Algebra Summer Packet 017 Dear Future Algebra student, Rising Algebra Students Stone Middle School 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 also attach the links to the video lesson for each topic. If you need a refresher on particular topics, please watch the video and practice some problems on each link. We recommend completing the packet by the middle of August. Be sure to bring your completed packet with you on the first day of school. Your math teacher will expect you to be able to solve problems like these when school begins. The packet problems will be reviewed during the first week of school and students will be assessed on the skills. If you are not able to complete a majority of these problems on your own, please contact the main office (70-61-5500) and ask to speak with Student Services regarding your math course selection for the coming school year. Show all of your work when answering these questions. Attach any additional work to this packet. Please circle your final answers. Sincerely, Stone Middle School Mathematics Department Name: Date: 1
Algebra Summer Packet 017 If you get stuck or need a refresher on a particular concept, the following websites are good resources: o http://www.purplemath.com/ o http://www.khanacademy.org/ ORDER OF OPERATIONS Order of operations is the law. Every problem must be done using order of operations. Make sure you know the order: Watch the video : https://www.khanacademy.org/math/algebra-basics/basic-alg-foundations/algbasics-order-of-operations/v/introduction-to-order-of-operations 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 1. 10 (16 + 9) 6 5. 16(4 + 5) (7 10). 5 + 0 6 4 6. 1 (5 81) 5. (6 7 7 ) 4. ( + ) (6 ) 7. (10 + ) 1 (4 9)
Algebra Summer Packet 017 ABSOLUTE VALUE Absolute value is the distance from 0. It is always positive. Directions: Find the absolute value of each number or expression. 8. 5 9..4 10. 101.101 11. 5 Evaluate the inside first before taking the absolute value. 1. 8 10 1. 1 14. 4+ 18 6 15. 5+ 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. No points will be given for problems with no credit. Helpful tips: x means times x. xyz means x times y times z. Watch for positive and negative numbers. Simplify your signs. Squaring a negative number will be positive. Example: Evalute x when x = ( ) (4) = 1. Visit the following website: https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1- substitution/e/evaluating_expressions_
Algebra Summer Packet 017 Directions: Evaluate the expressions using the given variables 16. What is the value of 4x y if x = and y =? 17. What is the value of x + 8 if x = 1? 18. What is the value of 1 a b+ 1 if a = 6 and b =? 19. What is the value of n m if 5 m = and n =? 7 0. What is the value of 4 x + y if x = and y = 4? b 1. What is the value of if a = and b =? a 4
Algebra Summer Packet 017. What is the value of b 4ac if a = 1, b =, and c = 1?. What is the value of a 4b 1c 1 if a = 4, b = 1, and c =? 4. What is the value of 4x y if x = and y =? 5. Evaluate c d c d if = 1 and = 5. SIMPLIFYING EXPRESSIONS Distributing: The distributive property a( b + c) = ab + ac states that a number being multiplied by a parenthesis must be distributed to each number in the parenthesis. The key operation in the distributive property is to multiply. If a is a negative number, make sure to carry the negative when you multiply with each value in the parenthesis. Examples: ( x + 4) ( x) + ( 4) x + 8 1 (4 x y ) 1 1 4x y x y (5 y) ( 5) + ( y) 15 + 6y Directions: Simplify the expressions using the distributive property 5
Algebra Summer Packet 017 Watch the video : https://www.khanacademy.org/math/algebra-basics/alg-basics-algebraicexpressions/alg-basics-distributive-property/v/distributive-property-with-variables-exercise 6. 5(m 6) 7. 7(5k 4) 8. (1+ v) 5 9. 1 (9x 0 y) 0. 6(7 + x) 1. 15( x+ y z) Like terms: Like terms are terms that have the exact same combination of variables. Like Terms 5x and x xy and 0.5xy 5y and 18y 5 5 xy z and 0.15xy z 8 and Unlike Terms x and 4xy 6z and 5z xy and z and 1 xy. Give an example of two terms that are like and two terms that are unlike Combining Like Terms: Combining terms means you add the coefficients of each like term. Examples: x+ 5x= + 4y + 6y = 7x 1+ 10y xy + y + 4xy = 6xy + y Helpful tips: 6
Algebra Summer Packet 017 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. A variable without a coefficient in front is automatically 1. Watch the video on the following link: https://www.khanacademy.org/math/cc-sixth-grade-math/cc- 6th-equivalent-exp/cc-6th-combining-like-terms/v/combining-like-terms- Directions: Simplify the expressions by combining like terms. x+ 11+ 6x 6. 1r+ 5+ r+ 4 4. v+ 1v 7. n 4 9 5. 5n+ 11n 8. 6y 4+ y 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: + ( x + ) + x + 6 x + 8 1 (4 x+ 10) + ( x+ ) x+ 5+ x+ 6 4x + 11 Directions: Simplify expressions by distributing and then combining like terms 9. 10(6a 1) + 9a 41. 5( n+ 4) + ( n+ ) 40. 5n+ (6 + 7 n) 7
Algebra Summer Packet 017 TRANSLATING EXPRESSIONS There are many ways to represent expressions. It can be expressed in: There are several key words to represent our four main operations. List some key words that can represent each operation. example: plus, sum Adding example: less than Subtracting example: times Multiplying example: 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. o two times the sum of a number n and 6 must be written as ( n + 6) Translating From Verbal Expressions to Symbols and Numbers 8
Algebra Summer Packet 017 Directions: Translate the following verbal sentences into symbols and numbers. You may use any letter to represent the number unless otherwise indicated. 4. the sum of a number and four 4. two times the sum of a number and four 44. two less than the sum of six and a number 45. six less than the quotient of a number n and four 46. three more than the product of five times a number 47. the sum of some number x and five divided by the difference of some number y and three 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 9
Algebra Summer Packet 017 Example: x 5= + 5 + 5 x = 8 48. v + 8 = 6 51. 104 = 8x 49. 15 + n = 9 b 5. = 6 18 50. v 15 = 7 5. 17x = 04 Watch the video: https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-twosteps-equations-intro/v/why-we-do-the-same-thing-to-both-sides-two-step-equations 10
Algebra Summer Packet 017 Solving two-step equations Directions: Solve the two-step equations. Remember, undo-ing adding and subtracting comes before undo-ing multiplying and dividing a Example: 6= + 4 a 4 4 = 4 4 16 = a 54. x 4 = 11 58. 1 x 1 = 4 4 55. 5 5x = 0 59. 7n + 4 = 11 k 56. 5 = 11 60. 8x = 1 57. x = 1 4 61. + x = 5 11
Algebra Summer Packet 017 Solving Multi-Step Equations Sometimes equations require more than the four basic operations. If you ever see a number with parenthesis (like ( x + ) ) you must distribute If you ever see like terms on the same side, you must combine them first ( x + 4+ 5 should be written as x + 9) Example: ( x + 1) 4 = 11 6x + 4 = 11 6x 1 = 11 + 1 + 1 6x = 1 x = Distribute first Combine like terms Solve a two steps equation Directions: Solve the multi-step equations below. 6. ( n + 5) = j 65. 5 + 9 = 14 6. 10 = 10( k 9) 66. 1 (8 x + 6) = 1 64. x+ 4 + x 5 = 11 67. ( x+ 1) + (x 5) = 5 1