Summer Packet

Transcription

1 Summer Packet The purpose of this summer work is to help prepare you for your upcoming math class. The work will tap into your prior knowledge and review past content, concepts, and skills. Our expectation is that you arrive on the first day of school able to demonstrate mastery of the material in this packet. In order to achieve this, please allow yourself plenty of time to work on the problems, use your resources (such as the review materials provided, Khan Academy, or the math faculty here at the school during the summer to specifically help with the summer work (July 17 Aug 17th on Tues and Wed from 8:30 to 10:30)), and work each problem to completion. You will use Khan Academy to complete the summer work for Algebra 2 Accelerated. This work will be due on Friday, September 8 th, and will be 3% of your first quarter grade. 10% will be deducted for each day it is late. Summer work will not be accepted after Sept. 13 th. Each math problem in the packet will be graded as follows: Summer Work Assignments Khan Academy (found on page 2) In the event you do not have access to technology, you may complete the Written Packet (found on page 3 to 22) Grading Evidence Perseverance Two points will be awarded for each correct answer in a row. (See page 2 for more details.) Two points will be awarded for the correct answer. Students will complete five problems in a row correctly per each topic assigned. Students will complete five problems correctly per topic. Students have an infinite amount of problems to attempt on Khan Academy. If students are struggling, they can access helpful videos on Khan and/or example problems. Students will show their work when solving a problem. If they are struggling, they will seek out extra help. Your teacher might choose to give a non-graded assessment on the first week of school in order to target remediation strategies and requirements. A note from your Algebra 2 Accelerated teacher: This packet will help you to sharpen your skills and be ready for the first day of the school year. These problems shouldn t take too long. HAVE A GREAT SUMMER!!!! 1

2 Khan Academy YOU MUST LOG IN TO HAVE KHAN ACADEMY GIVE YOU CREDIT FOR YOUR WORK. How to Log Into Khan Academy to complete your summer work: If you do not have an account yet: 1. Go to khanacademy.org 2. Click on Start Learning Now 3. Click on Sign in with Gmail 4. Create an Account with your gapps account 5. Type in the Search Engine Bar The Topic you would like to complete or click on the link provided If you have an account already with your gapps 1. Go to khanacademy.org 2. Click on the log in button on the top right hand side of the screen 3. Log in with your and password 4. Type in the Search Engine Bar the Topic you would like to complete or click on the link provided Summer Work Topics for Algebra 2- YOU MUST LOG IN TO HAVE KHAN ACADEMY GIVE YOU CREDIT FOR YOUR WORK. SEE ABOVE. a. Special Products of Binomials b. Graphs of Two Variable Inequalities c. Linear Models Word Problems d. Two Step Equation Word Problems e. Linear Equations with Unknown Coefficients f. Simplify Square Root Expressions: No Variables (advanced) g. Equations with Parentheses h. Pythagorean Theorem i. Adding and Subtracting Negative Fractions j. Simplify Rational Expressions: Common Monomial Factors *Khan Academy may ask for less than five in a row on some sections instead of five correct in a row. You may have to click on practice again in order to complete five problems for these sections. Students MUST complete five problems in a row correctly for all of the topics above to earn full credit. Partial credit will be awarded as described below. If you struggle on any of the problems, please reference the videos for each topic and/or look for hints found on the right hand side of your screen when attempting a problem. Please note you do not have to complete all problems in one sitting. Khan Academy will remember where you left off. Be sure to log-in every time you do additional work! Grading for Khan Academy for each topic: Credit can only be awarded for any work completed after June 1 st, correct in a row: 0 points 1 correct in a row: 2 points 2 correct in a row: 4 points 3 correct in a row: 6 points 2

3 4 correct in a row: 8 points 5 correct in a row: 10 points Written Packet (Only do this packet if you do not have access to technology to complete the Khan Academy assignment.) Polynomial Special Products 2 Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Simplify the following binomials. Determine the answer that is best. SHOW ALL WORK! 1. ( 8x + 10)(10x 10) a. 2x x b. 80x x c. 2x x 2. (3x + 7)( 4x + 7) a. 12x 2 7x + 49 b. x x + 14 c. x 2 7x (4x + 7) 2 a. 8x x + 49 b. 8x c. 8x (5x + 10)( x + 3) a. 5x 2 + 5x + 30 b. 4x x + 13 c. 4x 2 + 5x (8x + 5)(10x + 8) a. 80x x + 13 b. 18x x + 40 c. 18x x

4 6. (9x 9)(10x + 5) a. 90x 2 131x 4 b. 90x 2 31x 4 c. 90x 2 45x ( 4x 3) 2 a. 16x x 6 b. 16x 2 6 c. 8x (6x 7)(8x + 3) a. 14x 2 18x 21 b. 14x 2 66x 21 c. 14x x ( 4x 4)( 5x + 7) a. 20x 2 48x + 3 b. 9x x + 3 c. 20x 2 19x ( 8x 9)( 3x 3) a. 24x x 12 b. 11x x + 27 c. 11x 2 3x 12 4

