Algebra Prep. Summer Review Packet

Transcription

1 (Name) Algebra Prep. Summer Review Packet For students entering Algebra Prep. This summer math packet was developed to provide students an opportunity to review grade level math objectives and to improve math performance. DUE: FIRST WEEK OF SCHOOL Algebra Prep Page 1 Summer, 01

2 Dear student, Happy summer vacation! The start of the new school year is just around the corner. We want you to be as prepared as possible for the school year. It is important that you have a smooth transition to your new math class right at the beginning of the school year. With this in mind, we are providing a review summer packet of previously taught skills for you to complete over the summer. It is your responsibility to complete the packet before the start of the school year. Your new math teacher is expecting to see all work necessary to solve the problems in this packet. Work space is provided. However, if you use lined paper, please attach it to your packet. Your signature at the bottom of this page signifies that you have completed all work to the best of your ability and tried your best to complete the packet. If you have trouble on some of the information, seek assistance from a parent/guardian or other adult who may be able to assist you! Best wishes and we will see you soon! Sincerely, FOMS Mathematics Department Dear Parent/Guardian, It is important to us that your child has a smooth transition into a new math course. With this in mind, we are providing a practice workbook of previously taught skills for your child to complete over the summer. By doing so, it is our goal to increase your child s retention of mathematics skills and to assure a clear understanding of expectations we have for students in the upcoming year in math. Please encourage and monitor your child s completion of this workbook. Please make sure that ALL WORK IS SHOWN on each page or on attached paper. Remember, the goal is to work on it consistently throughout the summer and not to rush to finish it quickly. Students are to submit their workbooks to their math teachers within the first week of school. The packet will be assessed for a completion grade. Please sign and date the bottom of this document stating that your child has completed the summer math packet to the best of his/her ability. A list of suggested supplies and resources is also attached to this summer packet. The math department will be using graphing calculators for classroom instruction, homework completion, and MCPS assessments. Students may choose to purchase their own to bring back and forth to school. It is recommended that you purchase the graphing calculator during the summer so that your child can become acquainted with it before school starts in the fall. Thank you for your support! Suggested M ath Supplies for an Algebra Prep. Student: # pencils Paper (refill as needed) Graph Paper Protractor- basic and clear Compass Scientific Calculator Sincerely, FOMS Mathematics Department Please fill in the following information when the summer math packet is complete: Student Signature Grade: Date: Parent/Guardian Signature Date Algebra Prep Page Summer, 01

3 Whole Number Operations- Help Page Whole Numbers- Addition and Subtraction Help Adding numbers with different places requires lining up the units column. Your problem should always be justified on the rig ht side. The key to adding is regrouping. If a column adds up to more than ten, then the tens digit of the sum needs to be includ ed in the next column. Examples: = 1 (I have to carry the 1) = 16 (I have to carry the 1) = 8 (I don t have to carry because my number is less than 10) Subtracting numbers with different places requires lining up the units column. Your problem should always be justified on the right side. The key to adding is regrouping. If a column adds up to more than ten, then the tens digit of the sum needs to be included in the next column. Examples: I cannot subtract 6 7, so I must borrow from the and make the 6 a 16. I cannot subtract, so I must borrow from the and make the a I can subtract 1 so I do not have to borrow. Whole Numbers- Multiplication Help Step #1 Step # Step # Line up the numbers vertically (right justified). Multiply each digit in the top line by the ones digit in the bottom line (far right). Carry when necessary. x = (carried) = 16. I write the 16 next to the x Whole Numbers- Division Help You can always use the mnemonic device to help you remember the steps. Write a 0 under the last term you multiplied by ( in the example) as a place holder. Then multiply each digit of the top line by the tens digit in the bottom line. 1 6 x Add the numbers together. Carry when necessary. 6 x Th e an sw er is 1,10 Daddy Mommy Sister Brother Then repeat the Step 1: Divide Step : Multiply Step : Subtract Step : Bring down process over again! Round 1 Round Round Div ide: 76 1 is about M ultiply: 1 x 6 = 7 Subtract: 76 7 = x 6 = 18 I place the 8 below and carry the 1. Br ing Down: Br ing the 0 down. Multiply x 6. Place below and carry the11. Multiply x and add the carried Div ide: 76 1 is about M ultiply: 1 x 6 = 7 Subtract: 76 7 = Br ing Down: Br ing the 0 down Div ide: 76 1 is about M ultiply: 1 x 6 = 7 Subtract: 76 7 = Br ing Down: Br ing the 0 down. Repeat the steps! Repeat the steps! The final answer is 6! Algebra Prep Page Summer, 01 0 P L A C E H O L D E R

