Algebra 2 Level 2 Summer Packet

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1 Algebra Level Summer Packet This summer packet is for students entering Algebra Level for the Fall of 01. The material contained in this packet represents Algebra 1 skills, procedures and concepts that we expect students to know as they enter Algebra. Students are expected to complete this packet by the first day of school. We strongly suggest that students not wait until the last minute to do the packet. Completed packets will be collected and graded. Completing this packet is worth % of the student s first marking period grade. No credit will be given unless all work is shown. Whereas in past years we have been able to review Algebra 1 content during the first month and a half of the school calendar year, changes in the New Jersey Common Core Content Standards require us to significantly reduce the time spent reviewing Algebra 1. This is necessary in order to adequately cover the scope of Algebra content that is specified by the New Jersey Common Core Standards. Completion of this packet will ensure a smooth transition into new Algebra topics that we need to cover right away. Teachers teaching Algebra Level will use this summer packet to conduct an abbreviated review of prerequisite Algebra 1 content, followed by an exam on the majority of the prerequisite material within the first two weeks of the school year. That exam will be worth 10% of the first marking period grade. This summer packet is specifically designed to review the following topics: Interpreting graphs and plotting data on the coordinate plane Choosing appropriate scale for plotted data based on the size of the graphing area and data given Using data to model real-world situations Multiplication of polynomials and combining of similar terms Proper use of fractions and and rational expressions without introduction of decimals Using the least common multiple of denominators to clear fractions prior to solving an equation Interpretation of dividing by a fraction as multiplying by its reciprocal Proper manipulation of negative integers without the use of a calculator Translation of mathematical expressions into verbal sentences and vice versa Recognition of functions based on tables, graphs, and diagrams of data sets Modeling a real-world situation as a solvable equation with a single independent variable Identifying and modeling direct variation situations with linear equations Expressing the equation of a line in point-slope and slope-intercept form Interpreting data given in the form of a table and drawing conclusions from the table Identifying the x and y intercepts of a linear functions and deciphering their significance in the context of a problem

2 Algebra Level : Summer Assignment: Plotting Data on a Coordinate Plane 1) Plot each data set on a coordinate plane. Make sure to put the dependent event on the y-axis. Before plotting, make sure you decided on a suitable scale for each graph. Data Set 1: Number of hot dogs sold by a street vendor in Manhattan each month Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Hot Dogs y x

3 ) Data Set : Average height of children from birth to 10 years old Age (years) birth Height (inches) y x ) Data Set : Washing cars at a car dealership. Employees Time wash 6 cars (hours) y x

4 Algebra Level : Summer Assignment: The F.O.I.L. Method and Distribution Multiply. Simplify your answer completely. Show your work. 4) xx ( ) ) ( x ) 6) 1 (8 x 4) 7) ( x) ( x) Multiply Using the F.O.I.L. method of distribution. Simplify your answer completely. Show your work. 8) (x1)( x) 9) (x)( x ) 10) ( a )(4 a) ) ( z )( z ) 4

5 Algebra Level : Summer Assignment: Working with Fractions (All responses should be given as fractions or whole numbers. No decimals) Reduce each fraction to lowest terms by factoring the numerator and denominator. 1) 4 1) 10 14) 7 1) 1 1 Convert each mixed number into a fraction ) 17) 18) ) 7 Multiply. Give answer in lowest terms. 0) 1 4 1) 1 8 ) 6 4 Divide. Give answer in lowest terms. Hint: Flip and Multiply. ) 1 1 4) 8 ) Clear all fractions from the equation. (You do not have to solve for x.) Hint: Distribute the denominator to both sides. 6) 6 4 x 7) x x 1 8) x 6x 1 x Solve for x. Show your work. (Finish on the back if you need more space.) 9) 1 8 x 0) x 1 x ) 7 x

6 Simplify to a single fraction or whole number. Use no decimals. Reduce all answers to lowest terms. Show your work. s s s s 4) 8 ) ) s s s s ) s s 1 6) ) Solve for x. Use no decimals. Show your work. (Finish on the back if you need more space.) 1 8) 4 x 9) x x6 40) 7 1 x x x 41) x x 4 4 6

7 Algebra Level : Summer Assignment: Negative Number Manipulation Simplify each expression fully. 4) 4) 4 44) 7 4) 6 46) 9 47) ) 49) 0) 1) x ) 7 x y z ) a b 4c 7

8 Algebra Level Summer Packet: Part : Short Answer: 47 Questions 1. Define a mathematical expression. Give an example of a verbal expression translated into a mathematical expression.. Write an algebraic expression to represent the area of the rectangle. Then evaluate it to find the area when centimeters. m - m Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used.. three times the sum of 4m and n increased by 1 times m 4. Paul bought 14 gifts from a store. Each gift cost $.6. He got them gift wrapped for $ each. Write and evaluate an expression to determine the total amount he spent.. Lisa earns $7.1 per hour working after school. She needs at least $ to buy a stereo system. Write and solve an inequality to find the minimum number of hours she must work to buy the stereo. Express the relation shown in each table, mapping, or graph as a set of ordered pairs. Then write the inverse of the relation. 6. x y

