Transcription
Mukilteo School DistrictSeventh Grade AdvancedMathematicsReview & Practice
Dear families,As our community works to understand and respond to the effects of COVID-19,the Mukilteo School District sincerely appreciates your patience as we navigatethis period of unprecedented school closures.Attached to this letter is a packet of materials to help you supplement your child’seducation while away from the formal school environment. Please feel free to usethe grade-level packets to review and practice previously taught skills inEnglish/Language Arts, Mathematics and Science. They are not required, nor willthey be graded. Answer keys are included in the packets so that your child cancheck their own work. Students are encouraged to skip around and find topics ofinterest and practice rather than complete them from beginning to end. If youfind that your child’s grade level is too challenging, or not challenging enough, youare welcome to work outside of their current grade level.It is highly encouraged that your child continues to review and practice previouslytaught skills and remain engaged in learning. We hope these packets add to whatyou are already doing to support your child in learning during this challengingtime.Sincerely,The Curriculum and Instruction DepartmentMukilteo School District
REVIEW: Finding the Percentof a NumberNameKey Concept and VocabularyVisual Model40% of 60 is 24.Write percentas decimal orfraction andmultiply.0.4 60 2425— 60 24Finding apart.Skill Examples0%20%40%60%80%100%01224364860Application Example1. 30% of 50:0.3 50 152. 45% of 80:0.45 80 365. 28% of the 200 people who answereda survey own a dog. How many of the200 people in the survey own a dog?0.28 200 563. 110% of 40: 1.1 40 444. 25% of 240: 0.25 240 60PRACTICEMAKES56 of the 200 people own a dog.PURR-FECT Check your answers at BigIdeasMath.com.Find the percent of the number.6. 25% of 40 7. 20% of 35 8. 65% of 110 9. 125% of 20 1310. 33—% of 60 11. 95% of 400 12. 200% of 31 13. 18% of 90 14. 1% of 800 15. 60% of 60 16. 100% of 59 17. 1000% of 59 Write the question represented by the model. Then answer the question.18. 0%020%40%60%80%100%183654729019. swer:Answer:20. ENDANGERED SPECIES Sixty percent of a species of butterfly died due to loss of habitat.Originally, there were 10,000 butterflies. How many are left?21. SALES TAX You buy 4 breakfast sandwiches at 2.59 each, 4 hashbrowns at 1.10 each, and4 bottles of orange juice at 1.25 each. The sales tax is 6%. Find the total cost of the 4 meals,including sales tax.Copyright Big Ideas Learning, LLCTopic 10.4
REVIEW: Percents and ProportionsKey Concept and VocabularyTo represent “a is p percentof w,”use a proportion.part of thewholewholeawp100Proportion3650Visual Model0%20%40%60%80%09182736— —Application Examplep1003. A basketball player makes 45%, or 9 shots,of her attempted shots. How many shotsdid the basketball player attempt?p 100100 — 100 — 20100— — 900 45w90045 45w4520 wa 7.2The basketballplayer attempted20 shots.So, 7.2 is 20% of 36.MAKES — —a2036 — 36 —36100PRACTICE451009 100 w 45So, 36 is 72% of 50.a369w— —72 p2.4527 is 60% of 45.— — 3650100%percentSkill Examples1.NamePURR-FECT Check your answers at BigIdeasMath.com.Write and solve a proportion to answer the question.4. 68 is what percent of 80?5. What number is 25% of 116?6. 36 is 16% of what number?7. 48 is what percent of 128?8. What number is 64% of 40?9. 77 is 55% of what number?10. PLAY Students are auditioning for a play. Of the 60 students auditioning, 12 will get apart in the play. What percent of the students who audition will get a part in the play?11. HOMEWORK You have completed 60% of your English homework. The assignmenthas 25 questions. How many questions are left?Copyright Big Ideas Learning, LLCTopic 18.5
