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Name:Due: January 27, 2015Math 80__OWNCSMidterm Review SheetMath 8Unit 1: Operations with Rational Numbers (Prerequisites Skills) Operations with integersOperations with decimalsOperations with fractionsOperations with percentsTwo-Way Frequency TableOperations with IntegersAdding & Subtracting IntegersExamplesSame sign:Different signs:Double negatives:Multiply and Dividing IntegersExamplesSame sign: Different signs:Operations with DecimalsAdding and Subtracting Decimals ExamplesLine up the ________________.Add or SubtractBe careful of the positive and negative signs! (Refer to adding and subtracting integers when dealing with positive and negative decimals!!!)Multiplying DecimalsExamplesMultiply the NumbersCount the decimals places fromthe ________________.Move that many places in yourfinal answer.Dividing Decimals ExamplesMake the ________ a whole number.Move the same number of decimalplaces in the __________________.Divide.Operations with FractionsAdding and Subtracting FractionsExamplesFind the _________________.Create equivalent fractionsAdd or subtract the ____________.Keep the ________________.Multiplying and Dividing FractionsExamplesChange mixed numbers to_____________.If dividing, changing to multiplying and use the _________________ of the 2nd fraction.Cancel common ___________________Multiply acrossOperations with PercentsChanging Ratios to PercentsExamplesCreate a ____________________.Cross multiply and solveORUse equivalent fractionsTwo-Way Frequency TableFrequency TableExamplesShows how often each item occurs3200400170180in a set of categorical dataRead each question carefullyLook for relationshipsHow many friends did you survey?What percent of kids who like bowling were female?What type of party would please the most people? Explain.Practice for Unit 1 – Create work boxes and show all work on separate piece of graph paper!!!A survey was done to determine what type of special class students liked. MusicArtFilmTotal6th Grade4231227th Grade1512418th Grade244118TotalComplete the table.How many students were surveyed? How many students chose music?What percent of students chose music?How many students were surveyed in the 8th grade?How many students in 8th grade chose art?What percent of students in 8th grade chose art?How many students were surveyed in the 6th grade?How many students in the 6th grade chose art?What percent of students in the 6th grade chose art?Using the table, is there a relationship between the grade and the class chose? Justify your answer.Unit 2: Exponents Exponential Form vs. Expanded FormEvaluating a Number to a Power?Negative ExponentsZero ExponentsLaws of ExponentsProduct RuleQuotient RulePower RuleExtended?Power RuleWriting in Scientific NotationOperations with Scientific NotationExponential Form vs. Expanded FormExponential FormExamplesExpanded FormExamplesExponentsEvaluating a Number to a PowerExamplesWrite in ______________________._______________ the base n times.Negative ExponentsExamplesUse the _______________________.Make the exponent positive.Zero ExponentsExamplesAny number to the zero power is _____.Laws of Exponents Product RuleExamples______________ the exponents.______________change the base.Quotient RuleExamples______________ the exponents.______________change the base.Power RuleExamples______________ the exponents.______________change the base.Extended?Power RuleExamples______________ the exponents.______________change the base.Scientific NotationWriting in Scientific NotationExamplesa x 10ba: ____ digit in front of decimalb: the number of places the decimal point is moved______ exponent of 10: very big number______ exponent of 10: very small numberOperations with Scientific NotationMultiplying with Scientific NotationExamples______________ the coefficients.______________the exponents.Rewrite in _______________________.Dividing with Scientific NotationExamples______________ the coefficients.______________the exponents.Rewrite in _______________________.Adding with Scientific NotationExamplesRewrite the numbers with the same ______________________.Add the ______________________.Subtracting with Scientific NotationExamplesRewrite the numbers with the same ______________________.Add the ______________________.Practice for Unit 2 – Create work boxes and show all work on separate piece of graph paper!!!Directions: Evaluate.12) (-2)513) 14) 7-215) 80 =Directions: Simplify.16) 54 5317) 79 7-618) (34)719) (22)-320) 21) 22) 23) 24) Directions: Perform the indicated operation.25) (8 x 10-6) + (4 x 10-5)26) (9 x 108) - (6 x 106)27) (5 x 10-3)(4 x 10-2)28) (2.1 x 10-8) (7 x 10-9)Unit 3: Solving Equations Simplifying Expressions?Distributive PropertyCombining Like TermsIsolate the VariablePropertiesInverse OperationsIdentitiesSolving One-Step EquationsSolving Two-Step EquationsDistributive PropertyCombining Like TermsVariables on Each SideSolving Equations with Decimals and FractionsSimplifying ExpressionsDistributive PropertyExamplesCombine the ______________.Keep the _____________.Combining Like TermsExamples__________________ the coefficient to each ___________________ inside the ______________________.Solving EquationsInverse Operations_____________________________________________ ________________Steps to Solve EquationsExamples______________ PropertyCombine _______________________________ Operations __________________________ __________________________ No SolutionExamples___________________ cancel___________________ statementa bInfinite SolutionExamples___________________ cancel___________________ statementa = aHow to CheckExamples___________________ the value for the ___________________ on each side of the ___________________ .Is it _______________?Yes: ___________________ No: ___________________ Practice for Unit 3 – Create work boxes and show all work on separate piece of graph paper!!!Directions: Evaluate the expressions. Use x = -4, y = ? , and z = 829) 5z30) z – 231) 7xy2Directions: Simplify the expressions.32) 7x – 10x 33) x + x – 634) 8x – 4 + 7x + 9Directions: Simplify each expression.35) 7x – 9 + 3x + 436)8h – 3 – 4h + 9 37)-3p + 7 – 6p + 4 + p38)-5x + 9 + 3x – x – 4 + 8Directions: Solve each equation.39) -9x – 3x = 3640) y – 4 – 8 = 1041) 2k – 6 + 3k = 1442) 2m – 7m + 6 = -4Directions: Simplify each expression.43) 7(x – 4)44)-6(2x – 3)45)5(2x + 1) – 3x 46)-2(3x + 4) + x – 9 Directions: Solve each equation.47) 2(x – 7) = 2248)-4(y – 3) = 2049)3(2b – 1) = 5750)2(10 – m) = 30Directions: Solve the equation.51) 5x – 4 = 5x – 4 52) 3x + 7 = 3x – 2 53)3x + 7 = 754)x – 8 = x + 1 55) 3(2x + 8) = 6x + 2456) -6(x – 4) = 6x + 24Directions:Define the variable.Set up expressions.Set up the equation.Solve the equation.Reread the question.Four times a number increased by five is 29. Find the number. Three less than twice a number is -11. Find the number.Teddy bought a bat for $10 and x baseballs for $4 each. If he spent $22, how many baseballs did he buy?Ms Calbo has a tutoring company. She charges $20 per hour plus a $10 application fee. If someone paid him $190, how many hours did she tutor?Mr. Brown buys the basketball teams pizza every month for winning. In December, he bought 4 more than twice the number of pizzas he bought in November. If he bought 22 pizzas in December, how many pizzas did he buy in November?The Falcons won eight games more than they lost. If they played 78 games, how many games did they lose? Jacey wants new carpet in her bedroom. Carpet Plus charges $100 plus $8 per square foot. The World of Carpet charges $75 plus $10 per square foot. Find the number of square feet for which their prices are equal.Unit 4: Volume Cross Section of 3-D FiguresArea of 2-D FiguresArea of Compound ShapesVolume?PrismCylinderPyramidSphereSurface AreaSolving for Unknown MeasurementComparing Volumes and Determining the DifferenceComposite FiguresAreaRectangleTriangleCircleVolumePrismCylinderPyramidConeSpherePractice for Unit 4 – Create work boxes and show all work on separate piece of graph paper!!!65)64)63)Directions: Find the area or volume of the figure. If necessary, leave in terms of .27432001104901198883048066)67)25146001333502343151587568)69) 70)71) 2529840-4445 243840-4445-2286005651578) What is the effect on the volume when the height is doubled? What is the effect on the volume when the radius is doubled?Directions: Find the height of the solid.79) V = 3,000 ft3 80) V = 162 cm3321055911112581) V = 141.37 in382) V = 448 ft3Directions: Find the radius of the cylinder.7) V = 48 in38)V = 770 cm3Height = 3 inHeight = 5 cm9) V = 150 in310)V = 792 cm3Height = 6 inHeight = 7 cmUnit 5: Intro to Functions What is a Function?Identifying Functions and Non-FunctionsInterpreting Time-Distance GraphSketching GraphsWhat is a Function?FunctionsExamples__________ do not repeatEvery _________ has one __________.Pass the ________________________.Can be represented____________________.____________________.____________________.____________________.Inputs are _______________________.Outputs are______________________.Interpreting Time-Distance GraphsExamplesDefine and label the _____________.You may not always need ____________.Determine the __________ __________ should be _______ or _____________.Sketch the function based on the informationgiven.Remember the ____________ the graph, the the greater the ________________________.Unit 6: Linear Functions Defining and graphing linear functionsDetermining if a point is a solution to the linear functionDefining slope when given pointsSlope-intercept formDetermining slope and intercept from an equation Defining and Graphing Linear FunctionsGraphing Linear FunctionsExampleSolve for ________.Create a ____________ _______ ____________.Plot the points on a coordinate grid.Should yield a _____________________ line.All points on the line are ____________to the function.Label graph and axes.Special Cases3429000128905Determining if a Point is a Solution ExampleSolve for __________.Create __________________________OR _____________________________OR _____________________________.If yields a __________ statement thenpoint ________ a solution.Defining SlopeDefining Slope Given a GraphExamplesSlope is represent by ___________._________OR_________Defining Slope Given Points_________Describing SlopePositive Slopex ____________________ asy ____________________Negative Slopex ____________________ asy ____________________Zero Slopex ____________________ asy ____________________Undefined Slopex ____________________ asy ____________________Slope – Intercept Form01696085342900016960853429000421068504210685 ................
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