Entering all sections of Algebra I Summer Math Packet

Transcription

1 Entering all sections of Algebra I Summer Math Packet This packet is designed for you to review all of your algebra skills and make sure you are well prepared for the start of Algebra or Honors Algebra I in the fall. We anticipate this packet will take about 10 hours to complete. Please complete each problem in order on separate paper. This assignment is due on the third day of class in the fall. At that time a short quiz will be given with problems taken directly from this summer assignment (including the ixl sections below). A portion of the quiz grade will be based on the completeness of your work from this packet. In addition to the written work, you need to complete the following ixl sections to a score of 60%. Please note that if at any point during the summer the name of the section does not match the numbers below, go by the section name. If ixl becomes frustrating, REACH OUT TO A TEACHER FOR HELP! This ixl assignment is meant to help you recall graphing transformations without having to do lots of tedious hand graphing. From the 8th tab on ixl: Number theory S.3 Write variable expressions: word problems Z.4 Add and subtract polynomials A.6 Least common multiple A.7 GCF and LCM: word problems J.1 Convert between percents, fractions, and decimals A.5 Greatest common factor V.3 Graph inequalities on number lines ** Please show all of your work as was required of you throughout the entire school year. Remember No Work-No Credit. We are really looking forward to the upcoming school year and hope you are too! Questions? any of us at the following: Barbara.Filler@stewardschool.org Jennifer.Maitland@stewardschool.org Todd.Serr@stewardschool.org Karen.Hudson@stewardschool.org Mark.Nugent@stewardschool.org

2 I.Writing Algebraic Expressions In algebraic expressions, letters such as x and w are called variables. A variable is used to represent an unspecified number or value. Practice: Write an algebraic expression for each verbal expression. 1. Four times a number decreased by twelve. Three more than the product of five and a number 3. The quotient of two more than a number and eight 4. Seven less than twice a number II. Order of Operations To evaluate numerical expressions containing more than one operation, use the rules for order of operations. The rules are often summarized using the expression PEMDAS Practice: Evaluate each expression [5 (3 7 4)] (4) ( 8) - 1-

3 5. 50 (1 3 ) (6 1) (5 ) III. Evaluating Algebraic Expressions To evaluate algebraic expressions, first replace the variables with their values. Then, use order of operations to calculate the value of the resulting numerical expression. Practice: Evaluate each expression. 1. 5x y y when x 4 and y 4. 3xy 4 7x when x and y 3 3. ( z x) x when x and z y z x y z when x 1, y 9, and z 4 - -

4 IV. The Real Number System The Real number system is made up of two main sub- groups Rational numbers and Irrational numbers. The set of rational numbers includes several subsets: natural numbers, whole numbers, and integers. Real Numbers- any number that can be represented on a number- line. o Rational Numbers- a number that can be written as the ratio of two integers (this includes decimals that have a definite end or repeating pattern) 3 7 Examples:, 5,,, 0.53, Integers--- positive and negative whole numbers and 0 Examples: -5, -3, 0, 8, Whole Numbers --- the counting numbers from 0 to infinity Examples: {0, 1,, 3, 4,.} Natural Numbers --- the counting numbers from 1 to infinity Examples: {1,, 3, 4, } o Irrational Numbers --- Non-terminating, non-repeating decimals (including, and the square root of any number that is not a perfect square.) Examples:, 3, 0, Practice: Name all the sets of which each number belongs

5 V. Integers Adding Integers with the SAME SIGNS (both numbers are positive or both numbers are negative) "Same Sign - Find the Sum" Add the numbers and keep the same sign. Example: -6 + (-) = -8 Adding Integers with DIFFERENT SIGNS (positive + negative or negative + positive) "Different Signs - Find the Difference" Subtract the numbers and keep the sign of the number with the highest absolute value. Example 1: -8 + = -6 Example : = 3 Multiplying and Dividing TWO Integers with the SAME SIGNS The answer is always POSITIVE. Example 1: Example : 9 Multiplying and Dividing TWO Integers with DIFFERENT SIGNS The answer is always NEGATIVE. Example 1: Example : 30 ( 6) (-6) (-14) (-9) (-9)(7) ( 8)