5 Graphing 2 Variable Inequalities Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Answer each question completely. SHOW ALL WORK! 1. Graph y < 4 x 8 and determine if the points ( 8, 3) or ( 9, 7) are solutions Graph y > 1 x + 6 and determine if the points ( 7,8) or ( 8, 3) are solutions Graph 2x + 2y < 14 and determine if the points ( 7,1) or ( 6,5) are solutions. 5

6 4. Graph x + 4y 36 and determine if the points (6,7) or (9,4) are solutions. 5. Graph y x + 4 and determine if the points (5, 4) or (8,0) are solutions Graph y > 5x + 5 and determine if the points (0,5) or ( 5,9) are solutions. 6

7 7. Graph y < 3 x + 2 and determine if the points ( 4,8) or (9, 9) are solutions Graph y < 5 x 8 and determine if the points (7,0) or ( 6, 3) are solutions Graph y x 3 and determine if the points (8,4) or (9, 4) are solutions. 7

8 10. Graph 3x y < 7 and determine if the points ( 5,8) or (9,3) are solutions. 8

9 Linear Models Word Problems Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Answer each question completely. SHOW ALL WORK! 1. Mariana tried to drink a slushy as fast as she could. She drank the slushy at a rate of 4.5 milliliters per second. After 17 seconds, milliliters of slushy remained. How much slushy was originally in the cup AND how long did it take Mariana to drink all the slushy? 2. William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it s completely full. If he uses 85 marbles, he will have to add 20.9 liters of water. What is the volume of each marble AND how much water is necessary if William uses 200 marbles? 3. Agent Bourne transferred classified files from the CIA mainframe into his flash drive. The drive had 36.5 megabytes on it before the transfer, and the transfer happened at a constant rate. After 125 seconds, there were 549 megabytes on the drive. The drive had a maximum capacity of 1000 megabytes. What was the speed of the transfer AND how long did it take the drive to be completely full? 4. Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After reading for 4 hours, he had 330 pages left to read. How long is the book AND how long did it take Naoya to read the entire book? 5. Renata moved to her new home a few years ago. Back then, the young oak tree in her back yard was 190 centimeters tall. She measured it once a year and found that it grew at a constant rate. 3 years after she moved into the house, the tree was 274 centimeters tall. How fast did the tree grow AND how many years passed from the time Renata moved in until the tree was 344 centimeters tall? 9

10 6. Andrei has a glass tank. First, he wants to put in some marbles, each of which has a volume of 0.04 liters. Then, he wants to fill the tank with water until it s completely full. If he uses 50 marbles, he will have to add 33 liters of water. What is the volume of the tank AND how many marbles does he need to fill the tank if he has exactly 20 liters of water? 7. Alexandra has a stand in the marketplace where she sells ground cumin. She has a fixed amount of weekly expenses, and she sells her cumin for $7.20 per kilogram. If she sells 90 kilograms of cumin, her weekly net profit is $414. What are Alexandra s weekly expenses AND how much cumin does Alexandra have to sell to cover her weekly expenses? 8. Shryia read a 481 page long book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 403 pages left to read. How fast was Shryia reading AND how long did it take her to read the entire book? 9. A battery was charged. Each minute, the percentage of the battery s capacity that was charged increased by 2.5 percent. After 17 minutes of charging, the battery was 61.5 percent full. How full was the battery when the charging began AND how long did it take the battery to be fully charged? 10. A big cruise ship dropped anchor off the Caribbean island of Barbuda. The heavy anchor was released from a height of 54 meters above the water s surface, and it fell at a constant rate. After 35 seconds, the anchor was 9 meters below the water s surface. How fast did the anchor drop AND how long did it take the anchor to reach the water s surface? 10

11 Two-Step Equations Word Problems Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Answer each question completely. SHOW ALL WORK! 1. The perimeter of a rectangle is 34 units. Its width is 6.5 units. Write an equation to determine the length, l, of the rectangle AND find the length of the rectangle. 2. Carl is boarding a plane. He has 2 checked bags of equal weight, and a backpack that weighs 4 kilograms. The total weight of Carl s baggage is 35 kg. Write an equation to determine the weight, w, of each of Carl s checked bags AND find the weight of each of his checked bags. 3. Fabio and Carlos play on a basketball team together. Last game, Fabio had 7 points less than 2 times as many points as Carlos. Fabio scored 31 points in the game. Write an equation to determine the numbers of points, c, Carlos scored last game AND find the number of points Carlos scored last game. 4. Josh is hiking Glacier National Park. He has now hiked a total of 17 km and is 2 km short of being ½ of the way done with his hike. Write an equation to determine the total length (in kilometers), h, of Josh s hike AND find the total length of Josh s hike. 5. Raymond just got done jumping at Super Bounce Trampoline Center. The total cost of his session was $ He had to pay a $7 entrance fee and $1.25 for every minute he was on the trampoline. Write an equation to determine the number of minutes, t, that Raymond was on the trampoline for AND find the number of minutes he was on the trampoline for. 6. Tim answered all the questions on his math test but got 10 answers wrong. He received 4 points for every correct answer, and there was no penalty for wrong answers. His score was 76 points. Write an equation to determine the total number of questions, q, on Tim s math test AND find the total number of questions of his math test. 11

