Any person who wishes to copy any part of this book must have written permission from Mrs. Gismondi, who created, designed and compiled this work.

3 Keystone Algebra 1 Exam Eligible Content 2

4 DIRECTIONS FOR RATIONAL NUMBERS 3

5 Simplify each of the following: Absolute Value & Opposites 1. ( 4 ) 16. ( 8 ) 31. [ ( 6 ) ] 46. [ ( 3) ] 2. ( 9 ) 17. ( ) 32. ( 9 7 ) 47. ( 6 2) 3. ( ) 18. ( ) 33. ( 36 / 6 ) 48. ( 7 / 7 ) 4. ( 8 / 4 ) 19. ( 15 8 ) 34. ( 3 0 ) 49. ( ) 5. ( ) 20. ( 5 4 ) 35. ( 6 1 ) 50. ( 14 8 ) / / / 16 4

6 Add integers

7 Subtract Integers

8 Multiply & Divide

9 All Operations / / / / / / / / / /

10 9 Decimal Rationals Review

11 10 Fractions Rationals Review

12 11

13 12

14 13

15 Simplify the following: Matrix Operations

16 Evaluate Algebraic Expressions Evaluate the following showing all math steps and the matching steps in order of operations. Do work in your spirals. Examples: Evaluate the following when a = 3, x = 6, y = 5. x + y ax y 4 ( xy 7 ) substitution 3 6 ( 5) subst 4( 6 ( 5) 7 ) subst / 4 37 ( ) N / Evaluate the following when a = 3, b = 4, c = 2, h = 10, k = 16, x = 6, y = 5, z = ax + b 2. cy b 3. b ( x a ) 4. a 2 b 5. ab 2 6. bc + ax 7. ( x b ) ( y + a ) abc 9. x / a + b / c 10. y 2 ab 11. ( hk ) / ( cb ) 12. h 2 / y x 2 + ax + k 14. y 3 ch 15. c ( bk h ) 16. ( h b ) ch ax z ( abh cxy ) 19. zh + bk + ax 20. kz cx hb 21. zx ab + ck 22. k / b + h / y 23. z / c + k / c 24. yz / bc 25. k 2 bk + a 26. h 2 + ak b 27. z 2 + cz + hx 28. c 2 + 9c h y b 2 b 31. ( kx ) / ( ab ) 32. k x / a b 33. ( kx ) / c 2 15

17 Closure Take two numbers from a set and perform an operation. If the answer is always in the set, then the set is closed. Properties Identity Property: For all real numbers a, a + 0 = a and 0 + a = a For all real numbers a, a 1 = a and 1 a = a Additive Inverse Property For every real number, there is exactly one real number a, such that a + (-a) = 0 and a + a = 0. Multiplicative Inverse Property For every non-zero real number a, there is exactly one number 1 a, such that a 1 1 and 1 = a = 1. The number 1 a is called the reciprocal or multiplicative inverse of a. a a Multiplicative Property of Zero The product of any real number and zero is zero. a 0= 0 Other Properties of Zero Zero divided by any nonzero real number is zero. 0 = 0 a Division by zero is undefined. (Division by zero cannot be done.) Commutative Property. For all real numbers and b, a + b = b + a and a b = b a Associative Property Distributive Property For all real numbers a, b and c, (a + b) + c = a + (b + c) and (a b) c = a (b c). For all real numbers a, b and c, a(b + c) = ab + ac and a(b c) = ab ac. Properties of Equality For all real numbers a, b and c: Reflexive Property a = a (A number equals itself.) Symmetric Property If a = b, then b = a. Transitive Property If a = b and b = c, then a = c. Substitution Property If a = b, then a can be replaced by b and b can be replaced by a. Additive Property of Equality: If a = b then a + c = b + c. Multiplicative Property of Equality: If a = b then a c = b c. Underlined Properties are on the Keystone Algebra 1 Exam. 16

