Use your TI-84 graphing calculator to check as many problems as possible.

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1 Name: Date: Period: Dear Future Algebra Honors student, We hope that you enjoy your summer vacation to the fullest. We look forward to working with you next year. As you enter your new math class, you will be expected to have mastered certain skills. Some of these topics might need refreshing. So that you may be better prepared to begin your new math class this fall, the math department has prepared this review packet for you. Please use these problems as an indicator of weak areas and spend some time this summer reviewing at your own pace. We suggest completing a few problems each day, instead of waiting until the end of the summer to complete the problems. We recommend completing the packet by the middle of August. Be sure to bring your completed packet with you on the first day of math class. Your math teacher will expect you to be able to solve problems like these when school begins. If you are not able to complete a majority of these problems on your own, please contact the main office and ask to speak with Student Service regarding your math course selection for the coming school year. Show all your work when answering these questions. Attach any additional work to this packet. Please circle your final answers. Sincerely, Shenendehowa Mathematics Department If you get stuck or need a refresher on a particular concept, the following websites are good resources: Use your TI-84 graphing calculator to check as many problems as possible. 1

2 FRACTIONS In honors algebra, you will work with many fractions. Make sure you know how to do ALL operations of fractions (adding, subtracting, multiplying, and dividing), how to convert between mixed and improper fractions, and how to simplify fractions. ADDING AND SUBTRACTING: Directions: add and subtract the following fraction problems. Simplify answers into integers or simplified improper fractions. Helpful tips: In order to (+) and (-) fractions denominators must be the same Put whole number over 1 Simplify your signs MULTIPLYING: Directions: multiply the following fraction problems. Simplify answers into integers or simplified improper fractions. Helpful tips: Denominators do not have to be the same when multiplying. Make mixed fractions into improper fractions before multiplying You may simplify to make multiplication easier Remember to multiply across (numerators with numerators, denominators with denominators) Put whole numbers over 1 Simplify your signs

3 DIVIDING: Directions: divide the following fraction problems. Simplify answers into integers or simplified improper fractions. Helpful tips: You need to change division to multiplication and change the second fraction to its reciprocal ORDER OF OPERATIONS Order of operations is the law. Every problem must be done using order of operations. Make sure you know the order: Parenthesis Exponents Multiplication/Division (whichever comes first left to right) Addition/Subtraction (whichever comes first left to right) Directions: Evaluate the expressions using order of operations (16 + 9) (4 + 5) 3(7 10) ( ) ( 10+2) ( ) (3 6) 19. 3[ 7( ) ] 18 3

4 20. Absolute value is the distance from. ABSOLUTE VALUE 21. Absolute value of a number is always zero or. 22. Find the absolute value of each number or expression. a. 5 b. 3.4 c d Evaluate each: a b c d Matt said absolute value means to take the opposite of a number. Is he correct? Explain your answer. EVALUATING EXPRESSIONS Evaluating an expression means you are replacing variables with numbers in each problem. Evaluating expression is a basic skill in algebra that you need to master early on. Remember to follow the order of operations. When you evaluate expressions it is required that you show all steps. Helpful tips: 2 means 2 times x. xyz means x times y times z. Watch for positive and negative numbers. Simplify your signs. Example: Evaluate 3xx 2 when x = 2 3( 2) 2 3(4) 12 Directions: Evaluate the expressions using the given variables 25. What is the value of 2xx if x = 1 4

5 26. What is the value of 1 a 2 b + 1 if a = 6 and b = 3? What is the value of 4 xx 2 + yy 2 if x = 3 and y = 4? 28. What is the value of bb if a = 2 and b = 3? 2aa 29. What is the value of 3aa 4bb2 cc if a = 4, b = 1, and c = 1 3? 30. Evaluate cc dd 2 if c = 1 and d = Explain the difference of 2 2 vs. ( 2) 2 5

