Algebra 2 Pre-AP Summer Packet. PART I Solve the equation. Show all work on a separate sheet of paper. 1.) 5w 2 2w 5. 2.) 5b 4 2b 8. 6.

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1 Algebra 2 Pre-AP Summer Packet PART I Solve the equation. Show all work on a separate sheet of paper. 1.) 5w 2 2w 5 2.) 5b 4 2b 8.) 2z 6z 25 4.) 2c14 6 4c 5.) p5 25 4p 6.) 17 6r 25 r 12 r 2 r 5 r 7.) 2b 4b 2 8.) m5 6m 1 9.) 1 w 4 4 w 4 4w 11.) w 2 4 w 1 12.) 2 k 1 k ) 1.) 2.25b b ) 5x 4 5x ) x 5 x ) 52 x 2x 7 x 17.) 24 x 7 6x 1 18.) x x 9 2x 5 19.) 6 42 x 26x 4 2.) 25x x x 2 21.) 2x 1 x 9 4 x 22.) y2 y ) 6x2 x ) x x Solve for x. Then find the length of each side of the figure. 25.) Perimeter = ) Perimeter = 15

2 Solve for x unless otherwise stated. State restrictions if necessary. Show all work on a separate sheet of paper. 27.) Solve for "r" y r a 28.) Solve for "H" V 1 a b x x 2 r H 29.) 1 ; when.) x y 2 z; solve for y 1.) I prt; solve for t 2.) 5a6b 9; solve for b Mm.) de 4 f 5 g; solve for e 4.) F G ; solve for M 5.) qr s t; solve for q r ; solve for F 7.) 9 6.) C F ax b c 8.) d x e x 9.) y px c bk 4.) h 4; when r 41.) cx dx e r 42.) Solve the equation ax b cx d for x in terms of a, b, c, and d. Under what conditions is there no solution? Under what conditions are all real numbers solutions? For each of the following, define the variable(s), write an equation, and solve. EX 1.) The table shows the number of seats in each of the first four rows of an auditorium. The remaining 1 rows follow the same pattern. Find the number of seats in the last row. Row Number of Seats EX 2.) You are hanging three pictures on a wall that is 16 feet wide. The widths of the three pictures are 2,, and 4 feet. You want the space between the pictures to be the same, and the spaces to the left and right of the group to be 6 inches more than the space between the adjacent pictures. How should you position the pictures? EX.) Your long distance phone charges 8 cents per minute for weekday and daytime calls. It charges 5 cents per minute for night and weekend calls. If you made a total of 22 minutes of long-distance calls during one billing cycle, and your bill was $1.16, how many minutes of night and weekend calls did you make? EX 4.) The Chans invested twice as much money at 8% as at 6%. If the total of the simple interest for one year is $66, what is the amount the Chans invested at 6%?