18 17

19 Name the property used in each step. Algebraic Proofs 18

20 Write a P for positive or N for negative above each term then simplify the following: Algebraic Expressions 1. 2a + 4a + 8a 2. 5x + 6x + 9x 3. 3n + 9n + 11n 4. 5y + 6y + 14y 5. 6p + 9p 5p 6. 2w + w + w + 4w 7. 8x + 17x + x 8. 4g + 9g + 8q 9. 3c + 9c + c + 7c 10. 8w + 8f + 8w 11. 9a + 8m + 3m 12. 5w + 15v + 8w j + 9h + 9j + 7j 14. 2x + x + 3x f + 5y + 3f + 4y 16. 4x + 7y + x + y x x + 17x c + 2c + 8c + c 19. 9w 4w 20. 4x 3x 21. 2c + 6c 22. 5x 8x 23. 3x 12x 24. 3w 8w 25. 6p 2p 26. 3k 9k x 19x 28. x x 29. x 2x 30. c + 3c 31. 5x 2x 32. 3x 2x 33. 4w 9w 34. 5p p 35. 6k 5k 36. x 9x 37. 8x x x j g 5 3g q x x k g 2 2g 46. 4q x 6x p 6 2p 49. 4x + 7 4x w 6 + 3w x + 7 4x x + 5x l k r + 5s 6r 2s m + 4n 16m 56. 5y 9 3y q 2w + 9w 8g b 4b 6b 9b 59. 6h v + 27v + 5h f 7g + 18f + 4f 61. 2k k 14k 62. 7m - 2m 8m m x x 64. 6c + 2h 9c + 3h v + 4v 8 9v b + 4b + 30b 67. 2x + 6 x w 5 3w x 1 2x r + 4s 7r s m n 23m 4n 72. 2y 7 4y g 8w + 2w 4g b 3b b 5b 75. 3h v + 9v + 17v + 9h 76. 4f 5q + 13f 6f 77. 9k k 18k 78. 6m 4m 8m m x x 80. 5c + 3h 5c + 4h 81. 4x 6x 7x 9x 19

21 Simplify the following using the Distributive Property: 1. 2 ( x + 6 ) ( 2x + 5 ) m 8 ( 7w + 6m ) 2. 5 ( x 8 ) ( 4 + 8x ) x + 8 ( 3x 4 ) 3. 6 ( 8 x ) ( x + 13 ) + x 37. 6w 5 ( 9w + 6 ) 4. 3 ( 2 g ) ( 5x + 12 ) + 6x ( 2 + 3n ) 5. 8 ( x ) ( x 11 ) ( 7n 8 ) 6. 9 ( 5 + 8x ) 23. 2m 7( 8w + 9m ) ( 11x 4 } 7. 8 ( 9 3y ) 24. 6x 6 ( 6x 7 ) ( 4 8x ) 8. 4 ( 8 6y ) 25. 2w + 7 ( 7w 9 ) ( 4z + 8 ) + ( 11z + 4 ) 9. 5 ( 3x + 7 ) ( 2n + 3 ) ( 6 + 5x ) + 3 ( 4 + 8x ) ( 8x + 7 ) ( 3 9c ) ( 5 3w) ( 5w + 4 ) ( 2 3x ) ( 2x + 8 ) ( 2c + 8 ) ( 9 5c ) ( 7 4x ) ( 4 + 7x ) ( 3y 3p ) + 2(5p + 4y ) ( 3x 7 ) ( 2x 11 ) 10x ( 3x + 7 ) + ( 5x 4 ) ( x 5 ) ( 5 + x ) ( 8 3h ) 3 ( h 2 ) ( 9 11x ) ( 6x + 8 ) 3x ( 5 8d ) + 7 ( d + 9 ) ( 2 5x ) ( 3x 2y ) + 9y ( k + m ) ( k + m ) ( 3x + 2y ) 34. 7y 4 ( 2y 9 ) 51. 4(2x 7) 5 (6 3x) 20

