Released Assessment Questions, 20 15

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1 Released Assessment Questions, Grade 9 Assessment of Mathematics Applied: For use with Assistive Technology: Listen as your teacher reads the instructions. Some key points are listed below. Make sure you have the Formula Sheet for reference. The diagrams in this booklet are not all drawn to scale. Answering Multiple-Choice Questions: Answer all multiple-choice questions. If you fill in more than one answer to a question, or leave a question blank, the question will be scored zero. Incorrect answers will also be scored zero. Answering Open-Response Questions: Do all of your work for each question in the space provided for the question only. Write your solutions, including all calculations, clearly and completely. Attention: The format of this document differs from that of the actual assessment booklets, as the questions are sorted by strand. There are more multiple-choice and open-response questions in this document than in a regular booklet. You are now ready to start. Education Quality and Accountability Office, 2 Carlton Street, Suite 1200, Toronto ON. M5B 2M9 Telephone: Web site: Queen s Printer for Ontario.

2 Multiple-Choice, question 1 to 18: Question 1: Which of the following ratios is equivalent to: 2 to 5? A: 5 to 2: B: 2 to 7: C: 14 to 35: D: 22 to 25: Question 2: The ratio of boys to girls in Mandy s mathematics class is 3 to 12. This ratio is the same in Mandy s science class, in which there are 20 girls. How many boys are there in Mandy s science class? A: 5: B: 8: C: 11: D: 15: Question 3: Jake and Minh buy food for a fundraiser. One case of 24 hamburgers costs 37 dollars. One case of 12 drinks costs 9 dollars. How much will the food for 72 meals cost if each meal is made up of 1 hamburger and 1 drink? A: 2 hundred76 dollars: B: 1 hundred65 dollars: C: 1 hundred38 dollars: D: 92 dollars:

3 Question 4: A school orders 120 calculators. The school receives a shipment containing 80% of the order, and 1 out of every 3 of these calculators is black. How many black calculators has the school received in this shipment? A: 32: B: 40: C: 50: D: 96: Question 5: What is the value of negative 5 minus negative 3? A: negative 8: B: negative 2: C: 2: D: 8:

4 Thetwolinesegmentsarethesamelengthandareachlabeledp.Thetotalengthofthislonglineismisingandshownwithanotherline. Question 6: A line, square and cube are pictured below. Line: Square: Cube: Which of the following statements describes one of the above? A: The length of the line is p tothepowerof2. B: The area of the square is p tothepowerof2. C: The volume of the cube is 3p. D: The perimeter of the square is 2p.

5 Thehorizontalaxis,labeledTemperatureindegresCelsius,t,startsatnegative20andgoesupto60.Everyothergridlineislabeledinincrementsof20.Theverticalaxis,labeledVolumeinLitres,capitalV,startsat0andgoesupto4.Everyothergridlineislabeledinincrementsof1.Threpointsareshownonthegraph.Herearethecordinatesforeachpoint. CapitalP:(negative175,0decimal5): plus plus plus ket: Question 7: Which of the following is a simplified form of the expression below? 7: (bracket3x plus 5) brac A: 56x: B: 10x, 12: C: 21x, 5: D: 21x, 35: Question 8: Information about the volume of a particular gas and its temperature is shown on the graph. CapitalQ:(125,2): CapitalR:(525,4): Which of the following is true about the information represented in this graph? A: The volume of the gas is less at capital B: The volume of the gas is greater at capit R than at capit C: The temperature of the gas is lower at capital D: The temperature of the gas is higher at capital al P. al Q than at capital R. P than at capital Q than at capit Q. al R.

