SAT #2 - PRACTICE PROBLEMS – Remainder and Averages



ALGEBRA II – 2018-19December 3, 2018Today’s Agenda (Day 67)Homework Check: SAT #2 Practice ProblemsClass ActivitySection 5.5 – Solving Polynomial FunctionsSum and difference of cubesFactor by groupingCombine cubes and squaresSolve polynomial functions by graphingQuadratic formSolve equations in Quadratic formHOMEWORK:Review Ch 5 – Polynomials and Polynomial FunctionsComplete Section 5.5 Exercise, p. 346 [#15, 20, 22, 24, 26, 28, 30, 32, 34, 36, 40, 42, 44, 47]Complete Term 2 Project: In PAIRS, complete either “Hot, Hot, Hot” or “On Target” - see descriptions below on p. 2 or p. 5 of documentREMINDERS:SAT #2 Practice Problems – Dec. 3Section 5.5 Exercise – Dec. 4Chapter 5 Test Dec. 5 December 7Term 2 Project – Dec. 8; 11:59:59 pmPrepare for Mid-terms (covers chapters 1 – 5 AND SAT-type of questions)SAT #2 - PRACTICE PROBLEMS – Remainder and Averages1.When x is dived by 4, the remainder is 3. What is the remainder when 7x is divided by 4?(A) 0 (B) 1 (C) 2 (D) 3 (E) 42. When n is divided by 11, the remainder is 7. What is the remainder when 5n is divided by 11?(A) 0(B) 2(C) 4(D) 7(E) 93. When is divided by 5, the remainder is 2. When m is divided by 5, the remainder is 1. What is the remainder when m + n is divided by 5?(A) 0 (B) 1 (C) 2 (D) 3 (E) 44. If a = 4b + 26, and b is a positive integer, then a could be divisible by all of the following EXCEPT:(A) 2 (B) 4 (C) 5 (D) 6 (E) 75. If the remainder when x is divided by 5 equals the remainder when x is divided by 4, the x could be any of the following EXCEPT:(A) 20 (B) 21 (C) 22 (D) 23 (E) 24 1.The average weight of five packages is 30 pounds. Four of the packages weigh 10, 20, 40, and 45 pounds. What is the weight of the fifth package (in pounds)?(A) 15(B) 25(C) 35(D) 39(E) 482.A is a number. The numbers A?2, A?1, A+1, and A+2 are averaged. What is the average (arithmetic mean) of these four numbers?(A) A +0.5(B) A ? 0.5(C) A(D) 0(E) 13.Carol needs to buy six gifts for Christmas. She has $100 to spend on these gifts. She has already bought four gifts, costing $15, $20, $12, and $13. What is the average amount that she can spend on the remaining gifts?(A) $40(B) $20(C) $15(D) $17(E) $304.A survey of Town X found an average (arithmetic mean) of 3.2 persons per household and a mean of 1.2 televisions per household. If 48,000 people live in Town X, how many televisions are in Town X?(A) 15,000(B) 16,000(C) 18,000(D) 40,000(E) 57,6005.The average (arithmetic mean) of the first 3 numbers in a certain series is 10. If the average of the first 2 numbers is 10, what is the third number?(A) 0 (B) 5 (C) 10 (D) 20 (E) It cannot be determined from the information given.47651035619156.Ifxis the average (arithmetic mean) ofaandb, then in terms ofxandc, what isthe average ofa,b, andc?(A)x+c)B(x+c2()Cx+c3()D2x+c2()E2x+c3006.Ifxis the average (arithmetic mean) ofaandb, then in terms ofxandc, what isthe average ofa,b, andc?(A)x+c)B(x+c2()Cx+c3()D2x+c2()E2x+c3ALGEBRA II – 2018-19TERM 2 PROJECT.AChapter ProjectGo to the following Web sites to find information to help you complete this project.You can review how to enter data and use formulas in?spreadsheets.Learn more about running a small business from the?Small Business Association.Beginning the Chapter ProjectSuppose you are the owner of the Sizzlin' Sauce Company. Your company makes two different kinds of sauce, Red Hot Sauce and Scorchin' Hot Sauce. As the owner of a small but successful business, you want to minimize costs, maximize profit, and create satisfied customers by filling orders promptly.As you work through the project, you will use systems of equations and a spreadsheet to analyze production levels and make decisions. You will write a report detailing your choices.List of MaterialsCalculatorGraph paperActivitiesActivity 1: GraphingTo fill an order for Sizzlin' Sauce sauces, you bought 1050 green peppers and 1200 hot chili peppers.Write and graph a system of inequalities to represent how many pints of each kind of sauce you can make. Use the recipes below.Select one solution of the system and determine how many peppers you will have left over.Sizzlin' Sauces RecipesScorchin' Hot Sauce IngredientsRed Hot Sauce IngredientsYield: 1 pint1 pint tomato sauce with onions4 green peppers, diced8 hot chili peppers, seeded and dicedYield: 1 pint1 pint tomato sauce with onions5 green peppers, diced4 hot chili peppers, seeded and dicedActivity 2: AnalyzingSuppose you make $1.20/pt profit on Red Hot Sauce and $1.00/pt profit on Scorchin' Hot Sauce. Using the restrictions from Activity 1, decide how much of each sauce you should make and sell to maximize your profit. What is the maximum profit?Activity 3: ResearchingVisit a local grocery store to estimate the cost of each sauce ingredient. Remember that buying in large quantities can save you money.Find the cost to produce 1 pt of each type of sauce.What selling price will you set for each sauce to maintain your profit?Activity 4: OrganizingYou can sell your sauce to a supermarket chain, a local grocery store, and a specialty store. The supermarket chain will buy 288 pints at a time, every eight weeks. The grocery store will buy 60 pints every four weeks, and the specialty store will buy 24 pints each week.How much sauce should you produce each week to fill these orders? Presume that you want to produce the same number of pints each week, and that the type of sauce is not a factor in filling these orders.Design a spreadsheet to track your stock of sauce after each week. Use cell formulas.Finishing the Chapter ProjectThe activities should help you to complete your project. Your report should include your analysis of the cost of producing Sizzlin' Sauces. Include your profit analysis and production spreadsheet. Illustrate your reasoning and decisions with graphs.Reflect and RevisePresent your analysis to a small group of classmates. After you have heard their analyses and presented your own, decide if your work is complete, clear, and convincing. If needed, make changes