22 Solve the following equations showing all the work. 1. a 11 = b 8 = y + 7 = x + 18 = m = n = c 30 = d 24 = p + 18 = s + 90 = t = = z v 37 = w 94 = k = h = = x = y a = b 32 = x = = 3 a = 5 g h = = 18 k = p m = r = = 81 z = y x = y = c = a = b= t = r = s = = 4 k = 7p 41. c d 2 = 1 = f = p = = u n 1 = x 1 = y 2 = z + 4 = a = z 5 = y 7 = = 4x y = = 8 2z = 3 + 5a 57. 6x + 25 = = 2c y = n 14 = x + 3 = m = z = = 6 2x x = x 7 = y 5 + = x 7 = y = = 10 + z = 7x + 8 5x 72. 6y + 8 5y = = 8z + 8 9z = 5x 7x y + 7 5y = = 3p 9 7p

23 Solve the following equations. Show all work for each y 18 = 3y 98. y + 11 = 2y c 9 = 8c 99. 2y + 3 y = 11 + y 79. 8n 12 = 5n x = 4x x m = 14 9m ( y + 7 ) = x = 10 4x ( x 2 ) = z = 35 9z ( a + 2 ) = p = 5p x + 9 = 2 ( x 3 ) r = 3r ( y + 3 ) = 12 y c + 36 = 8c a = 3 ( 2a + 1 ) 86. 7z 9 = 3z ( 3 2c ) = 10 4c t = 8t = 12 ( 6 + c ) 88. 3x + 7 = x ( x 1 ) = 2x + 4 ( x 1 ) y = 5y ( 2x 5 ) = 2 ( x + 2 ) + 3x a + 8 = 2 + 9a 111. ( 3 2n ) + 7n = 3 ( n + 3 ) 91. 9x 5 = 6x ( y + 8 ) 5 = 4 ( y + 2 ) 6y x = x ( c + 4 ) 6c = 2 ( 4 2c ) n = n y 3 ( 4 2y ) = 6 ( y + 1 ) x = 5 + 3x ( 3 4z ) + 7z = 12z ( z + 2 ) 95. 4y + 2 = 2y y ( 6 2x ) + 4x = ( 2x 6 ) 96. 8c 12 = 15c 4c x ( 9 4x ) = 3 ( x 11 ) 97. 5x 3 = 7x x r + 3 ( 7 r ) = ( r + 4 ) 22.

24 Solve the following using the LCM Method. Show all work in your notebook. LCM Method c = y = 2 15 y = 2 3 c c = y 1 2 = = 3 2 a x + 7 = = 1 2 x x + 6 = 3 4 x y 4 = 1 5 y x 3 = 2 3 x r 1 = 2 5 r a = 2a x 3 7 x 2 = x y 4 2y 9 3 = y b 4 2b 1 2 = b x 3 6 5x 4 5 = x 5 8 2x 7 12 = 9 x x 5 4x + 5 = = 6x 2 3x

25 Solve the following using the Decimal Method. Show all work in notebook. Decimal Method x = x = c = m = d 2.6 = = 0.15 x x 7.3 = y = z = 0.07z = x y + 2 = y x 0.11 = 0.03 x n = n z = 0.8 z x = 1.4 x c 5.1 = c Solve the following using the LCM and Decimal Methods. Show all work in your notebook. 17. x x = k 8 = k 19. x 3 6 = h 5 + h 7 = y = 5 6 y x = 2 3 x y y = x x = 6 24.