4 a) Whole Number Operations b) See previous page for assistance. c) d) 8, 8 7 7, 6 0 +, , 8 9 +, 0 7, 9 6, , , 1 e) 89,76 9,880 f), g) 9,17 17,8 h) 1, i) 8 1 j) 67 x 9 k) 09(9) l) (7)(9) m) 1,08 n) 6,170 o) p) Algebra Prep Page Summer, 01

5 Hints: Example: 16 0 Understanding Fractions Simplifying Fractions Mixed Numbers Into Improper Fractions Improper Fractions Into Mixed Numbers Example: Example: or x Look for a number that can be divided evenly into the top & bottom number (common factor). Divide top & bottom number by the common factor. Repeat until 1 is the only common factor. 1) Multiply the denominator (bottom number) times the whole number. ) Add that number to the numerator (top number). Divide the numerator (top) by the denominator (bottom). Note: The remainder is the numerator and denominator doesn t change. Simplify each fraction or mixed number. Show all work. 1 a) 0 b) 8 8 c) 0 d) 0 1 e) 60 9 f) Write each mixed number as an improper fraction. a) 9 7 b) 1 8 c) d) 8 1 e) 11 f) 7 9 g) h) Write each improper fraction as a mixed number. a) 1 b) 19 c) 11 d) e) 7 f) 77 8 g) h) 6 Algebra Prep Page Summer, 01

6 Fractions, Decimals and Percents Changing Fractions to Decimals Changing Decimals to Percents Changing Percents to Decimals 1) Take the top number and divide it by the bottom number. ) Keep adding zeros until the decimal terminates or the numbers repeat. ) If the numbers repeat, draw a repetition bar over top. Take the decimal and multiply it by 100. Trick: Move the decimal places to the RIGHT Take the percent and divide it by 100. Trick: Move the decimal places to the LEFT Terminating Repeating Work 0. x x *. 0 0 % Trick 0.. % Work % Trick ) Change each fraction to a decimal. Show all work. Use lined paper (if necessary) a) b) c) d) e) f) ) Change the decimal to a percent. Show all work or use trick. a) 0. b) c) 1.0 d) 1.08 ) Change each percent to a decimal. Show all work or use trick. a) % b).1% c) 8% d) 1.% Algebra Prep Page 6 Summer, 01

7 Simplifying Fractions and Mixed Numbers A fraction is in simplest form when its numerator and denominator have no common factor other than one. There are two ways you can simplify fractions: Choice One: Common Factors You can divide the numerator and denominator by common factors until the only common factor is 1. The best order of common factors is,,,, 9, and then divide. Example: = 16 1 = 8 6 = Choice Two: Greatest Common Factor You can also divide the numerator and denominator by the greatest common factor. You can find the greatest common factor by drawing the LCD table and multiplying together the common factors. Example: 8 = GCF = = 8 Simplify the following fractions and mixed numbers. Show all work. 6 = a) = b) 16 = c) d) = e) = f) = g) 8 = h) = i) = j) = k) 7 = l) = Algebra Prep Page 7 Summer, 01

8 Decimals (All Operations)- Help Page Adding Decimals Write the problem up and down! Line up the decimal points Add. Remember to carry when needed. Erase any extra zeros at the end of your final answer Subtracting Decimals Write the problem up and down! Line up the decimal points. Subtract. Remember to borrow when needed. Erase any extra zeros at the end of your final answer Multiplying Decimals Write the problem up and down. DO NOT LINE UP YOUR DECIMALS!!!!! Multiply carefully! Place the decimal in the final answer. Count the places to the right of the decimal point in each number. Count the same number of places from right to left in the answer, then place the decimal pt. Sometimes you ll need to fill places with zeroes x x # after decimal pt. # s after decimal pt. Move decimal spaces right..0 =. (Cut off an y zeros at th e en d after th e decimal poin t) Dividing Decimals Write the problem across. The first number goes into the division symbol. The second number goes outside of the house. Dividing by Whole Numbers 1) Bring up the decimal point. ) Divide until there is no remainder Dividing by Decimals 1) Move both decimal points to the right until the outside number is whole. ) Bring the moved decimal pt up. ) Divide until there is no remainder Problem Answer 0.07 Algebra Prep Page 8 Summer, 01

9 Decimals- All Operations See Decimals All Operations Page for assistance (page 1). 1) ) ) ) ) 18.9 x 1. 6) 7. x 0.8 7) 16.7 x 0. 8) 68 x. 9) ) ). 1. 1).99. Algebra Prep Page 9 Summer, 01