REVIEW: Estimating andFinding a TipNameKey Concept and VocabularyTo find the tip on a food bill ata restaurant, write the percentas a decimal or fraction andmultiply it by the cost of thefood bill.TipVisual Model0%20%40%60%80%08162432100%40A 20% tip on a food bill of 40 is 8.Application Examples1. Your food bill at a restaurant is 8.49. Youleave a 15% tip.Estimate: Round 8.49 to 10.0.15 10 1.5The estimate for the tip is 1.50.2. Your food bill at a restaurant is 15.83. Youleave a 20% tip.Estimate: Round 15.83 to 16.0.2 16 3.2The estimate for the tip is 3.20.Actual: 0.15 8.49 1.27Actual: 0.2 15.83 3.17The actual tip is 1.27.The actual tip is 3.17.PRACTICEMAKESPURR-FECT Check your answers at BigIdeasMath.com.Estimate the tip. Then find the actual tip.3. Food bill: 33.65; Tip: 15%4. Food bill: 44.28; Tip: 20%5. Food bill: 11.17; Tip: 15%6. Food bill: 12.37; Tip: 20%7. Food bill: 23.16; Tip: 15%8. Food bill: 16.21; Tip: 20%9. Food bill: 37.54; Tip: 25%10. Food bill: 25.96; Tip: 20%11. Food bill: 28.93; Tip: 15%12. Food bill: 72.79; Tip: 25%13. Food bill: 19.82; Tip: 23%14. Food bill: 51.56; Tip: 30%Copyright Big Ideas Learning, LLCTopic 10.8
REVIEW: Estimating andFinding a Sales TaxKey Concept and VocabularyTo find the sales tax on anitem, write the percent asa decimal or fraction andmultiply it by the price ofthe item.SalesTaxNameVisual Model5%0%20%2.501.25540%7.560%80%10 12.5 15 17.5 20 22.5100%25Using a sales tax of 5%, the sales taxon a 25 shirt is 1.25.Application Examples1. A DVD costs 20 before tax. The sales taxis 7%.Estimate: Round 7% to 5%.0.05 20 1The estimate for the sales tax is 1.Actual: 0.07 20 1.42. A bicycle costs 115 before tax. The sales taxis 9%.Estimate: Round 9% to 10% and 115 to 120.0.1 120 12The estimate for the sales tax is 12.Actual: 0.09 115 10.35The actual sales tax is 10.35.The actual sales tax is 1.40.PRACTICEMAKESPURR-FECT Check your answers at BigIdeasMath.com.Estimate the sales tax. Then find the actual sales tax.3. BASEBALL CARDS The pack of baseball cards costs 3.75 before tax. The sales tax is 4%.4. TELEVISION A television costs 400 before tax. The sales tax is 8%.5. MP3 PLAYER An MP3 player costs 89 before tax. The sales tax is 6%.6. COUCH A couch costs 675 before tax. The sales tax is 5%.7. GUITAR A guitar costs 299 before tax. The sales tax is 9%.8. TABLE A table costs 50 before tax. The sales tax is 4.5%.9. JEANS A pair of jeans costs 39 before tax. The sales tax is 5.5%.Copyright Big Ideas Learning, LLCTopic 10.7
REVIEW: Estimating andFinding a DiscountNameKey Concept and VocabularyA discount is a decrease in theoriginal price of an item. To findthe discount, write the percentas a decimal or fraction andmultiply it by the original priceof the item.Visual ModelDiscount0%20%40%60%80%015304560100%75The sale price of a 75 necklace witha 60% discount is 75 45 30.Application Examples1. The original price of a book is 18.79.The discount is 20%.Estimate: Round 18.79 to 20.0.2 20 4The estimate for the discount is 4.Actual: 0.2 18.79 3.76The actual discount is 3.76.The sale price of the book is 18.79 3.76 15.03.PRACTICEMAKESPURR-FECT 2. The original price of a pair of in-line skatesis 209.99. The discount is 15%.Estimate: Round 209.99 to 200.0.15 200 30The estimate for the discount is 30.Actual: 0.15 209.99 31.50The actual discount is 31.50. Thesale price of the pair of