26 Use the verbal model format to solve the following. Show all work. 1. Seven more than three times a number is eighteen. Find the number. 2. Jason has fourteen more than three times Evelyn s amount. Together they have 130 marbles. How many marbles does each have? 3. Seven times the difference between eleven and twelve times a number is four. Find the number. 4. April has 9 computer games. This is seven less than twice the number of Sam s games. How many does Sam have? 5. The quotient of nine times a number and fourteen is seven. Find the number. 6. George has twelve books more than Jonathan. Together, they have 44 books. How many books does each have? 7. Six more than half a number is forty-two. Find the number. 8. Seven is to nine as fourteen is to what number? 9. Eleven is to thirty-three as what number is to twenty? 10. What number is to forty-nine as three is to seven? 11. Fifty-one is to what number as thirty-four is to two? 12. Arthur has 23 books. This is twelve books less than Jonathan. How many books does Jonathan have? 13. One number is sixteen more than five times a second number. Their sum is 58. Find the numbers. 14. Eleven is twice the sum of eight times a number and twelve. Find the number. 15. Greg earned 4 more points than twice Matt s amount. Together, they earned 19 points. How many points has each earned? 16. Find the radius of a sphere with the volume of 1365 feet The measures of two angles of a triangle are 41 and 83. Find the measure of the third angle. 18. Find the height of a prism if its volume is 2295 ft 3, its width is 15 ft and its length is 17 ft. 19. A triangle has a height of 38.2 m and an area of m 2. Find its base. 20. Find the number such that the sum of twice a number and three is to six as the difference between seven times the same number and five is to eight. 21. Eleven is to a number as seven is to the sum of four times that number and five. Find the number. 22. Four of the angles in a pentagon measure 89, 109, 73, 154. Find the measure of the other angle. 23. What was the cost of the meal if an 18% tip was $10.99? 25.

27 Use the verbal model format to solve the following. Show all work. 24. What was the original cost of a dress during a 25% off sale if the savings was $22.50? 25. How many towels did Stephanie purchase for $89.70, if each towel cost $5.98? 26. The sum of five and six times a number divided by three is the same as the difference between seven times the same number and four divided by eight. Find the number. 27. The sum of a number divided by four and nine times a number divided by six is the same as the difference between five times a number and seven divided by two. Find the number. 28. A company reimburses $49 plus forty-five cent for each mile a salesman drives. If the reimbursement check was for $121, how many miles did the salesman drive? 29. A coat, originally marked $159, was sold for $ during a sale. What was the rate of the discount? 30. A stereo cost $289. The final bill after sales tax was $ What was the rate of the sales tax? 31. The check in a restaurant came to $58.45 and Mr. Jones left $69. What was the rate of the tip? 32. Marcy paid $146 for her purchases including a 7% sales tax. What was the original cost of her purchases before the sales tax? 33. Mr. Brown paid $136 for a suit during a 25% off sale. What was the original price of the suit? 34. A repair man charges a service fee of $60 plus $35 for each hour he works on the item. If the final bill was $147.50, for how many hours did he work on the item? 35. The page of your school yearbook is 8 ½ inches by 11 inches. The left and right margins are ¾ inch and inches, respectively. The space between pictures is inch. How wide should you make each picture to 8 16 fit three across the page? 36. You are shopping for earrings. The sales tax is 5%. You have a total of $ What is your price limit for the earrings? 37. You want to include four photos on the cover of a program for the school play, two across the page. The cover is 6 1/2 inches wide, and the left and right margins are ¾ inches each. The space between the pictures is ½ inches. How wide would you make the pictures? 38. Find the missing radius of the cylinder: 39. Find the missing side of this cube. 25 feet Volume = Volume = 4505 ft m 3 26.