6 VI. Fractions

7 VII. The Distributive Property The Distributive Property states for any number a, b, and c: 1. a(b + c) = ab + ac or (b + c)a = ba + ca. a(b c) = ab ac or (b c)a = ba ca Practice: Rewrite each expression using the distributive property. 1. 7( x 4). 3(x 5) 3. 4(5x 9) 4. 1 (14 6 y ) 5. 3(7x 3x ) 6. 1 (16 x 1 y 4 z ) 4 VIII. Combining Like- Terms Terms in algebra are numbers, variables or the product of numbers and variables. In algebraic expressions terms are separated by addition (+) or subtraction (- ) symbols. Terms can be combined using addition and subtraction if they are like- terms. Like- terms have the same variables to the same power. Example of like- terms: 5x and 6x Example of terms that are NOT like- terms: 9x and 15x Although both terms have the variable x, they are not being raised to the same power To combine like- terms using addition and subtraction, add or subtract the numerical factor Example: Simplify the expression by combining like- terms 8x + 9x 1x + 7x = (8 + 7)x + (9 1)x = 15x + 3x = 15x 3x - 6-

8 Practice: Simplify each expression 1. 5x 9x +. 3q + q q 3. c + 4d 7d 4. 5x + 6x 1x 9x + 5. (3x 4y) + 5(x + 3y) 6. 10x 4(x + ) IX. Solving Equations with Variables on One- Side Practice: Solve each equation = b y = - 7-

9 3. 8k = x = n 8 = n 38 d 7. 3k m n 85 n x ( x 4) x 4 5x 8-8-

10 X. Percent of Change Practice: State whether each percent of change is a percent of increase or percent of decrease. Then find each percent of change. 1. original: 50 new: original: 7.5 new: 5. original: 14.5 new: original 50: new:

11 XI. Percent of Change (Continued) Practice: Find the final price of each item. When a discount and sales tax are listed, compute the discount price before computing the tax. 1. Two concert tickets: $8 Student discount: 8% 4. Celebrity calendar: $10.95 Sales tax: 7.5%. Airline ticket: $48.00 Frequent Flyer discount: 33% 5. Camera: $ Discount: 0% Sales tax: 5% 3. CD player: $14.00 Sales tax: 5.5% 6. Ipod: $89.00 Discount: 17% Tax: 5% - 10-

12 XII. Simplifying Exponents Simplify x x x m 4m 3m 4. 5y 6y 5. 8m 3 m xy 6xy x x xy 9. 9xy 7x m p - 11-

13 XIII. Solving Word Problems Practice: Write an algebraic equation to model each situation. Then solve the equation and answer the question. 1. A video store charges a one- time membership fee of $11.75 plus $1.50 per video rental. How many videos did Stewart rent if he spends $7.00?. Nick is 30 years less than 3 times Ray s age. If the sum of their ages is 74, how old are each of the men? 3. Three- fourths of the student body attended the pep- rally. If there were 130 students at the pep rally, how many students are there in all? 4. Sarah drove 3 hours more than Michael on their trip to Texas. If the trip took 37 hours, how long did Sarah and Michael each drive? - 1-

14 XIV. Graphing Linear Equations 1. y = 3x y x 3 3. x y y x 4-13-

15 XV. Finding Slope rise Slope( m) run When given two ordered pairs ( x1, y 1) and ( x, y ), use the slope formula of y y1 m. x x 1 Find the slope of the line through each pair of points. 1) (4, 17), (-, 13) ) (-8, 5), (-1, -4) 3) (-0, 8), (-16, 16) 4) (-8, -1), (-7, -7) 5) (3, 9), (3, 1) 6) (10, -), (-1, 5) Determine the slope of the line in each graph. 7) 8) - 14-