in-line skatesis 209.99 31.50 178.49.Check your answers at BigIdeasMath.com.Estimate the discount. Then find the actual discount and the sale price.3. TRUMPET The original price of a trumpet is 319.29. The discount is 25%.4. SHOES The original price of a pair of shoes is 47.99. The discount is 40%.5. LAMP The original price of a lamp is 17.09. The discount is 15%.6. RING The original price of a ring is 96.75. The discount is 60%.7. ELECTRONICS The original price of a home theater system is 243.89. The discount is 75%.8. BASEBALL The original price of a baseball glove is 26.99. The discount is 30%.9. SEWING MACHINE The original price of a sewing machine is 182.96. The discount is 20%.Copyright Big Ideas Learning, LLCTopic 10.6
REVIEW: Simple InterestNameKey Concept and Vocabularytime inyearsI PrtSimpleInterestVisual Model1 month112principalrate asdecimalSkill ExamplesI (200)(0.10)(4) 8013t —6 months1 year2 yearst 1t 212t —4. You deposited 500 in a savings accountfor 10 years. The account paid 6% simpleinterest. How much interest did you earn?2. P 250, r 0.04, t 0.5 yearP 500, r 0.06, t 10 yearsI (250)(0.04)(0.5) 53. P 2000, r 0.05, t 20 yearsI (2000)(0.05)(20) 2000MAKES14t —Application Example1. P 200, r 0.10, t 4 yearsPRACTICE4 monthst — 100 ( 1000)(0.05)(2)interest3 monthsPURR-FECT I (500)(0.06)(10) 300You earned 300 in interest.Check your answers at BigIdeasMath.com.Find the simple interest.5. Principal: 400, Rate: 5%, Time: 3 years6. Principal: 100, Rate: 3%, Time: 6 months7. Principal: 1000, Rate: 2%, Time: 4 months8. Principal: 250, Rate: 10%, Time: 6 months9. Principal: 500, Rate: 8%, Time: 9 months10. Principal: 600, Rate: 1%, Time: 8 yearsIn which savings account do you earn more simple interest?11. a. Deposit 200 at 6% for 3 years.b. Deposit 200 at 8% for 18 months.12. a. Deposit 1000 at 4% for 5 years.b. Deposit 1000 at 5% for 4 years.13. SAVINGS You deposited 600 in a savings account for 5 years. The account paid4% simple interest. How much interest did you earn?14. LOAN You borrowed 1000 for 2 years. You are charged 5% simple interest.How much interest do you owe?Copyright Big Ideas Learning, LLCTopic 18.4
NameDateOperations with Rational NumbersTo add, subtract, multiply, or divide rational numbers, use the same rules for signs as you usedfor integers.5 2Find (a) — — and (b) 7.3 ( 4.8).6 3Example 1a. Write the fractions with the same denominator, then add.5 25 4 5 4 11 — — — — — — —6 36 6666b. To subtract a rational number, add its opposite.7.3 ( 4.8) 7.3 4.8 12.1 The opposite of 4.8 is 4.8. Find (a) 2.25 8, (b) 2.25 ( 8), and (c) 2.25 8.Example 2 a. 2.25 8 18 b. 2.25 ( 8) 18c. 2.25 8 184 3Find — —.9 4Example 3To divide by a fraction, multiply by its reciprocal. 164 34 44 4 — — — — — —9 49 39 3273 4The reciprocal of — is —.4 3PracticeCheck your answers at BigIdeasMath.com.Add, subtract, multiply, or divide.1. 7.5 3.8 5. 6 4.75165632 ( —8 ) 6. 3.2 ( 4.8)7109. — —13. —2. 18.3 ( 6.7)( 35 )10. — —13. 0.6 0.854.6.13 ( 2.82)7. 1.8 ( 9)8.3.6 ( 1.5)492312.5 1 — —6 458( 14 )16.4 2 — —7 511. — — 3 74 1214. — —15. — —17. TEMPERATURE The temperature at midnight is shown. The outsidetemperature decreases 2.3 C over the next two hours. What is the outsidetemperature at 2 a.m.?518. SNOWFALL In January, a city’s snowfall was —8 foot below the historicalOUTIN3—4average. In February, the snowfall was foot above the historical average.Was the city’s snowfall in the two-month period above or below the historicalaverage? By how much?Copyright Big Ideas Learning, LLCTopic 3.2