12 7. 64 is 4 times the difference between Sarah s age, a, and 44. Assume Sarah is older than 44. Write an equation to determine Sarah s age, a, AND find Sarah s age. 8. Ann took a taxi home from the airport. The taxi fare was $2.10 per mile and she gave the driver a tip of $5. Ann paid a total of $ Write an equation to determine the distance (in miles), x, between the airport and Ann s home AND find the distance between the airport and Ann s home. 9. Tony misplaced 7 stamps from his collection. He knows that each stamp of his is worth $0.15 and that the total value of them is now only $5.55. Write an equation to determine the number of stamps, s, that Tony originally had AND find the number of stamps he originally had. 10. Floyd is an aspiring music artist. He has a record contract that pays him a base rate of $200 a month and an additional $12 for each album that he sells. Last month he earned a total of $644. Write an equation to determine the number of albums, a, Floyd sold last month AND find the number of albums Floyd sold last month. 12

13 Linear Equations with Unknown Coefficients Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Solve the following equations for the specified variable. Determine the answer that is best. SHOW ALL WORK! 1. x: 3xyz 8y + 10z + 10 = 10y + 4z 9 a. x = 2y+6z 1 3yz b. x = 2y+6z+19 3yz c. x = 18y+6z+19 3yz 2. r: 3r+7s 4 = 7r 3t 5 a. r = 12t 35s 43 b. r = 12t 35s 13 c. r = 12t+35s a: 7abc + 4b + 7c + 7 = 7b 6c 6 a. a = 11b c 1 7bc b. a = 3b+13c+13 7bc c. a = 3b+13c 1 7bc 4. r: 5rs + 10rt r + 3 = 7s + 2 a. r = 7s 1 5s+10t 1 b. r = 7s+5 5s+10t 1 c. r = 7s 1 5s 1 5. r: 8rs + 5rt + 10r + 8 = 9s + 4 a. r = b. r = 9s 8s+5t s+5t+10 c. r = 9s 4 8s+3t+10 d. None of the abov 13

14 6. r: 9r 9s 10 = 5r 3t 9 a. r = 30t 81s 131 b. r = 30t 81s 31 c. r = 30t 81s f: fgh 4g 3h + 1 = 3g 5h + 10 a. f = g+2h 9 gh b. f = g+2h 11 gh c. f = 7g+8h 9 gh 8. x: 6xy 7xz + 8x + 3 = 6y + 6 a. x = 6y+3 y 7z+8 b. x = 6y+3 6y 7z c. x = 6y+3 6y z+8 9. m: 4m 4n 5 = 7m+4p 4 a. m = 20p 16n 19 b. m = 20p 16n 51 c. m = 20p+16n f: 8fg 9fh 3f 3 = 5g 6 a. f = 5g+3 g+9h+3 b. f = 5g+3 8g+9h+3 c. f = 5g+3 17g+9h+3 14

15 Simplifying Square Root Expressions Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Simplify the following expressions. SHOW ALL WORK!

16 Equations with Parenthesis Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Solve the following equations for the specified variable. Determine the answer that is best. SHOW ALL WORK! 1. y: 4( 2 + 2y) = 2 16y 6. r: r = r 1 ( 9r 2) t: 24 16t = 5t 3(9t 4) 7. n: ( 4 3 5n 2 ) = n 2 3. k: 7 = 4k ( 2k 1) 8. z: z = 3.2( 6z 1) 4. r: 11 r = (2r 3) 9. p: 4p (4 5 4p 3 ) = p 3 5. r: 2 = 4r 2( 4r + 2) 10. n: ( n) = n 16

17 Pythagorean Theorem Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Determine the value of the indicated side by using the Pythagorean Theorem. SHOW ALL WORK! A 3. A 17

18 4. A 5. A 6. A 18

19 7. A 8. A 9. A 19

20 10. A 20

21 Adding and Subtracting Negative Fractions Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Simplify the following. SHOW ALL WORK!

22 Simplifying Rational Expressions Directions: You are strongly encouraged to complete all problems, however in order to earn full credit five of the following problems must be done CORRECTLY. Simplify the following. SHOW ALL WORK! 1. 12y 5 72y 5. 99r 5 132r r 4 144r t 5 32t n 3 20n k 99k z 4 110z r 3 60r p 2 36p n2 10n 2 22