Alegbra 1 HONORS Summer Packet

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:Welcome to Algebra 1 Honors!This summer packet is for all students enrolled in Algebra 1 Honors atHerndon Middle School for Fall 2019. The packet contains prerequisite skillsthat you will need to be successful in Algebra 1 at the honors level.Please spend some time this summer keeping these skills and concepts freshin your mind. The packet is due the first week of school when you will have anassessment on the content. This assignment should be completedWITHOUT the use of a calculator.Have a great summer – we are looking forward to seeing you in August!As you work through the packet, keep track of the following:“Things I learned, but forget how to do:”“Things I never learned:”1

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:A. The Real Number SystemAll Real Numbers can be classified by the following:Rational Numbers: Any value that can be written as a fractionabIrrational Numbers: Any value that cannot be written as a fraction.Integers: Any positive or negative whole value and zeroWhole Numbers: Any positive whole value and zeroNatural / Counting Numbers: Any positive whole ------------------------------------Exercises: Label the diagram.Classify each of the following in the most specific subset.1.72. 163. 04. 0.3105.56. 2.74677.8.3 14 5 1014 / ---------------B. The Order of Operations: Follow the Order of Operations when simplifying expressions:1.2.3.4.Simplify all grouping symbols: parenthesis, brackets, braces, fraction bars, absolute value and radical signsSimplify all exponents and radicals.Do multiplication and division in order from left to right.Do addition and subtraction in order from left to : Simplify:9. 12 6 212. 5 6(4 1) 10. 24 4(2)13.11.3(4 2)2(4 3)139(2 1) 2 5(4 2) 95 414. 2 25 10 2(6) 42

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:C. Operations with IntegersReview sign rules for operations with positive and negative values:Positive Positive Positive Positive Negative Negative Positive Negative Negative Negative Positive Negative Hmmmmm?Describe why the sum of a positive and negativevalue can be either positive or ses: Simplify (you will need to be able to simplify these types of problems without a calculator).15. 4 1823. 56 / 816. 5 524. 121 ( 11)17. 7 3 1125. 108 1218. 3 7 4 626. Find the average of -8, -5, 4, 13, -12 and -419. 7 6 27.5 15 33 7 220. 2 ( 9)28. 4 2 12 / 621. 30(7)29. (3 2) 2 7 422. 2 4 3 30. 36 12 / 4i223

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:D. Operations with Real NumbersReview rules for operations with fractions:-Adding and subtracting fractions: Find a common ; add or subtract theonly.-Multiplying fractions: multiply numerators, multiply denominators. Simplify by dividing common factors-Dividing fractions: multiply the dividend (first value) by the reciprocal of the divisor (second : Simplify (you will need to be able to simplify these types of problems without a calculator).1 131. 3 2172338.16 39.2 45532.3 33.13 5 16 840.2 12334.1 23 5 341.31 25735.13 5 264142. 3 7936.3 12 4 243.37.14 7844.2 1 2 1 3 4 5 152 1 2 1 3 4 5 154

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:E. TranslationsFill in the chart with the math symbol or operation that represents each term:Sumdifferenceproductoftwicequotientmore thantimessquareless thandividedsquare rootExercises: Translate the following expressions into math symbols, and then simplify the expression.45. Four more than twice seven.49. Six squared less the product of five and six.46. Six less than five times three.50. Five less than the square root of sixteen.47. Twenty five divided by the difference of sevenand two.51. One third of a number minus seven.48. One half of the sum of twenty and four.52. The sum of a number and 3 divided by ----------------F. Evaluating ExpressionsReplace each variable with its given value and simplify. Use parenthesis when substituting the value topreserve negative : Evaluate each of the following expressions for the given values of the variables:c 0a 5b 2f 3d 4e 153. 3a 4e56. a f f a54. 2(d 2)57.55. b 2 2df2b 4d358. 5a 6d bf65

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:G. Factors and MultiplesFactor: a value that can be evenly divided into another value.Multiple: a value that is evenly divisible by a factorGCF – the greatest common factor of valuesLCM – The least common multiple of valuesPrime: a number that is only divisible by 1 and itself (1 is a unit, not prime. 2 is the smallest prime value.)Prime Factorization: A listing of all the prime factors of a value; expressed in simplest form with ises: Show the prime factorization using a factor tree, then express the factors using exponents.72Calculate the GCF of the following:196375Calculate the LCM of the following:59. 12, 24, 3661.4, 8, 960.62.5, 15, 1221, 14, ----------------H. ExponentsExercises: Use exponents to simplify each expression:63. x x x x67.64. 2 x 2 x 2 x68.x5x98065.y8 y6 y69. 3 x (4 x )66. x 70.4 234 2x y 326

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:I. Properties of Real NumbersA.B.C.D.E.Commutative Property of AdditionCommutative Property of MultiplicationAssociative Property of AdditionAssociative Property of MultiplicationAdditive Inverse PropertyF.G.H.I.Multiplicative Inverse PropertyAdditive Identity PropertyMultiplicative Identity PropertyDistributive Property of Multiplication overAddition and cises: Write the letter of the Property of Real Numbers that justifies each step.71. 6 0 (-6)6 (-6) 00 00Given72. 4(1/4 1)4 1/4 4 11 4 11 44 15Given73. (1/5 7) 5(7 1/5) 57 (1/5 5)7 1774. 8(1/8 1)8 1/8 8 11 8 11 --------------------------J. Distributive Property and Combining Like TermsUse the Distributive Property when an expression with the addition or subtraction of terms is a factor.Examples:Non-example:2(5 x)(3) 30 x8( x 2 y 3) 8 x 2 8 y 24The two is not distributed since there is only 4(3a 7b) 12a 28bmultiplication and no addition or subtraction.Combining Like Terms: - Like terms have exactly the same variables raised to the same power.- Combine by adding or subtracting the ercises: Simplify.75. 7(3 x 2 5 x 9)79. 14 x 2 6 x 8 6 x 2 x 1176. 4a (3 x 2)80. 7(3 2 x) 8 (4 x 9)77. x 2 x x x y278. 3 x (2 x 4) 3(2 x 5) 4 x 181. 14 7 a 1782. ( x x x x 2 x)7