REVIEW: Writing and GraphingInequalitiesNameKey Concept and VocabularyVisual Modelx 2x 2: All numbers greater than 2x 2: All numbers greater thanor equal to 2x 2: All numbers less than 2 5x 2: All numbers less thanor equal to 2 5 4 3 2 1012345x 2Skill Examples 4 3 2 1012345Application Example1. x 0: All positive numbers5. A sign at a clothing store reads “Savingsup to 70%.” Let S represent the percent ofsavings. Write an inequality to describe S.2. x 0: All nonnegative numbersS can be equal to 70%.3. x 0: All negative numbersOr S can be less than 70%.4. x 0: All nonpositive numbersAn inequality is S 70%.PRACTICEMAKESPURR-FECT Check your answers at BigIdeasMath.com.Write an inequality for the statement.6. All numbers that are less than 247. All numbers that are at most 38. All numbers greater than 109. All numbers that are no more than 510. All numbers that are at least 1111. All numbers less than or equal to 8Graph the inequality.12. x 1 5 413. x 4 3 2 101234514. x 3 5 5 4 3 2 1012345 4 3 2 101234515. x 0 4 3 2 1012345 516. A sign at a shoe store reads “Savings up to 60%.” Let P representthe percent of savings. Write an inequality to describe P. 45Shoe SaleSavingsup to 60%Copyright Big Ideas Learning, LLC 665Topic 17.4
REVIEW: Properties of InequalityNameKey Concept and VocabularyAddition Properties of Inequality:Subtraction Properties of Inequality:If a b, then a c b c.If a b, then a c b c.If a b, then a c b c.If a b, then a c b c.Multiplication and DivisionProperties of Inequality when c 0:Multiplication and DivisionProperties of Inequality when c 0: If a b, then a c b c. If a b, then a c b c. If a b, then a c b c.InequalitiesIf a b, then a c b c.a bcca bIf a b, then — —.cca bcca bIf a b, then — —.ccIf a b, then — —.If a b, then — —.Skill Examplesx41. Solve — 2 12.x4— 2 12 2x4 2 4 10 4x 40PRACTICE 7v 21 28Write the equation.x— 104—2. Solve 7v 21 28.Write the equation.Subtraction Property of Inequality 21 21Addition Property of InequalitySimplify. 7v 49Simplify.Multiplication Property of Inequality— — 7v 7Division Property of Inequalitywhen c 0v 7Simplify.MAKES49 7PURR-FECT Simplify.Check your answers at BigIdeasMath.com.Solve the equation. Identify the properties used.m2m —23. 3x 5 44. 1 — 33xxmWrite and solve an inequality that represents the value of x.5. Area 44 ft26. Area 64 m25Źx8 ft16 mxà2Copyright Big Ideas Learning, LLCTopic 24.3
REVIEW: Sample SpaceNameKey Concept and VocabularyThe set of all outcomes ofan experiment is called thesample space.OutcomesThe sum of the probabilitiesof all outcomes in a samplespace is 1.Visual ModelPA hat contains 3 tiles with theletters P, R, and O.O RExperiment: Draw a tile.Sample Space: PRO13—13—Probabilities:—13131313Sum of Probabilities: — — — 1Skill ExamplesApplication Example1. You flip a coin. The sample space of theexperiment is Heads (H), Tails (T).2. You roll a number cube. The sample spaceof the experiment is 1, 2, 3, 4, 5, 6.3. You flip a coin and roll a number cube. Thesample space of the experiment is H1, H2,H3, H4, H5, H6, T1, T2, T3, T4, T5, T6.PRACTICEMAKESPURR-FECT 4. A referee flips a coin twice. Find the samplespace. Show that the sum of the probabilitiesof all outcomes is 1.The sample space is HH, HT, TH, TT.14The probability of each outcome is —.14141414— — — — 1Check your answers at BigIdeasMath.com.Find the sample space of the experiment.5. Drawing a marble6. Rolling a cube with letters of the word sample7. Rolling a number cube twice8. Flipping a coin and rolling the cubein Exercise 69. BILLIARDS The three balls shown are left on a billiards table. You choosea ball at random, set it aside, and then choose another ball. Find thesample space. Show that the sum of the probabilities of all outcomes is 1.Copyright Big Ideas Learning, LLCTopic 20.5