10 Same Sign: You add Pos + Pos = Pos Neg + Neg = Neg Different Signs: You subtract The number that looks bigger deter mines whether the answer is negative or positive. Integer Operations Addition Subtraction Multiplication Division a) Keep the first number. e) Positive x Positive = Positive b) Switch the minus sign to f) Negative x Negative = Positive a plus sign g) Positive x Negative = Negative c) Change the sign of the h) Negative x Positive = Negative second number. i) Anything x zero = zero d) Then follow the rules of adding. j) Positive Positive = Positive k) Negative Negative = Positive l) Positive Negative = Negative m) Negative Positive = Negative n) Anything zero = NOT POSSIBLE o) Zero Anything = ZERO 1) Find each sum (add). Show all work! a) b) -0 + c) d) ) Find each difference (subtract). Show all work! a) -1-0 b) 1 0 c) -10 d) -1 ) Find each product (multiply). Show all work! a) 0 x - b) - c) (-10)(-10) d) -8 - Note: All of the ques tions lis ted above involve multiplication. You can s ee multiplication written in many different ways! ) Find each quotient (divide). Show all work! a) 80 - b) 90 6 c) 100 d) 1 Note: All of the ques tions lis ted above involve divis ion. You can s ee divis ion written in many different ways! ) Simplify the following expressions using the integer laws. 6 a) b) -6(9 11) c) - + d) (- + 7) (-16 + ) 1 e) 1( ) + f) (-³) (- - -6) g) 6 8 h) 7 6 Algebra Prep Page 10 Summer, 01

11 Order of Operations Helpful Hints- Order of Operations Example #1 Example # 1) Underline the step you are completing. ) Bring down all other numbers and operations. Go in order! Remember: Please Excuse My Dear Aunt Sally! ()³ (10 ) ()³ (10 6) + 8 ()³ + 8 (8) ( 1) P E M D A S Parenthesis Exponents Multiply or Divide (Left to Right) Add or Subtract (Left to Right) Simplify the following expressions using order of operations. a) 600 b) (1 1)² - 0 c) d) 6 e) (6 )² f) ( ) ( ) + 6 g) (1 10) h) 1 + (²) (1 ) i) (² - ) ² + 7 Algebra Prep Page 11 Summer, 01

12 Solving One & Two Step Equations Solving One Step Equations Get the variable (letter) by itself by doing the opposite operation on both sides of equal sign. Solving Two Step Equations Steps: 1) Get rid of the number that is added or subtracted by doing the opposite operation. ) Get the variable by itself by doing the opposite of the multiplication or division. Examples Addition: x + 7 = 9 Subtraction: x 1 = 8 x + 7 = x = x - 1 = x = 0 x + 7 = x = 6 x = Examples x - 7 = x = 11 x = Solve each equation using the steps above. 1) y + 1 = ) x 1 = 1 ) 8 a = ) h = 6 ) x 6 = 1 6) y + = 9 7) 1 + x = 8) y 9) w = = 1 10) y 8 = Algebra Prep Page 1 Summer, 01

13 Solving One & Two Step Inequalities Solving Inequalities Follow the same steps that you would use when solving equations. However, there is one extra step. NOTE: If you multiply or divide both sides of inequality by same POSITIVE NUMBER, direction of in equality sign does n ot ch an ge. If you multiply or divide both sides of inequality by same NEGATIVE NUMBER, direction of in equality sign REVERSES. Ch an ge th e Sign x - > + + x > 8 x > Don t Ch an ge th e Sign -x - > + + -x > x < - Graphing Inequalities Look at the final solved answer. 1) If the final solved answer has: < or > or Use an open dot ( ) Use an open dot ( ) ) If the final answer has: < or or Arrow goes to left. Arrow goes righ t. x x -6 x - -x +10 < x < x > by - switch the > to a < ) Solve and graph. a) -d b) c 18 < - c) x > 7 ) Which of these graphs represents the solution set for the inequality below? x 10 A) B) C) D) ) Which of these graphs represents the solution set for the inequality below? A) B) C) D) x 9 ) What does each sign mean? a) < b) c) d) e) > f) = Word Bank greater than or equal to not equal to less than or equal to less than equal greater than Algebra Prep Page 1 Summer, 01