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:K. Solving Multi-step EquationsSolve for the variable by isolating it on one side of the equation.Steps:- Simplify each side of the equation-Use addition or subtraction to combine and isolate variable termUse multiplication or division to eliminate coefficients.Example:4(y 5) – y 114y 20 – y 113y 20 113y -9y -------------------------------------Exercises: Solve:83. 21 3(2 a )89. 5 x 2( x 1) 1090.11(8 10 x) x 54285. 9(3 – x) 2x – 691.x 5 8 286. 12x – 15 x - 792.5 13 6 x87. 3( x 5) x 593.12 27 4x 984. 3x – 18 -3288. 8 x 3(2 3 x) 28294. ( x 4) ( x 3)78

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:L. Solving InequalitiesExample: Solve. Remember when you multiply or divide each side of an inequality by a negative number,you must reverse the inequality symbol to maintain a true statement.Exercises:95. 5 x 4 4 x 699. 7 x 1 26 2 x96. 2m 3m 8597. 4c 13 c 298. 2 3 x 2100.2x 3 75101.4 y 2 8 y (6 y 10)102.5(2h 6) 7(h 7) ----------------M. FunctionsUse the function tables given to find the function rules.103.104.X45678Rule: ?-12-15-18-21-24X12345Rule: ?14710139

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:N. Applications: Show all work to solve.105.The length of a rectangle is 3x – 5 and its width is x. Find the length and width if the perimeteris 38 meters.106.A plumber is paid 50 to make a house call. She charges 80 per hour of work once she isthere. How much does she earn for a 4-hour job?107.Tina is having her car repaired. The mechanic said it would cost at least 480 for parts andlabor. If the parts cost is 105 and the mechanic charges 60 per hour, what is the minimum number ofhours the mechanic is planning to work on the car?108.What is 50% of the sum of the first 10 odd numbers?109.Insert the fewest number of grouping symbols to make the following equation true:24 3 9 5 2 6110.If eight students scored 100 on a test, twelve scored 90, and eight scored 80, what was the meanof the students’ scores?111.If the price of a shirt is reduced by 20% to 14.40, what was the original price?112.Evaluate113.If 24 students in a class of 30 students were present, what percent of the students were absent?11 3a if a .a2114.Karen opened a checking account by depositing 500. She wrote checks for 13.85, 28.14 and 230.18. She made a deposit which was a tenth of the opening balance. What is the balance in heraccount?115.A rubber ball bounces exactly half as high as it did on the previous bounce. It bounces 128 feethigh on the first bounce. How high does it bounce on the 12th bounce?10

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:O. Reading Charts and Graphs116.The box and whisker plot shows the results of testsgiven on two different days. On which day were more than75% of the scores higher than the median of the other day’sscores? Explain your choice.117.The graph shows a comparison of hours spent onschoolwork.a. How many hours do Japanese students spend on theirschoolwork at home?b. What percentage of schoolwork time is spent by the Frenchstudents in doing their work in class?118.The computer age has advancements occurring in technology on a daily basis. Which of thefollowing graphs would best represent the age of a computer compared to its value? Explain yourreasoning.119.The graph represents a sugar cube as it is eatenby several ants.What is the approximate surface area of the cube afterthe ants have been eating the cube of sugar for 8minutes?11

Herndon Middle SchoolAlgebra Honors Summer AssignmentName:P. Graphing on the Coordinate PlaneThe first value in an (x, y) ordered pair represents the distance horizontally from zero. If the value is positive,start at the origin (0, 0) and count to the right. If the value is negative, count to the left.The second value in an (x, y) ordered pair represents the distance vertically from zero. If the value is positive,start at the origin (0, 0) and count up from zero. If the value is negative, count down.Plot and label each of the (x, y) ordered pairs on the coordinate plane.A (2, 2)F (-2, 7)K (6, 7)P (6, -2)U (-7, -6)B (1, -2)G (5, -2)L (-3, -2)Q (-5, -4)V (-1, -2)C (-3, -6)H (6, -6)M (-7, -2)R (6, 2)W (-1, -6)D (-5, -1)I (3, -6)N (-2, 2)S (3, -2)X (-5, -6)E (-6, 2)J (-6, 7)O (2, 7)T (1, -6)Y (-7, -4)Z (4, -6)Connect the following sets of points by drawing a line segment between the coordinates.AR will connect points A(2, 2) and R(6, 2).The line segments will form letters thatspell a JEWhew! Feel ready for algebra? Believe itor not, you will use all of these skills thisyear. We will check the answers in class –be ready with questions! – See you soon!12

Prime: a number that is only divisible by 1 and itself (1 is a unit, not prime. 2 is the smallest prime value.) Prime Factorization: A listing of all the prime factors of a value; expressed in simplest form with exponents. -----Exercises: Show the prime factorization using a factor tree, t