REVIEW: Tree DiagramsNameKey Concept and VocabularyHHTTHFlip a coin2 times.4 possibleoutcomes:HH, HT, TH, TTVisual ModelTreeDiagramHHTSkill ExampleHTTHTTApplication Example1.Draw 2 marbles froma sack containing:2. You are drawing 2 marbles from a sack that. In how many ways cancontainsyou draw 2 green marbles?There are 2 GG’s in the tree diagram.GGGRGGPRACTICEGRRGMAKESThere are 2 ways to draw 2 green marbles.RGPURR-FECT Check your answers at BigIdeasMath.com.Draw a tree diagram to show all the outcomes.3. Flip a coin 3 times.4. Draw 2 marbles from a sack with5. You flip a coin 3 times. In how many wayscan you get 2 heads and 1 tail?6. You draw 2 marbles from a sack withIn how many ways can you draw2 green marbles?22ACopyright Big Ideas Learning, LLC343A.47. CARDS You draw 2 cards from the hand at the right.In how many ways can you end up with a sum of 5?(For instance, A 4 5.).Topic 20.1
REVIEW: Circles and CircumferenceNameKey Concept and VocabularycumferencecirCeret RmadiuasDiVisual ModelC πdCirclesC 2πrCircumference of a Circle:C 2πrπ 3.14r â 12 2π(12) 24π227π — 75.4Skill ExamplesApplication Example2.1.dâr â 2.4 in.3ft43. Find thedistance aroundthe soccer ball.22.3 cmC π(22.3)C 2π(2.4)()34C π — 4.8π 2.4 ft 15.1 in.PRACTICEMAKESPURR-FECT 70.0 cmThe distance is about 70 centimeters.Check your answers at BigIdeasMath.com.Find the circumference. Round your answer to the nearest tenth.4.5.6.7Circumference 7.Circumference 8.4.1 cmCircumference 2 8 in.7925 mi74.6 in.Circumference 9.0.42 in.Circumference 1.25 ft1Circumference 10. RACETRACK A circular racetrack has a circumference of one mile. What is the diameterof the racetrack in feet?11. OLD OAK TREE You have 110 inches of yellow ribbon. The diameter of the old oak treeis 38 inches. Do you have enough yellow ribbon to wrap around the old oak tree? Explain.Copyright Big Ideas Learning, LLCTopic 11.3
REVIEW: Areas of CirclesNameKey Concept and VocabularyVisual ModelAreaA πr 2Area of a Circle:π 3.14rA πr 2râ4 π(4)2227π — π(16) 50.2Skill ExamplesApplication Example2.1.dâr â 2.4 in.3ft43. Find the areaof a dime.A π(0.9)2 2.5 cm2A π(2.4)2()3 28A π — 18.1 in.2PRACTICE1.8 cmThe area is aboutbout2.5 square centimeters.2 0.4 ftMAKESPURR-FECT Check your answers at BigIdeasMath.com.Find the area. Round your answer to the nearest tenth.4.5.6.72 8 in.4.6 in.10.4 in.Area Area 7.Area 8.9.4.1 cm1.5 ft1.5 ftArea Area 10. BASKETBALL Find the area of the center circleon a basketball court.11. BASKETBALL Find the area of a free throw regionon a basketball court.Copyright Big Ideas Learning, LLC1.5 ftArea centercircle12 ftfreethrowTopic 11.4
REVIEW: AreaNameKey Concept and VocabularyRectangle:A bhParallelogram:A bhTriangle:1A —bh2Trapezoid:1A —(B b)h2Visual ModelAreaFormulasArea of a Rectangle:A bh 120 square unitsbase â 12Skill Examples1.Application Example2.4 in.1.2 cm 1240 ft 2400 ft21A —(3.8)(2.4)2A —(1.6 1)(1)60 ftA 60 403.8 in.1.6 cmThe area is 2400 square feet.2 4.56 in. 1.3 cm2PRACTICE3. Find the area ofthe apartment.2.1 cm1 cmheight â 10 (12)(10)MAKESPURR-FECT Check your answers at BigIdeasMath.com.Find the area of the figure.4.50 ft5.6.30 ft10.6 in.1ft413.5 in.Area 1ft23ft8Area Area 7.8.5 cm 6 cm9.8 yd2 ft6 yd4 cm5 cmArea 143 ft2 yd2 ydArea Area 10. CARPET You are carpeting a rectangular room that is 3.5 yards by 4.5 yards. The carpetcosts 15 per square yard. How much will it cost to carpet the room?11. COLORADO Colorado is approximately a rectangle that is 280 miles by 380 miles.Is the area of Colorado greater than or less than 100,000 square miles? Explain.Copyright Big Ideas Learning, LLCTopic 11.2