6 Numberofcarsold,1: Totalpay,2hundred50dolars: Numberofcarsold,4: Totalpay,6hundred50dolars: Numberofcarsold,5: Totalpay,7hundred50dolars: Numberofcarsold,1: Totalpay,2hundred50dolars: Numberofcarsold,4: Totalpay,10dolars: Numberofcarsold,5: Totalpay,1thousand2hundred50dolars: Numberofcarsold,1: Totalpay,3hundred50dolars: Numberofcarsold,4: Totalpay;1thousand40dolars: Numberofcarsold,5: Totalpay,1thousand7hundred50dolars: Numberofcarsold,1: Totalpay,3hundred50dolars: Numberofcarsold,4: Totalpay,6hundred50dolars: Numberofcarsold,5: Totalpay,750dolars: Question 9: Each week, a salesperson is paid a base salary of 2 hundred50 dollars plus 100 dollars for each car sold. Which of the following shows information that is all correct about the salesperson s total pay for a week? A: B: C: D:

7 AndtheverticalaxisislabeledHeightofwater,capitalH.Noscaleishownoneitheraxis.Theorigin,labeled0,isonthebotomleftcornerofthegraph.A,linestartshalfwayupthecapitalHaxis,andgoeshorizontalytotheright. AndtheverticalaxisislabeledHeightofwater,capitalH.Noscaleishownoneitheraxis.Theorigin,labeled0,isonthebotomleftcornerofthegraph.A,curvestartsathetopofthecapitalHaxisandcurvesdowntotherightslowlyatfirst,thencurvesoitisalmostverticalathendasitreachesthendofthet-axis. A n d t h e v e r t i c a l a x i s i s l a b e l l e d H e i g h t o f w a t e r, c a p i t a l H. N o s c a l e i s s h o w n o n e i t h e r a x i s. T h e o r i g i n, l a b e l l e d 0, i s o n t h e b o t t o m l e f t c o r n e r o f t h e g r a p h. A l i n e s t a r t s t h r e e q u a r t e r s u p t h e c a p i t a l H a x i s a n d g o e s d o w n, d i a g o n a l l y, t o t h e r i g h t. AndtheverticalaxisislabeledHeightofwater,capitalH.Noscaleishownoneitheraxis.Theorigin,labeled0,isonthebotomleftcornerofthegraph.A,curvestartsathetopofthecapitalHaxisandcurvesdowntotherightquicklyatfirstandthencurvesoitisalmosthorizontalathendasitreachesthendofthet-axis. Question 10: Rita measures the height of the water in a swimming pool as it is pumped out at a constant rate. Which graph best represents the height of the water? A: B: C: D:

8 n,1:capitalc,1: n,2:capitalc,3: n,3:capitalc,6: n,4:capitalc,10: n,1:capitalc,negative1: n,2:capitalc,negative2: n,3:capitalc,negative1: n,4:capitalc,negative2: n,0:capitalc,0: n,1:capitalc,1: n,2:capitalc,4: n,3:capitalc,9: n,0:capitalc,0: n,1:capitalc,3: n,2:capitalc,6: n,3:capitalc,9: Question 11: Use first differences to determine which table of values shows data from a linear relationship. A: B: C: D:

9 Thehorizontalaxis,labeledTimeinminutes,t,startsat0andgoesupto8.Everyothergridlineislabeledinincrementsof2.Theverticalaxis,labeledVolumeofwaterinLitres,capitalV,startsat0andgoesupto50.Everyothergridlineislabeledinincrementsof10.Fivepointsareploted.Alineisdrawnthroughalofthesepoints.Thecordinatesofthesefivepointsare: 0,50: 2,450: 4,40: 6,350: 8,30: Averticaldotedlinelabeledriseisdrawnfromthepoint(4,40),whichisontheline,downtothepoint(4,30).Fromthepoint(4,30),ahorizontaldotedlinelabeledrunisdrawntothepoint(8,30)whichisontheline.Arightriangleisdrawnathepoint(4,30)wherethesetwodotedlinesmet. Question 12: The graph below shows information about the linear relationship between the volume of water in a tank and time. What is the rate of change in this relationship? A: negative 0. Decimal0 4 litres per minute: B: negative 0. Decimal5 litres per minute: C: negative 25 litres per minute: D: negative 50 litres per minute:

10 Thehorizontalaxis,labeledTime(inminutes),t,startsat0,andgoesupto5.Everyothergridlineislabeledinincrementsof1.Theverticalaxis,labeledDistancebelowthesurfaceinmetres,capitalD,startsat0,andgoesupto40.Everyothergridlineislabeledinincrementsof8.Alineishownonthegraph.Herearethecordinatesoftwopointsontheline: 0,0: 5,40: Timeishown.Thehorizontalaxis,labeledTimeinminutes,t,startsat0,andgoesupto10.Everyothergridlineislabeledinincrementsof2.Theverticalaxis,labeledDistancebelowthesurface(inmetres),capitalD,startsat0,andgoesupto10.Everyothergridlineislabeledinincrementsof20.Alineishownonthegraph.Herearethecordinatesoftwopointsontheline: 0,0: 10,10: Question 13: The relationship between the distance below the surface and time for two scuba divers is shown by the graphs below. How much faster is diver B diving than diver A? A: 0 metres per minute. B: 2 metres per minute. C: 10 metres per minute. D: 12 metres per minute.

11 Question 14: The equation C = 45 plus 3d represents the relationship between total cost, C, in dollars, and the number of days, d. Which of the following is true about this relationship? A: The total cost is 48 dollars per day. B: The total cost is 45 dollars for 3 days. C: The total cost is made up of a 45-dollar fixed fee and 3 dollars per day. D: The total cost is made up of a 3-dollar fixed fee and 45 dollars per day. Question 15: The total cost of a cellphone plan, capit Capital C = 10 plus 0. Decimal1 5n: where n is the number of text messages sent. If 25 text messages are sent, what is the total cost? alc, in dollars, is determined by the equation: A: 13 dollars and 75 cents: B: 35 dollars and 15 cents: C: 100 dollars: D: 2 hundred53 dollars and 75 cents: Question 16: Amanda has a snow-shovelling business. Advertising costs her 5 dollars in total. She charges 15 dollars per driveway. Which equation represents the relationship between her profit, capitalp, and the number of driveways that she shovels, n? A: c apital P = 10n: B: capit alp = C: capit alp = 20n: 15n minus 5: D: capit alp = 5n minus 15:

12 NumberofYearboks.Thehorizontalaxis,labeledNumberofyearboks,n,startsat0,andgoesto80.Everyothergridlineislabeledinincrementsof20.Theverticalaxis,labeledTotalcostindolars,capitalC,startsat0,andgoesupto60.Everyothergridlineislabeledinincrementsof10.Adiferentlineisdrawnoneachgraph.Onlythecordinatesoftwopointsoneachlinewilbegivenwitheachanswerchoice. 0,250:and:50,350: NumberofYearboks.Thehorizontalaxis,labeledNumberofyearboks,n,startsat0,andgoesto80.Everyothergridlineislabeledinincrementsof20.Theverticalaxis,labeledTotalcostindolars,capitalC,startsat0,andgoesupto60.Everyothergridlineislabeledinincrementsof10.Adiferentlineisdrawnoneachgraph.Onlythecordinatesoftwopointsoneachlinewilbegivenwitheachanswerchoice. 0,250:and:50,50: Question 17: Last year s relationship between the total cost of producing yearbooks, capital C, and the number of yearbooks produced, n, is represented by the equation below. Capital C = 1 hundred50 plus 5n: This year, the initial cost is increased but the cost per yearbook is decreased. Which graph could represent this year s relationship between total cost and the number of yearbooks? A: B:

13 Thehorizontalaxis,labeledNumberofyearboks,n,startsat0,andgoesto80.Everyothergridlineislabeledinincrementsof20.Theverticalaxis,labeledTotalcostindolars,capitalC,startsat0,andgoesupto60.Everyothergridlineislabeledinincrementsof10.Adiferentlineisdrawnoneachgraph.Onlythecordinatesoftwopointsoneachlinewilbegivenwitheachanswerchoice. 0,150:and:60,30 Thehorizontalaxis,labeledNumberofyearboks,n,startsat0,andgoesto80.Everyothergridlineislabeledinincrementsof20.Theverticalaxis,labeledTotalcostindolars,capitalC,startsat0,andgoesupto60.Everyothergridlineislabeledinincrementsof10.Adiferentlineisdrawnoneachgraph.Onlythecordinatesoftwopointsoneachlinewilbegivenwitheachanswerchoice. 0,10:and:50,450: C: D:

14 Thehorizontalaxis,labeledNumberofrides,n,startsat0andgoesupto10.Everyothergridlineislabeledinincrementsof2.Theverticalaxis,labeledTotalCostindolars,capitialC,startsat0andgoesupto40.Everyothergridlineislabeledinincrementsof8.Fivepointsareploted.Herearethecordinatesofeachpoint: (0,8): (1,12): (2,16): Question 18: An amusement park has two options for rides. All-Day Pass: The total cost is 36 dollars for unlimited rides. Pay-as-You-Go: Information about the linear relationship between the total cost and the number of rides is shown on the graph. (3,20): (4,24): Which of the following is a correct comparison of these two options? A: Pay-as-You-Go is cheaper for 8 rides. B: The All-Day Pass is always more expensive. C: The All-Day Pass is cheaper if the number of rides taken is less than 6. D: Pay-as-You-Go is more expensive if the number of rides taken is more than 7.

15 Eachboxshowsacostforthecerealinsideofit.ThecostontheSmalBoxiszerodecimalzerozeronineightcentspergram.ThecostontheLargeBoxisfivedolarsandtwentyfivecentsfor480grams. of Open-Response, question 19 to 25: Question 19: Healthy Start A grocery store sells Healthy Start cereal in two different sized boxes as shown below. What is the difference in the cost of 100 grams Show your work. of cereal in these two boxes? The difference in the cost for 100 grams cereal in these two boxes is, [ bl ank spac e].

16 represents represents represents 1 = Question 20: Banking on a Car: Juan borrows money from his mom to buy a used car. His mom uses the equation shown below to determine the number of monthly payments Juan will make to pay her back. 1. decimal 3 T, 75n plus d: In the equation, T, the total cost of the car before tax, in dollars, n, the number of monthly payments and: d, the amount of his down payment, in dollars. How many monthly payments will Juan have to make to pay his mom back fully for a car that costs 2000 dollars before tax with a down payment of 5 hundred35 dollars? Show your work. The number of monthly payments is [blankspace]

17 DayandTotalnumberofpeniesinSheldon sjar. Day:1,TotalnumberofpeniesinSheldon sjar,1: Day:2,TotalnumberofpeniesinSheldon sjar,3: Day:3,TotalnumberofpeniesinSheldon sjar,7: Theverticalandhorizontalaxesaredrawnonthegrid.Theaxesmetinthebotomleftcornerofthegrid. Linear, Non-linear Question 21: Jar of Pennies: Sheldon creates a pattern by placing pennies in a jar. Each day he adds twice as many pennies as he did the day before. On Day 1, he places 1 penny in the jar. On Day 2, he adds 2 more pennies, for a total of 3 pennies in the jar. On Day 3, he adds 4 more pennies, for a total of 7 pennies in the jar. On Day 4, he adds 8 more pennies to the jar. He continues adding pennies using this pattern. Complete the table of values with the total number of pennies in Sheldon s jar on Days 4 and 5. Day:4,TotalnumberofpeniesinSheldon sjar,[blankspace]: Day:5,TotalnumberofpeniesinSheldon sjar,[blankspace]: Is the relationship between the total number of pennies in Sheldon s jar and the day number linear or non-linear? Circle one: Justify your answer. You may use the grid if you wish.

18 Numberofweksincehaircut,0: Lengthofhair,blank: Numberofweksincehaircut,1: Lengthofhair,4milimetres: Numberofweksincehaircut,2: Lengthofhair,blank: Numberofweksincehaircut,5: Lengthofhair,blank: Initial Question 22: What a Haircut! Cody gets a haircut. He measures the length of his hair as it grows back and discovers that it grows at a rate of 3 milimetres per week. Complete the following table of values for the linear relation between the length of Cody s hair and the number of weeks since his last haircut. State the rate of change and the initial value for this relationship. Rate of change: [blankspace] value: [blankspace] Write an equation to represent this linear relation, where capit al L is the length of Cody s hair, in milimetres, and n is the number of weeks since his haircut. Capital L = [blankspace]

19 spac e] Question 23: Cellphone Plans: A company offers two different cellphone plans. Plan A: 17 dollars per month for the cellphone, plus 25 cents per minute for additional talk time Plan B: 20 dollars per month for the cellphone, plus 15 cents per minute for additional talk time Both plans include 200 minutes of talk time for free. Determine the difference in total cost between the two cellphone plans for 237 minutes of talk time in one month. Show your work. The difference in total cost for 237 minutes of talk time is [blank