6 SIMPLIFYING EXPRESSIONS 32. Directions: Simplify the expressions using the distributive property. a. 5(3mm 6) b. 7(5kk 4) c. (1 + 2vv)5 d. 1 (9xx 30yy) e. 15(xx + 2yy 3zz) 3 Combining like Terms: Combining terms means you add the coefficients of each like term. Like terms: Like terms are terms that have the exact same combination of variables. Like terms 5x and 2x 3xy and 0.5xy 5yy 2 and 18yy 2 2xyy 2 zz 5 and 0.15xyy 2 zz 5 8 and 2 3mn and 4nm Unlike terms 2x and 4xy 6zz 2 and 5z 3xyy 2 and 1 2 xx2 y z and Give an example of two terms that are like and two terms that are unlike Helpful tips: Identify like terms first by using colors, highlighters, or marking them with circles, squares, etc. The sign of a term is in FRONT of it. Make sure you carry it through in your operations. It is usual to have more than one term in your final answer. 34. Simplify the expressions by combining like terms a. 2x x b. 12r r + 4 c. v + 12v d. 5nm + 11mn Distributing and combining Like Terms: There will be many problems in algebra when you will have to distribute and combine like terms. The distributive property must be done first before combining like terms. Examples: 3 + 2(xx + 3) 3 + 2x + 6 2x (4xx + 10) + 2(xx + 3) 2x x + 6 4x

7 Directions: Simplify expressions by distributing and then combining like terms (6aa 1) + 9a (40xx 28yy) + 5y m ( 2n + 4) + 2n( m + 3) TRANSLATING EXPRESSIONS There are several key word to represent our four main operations. List some key words that can represent each operation. 38. Ex.: plus, sum more than Adding Ex.: less than Subtracting Ex.: times Multiplying Ex.: divided by Dividing Important MUST KNOWS in translating expressions: When an expression uses less than or more than, it says that the order of the term must be switched. o 5 less than a number x must be written as x 5 When an expression uses the it indicates there are parenthesis. 7

8 o two times the sum of a number n and 6 must be written and 2(nn + 6) Translating From Verbal Expressions to Symbols and Numbers Directions: Translate the following verbal sentences into symbols and numbers. You may use any letter to represent the number unless otherwise indicated. 39. the sum of a number and four 40. triple the difference of a number and four 41. two less than the product of six and a number 42. the quotient of a number and four, diminished by six 43. half of a number exceeded by five 44. the sum of a number x and five, divided by the difference of a number y and three Translating From Word Problems to Symbols and Numbers Directions: Translate the following word problems into symbols and numbers. Example: Carlos signed up for a cell phone plan that is $30 a month and $0.45 per minute. Answer: m 45. On Monday, Jan had 72 eggs in her bakery. Each day she uses 12 eggs. Write an expression that could be used to model the number of eggs Jan has in x days. 46. Amir has saved up $75.00 to buy a new gaming system. He plans to save $10 each week until he can afford to buy the system. Write an expression that could be used to model this situation. 47. The Speedy Car Rental Company charges $35 per day plus $0.10 per mile. Write an algebraic expression that could be used to model this situation. 8

9 SOLVING EQUATIONS Solving equations means you are finding the value of the variable that makes the equation true. The steps in solving equations are opposite of the order of operations. Eliminate adding and subtracting first Eliminate multiplying and dividing second In order to undo operations, you must perform the opposite operation to both sides of the equation (addition and subtraction are opposites and multiplication and division are opposites) Solving one-step equations Directions: Solve the one step equations Example: x 5= x=8 48. v+8= =8x n= bb = v 5= x= Solving two-step equations Directions: Solve the two-step equations. Remember, undo-ing adding and subtracting comes before undo-ing multiplying and dividing Example: 6 = aa (4 ) 4= aa (4) 4 16=a 54. 3x 4= n= kk 3 5= xx 2 =12 9