REVIEW: Surface Areas of PrismsNameKey Concept and VocabularyVisual ModelSurfaceAreahNet for a Rectangular PrismwhhwwhhwhwS 2ℓw 2ℓh 2whwwSkill ExamplewApplication Example1.2. Find the surface area of the block.(3 ft ) 12 20 12 162 ft4 ft12S 2 — 3 4 4 5 3 4 4 4 16 24 12 5 cm 60 cm2S 2(4 2) 2(4 3) 2(2 3)The area is 60 cm2.2 52 ft4 cm4 cm3 cmPRACTICEMAKESPURR-FECT Check your answers at BigIdeasMath.com.Find the surface area of the prism.3. Rectangular Prism4. Rectangular Prism1 ft5. Rectangular Prism3 cm3 in.5 ft10 ft9 cmS 4 in.6 cm6. Triangular Prism5 in.S S 7. Triangular Prism8. Triangular Prism5.7 mm5m5 cm3 mm5m4m4 cm7m6mS 5 cm3 cmS 4 mm4 mmS 9. AQUARIUM How much glass is used to makethe four sides of the aquarium?2 ft10. AQUARIUM How much glass is used to makethe base of the aquarium?1.5 ftCopyright Big Ideas Learning, LLC4 ftTopic 12.21
REVIEW: Surface Areas of CylindersNameKey Concept and VocabularyVisual ModelSurfaceArearNet for aCircular CylinderhrhrS 2πr 2 2πrh2Ĭ rSkill Example1.Application Example2. Find the surface area ofthe soup can.3 ft2 ft 4.5π 15π 5 in. 19.5π in.2The area is 19.5π square inches. 30π ft2PRACTICE S 2π 1.52 2π 1.5 5S 2π 32 2π 3 2 18π 12π3 in.MAKESPURR-FECT Check your answers at BigIdeasMath.com.Find the surface area of the circular cylinder.3. Circular Cylinder4. Circular Cylinder5 mm5. Circular Cylinder12 cm6 ft6 cm7 ft2 mmS S 6. Circular CylinderS 7. Circular Cylinder8. Circular Cylinder9 in.14 m10 ft2m6 ft4 in.S S S 9. OIL TANKER TRUCK The truck’s tank is a stainless steelcylinder. How many square feet of stainless steel areneeded to make the tank?10. OIL TANKER TRUCK What percent of the stainless steel inthe tank is used to make the two ends?Copyright Big Ideas Learning, LLCLength â 50 ftRadius â 4 ftTopic 12.3
REVIEW: Volumes of PrismsNameKey Concept and VocabularyVisual ModelBasehVolumeVolume of aRectangular PrismV Bh ℓwhw3 V 2 4 3 24 units342Skill ExampleApplication Example1.2. Find the volume of the block.3 ft5 ft(2 ft12 ) 5 — 3 4 V 5 2 35 cm 30 cm3 30 ft3PRACTICE4 cmV Bh3 cmThe volume is 30 cubic centimeters.MAKESPURR-FECT Check your answers at BigIdeasMath.com.Find the volume of the prism.3. Rectangular Prism4. Rectangular Prism1 ft5. Rectangular Prism3 cm3 in.5 ft10 ft9 cm4 in.5 in.V 6 cmV 6. Triangular Prism7. Triangular PrismV 8. Triangular Prism3 mm4 cm4 mm4m7m6 cm6m3 cmV V V 9. AQUARIUM How much water is needed to fillthe aquarium?10. AQUARIUM There are about 7.5 gallons in1 cubic foot. How many gallons of waterdoes the aquarium hold?Copyright Big Ideas Learning, LLC4 mm2 ft1.5 ft4 ftTopic 13.1
REVIEW: Volumes of PyramidsNameKey Concept and VocabularyVisual Model1V — Bh3height, hVolumeThe volume of a pyramid isone-third the volume of theprism that has the samebase and height.area of base, BBSkill Example1.Application Example131 — (8 10) 73560 —32 186 — in.332. Find the volume ofthe square pyramid.V — Bh7 in.8 in.10 in.PRACTICEhMAKES 13V — ( 40 ) 30230 m 16,000 m340 mThe volume is 16,000 cubic meters.PURR-FECT Check your answers at BigIdeasMath.com.Find the volume of the pyramid.4.3.4 mm5.8 in.2 ft2 ft1 ftB â 15 mm2V 6.V 7.4 cm6 in.V 8.15 mm7 ft8 ft5 cm10 in.3 cmV 14 mm20 mm6 ftV V 9. PYRAMID The pyramid has a volume of 2000 cubic feet.Find a set of possible dimensions for the pyramid.hw , ℓ , h wCopyright Big Ideas Learning, LLCTopic 13.3
