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SUMMER STUDY PACKET ALGEBRA II Dear prospective Algebra II student, This summer packet is designed to help you practice the concepts you learned in Algebra I and Geometry so that you are prepared to study Algebra II this fall. The content and philosophy of this summer packet is consistent with the math department goals and will enable you to: (1) value mathematics, (2) become confident in your ability to do mathematics, (3) become mathematical problem solvers, (4) communicate mathematically, and (5) reason mathematically. You are responsible for knowing how to do all the exercises noted before the first day of classes. If you do not know how to solve a problem you are expected to use the sources available to you (notes, handouts, books, Internet, etc.) to figure it out independently. The best study routine during the summer months is to constantly review topics and do a few problems each day, not attempt to do the entire packet the day before school starts. For your convenience, the answers to all of the exercises are included at the end of the document. Unless specifically stated or unless you are to give a decimal approximation to a square root, you should not use a calculator to do these exercises. You may, however, use your calculator to check your answers. Use separate sheets as necessary to show your work in a neat and organized way. Do not try to show all work on these worksheets; there isn’t enough room! The topics covered in this packet are: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Connections to algebra Properties of real numbers Order of operations Solving linear equations Graphing linear equations and functions Writing linear equations Solving and graphing linear inequalities Systems of linear equations Exponents and exponential functions Quadratic equations and functions Polynomials and factoring Rational equations and functions Radicals and trigonometry 1 This summer assignment will not be collected. You are responsible for knowing how to solve every single problem. Motivated students can work additional problems to gain confidence and familiarity with the more difficult topics at the following websites: 1. http://www.khanacademy.org/4 4 2. http://www.algebralab.org/lessons/lesson.aspx4 4 3. http://www.purplemath.com/modules/index.htm4 4 4. http://www.classzone.com/books/algebra_1/index.cfm?state=VA 4 4 Important: You will have a test on this summer packet study material during your second math class of the year. The test will consist of approximately twenty free response questions. You will not be able to use your calculator on the test. This exam will not count towards your math grade; however, those students who fail the exam will be obliged to attend remedial sessions during lunch or after school until they pass a similar exam.4 4 If you have any questions, please email [email protected] or [email protected]. Enjoy your summer and do your best! Sincerely, The ASFG Math Department 2 Solve each equation. 1) x 2) k 3) k 4) n State the quadrant in which the terminal side of each angle lies. 5) ° 7) ° Simplify each expression. 6) 8) ( r ) ( b ) x) n) n 9) r 11) b 13) ( ( 15) Divide. ° ° ( 10) 12) 14) 16) (n (k 17) ( k k k ) k 19) ( b b b ) b Solve each equation. 18) 20) ( x ( n ( m ) 21) m (n ) 23) n Solve each equation with the quadratic formula. 22) 24) p a n) ) ) k (a ) x) x ( p) 31) (y ) x y 30) x y ( y ) 32) x y yx Evaluate each function. 33) h(n) 35) h( x) n x ; Find h( x; Find h( ) ) ©Y LKOuctGaA uStopfOtawSaYrdem vL0LQCe.p n jAElKlT drMi2gOhgtwsY XrXe8sEeurIvfetdl.U H AM5aZdNeh UwoivtehZ kIknAfhixnSiUtDeR ZA3lngqe0bvrpa1 Y2t.J ( ( x m n m n y x y 34) f (a) 36) w(n) -1- n nm x n p x) 25) r r 26) b b 27) x 28) n Simplify. Your answer should contain only positive exponents. 