28 Model 8 uses the model Predicted Value = Original Value + rate per unit the number of units, twice. As a result, a chart is the best way of organizing the data. In Model 8, one of the key pieces of data in the chart is equal to its corresponding part. The chart below will be used to solve most of the problems below. However, it must be personalized to reflect the data in the problem. Once the chart is complete, a verbal model can be written. A paragraph explaining each problem will be written. Original Value Rate per unit Number of units Predicted Value 1. Video Game Membership A local store charges $8 to rent a video game for three days. You must be a member to rent from the store, but the membership is free. A video game club in town charges only $3 to rent a game for three days, but the membership in the club is $50 a year. Which membership is more economical? 2. Bike Safety Suppose you live near a park that has a bike trail you like to ride. The Parks Department rents a bike with safety equipment for $5 a day. If you provide your own safety equipment, the bike rental is $3 a day. You could buy the equipment at a sports store for $28. How many times must you use the trail to justify buying your own safety equipment? 3. Catching Up with Sis Kate is always reminding her younger brother Tony that she is taller than he is. Kate is 63 tall and is growing at a rate of 1 inch a year. Tony is 60 tall and is growing at a rate of 2 1 inches per year. How 3 3 long will it take Tony to catch up with Kate? 4. Summer Swimming A new swimming pool is opening for 15 weeks during the summer. You can swim in the afternoon for $3 or buy a membership for $80 and pay only $1 for the afternoon session. You must decide whether to buy a membership or to buy daily passes. 5. Remote Control Cars The Fast Track Company manufactures toy remote-control race cars, which it sells for $18 each. The production cost for the company is $2000 per day plus $13 per race car. How many cars must the company sell in a day to break even? 6. The Gazelle and the Cheetah A gazelle can run 73 feet per second for several minutes. A cheetah can run faster (88 feet per second), but it can only sustain its top speed for about 20 seconds. Gazelles seem to have an instinct for this difference because they will not run from the prowling cheetah until it enters its safety zone. This is the distance the cheetah would need to run to overtake the gazelle in 20 seconds if both are running at top speed. How close should the gazelle let the cheetah come before it runs? 7. High School Enrollments Cleveland High is in the city and West Lake High is in one of the suburbs. Cleveland High s enrollment has been decreasing at an average rate of 75 students per year, whereas West Lake High s enrollment has been increasing at an average rate of 60 students per year. Cleveland High has 3150 students, and West Lake High has If enrollments continue to change at the same rates, when will the two schools have the same enrollment? 27. Heath Algebra 1

29 8. Running a Race Two runners are running on a 21 kilometer course. The first runs at 10 kilometers per hour, and the second runs at 15 kilometers per hour. If the first runner is 7 kilometers past the starting line before the second runner starts, how far does each run before they are side by side? 9. Left Behind An elephant herd is migrating to greener plains. The herd is moving at about 10 miles per hour. One elephant strays from the herd, stops, and is left behind. Then it senses danger and begins running at about 25 miles per hour to reach the others. It takes the stray elephant 5 minutes to catch up with the herd. How far had the herd traveled when the stray elephant became frightened? 10. Population Growth From 1987 to 1988 in the United States, the population of the western region increased by 982,000 and that of the Midwest region increased by 222,000. In 1988, the population of the western region was 50,679,000 and that of the Midwest region was 58,878,000. If the populations continue to change at the same rates, when will the populations of the western region and Midwest region be the same? 11. Savings and Spending Currently, you have $60 and your sister has $135. You decide to save $5 of your allowance each week, whereas your sister decides to spend her whole allowance plus $10 each week. How long will it be before you have as much money as your sister? 12. Temperature Change Suppose you live in Greenville, South Carolina, where the temperature is 69 0 F and going up at a rate of 2 0 F an hour. You are talking on the phone to a friend, who lives in Waterloo, Iowa, where the temperature is 84 0 F and going down at a rate of 3 0 F an hour. If the temperatures continue to change at the same rates, how long would you and your friend have to talk before they would be the same? Heath Algebra 1 Use the verbal model format to solve the following. Show all work ABC and DEF are similar. For each set of measures given, find the measures of the remaining sides. B 21. c = 11, f = 6, d = 5, e = 4 a 22. a = 5, d = 7, f = 6, e = 5 c 23. a = 17, b = 15, c = 10, f = a = 16, e = 7, b = 13, c = 12 A b C 25. d = 2.1, b = 4.5, f = 3.2, e = f = 12, d = 18, c = 18, e = 16 f E d 27. c = 5, a = 12.6, e = 8.1, f = 2.5 D e F Glencoe Algebra 1, p

30 29.

31 30. Pythagorean Theorem: c 2 = a 2 + b 2 Pythagorean Triples:

32 Which of the following are right triangles? 1. 3, 4, , 4, , 12, , 6, , 24, , 10, , 11, , 14, , 7, , 20, , 40, , 2.5, , 356, , 4, , 7, , 1.5, 0.8 Solve the following using the Pythagorean Theorem. Draw a picture. 1. A fire truck parks 15 ft away from a building. The fire truck extends its ladder 39 ft. How far up the building from the truck's roof does the extension ladder reach? 2. Carson found an old tent in the attic of his house and decided to set it up in the back yard. However, the support sticks for the tent are missing. If the tent is 60 inches across on the bottom and 34 inches on each side, how tall of a stick does he need to set up the tent? 3. A television has a rectangular screen with a diagonal measurement of 30 inches. If the screen has a height of 18 inches, what is the width of the screen? 4. Two ships leave port at the same time. Ship X is heading due north and Ship Y is heading due east. Six hours later they are 300 miles apart. If the Ship X had traveled 240 miles from the port, how many miles had Ship Y traveled? 5. Jeremy goes to White Water Amusement Park. While there he decides to go down the park's huge waterslide called Lightning. If the slide is 120 feet high and the base of the slide is 90 feet from the pool, then what is the length of the slide? In #6 to 10, find the length of each of these lines in a coordinate plane

33 Solve completely the following word problems using the verbal model format: Verbal Models 1 to 8 Review 1. The volume of a rectangular prism is m 3. If its length is 36 m and its height is 48 m, find its width. 2. Alice earned $54, which is $36 less than three times Sue s amount. How much does Sue earn? 3. John drove 450 miles in 7.4 hours. What was his average rate? 4. The final cost of a refrigerator (including an 8% tax) was $744. What was the original cost of the refrigerator? 5. The radius of a sphere is 6.2 inches. Find its volume. 6. Find the number such that six times a number less than nine is the same as four times the same number subtract one 7. The hypotenuse of a right triangle measures 36 feet and one leg measures 8 feet. Find the length of the other leg. 8. A tree cast a 25-foot shadow at the same time as a 6-foot pole casts a 2.5-foot shadow. How tall is the tree? 9. The waiter received a tip of $29.67, which represented 20% of the food check. How much was the check for the food? 10. The volume of a cone is m 3. If its height is 12 m, what is the radius of the cone? 11. A pair of jeans went on sale for $ What was their original cost if the discount rate during the sale was 33%? 12. The first number is twelve more than five times the second number. Their sum is 432. Find each number. 13. A simple recipe calls for 4 cups of flour for every 1.5 cups of sugar. Amanda only has 3 cups of flour. How much sugar must she use with 3 cups of sugar to keep the taste the same? 14. Julie saved $11.62 on an item that was marked $ What was the rate of discount? 15. Find the missing sides in these sets A. 19 ft B. 8 ft of similar triangles. y ft 12 ft 14 ft k ft 26 m 10 m 32m w m 12 m x m 16. Sloan made 35 more cards than five times Monica s amount. If he made 245 cards, how many did Monica make? 17. Seven times the difference between eight times a number and five is the same as four times the sum of eleven times that number and twelve. Find the number. 18. Jeanne ran 15 miles more than twice Alison s distance. Together they ran 72 miles. How far did each girl run? 19. Two boats left the same dock at the same time. One traveled due north at 11 knots per hour. The second traveled due south at 14 knots per hour. After how many hours were the boats 150 knots apart? How far had each boat gone? 20. What number is 84% of 26? 21. The sum of nine times a number plus three is to eight as the difference between seven and six times the same number is to six. Find the number. 22. A square has an area of 990 square feet. How long is one of its sides? 23. Fifty-five is to thirty-three as twelve is to what number? 24. A rancher rode 32 miles on horseback over 8 hours. At this rate, how far can he go in 10 hours? 25. Emily has $4536 and deposits $35 each week into that account. Joanne has $2936 and deposits $55 each week into her account at the same bank. If this continues, when will their savings accounts contain the same amount? 32.