REVIEW: Evaluating ExpressionsNameKey Concept and VocabularyVisual ModelEvaluatingExpressionsvariableExpression: 2x 2 3x 6Evaluate when x 2.2( 22 ) 3(2) 6 8 6 6 8Skill Examplesx2x 3Value of Expression12(1) 3522(2) 3732(3) 3942(4) 311Application Example1. When x 5, 3x 4 is 3(5) 4 19.5. For a Celsius temperature C the Fahrenheit95temperature F is —C 32. Find F when2. When x 1, 5x 7 is 5( 1) 7 2.C 25 .3. When x 3, 4x 2 is 4( 32 ) 36.9595—C 32 —(25) 324. When x 4, x 3 1 is 43 1 65. 45 32 77The Fahrenheit temperature is 77 .PRACTICEMAKESPURR-FECT Check your answers at BigIdeasMath.com.Evaluate the expression.6. When x 2, 3x 1 .7. When x 1, 3x 9 8. When x 4, x 2 5 .9. When x —, 3x 2 10. When x 3.1, 5x 0.5 1212. When x 10, x 2 8x 11 .11. When x 0, 4x 2 5 .1213. When x 2—, 6x 3 .Evaluate the perimeter when x 3.14.P 2x15.2x Ź 1xà1xP 3x Ź 12x Ź 116. CARDINAL The weight of the cardinal (in ounces) is 0.6x 11after its eats x ounces of bird seed. How much does it weighafter it eats 2 ounces of bird seed?Copyright Big Ideas Learning, LLCTopic 17.1
REVIEW: Simplifying ExpressionsNameKey Concept and VocabularyVisual ModelAlgebra TilesSimplifyingExpressionsCombine variable terms.2x 4 3x 1 5x 3áá ááá áááàáááááá5. The original cost of a shirt isx dollars. The shirt is on salefor 30% off. Write a simplifedexpression for the sale cost.2. 1 n 4 n 53. (2x 3) (x 2) x 1á30%Offx 0.3x 0.7x4. 2( y 1) 3( y 2) 5y 4MAKESáApplication Example1. 2x 5x 7xPRACTICEâáCombine numerical terms.Skill ExamplesźThe sale cost is 0.7x.PURR-FECT Check your answers at BigIdeasMath.com.Simplify the expression. (Remove parentheses and combine like terms.)6. 4x 6x 7. 3n 5 2n 8. 9x 3 6x 2 9. 3(x 2) 10. 7m 2m 5m 11. 2 (x 1) 12. (3x 6) x 13. 5 (1 n) 14. (x 6) (x 6) 15. (4x 2) 3(x 1) 16. (5x 4) 2(x 1) 17. 5(x 2) 2(x 2) Write a simplified expression for the perimeter of the rectangle or triangle.19.18.20.7x5n8xPerimeter 9nPerimeter 21. The original cost of a cell phone is x dollars. The phone ison sale for 35% off. Write a simplified expression for thesale cost.Copyright Big Ideas Learning, LLC18x18x21xPerimeter 35%OffTopic 17.3
REVIEW: Writing Expressionsand EquationsKey Concept and VocabularyNameVisual Model2 n 6Phrase: Two more than a numberExpression: 2 nTwoSentence: Two more than anumber is equal to six.morethanis equaltoanumbersix.Equation: 2 n 6Skill ExamplesApplication Example1. Five times a number: 5n2. Six less than three times a number: 3n 65. Write an equation for the following.“The price of 15 is the wholesale costplus a markup of fifty percent.”3. The sum of a number and one: n 1Let C be the wholesale cost.50% of C is 0.5C.4. A number divided by three: n 3An equation is 15 C 0.5C.PRACTICEMAKESPURR-FECT Check your answers at BigIdeasMath.com.Write the verbal phrase as a mathematical expression.6. The product of a number and two7. 10 subtracted from a number8. 19 less than twice a number9. The sum of a number and three,divided by four10. Five times the sum of a number and two11. Seven less than four times a numberWrite the sentence as an equation.12. Three times a number equals nine.13. The difference of a number and nine is four.14. Twelve divided by a number is four.15. The sum of a number and seven is eighteen.16. The volume of a cone is one-third the area of the base times theheight. A cone has a volume of 20π cubic inches. Write an equationthat can be used to solve for the height of the cone.Copyright Big Ideas Learning, LLChB 4π in.²Topic 17.2