9 Questions 7-11: Determine whether the relation is a function x y y x 10.{(, 9), (4, 8), ( 7, 4), (0, 4), (, 4), (, 9), (, 8) 11. y x 9

10 1. Bill earns $ more than Jack per day. Draw a graph showing Bill s earnings as a function of Jack s earnings. 1. The force, F, required to pull a block up an incline is given by, where x represents the weight of the block in kilograms. Write the equation in function notation and then find and. What do these values represent? Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form. 14. A square is a rectangle with all sides equal. 1. Katherine is 6 inches taller than Emily. If Katherine is 68 inches tall, write and use an equation to find Emily s height. 16. Mary bought a coat on sale for $6.7. The original price for the coat was $8. Write and solve an equation to find the amount of money Mary saved. 17. At a certain gas station, gas costs $.8 a gallon. Jason paid $.0 to fill his tank. Write and solve an equation to find how many gallons of gas he bought? 18. Eleven increased by three times a number equals 68. Write an equation for this situation and then find the number. 19. Henry and his brother each start a savings account. Henry begins with $00 and plans to deposit an additional $ per month. His brother begins with $10 and plans to deposit an additional $ per month. After how many months will the two brothers have the same amount in their accounts? 0. The team s ratio of games won to games played was to 8. If the team played 6 games, how many games did the team win? 1. A department store purchases a dress for $8. To sell the dress to the customers, the price is increased by 1%. What is the new price of the dress? Write an equation and solve for the variable specified.. Twelve more than a number, s, equals another number, p, minus 4. Solve for s.. An athlete runs 9 miles in 1. hours and then 14 miles in. hours. What is the average speed of the athlete? 4. Find the x- and y-intercepts of the graph of.. A country paid $41 million in interest on its national debt in 1940 and $191 million in What was the annual rate of change from 1940 to 1970? Explain the meaning of the rate of change. Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve. 6. If when, find y when. 7. What is the slope of a line that contains the point and has the same x-intercept as? 10

11 8. The table below shows the percentage increase in the sales of snack bars in a certain country in different years. Year 1 4 Sales (%) What would be the expected percentage increase in sales for the ninth year? eleventh year? 9. The cost of admission to an amusement park is $9.0 plus $1.0 per ride. Write a linear equation in slope-intercept form for the amount spent if r rides are taken. 0. The table of ordered pairs shows the coordinates of the two points on the graph of a line. x y Write an equation that describes the line. 1. Write the point-slope form, slope-intercept form, and standard form of an equation for a line that passes through with slope 4.. Determine whether and are perpendicular. Explain.. The table below shows Alex s best time for the 00-m sprint each year. Draw a scatter plot and determine what relationship, if any, exists in the data. 4. The length of the rectangle given below is more than the width of the rectangle. What are the possible values of x? Formulate a linear inequality to solve the problem. x in. 8 in.. Isabella works part time to earn money. She wants to earn at least $7 to buy a new computer. If she earns $11 per hour, how many hours must she work to reach her target? 11

12 6. Aaron s point totals in the first four of five basketball games were 1, 18, 19, and 1. How many points, t, must he score to have a mean point total of more than 16? 7. The water temperature for a manufacturing process should be kept at 140 F. A computer program uses the inequality, which describes the acceptable water temperatures, t, in Fahrenheit. What is the range of acceptable temperatures for the water? 8. Patrick has $10 to spend on gifts. He must buy at least 8 gifts. He plans to buy storybooks that cost $8 or $1. How many of each book can he buy? 9. The graph below shows the annual increase in salaries of employees A and B. 10 y Employee A Increase (thousand of dollars) Employee B x Year If the pattern continues, will the annual salary of the two employees ever be equal? Explain. 40. How many grams of pure silver and how many grams of an alloy that is 6% silver should be melted together to produce 6g of an alloy that is 80% silver? 41. The sum of two numbers is 4, and their difference is 6. What are the numbers? 4. Six times a number plus five times another number equals 6. The sum of the two numbers is 10. What are the numbers? 4. Emily has a total of 0 dimes and nickels. If the dimes were nickels and nickels were dimes she would have 0 cents less than she has now. How many of each coin does she have? 1

13 Use the table below that shows last week s sales of polo shirts at a local department store. Color Small Medium Large X-Large White Blue Green Create a matrix to show the number of polo shirts sold last week according to size and color. 4. Suppose the store decides to double their order of green polo shirts. Create a matrix representing the number of green polo shirts ordered in each size. 46. Suppose the store decides to triple their order of white polo shirts. Create a matrix representing the number of white polo shirts ordered in each size. 47. Patrick has $10 to spend on gifts. He must buy at least 8 gifts. He plans to buy storybooks that cost $8 or $1. How many of each book can he buy? 1

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