34 Solve completely the following word problems using the verbal model format: Verbal Models 1 to 8 Review 26. Two boats left the same dock at the same time. One traveled due north at 16 knots per hour. The second traveled due east at 15 knots per hour. After nine hours, how far apart were the boats? 27. A pyramid has a square base with an area of 289 feet 2 and a height of 7 yards. Find the volume of the pyramid. 28. The legs of an isosceles right triangle are each 11.5 inches long. How long is the triangle s base? 29. A 25-feet high statue and casts a 6-feet shadow while a building casts a 14-foot shadow. How high is the building? 30. The perimeter of a rectangle is 86 feet. Its length is 25 feet more than five times its width. What is the length and width of the rectangle? 31. John bought a $24.99 frying pan, a $48.89 set of dishes, and $19.56 of assorted cooking utensils. If he purchased all of these items during a 15% off sale, what was the final cost of all the items? 32. The diagonal of a rectangle measures 38 feet while the length is 21 feet. What is the width of the rectangle? 33. The page of your school yearbook is 8 ½ inch by 11 in. The left and right margins are ¾ in. and in, respectively. The space between pictures is 3 16 inch. How wide should you make each picture to fit three across the page? 34. The volume of a prism is 2536 in 3. Its length is 15 inches and its height is 13.5 inches. Find its width. 35. The first number is twelve times a second number while a third is three more than fourteen times the second number. The sum of all three numbers is Find the values of all three numbers. 36. A cylinder has a volume of feet 3 and a height of 20.1 feet. Find its radius. 37. Twelve times a number less than fifteen equals twenty-four times the same number plus one. Find the number. 38. Matt mows the 1200 ft 2 lawn in 85 minutes. At the same rate, how long will it take him to mow a 1600 ft 2 lawn? 39. Monroe traveled 125 miles on the first day, 479 miles of day 2, and 635 miles on day 3. If his average speed was 45 mph over the three-day period, how many hours was he actually driving during the trip? 40. Can the following dimensions form a right triangle? Prove your conclusion. 6 inches, 7 inches, 13 inches. 41. Jen works 4 hours less than twice Maggie s hours. If Jen works 42 hours this week, how long did Maggie work? 42. How far can a car travel on 14 gallons of gas if at the same rate, it can travel 1584 miles on 49.5 gallons of gas? 43. The volume of a sphere is yd 3. Its height is 3 feet. Find its radius. 44. The length of a rectangle is 42 meters less than six times its width. If the perimeter measures 1134 meters, find the length and width of the rectangle. 45. What is the original cost of a dress if you paid $ during a 15% off sale? 46. The area of a triangle is yard 2. If its base measures 14.8 yards, what is its height? 47. The population in Hargrove is 5,504 and is increasing at a rate of 15.2% each year. Across the state, Joshua has a population of 6,195 but is decreasing at a yearly rate of 19.8%. When will the populations be the same? 48. Mr. Roman is going to paint his house using a 20-foot ladder. He sets the base of the ladder 15 feet away from the house. How far up the side of the house will the ladder reach? 33.

35 Write an Equation for a Function Chapters 1 & 4 Find the first difference for x. Find the first difference for y. Find: Changein y Changein x Δ y = Δ x Find the y-intercept: the y-coordinate in (0, ) Write equation in the form: y = Δ y Δ x x + original value Find the missing values in this table: x y Change in y Change in x Find the missing values in each of these tables and, if possible, find the equation for the table. 1. x y x y x y x y

36 Find the missing values in each of these tables and, if possible, find the equation for the table. 5. x y x y x y x y x y x y x y x y

37 Relationship to Model 5 & 7 Problems Number of DVDs purchased Total Cost Find the equation that corresponds to these tables x y x y x y x y x y x y x y x y x y x y

38 37.

39 Scatterplots & Line of Best Fit The 1990 earnings per share and dividends per share for 35 electric utility companies (in the central United States) are shown in the table. 1. Enter the data into L1 and L2. 2. Create a scatterplot. 3. Write the line of best fit in space to right. 4. Write Correlation coefficient, r = Earnings Dividend Earnings Dividend Earnings Dividend Earnings Dividend The data in the table shows the age in years and the number of hours slept in a day by 28 infants who are less than one year old. 1. Enter the data into L1 and L2. 2. Create a scatterplot. 3. Write the line of best fit in space to right. 4. Write Correlation coefficient, r = Sleep Sleep Sleep Sleep Age (yrs) Age (yrs) Age (yrs) Age (yrs) (hrs) (hrs) (hrs) (hrs)

40 Keystone Algebra 1 Formula Sheet 39.

41 40.

42 41.

43 42.