14 Graphing on the Coordinate Plane Coordinate Plane Vocabulary Quadrant Quadrant 1 Quadrant Quadrant Helpful Hints for Graphing Steps to plot a point. Start at the origin (0, 0) 1. Move left or right to whatever number x is. sign positive (+) negative (-) direction right left. Move up or down to whatever number y is. Definitions: sign positive (+) negative (-) direction up down Ordered Pairs: set of numbers. The first number tells you to move left or right. The second number tells you to move up or down. Remember: CRAWL before you CLIMB!!! Origin: the center point You always start from (0, 0) and then move across and then up or down. 1) Give the coordinates of each point. a) H f) Q b) A g) L c) T h) C d) M i) X e) F j) J Q H M X 1 F L T - - C - J A ) State which quadrant each point is in. a) (,-1) b) (-1,-) c) (18,10) d) (-,9) e) (,11) f) (-6,17) ) Describe how to locate each point. a) (,-11) - b) (-8,-6) ) Plot and label each point. a) J (,-) b) E (, ) c) W (-1,-) d) R (1,0) e) B (-, ) f) Z (,) g) P (-,1) h) G (-,-1) i) Y (0,-) j) S (,-) Algebra Prep Page 1 Summer, 01 -

15 Problem Solving- Part 1 Addition Subtraction Multiplication Division Sum Positive Total Plus All together Incr eased by Add Addends In all Deposit Differ ence Mor e than Gr eater than Take aw ay Subtr act Less than Minus Withdraw Decr eased by less than Pr oduct Times In all Multiply Multiples Double (x ) Tr iple (x ) Tw ice (x ) Quotient Divide Goes into Factor s Pieces or Parts Per Shar e Equally Divisible Par t of Show all steps to solve each problem. 1) If Julia can assemble clipboards in minutes, how many clipboards can she assemble in 1 minutes? Final Answer: ) An airplane is approaching its final descent into the airport. If the plane descends at a rate of 0 feet per second, what is the change in altitude of the plane after twelve seconds? Final Answer: ) Elizabeth is planning a trip to Houston and has calculated $0.9 for lodging, $98 for food, and $11.0 for gasoline. How much will her trip cost? Final Answer: ) Keegan is a babysitter and earns $8.0 per hour. Last week, she worked 6 hours. What is her total pay? Final Answer: ) Aleia rides her bike for hours and minutes. If she started riding her bike at 11:0 a.m., at what time will she finish? Final Answer: Algebra Prep Page 1 Summer, 01

16 Bar Graph Statistics Review- Part 1 Hints: Basic Graph Information Circle Graph Line Graph Stem & Leaf Plot Bar Graphs compare data. Circle graphs show how a whole is broken into parts. Line graphs measure change in data over time. Stem & Leaf Plots shows groups of data arranged by place value Hints: Measures of Central Tendency Measure of Variation Mean Median Mode Range Sum of a set of numbers divided by the amount of numbers in the set Middle number (when numbers are in order from least to greatest) Number that appears most often highest number minus lowest number 1) State what type of graph you would use for each question. a) Taline wanted to display data on the number of CD players used each year from 1981 through b) Robert wanted to display data about the heights of the world s five tallest buildings. c) Alex wanted to create a graph showing the percentages of different juice sold in the United States. ) Make a stem-and-leaf plot of the data showing phone call lengths. Don t forget a title and key. Phone Call Lengths Find the mean, median, mode and range. Mean Median Mode Range stem leaf ) Use the stem and leaf plot to the right to answer the questions below. a) Name the highest score on the test. a) 96 b) 9 c) 100 d) 97 Science Test Scores (Question s 1 ) stem leaf b) Name the mode score a) 79 b) 9 c) 89 d) c) What is the range? 8/1 = 81% a) b) 7 c) d) no range Algebra Prep Page 16 Summer, 01

17 Amount of People Reading and Creating Graphs- Part ) Choose mode, median, mean, or range to best describe each statement below. a) Half of the students are on team 7-A. b) The average amount of time spent on homework is minutes c) Most of the students have Ms. OLaughlin for math d) The difference between the tallest and smallest building is 7 feet. ) Use the graph to choose the statement that is true. a) Jive Cola is more than twice as popular as Cool Cola. b) Jive Cola is less than twice as popular as Cool Cola. c) Jive Cola is times as popular as Cool Cola d) Zippy Cola is the most favorite Cola chosen Favorite Cola Jive Cola Zippy Cola Cool Cola Cola 6) Use the graph to answer the question below. A bank customer looks at the graph and states that the cost of stocks in April was over twice the cost of stocks in July. What should the bank manager do to make this graph accurate? a) His origin is incorrect. He should have started at 0. b) He should have used a different scale. c) He should have made a circle graph. d) He should have made a pictograph 7) Find the mean, median, mode, and range. 66, 6, 0,, 9, 6,, 1,, 7 Order: Least to Greatest 8) Find the mean, median, mode, and range. 17, 16, 1, 17, 17, 10, 10, 1, 10 Order: Least to Greatest Mean Median Mode Range Mean Median Mode Range Algebra Prep Page 17 Summer, 01

18 Algebra Prep Page 18 Summer, 01