REVIEW: Properties of EqualityNameKey Concept and VocabularyAddition Property of Equality:If a b, then a c b c.Visual ModelIf two sides of a scale weigh the same,the scale balances.Equality1111Subtraction Property of Equality:If a b, then a c b c.If you add or subtract the same amount oneach side of the scale, the scale still balances.Multiplication Property of Equality: If a b, then a c b c.44Division Property of Equality:1111If a b, then a c b c, c 0.Skill ExampleApplication Examplex42. Ski rental is 45 for 3 hours and 10 for eachadditional hour. You pay 75. Write andsolve an equation to find the number ofadditional hours you rented the skis.1. Solve — 3 7.x4— 3 7Write the equation. 3 3Addition Property of Equalityx4— 10x4— 4 10 4x 4010h 45 75Simplify. 45 45Write the equation.Subtraction Property of EqualityMultiplication Property of Equality10h 30Simplify.Simplify.— —10h10Division Property of Equality3010h 3Simplify.You rented the skis for3 additional hours.PRACTICEMAKESPURR-FECT Check your answers at BigIdeasMath.com.Solve the equation. Identify the properties used.3. 2y 9 13n44. — 2 10n42y — y n 5. COMPUTER You pay 87 to get your computer repaired. You are charged 37 for partsand 20 per hour of labor. Write and solve an equation to find the number of laborhours you were charged.Copyright Big Ideas Learning, LLCTopic 24.2
NameDateSolving Linear EquationsTo determine whether a value is a solution of an equation, substitute the value into the equationand simplify.Determine whether (a) x 1 or (b) x 2 is a solution of 5x 1 4.Example 1a.5x 1 2x 6b.?5(1) 1 2(1) 64 4 5x 1 2x 6?5( 2) 1 2( 2) 6Substitute. 11 10Simplify.So, x 1 is a solution.Substitute.Simplify.So, x 2 is not a solution.To solve a linear equation, isolate the variable.Example 2a.Solve each equation. Check your solution.4x 3 13b.4x 3 3 13 32y 16 y 6Add 3.4x 16Simplify.4x4Divide by 4.164— —x 42(y 8) y 6Distributive Property2y y 16 y y 6Simplify.Subtract y.y 16 6Simplify.y 16 16 6 16Add 16.y 22CheckSimplify.Check4x 3 13?4(4) 3 1313 132(y 8) y 6?2(22 8) 22 6 28 28Practice Check your answers at BigIdeasMath.com.Determine whether (a) x 1 or (b) x 3 is a solution of the equation.1. 5x 7 22. 4x 8 43. 2x 1 3x 4Solve the equation. Check your solution.4. x 9 247.5 —6 t 155. n 14 06. 16 4y8. 81 46 x9. 4x 5 110. x 5 11x11. 9(y 3) 4512. 6 7k 8 k13. 6n 3 4n 714. 2c 5 3(c 8)15. 18m 3(2m 8) 0w 6515 h38 3x516. — 817. — 1018. — x19. (8r 6) (4r 1) 1420. —23 y 3 921. —12 x — —2 x —101035722. MONEY You have a total of 3.25 in change made up of 25 pennies, 6 nickels, 2 dimes, andx quarters. How many quarters do you have?Copyright Big Ideas Learning, LLCTopic 6.2
REVIEW: Finding the Percentof a NumberNameKey Concept and VocabularyVisual Model40% of 60 is 24.Write percentas decimal orfraction andmultiply.0.4 60 2425— 60 24Finding apart.Skill Examples0%20%40%60%80%100%01224364860Application Example1. 30% of 50:0.3 50 152. 45% of 80:0.45 80 365. 28% of the 200 people who answereda survey own a dog. How many of the200 people in the survey own a dog?0.28 200 563. 110% of 40: 1.1 40 444. 25% of 240: 0.25 240 60PRACTICEMAKES56 of the 200 people own a dog.PURR-FECT Check your answers at BigIdeasMath.com.Find the percent of the number.1076. 25% of 40 7. 20% of 35 71.5 9. 125% of 20 258. 65% of 110 13380 12. 200% of 31 62 13. 18% of 90 20 11. 95% of 400 16.210. 33—% of 60 368 15. 60% of 60 14. 1% of 800 59059 17. 1000% of 59 16. 100% of 59 Write the question represented by the model. Then answer the question.18. 0%020%40%60%80%100%1836547290Question: What is 60% of 90?Answer:5419. 0%020%
Dear families, As our community works to understand and respond to the effects of COVID-19, the Mukilteo School Di