to improve your presentation.Extending the ProjectAre there other expenses you could expect in addition to those you have already considered? Estimate them. Modify your recommendations if necessary.Chapter Project ChecklistHave you done all of the following?Made sure that answers are reasonableChecked your work with a graphing calculatorDocumented your informationRemembered that you will produce the same amount of sauce every weekBesides the cost of ingredients, what information would need to be taken into consideration to accurately determine the profit? How would you go about finding this information?Scoring Guide3Correct inequalities are written and graphed. Calculations are accurate. Graphs are accurate and labeled correctly. Information is clear and thoroughly presented. The folder is well organized and provides useful information.2Minor errors are made in writing inequalities. Reasoning and explanations are essentially correct, but could be more thorough. The folder provides useful information, but needs to be better organized.1Inaccurate inequalities are written and graphed. The folder lacks organization. Graphs could be neater and more accurate. Explanations lack detail.0Major elements of the project are incomplete or missing. NEXT PAGE FOR TERM PROJECT BALGEBRA II – 2018-19TERM 2 PROJECT.BChapter ProjectGo to these Internet links for more information to help you complete this project.You can find out more about the?history of archery?by rolling your mouse cursor over "Home" on the menu bar. In the expanded menu, click on the "history of archery" link.You can use this?online graphing?utility to graph parabolas.Find more information about archery at the?USA Archery Association, and the?National Field Archery Association.Beginning the Chapter ProjectArchery has its roots in prehistoric times. Cave drawings in Spain, France, and North Africa show hunters using bows and arrows. In the Far East, people made bows by gluing wood, bone, and animal tendons together. Early Native Americans also used bows and arrows. Archery has also become a recreational sport. In 1992, at the Olympic Games in Barcelona, it was an archer who lit the Olympic flame.In this project, you will research topics such as how archers choose their arrows and how technology has changed the sport. You may want to finish your project by making a display or other presentation.List of MaterialsCalculatorGraph paperMeasuring tapeActivitiesActivity 1: GraphingAn archer releases an arrow at shoulder height.Measure the distance from the floor to your shoulder when you are standing. Suppose you release an arrow and it hits the target at a point 5 ft above the ground. Sketch a possible parabolic path of your arrow's flight using this information.Archery is one of only a few sports in which athletes using wheelchairs can compete with other athletes.Measure the distance from the floor to your shoulder while you are sitting in a chair. Suppose you release an arrow while sitting in a wheelchair, and it hits the target at a point 5 ft above the ground. Sketch the possible path of your arrow's flight.Describe the similarities and differences between your two sketches.Activity 2: AnalyzingIf an arrow randomly hits a target, you can find the probability that it will hit a given area by comparing this area to the total area of the target. Suppose an arrow randomly hits the target shown. Find the probability that the arrow will hit the following:the bull's-eye (yellow area)the red areathe black or white areaany area except the blue areaActivity 3: ModelingArchers need to use arrows that do not bend easily. The table shows how the weight of an arrow affects its spine, or the distance the center of the arrow bends when a certain constant weight is attached. Graph the data in the table to find a linear and a quadratic model for the data. Use the regression feature on your calculator to find each model. Which model is a better fit? Explain.Weight (in grams)140150170175205Spine (in inches)1.41.250.930.780.43Activity 4: ResearchingResearch the new styles of archery that use three-dimensional targets or moving video targets. Create one of these targets using readily available materials or a computer program.Finishing the Chapter ProjectThe activities should help you to complete your project. Present your project for this chapter as a visual display, a demonstration, or, if equipment is available, as a videotape.Reflect and RevisePresent your information to a small group of classmates. Decide if your work is complete, clear, and convincing. If needed, make changes to improve your presentation.Extending the ProjectInterview an archer. Find techniques archers use to increase the range and accuracy of a shot.Chapter Project ChecklistHave you done all of the following?Measured standing and sitting height to your shoulder.Subtracted areas of circles to find the area of a ring. Found the ratios of the areas of parts to the area of the whole to find each probability.Used residuals.Determined whether there is an archery club in your area.How might a videotaped presentation be more useful in studying parabolic paths of arrows than a real-life demonstration? What other objects in sports or real-life situations follow parabolic paths?Scoring Guide3Calculations are correct. Graphs are neat, accurate, and labeled correctly, and they clearly show the differences between the situations. Explanations are thorough and well thought out. The target is designed well and neatly made. The display is well organized.2Calculations and explanations are mostly correct, with some minor errors. Graphs are neat and mostly accurate with minor errors in scale. The target is designed adequately, but is not neatly made. The display presents clear information, but is not well organized.1Calculations contain both minor and major errors. Graphs are not accurate. Explanations lack detail. The target is poorly designed.0Major elements of the project are incomplete or missing. ................
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