29) n) n ( x a n ) ) ; Find f ( ; Find w( ) ) Worksheet by Kuta Software LLC Sketch the graph of each line. 37) x-intercept = , y-intercept = 38) x-intercept = 39) x y 40) 41) y x 42) y ©I RKDuxt9aU aSvojfitlwDaxrxeE 2L4LCCM.P A rAOlrlj PrdiLg5h2tasc nrOecsreprAvAeBdp.F L nMUaTdjea 1wzictWhR bICnYfIiLnniPtleL BA6lagre8bRrmaf u2w.9 -2- x , y-intercept = y x Worksheet by Kuta Software LLC Sketch the graph of each linear inequality. 43) y x 45) y 44) y x 46) y x Solve each system by graphing. 47) y x 48) y y x y 49) x y 50) x x y x Solve each compound inequality and graph its solution. 51) 53) 52) p x or x ©S JKCuktVaT iSGo2fTttwUaIrper pLfLlCH.3 Z SAmlRls wraiSgkhdtSs4 vrFecsXeircvEend4.K K PMqaudpeF XwDiStjh7 0IwnSfiiCnGictfe5 MAKlTgdejbMr8aZ E22.u 54) -3- x x y y m n or n Worksheet by Kuta Software LLC Write the slope-intercept form of the equation of each line. 55) 56) Find each product. ) 57) ( n )( v ) 59) ( v Evaluate each expression. 58) 60) 61) 62) ( )) 63) ( Solve each system by substitution. 64) 65) x 66) y ( x ( a ) )( a ) ( ) x y x y x y 67) The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 6 vans and 7 buses with 438 students. High School B rented and filled 6 vans and 6 buses with 384 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus. 68) The senior classes at High School A and High School B planned separate trips to Yellowstone National Park. The senior class at High School A rented and filled 7 vans and 6 buses with 375 students. High School B rented and filled 12 vans and 6 buses with 450 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus. 69) Mike and Nicole are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Mike sold 1 roll of plain wrapping paper and 12 rolls of holiday wrapping paper for a total of $218. Nicole sold 3 rolls of plain wrapping paper and 6 rolls of holiday wrapping paper for a total of $144. Find the cost each of one roll of plain wrapping paper and one roll of holiday wrapping paper. 70) Jimmy's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 11 adult tickets and 3 child tickets for a total of $75. The school took in $207 on the second day by selling 13 adult tickets and 12 child tickets. What is the price each of one adult ticket and one child ticket? Find the measure of each angle indicated. Round to the nearest tenth. 71) 72) A C 7.4 8 3.7 B A B 73) 3.5 C B A 74) C 10 4 7 C ©V 1KsuftGaa USTowfNt0w1aYrQeF bLVL5Cq.r R zARl8lK zrCixgVhktHsV frUexsaeHrBv4efdV.J n 6MFaEdhe6 5wXiStphL JIGnzfhiWnaiItbeS pAJlJgXeEb9rLaH I2v.u B -4- 16 A Worksheet by Kuta Software LLC Answers to 1) , 5) II 9) r 13) k 17) 21) 25) 29) 33) 37) x k , y x k 2) , 6) IV 10) 14) k x 18) 22) 26) 30) 3) , 7) III 11) b 15) n b b 19) n x , n m 34) 23) 27) , 31) x y 4) , 8) II 12) n 16) a b 20) n 24) 28) 35) 40) 41) 42) 43) 44) 45) 46) 47) ©R 2KLuttsal iS2oKfjtDw0ajrxek zLOLSCP.m A RAxlDl5 Drbi1gahstss3 hrlersIeor5vgemdR.L A FM5akdPez uwyixtuhq hIenofzienhiAtjew CAdlWgye5bHrgaL j2O.0 48) -5- , i 36) 39) ) i 32) 38) ( , n ( , ) Worksheet by Kuta Software LLC 49) 51) (, ) 50) p : 52) m : 53) x or x : 54) n or n : 55) y x 59) 63) 67) 69) 70) 73) (, 56) y ) x 57) v n n 60) a 61) 64) 65) ( , ) Van: 10, Bus: 54 68) Van: 15, Bus: 45 roll of plain wrapping paper: $14, roll of holiday wrapping paper: $17 adult ticket: $3, child ticket: $14 71) 46.6° 60.3° 74) 51.3° ©z MKmuVt2aF pSAomf4t5w0a1rte9 DLrLWC1.y D gAIlHlb brDiZgfhXtUsQ ZrMeCsPeLrlvteFdg.a C 5MqaGdeem 9wfijtvhc sIYnOfCiGnJiBtse1 QAqlvg6eqbtr7aZ k2I.y -6- 58) x 62) 66) ( , ) x 72) 42.8° Worksheet by Kuta Software LLC