10 y 1 4 = x = 2 3 Solving Multi-Step Equations Sometimes equations require more than the four basic operations. If you ever see a number with parenthesis (like 2(x+3)) you must distribute If you ever see like terms on the same side, you must combine them first (2x should be written as 2x+9) Example: 3(2x+1) 4=11 6x+3 4= 11 6x 1= x=12 x=2 Distribute first Combine like terms Solve a two-step equation Directions: Solve the multi-step equations below (n+5) = (8m+6)= x+4+3x 5= (x+1) =35 3(2x 5) 64. n 9 8 = 12 10

11 INEQUALITIES Solve the inequality. Graph the solution. Remember that when solving an inequality, if we multiply or divide each side of the inequality by a negative value, we must REVERSE the inequality symbol a x m > d > School Carnival You are in charge of purchasing helium balloons for a school carnival. You have been given $42 to buy the balloons. The balloons cost $1.60 each. a. Write and solve an inequality that gives the possible numbers b of balloons you can buy. b. What is the greatest number of balloons that you can buy? MEASURES OF CENTRAL TENDENCY 70. Tomato Plants The heights (in inches) of seven tomato plants are 36, 43, 53, 40, 38, 41, and 43. a. What is the range of the tomato plant heights? b. Find the mean, median, and mode(s) of the tomato plant heights. 11

12 c. Which measure of central tendency best represents the data? Explain. PERCENTS Solve each: 71. Identify the percent of change as an increase or decrease. Then find the percent of change. Original: 80 New: Subway - The price for a token to ride a city s subway system is changing from $1.25 to $1.50. Find the percent of change. 73. Research Paper - You have written 4 pages of a research paper. This is 80% of the number of pages you need to complete paper. How many pages is the paper supposed to be? SETS OF REAL NUMBERS Select the response that correctly answers the question. 74. Name the set(s) of numbers to which 1.68 belongs. a. Rational numbers b. Natural numbers, whole numbers, integers, rational numbers c. Rational numbers, irrational numbers d. None of the above 75. Name the set(s) of numbers to which -5 belongs. a. Whole numbers, natural numbers, integers b. Rational numbers c. Whole numbers, integers, rational numbers d. Integers, rational numbers 76. Which set of numbers is the most reasonable to describe the number of desks in a classroom? a. Whole numbers b. Irrational numbers c. Rational numbers d. Integers x 1 = 2.1 a. Inverse Property of Multiplication b. Multiplication Property of 1 c. Identity Property of Addition 12

13 d. Identity Property of Multiplication x = x a. Identity Property of Addition b. Multiplication Property of 0 c. Commutative Property of Addition d. Inverse Property of Multiplication = 1 a. Identity Property of Division b. Inverse Property of Addition c. Inverse Property of Multiplication d. Multiplication Property of (-8.2) = 0 a. Inverse Property of Addition b. Addition Property of 0 c. Identity Property of Addition d. Inverse Property of Multiplication = a. Inverse Property of Addition b. Associative Property of Addition c. Commutative Property of Addition d. Inverse Property of Multiplication 82. (ab)3 = a(b3) a. Inverse Property of Multiplication b. Associative Property of Addition c. Associative Property of Multiplication d. Commutative Property of Multiplication GRAPHING REVIEW Select the response that correctly answers the question. 83. What are the coordinates of Point A? a. (-1, 1) b. (1, 1) c. (-1, -1) d. (1, -1) 84. In which quadrant of on which axis would you find the point (-2, -4)? 13

14 a. Quadrant II b. Quadrant III c. Quadrant IV d. y-axi 85. The point (a, b) is in Quadrant II when a < 0. a. always b. sometimes c. never 86. Which of the scatter plots shows a positive correlation? Answer each: 87. Given y 3x = 5, identify slope and y-intercept. 88. Graph 2y = 6x + 4 using a table of values. 14

15 89. Write the equation of a line passing through points (4, -4) and (-2, 8). 90. What is the slope of the following line? 15