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MonroeTownshipMiddleSchool MonroeTownship,NewJersey MiddleSchool8th GradeRESOURCE*PREPARATION PACKET* Welcometo8thGradeMathematics!Our8thGradeMathematicsCourseisa comprehensivesurveycoursethatwillprovideyouwiththefundamentaltools ofmathematicalunderstandingthatwillsupportyouinallyourhighschool courses.Sinceyouwillbetaking8thGradeMathematicsaftersuccessful completionof7thGradeMathematics,theMonroeTownshipMiddleSchool8th GRADEPREPARATIONPACKETcontainsreviewmaterialofthe7thgrade concepts,skills,andproceduresthatshouldbemasteredBEFOREentering8th gradeinthefall.Essentially,thispacketprovidesareviewofthemajor7th gradetopicsaswellasapreviewof8thgradetopics.Thesectionsarebasedon theNJ2016StudentLearningStandards.Seeourtownshipwebsiteforgreat web-basedresourcesifyouneedarefresheronanyoftheproblems encounteredhereinthispacket. Herearesomewebsitesyoumightfindparticularlyuseful: • http://www.khanacademy.org/ • http://www.ixl.com/math/ • http://phschool.com/atschool/cmp2/program_page.html • http://www.studyisland.com/web/index/ Thiscollectionofproblemswillidentifythoseconceptsthatyouhavemasteredaswellasthose youwillneedtopracticeandreview.Youareexpectedtoseekextrahelpimmediatelyon thoseconceptswithwhichyouhavenotdemonstratedproficiency.Beresourceful–usethe onlineresources! ***SOLVETHESEPROBLEMSWITHOUTTHEUSEOFACALCULATORANDSHOWALLWORK*** YouwillberesponsibleforhandinginthecompletedpacketwithallworkshownONTHE FIRSTDAYOFSCHOOL.Theproblemshereareveryrepresentativeofthetypesofitemsyou willneedtohavemasteredBEFORE8thGradeMath…sowestronglyencouragethatyou includethispacketinyoursummerfestivities!Goodluckandenjoy!J MATH8PREPARATIONPACKETSCORE:___________of41points Page1 RatiosandProportionalRelationships7.RP Usethetablebelowfor#1. 1. Is the relationship between time and earnings proportional? Explain why or why not. (For #2) Use the map below. 2. What would be the approximate distance (in miles) to travel from Seattle to New York? (Hint: Set up a proportion.) Page2 3. Label the dimensions of rectangles 1, 2 and 3. Use the dimensions to prove which rectangles below are similar? Show your work! (Hint: Set up a proportion or use scale factor.) 4. If David walks 0.5 miles in 0.25 hours, then how fast does David walk in one full hour? In other words, what is David’s “unit rate”? (Hint: Set up a proportion) 5. An important category of percentage problems is markup & markdown problems. Solve the following: a. A sporting goods store pays its wholesaler $50 for a certain baseball glove and then sells the glove to customers at a retail value of $90. What is the markup rate? b. A sweater originally priced at $44 is marked down 25%. What is the sale price? TheNumberSystem7.NS 6. Fill in the missing fraction/decimal/percent conversions below. FRACTION DECIMAL PERCENT 0.12 7 8 125% Page3 7. Use the distributive property to write an equivalent variable expression. -7(2 x - 5) 8. Find the sum or difference. You MUST show ALL of your work to receive credit! (Hint: Find common denominators) a. 5 3 + 16 4 b. 5 3 5 -1 32 8 9. Find the quotient or product. You MUST show ALL of your work to receive credit! a. 9 20 • 5 1 b. 1 3 ÷ 2 4 10. Simplify and show all steps of work: 𝟏𝟎 − 𝟓𝟎 ÷ −𝟐×𝟐𝟓 + 𝟕 ×𝟐𝟐 Page4 Expressions&Equations7.EE 11. Simplify (Hint: combine like-terms): m + 0.5m 12. The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? (Hint: Draw a picture to help you.) 13. Felicia is planning a white water rafting trip. She compares two companies to find the better buy. a. Sinking Rivers charges two hundred dollars for insurance and fifteen dollars an hour to rent the raft. Write an equation to represent Sinking Rivers’ total cost (c) for any number of hours (h). c = _______________________ b. Floating Down the Stream charges thirty dollars an hour and one hundred and ten dollars for insurance. Write an equation to represent Floating Down the Stream’s total cost (c) for any number of hours (h). c = _______________________ 14. Solve: 2 x + 17 = 81 Geometry7.G 15. Illustrate each of the following terms by providing clear examples. a. Supplementary angles b. Complementary angles c. Vertical angles d. Adjacent angles Page5 16. Below is a grid with four quadrants. Plot the following points, and connect them with line segments. Point A (-2, -4) Point B (3, 4) Point C (3, -4) 17. On the same grid paper above, transform your figure ABC using the rule (2x, 2y). A’ ______________ B’ ______________ C’ _____________ 18. Are the triangles from question 16 and 17 congruent to each other? Explain. 19. What is the VOLUME of the cone? 20. formula: - 𝑉 = ×𝜋×𝑟 1 ×ℎ . What is the SURFACE AREA of a cylinder with a radius of 5 cm and a height of 7 cm? Draw a picture to help you. formula: 𝑆𝐴 = 2×𝜋×𝑟×ℎ + 2×𝜋×𝑟 1 Page6 StatisticsandProbability7.SP Match the following terms to their corresponding definition: 21. ________Probability A. The middle number of an ordered set of numbers. If there is an even number in the set, then it is the average of the two middle values. 22. ________Law of Large Numbers B. The “average” of a set of numbers – the sum of the set divided by the number in the set. 23. ________Random sample C. A number between 0 and 1 that describes the likelihood that an outcome will occur. It can be theoretical where it’s the ratio of the number of favorable outcomes (assuming they are equally likely) to the total number of outcomes or experimental where it’s the ratio of the number of favorable outcomes of a trial to the total number of trials in an experiment. 24. ________Mean D. 25. ________Median E. As more trials of an experiment are conducted, the experimental probability more closely approximates the theoretical probability. If is not at all unusual to have 100% heads after three tosses of a fair coin, but it would be extremely unusual to have 100% heads after 1,000 tosses. 26. ________Mode F. When you choose in such a way that gives every sample from a population an equally likely chance of being selected. The most frequently occurring value in a numerical set. 27. Each letter of the word “MATHEMATICS” is written on a separate slip of paper and placed in a hat. A letter is chosen at random from the hat. a. What is the probability of choosing “M” on your first try? b. Suppose you choose an “M” on your first try. You keep the slip of paper (do not replace it in the hat) and go for another letter. What is the probability of getting another “M”? Page7 28. Solve and graph the inequality below: 5𝑥 + 460 ≥ 1,000 29. Using the graph, identify the slope and y – intercept. Then write an equation that represents the linear relationship. Slope: ___________ y – intercept: ____________ equation: _________________ 30. Identify if the relationship represented in the tables below is linear. If the table is linear, write the equation of the line. linear / non-linear linear / non-linear Equation: ___________________ Equation: _________________ Page8