3 For each of the following, define the variable(s), write an equation, and solve. Show all work on a separate sheet. 1.) Twenty-four subtracted from six times a number is 88. Find the number. 2.) Five times a number decreased by twelve is 4 more than the original number. Find the number..) The sum of four consecutive odd integers is 184. Find the four integers. 4.) The sum of three integers is 242. The second number is three more than twice the first and the third number is nine less than five times the first. Find the integers. 5.) The length of one side of a triangular flower bed is ft less than twice the length of the shortest side and the length of the third side is ft greater than the length of the shortest side. If the perimeter is 6 ft, what is the length of the shortest side? 6.) The Leos invested part of $12, at 4% simple interest and the rest at 6% simple interest per year. The total interest for one year was $64. Find the amount invested at 4%. 7.) Victor bought $8.4 worth of stamps. He bought times as many $.17 stamps as $.25 stamps and 4 times as many $.2 stamps as $.25 stamps. Find the number of $.25 stamps he purchased. 8.) Denise drove to her parent s house at a rate of 7 km/h. She came back by the same route, but drove at a rate of 8 km/h. If the round trip took her hours, what is the distance between her house and her parent s house? 9.) Two planes leave Hobby Airport at noon. One flew east at a certain speed and the other flew west at twice that speed. The planes were 27 miles apart in hours. How fast was each plane traveling? 1.) Assume that a, b, and c are integers and a. Prove that the solution to the linear equation ax b c must be a rational number. 11) Write an equation that represents the table shown below. x y ) You have a piece of wood that is 72 inches long. You cut the wood into three pieces. The second piece is 6 inches longer than the first piece. The third piece is 6 inches longer than the second piece. Draw a diagram and then write and solve an equation to find the lengths of the three pieces. 1) You want to tape five posters on a wall so that the spaces between posters are the same. You also want the spaces at the left and right of the group of posters to be three times the space between any two adjacent posters. The wall is 15 feet wide and the posters are 1.5 feet wide. Draw a diagram and then write and solve an equation to find how to position the posters. 14) A moving company weights 2 boxes you have packed that contain either books or clothes and says the total weight is 44 pounds. You know that a box of books weighs 4 pounds and a box of clothes weighs 7 pounds. Write and solve an equation to find how many boxes of books and how many boxes of clothes you packed. 15) You are hanging fliers around a cylindrical kiosk that has a diameter of 5 feet. You want to hang 15 fliers that are 8.5 inches wide so they are evenly spaced. How far apart should the fliers be placed?

4 PART II Natural Numbers: N, counting numbers {1,2,, } Number Systems & Properties Whole Numbers: W, {,1,2, } Integers: Z, { -2, -1,, 1, 2 } Rational: Q, any number that can be expressed in the form a b, where a and b are integers and b Irrational: I, nonterminating, nonrepeating decimals Real Numbers:, union of Rational and Irrational Venn Diagram Q Z W N Real Numbers I Name all the sets of numbers to which each belongs. 1.) 2.) 81.) 11 4.) Graph each of the following on a number line. 5.) all whole numbers less than 5 6.) all integers between - and 4 7.) all integers between - and 4 inclusive 8.) all natural numbers greater than -2 9.) all real numbers less than or equal to 4 Properties of Real Numbers Property Addition Multiplication Commutative a b b a ab ba Associative ( a b) c a ( b c) ( ab) c a( bc) Identity a a aa a 1 a 1 aa Inverse a a a a ; 1 1 a1; a 1 a a Distributive of Multiplication over Addition a( b c) ab ac; ( b c) a ba ca Multiplicative Property of Zero a a

5 Name the property illustrated by each equation below. 1.) 5x 4y x 5x x 4y 11.) 5x y 5x 1y 12.) 2x y 2xy 1.) 6 ( 6) y y 5 x y 5x 5y 14.) 15.) x x x x ) n n n 17.) x2y 2 x y 18.) 1 4 y 1 y 4 19.) 4n 4n Complete the table. Place an x under the name(s) of the sets of numbers to which each number belongs. Natural Whole Integer Rational Irrational Real

6 Graph each of the following on a number line. 2. real numbers between -4 and whole numbers greater than integers between -6 and -2 inclusive 2. natural numbers less than real numbers less than 7 and greater than 2 True or False: If false, give an example of a number that shows the statement is false. 25. Every real number is irrational. 26. Every integer is a rational number. 27. Every rational number is an integer. 28. Every natural number is an integer. 29. Every irrational number is a real number.. Every real number is either a rational or an irrational number. Write the additive inverse and the multiplicative inverse for each of the following Tell whether the statement is always, sometimes, or never true for real numbers a, b, and c. Explain. 5. a b c a b c 6. abc ab c 7. a b c a b c 8. a b c a b c 9. ab c ab ac 4. ab c ab ac 41. Show that a c a b for nonzero real numbers a, b, c, and d. Justify each step in your reasoning. b d c d 42. Let a b and c d be two distinct rational numbers. Find the rational number that lies exactly halfway between a b and c d on a number line.