20 Thefrontfacehasaheightlabeledh,andalengthlabeled12centimetres.Adiagonalineisdrawnonthisfacefromonecornertotheopositecorneranditislabeled15centimetres.Thewidthoftherectangularbasedprismislabeled4centimetres. Hi nt: UsethePythagoreanTheoremaspartofyoursolutionproces. Question 24: Picture of a Prism: Determine the volume of the rectangular prism pictured below. Show your work. The volume of the rectangular prism is [blankspace]

21 ValueandJustificationusingeometricproperties: Value:x=[blankspace],Justificationusingeometricproperties,[blankspace]: Value:y=[blankspace],Justificationusingeometricproperties,[blankspace]: Question 25: Delightful Deck: Ursula is building a deck. A view of the surface of the deck from above is pictured below. Thetwoshapeshareasideandonotoverlap.Thebotomshapeisarightrianglewhichisitingonitsbaseanditsheightisontheright.Arightangleislabeledbetwenthesesidesonthebotomrightcornerofthetriangle.Thebotomleftcornerofthetrianglebetwenthebaseandthehypotenuseislabeledy.TheshapeontopoftherightriangleisaParalelogram.Thebotomsideoftheparalelogramisthehypotenuseofthetriangle.Therightsideoftheparalelogramismadebyextendingtheheightofthetriangleupwards.Theangleinthetoprightcorneroftheparalelogramislabeled65degresandtheangleinthetopleftcorneroftheparalelogramislabeledx. Complete the chart with the values of x and y. Justify your answers using geometric properties.

22 Multiple-Choice, question 26 to 31: Question 26: Which rectangle below has the smallest perimeter? A: B: C: D:

23 Therectanglehasabasethatislabeled54metresandawidththatislabeled30metres.Thetriangleisjoinedtotherectanglesothathesideofthetrianglethatisitsheight,isthewidthoftherectangle.Thisideofthetriangleisequalinlengthtothebaseofthetriangle.Arightangleislabeledbetwenthesetwoequalsides. mal 5 Question 27: Jensen is seeding his lawn. The shape of his lawn is shown in the diagram below. Each bag of grass seed covers 3 hundred10 metres squared. What is the minimum number of bags of seed that Jensen will need to seed his entire lawn? A: 5: B: 6: C: 7: D: 8: Question 28: Tennis balls have a radius of 3. deci centimetres. Which of the following is closest to the volume of 2 tennis balls? A: 88 centimetres cubed: B: 1 hundred80 centimetres cubed: C: 3 hundred59 centimetres cubed: D: 1078 centimetres cubed:

24 by by by by Question 29: The Snack Company sells popcorn in 2 different-sized boxes. Each box is in the shape of a rectangular prism. Box A has dimensions 10 centimetres Box B has dimensions 12 centimetres 20 centimetres 22 centimetres 24 centimetres. 20 centimetres. The price of the popcorn per centimetres cubed is the same for both boxes, and the price of each box is determined by the total volume of popcorn it can hold. If Box A s price is 6 dollars and 24 cents, what is the price of Box B? A: 5 dollars and 67 cents: B: 6 dollars and 24 cents: C: 6 dollars and 86 cents: D: 9 dollars and 62 cents: Question 30: A regular hexagon with one side extended is shown. Thesideofthehexagonbelowitsrightmostpointisextendedupandtotheright.Theanglebetwenthisextendedsideandthesideofthehexagonthatisabovethisrightmostpointislabeledx. What is the value of x? A: 30 : B: 60 : C: 120 : D: 240 :

25 Athirdlineisdrawn,whichstartsathetopleftofthediagram,crosestheparalelinesandendsathebotomrightofthediagram.Theangleabovethetoparalelineandtotheleftofthethirdlineislabeled36degres.Theangleabovethebotomparalelineandtheleftofthethirdlineislabeledx. Question 31: What is the value of x in the diagram below? A: 36 : B: 54 : C: 126 : D: 144 :