Academic. Grade 9 Assessment of Mathematics SAMPLE ASSESSMENT QUESTIONS

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1 Aemi Gre 9 Assessment of Mthemtis 211 SAMPLE ASSESSMENT QUESTIONS Reor your nswers to the multiple-hoie questions on the Stuent Answer Sheet (211, Aemi). Plese note: The formt of this ooklet is ifferent from tht use for the ssessment. The questions themselves remin the sme.

2 Gre 9 Assessment of Mthemtis, Whih of the following hs volume tht n e represente y s 3? s 3 Wht is the vlue of the expression 5(] )? ] ]6 ]1 Multiple-Choie s 4 Luke esigns gren in the shpe of right tringle s shown elow. s 3x s x The totl re of the gren is 96 m 2. Hint: A h 2 Wht vlue of m mkes the eqution 6 m true? s Whih is losest to the vlue of x in the igrm? 6 m 8 m 32 m 64 m Aemi 1

3 Multiple-Choie Gre 9 Assessment of Mthemtis, A squre n n equilterl tringle re piture elow. If the squre n the tringle hve the sme perimeter, wht is the vlue of x? (5x 3) (7x 1) 15 2 Aemi

4 Gre 9 Assessment of Mthemtis, 211 Open-Response 6 How High Is It? The yliner piture elow hs surfe re of 66 m m Use the following formul to etermine the height of the yliner: Surfe re = 2πr 2 1 2πrh Show your work. Aemi 3

5 Multiple-Choie Gre 9 Assessment of Mthemtis, Dehen hs ny-mking usiness. The grph elow shows the totl numer of nies his usiness hs proue y the en of eh y for the first four ys. Totl numer of nies proue C Totl Numer of Cnies Proue vs. Dy Dy 8 Krin hs jo t vieo store. The totl she is pi eh week is me up of n hourly rte plus $14 for trnsporttion. One week, she works 2 hours n is pi $215. Whih eqution represents the reltionship etween Krin s totl py, P, in ollrs, n the numer of hours she works, n? P n 1 14 P 5 14n P 5 1.5n 1 14 P 5 14n If this tren ontinues, whih of the following points represents y with more nies proue thn expete? (5, 5) (9, 85) (1, 13) (14, 14) 4 Aemi

6 Gre 9 Assessment of Mthemtis, Whih tle of vlues shows liner reltion etween C n n? Whih reltion oes not hve n initil vlue of 5? y 5 5 n n n n y x y 5 5x C C C C y x s Multiple-Choie The grph elow represents the reltionship etween Ren s istne from home n time. Distne from home (km) During whih setion of the grph oes Ren trvel the fstest? p q r w The tle elow represents liner reltion. Whih eqution represents this reltion? D Time, t p D 5 5t 2 D 5 1t q D 5 1t 1 5 D 5 5t 11 r Distne, D Time (min) w t Aemi 5

7 Open-Response Gre 9 Assessment of Mthemtis, 211 Follow the Bouning Bll This stter plot shows the reltionship etween the reoun height of ll n the height from whih the ll is roppe. R Reoun Height vs. Drop Height Reoun height (m) Drop height (m) h Drw line of est fit for the t on the gri ove. Determine n eqution for your line of est fit. Show your work. Eqution of line of est fit: 6 Aemi

8 Gre 9 Assessment of Mthemtis, 211 Open-Response f Getting Pi Hnnh s totl py inlues se slry n perent of her sles. The following tle shows her totl py for three ifferent sles levels. Sles ($) Totl py ($) Determine Hnnhʼs totl py when her sles re $47. Show your work. Aemi 7

9 Multiple-Choie Gre 9 Assessment of Mthemtis, 211 g Whih of the following nnot e n eqution of line? x 5 2 y 5 7 y 5 2x x 1 y j Nevenk n Jun su ive. The grph elow represents the reltionship etween the istne from the surfe, in metres, n time, in minutes, for oth ivers s they swim own from the surfe n then swim k up. Distne from Surfe vs. Time D h Whih of the following is the eqution of the line 6x 2y 12 in the form y mx? y 5 ]3x 6 Distne from surfe (m) y 5 3x t 1 y 5 ] x y 5 x Time (min) Jun Nevenk Whih sttement elow is true? Jun swims k up t rte of.5 m/min. Nevenk swims k up t rte of 4.5 m/min. Nevenk swims own fster thn she swims k up. Jun swims own n k up t the sme rte. 8 Aemi

10 Gre 9 Assessment of Mthemtis, 211 Multiple-Choie k Alex hs $15. She spens the sme mount eh week. After 6 weeks, she hs $3 remining. The reltionship etween the mount of money Alex hs n the numer of weeks is represente y line. Wht is the slope of this line? ]25 ]2 2 l Whih of the following represents the grph of the eqution 2x 2 4y 5 8? y x 25 y x y x y x Aemi 9

11 Multiple-Choie Gre 9 Assessment of Mthemtis, 211 s Whih eqution represents line tht hs the sme y-interept s 2x 1 3y 2 6 5? y x 1 2 y 5 2x 2 2 y 5 ] 1 2 x 1 6 y 5 ]2x 2 6 s Nte uys vieo-gme system. The system osts $3. Gmes ost $6 eh. He pys 13% tx on the system n on eh gme. He hs $85 in totl to spen. After he pys for the system, how mny gmes is Nte le to uy? extly 12 extly 9 no more thn 7 no more thn 3 1 Aemi

12 Gre 9 Assessment of Mthemtis, 211 Open-Response ss Hit the Slopes Consier the two reltions represente elow. Reltion 1 Reltion 2 4 y 3 2 5x 2y x Determine the slope of the line representing eh reltion. Show your work. Slope of line representing Reltion 1: Slope of line representing Reltion 2: Whih of these reltions is represente y the steeper line? Justify your nswer. Aemi 11

13 Open-Response Gre 9 Assessment of Mthemtis, 211 s How Mny Uniforms? The eqution C 5 2n 1 35 represents the reltionship etween the ost of shool volleyll uniforms, C, in ollrs, n the numer of uniforms orere, n. The uniform ompny requires tht the shool orer minimum of 15 uniforms. The shool hs mximum of $6 to spen on the uniforms. Determine the possile vlues for n n C in this sitution. Show your work. The possile vlues for n re. The possile vlues for C re. 12 Aemi

14 Gre 9 Assessment of Mthemtis, 211 Multiple-Choie sf Tom uses fening to rete retngulr horse enlosure. He uses the sie of rn s one of the sies of the enlosure. Brn sh Plo is esigning retngulr flg tht onsists of three oloure tringles. The piture elow shows the olours of the tringles n the ost of eh olour of mteril. With Re $.3/m 2 Green $.2/m 2 Blue $.1/m 2 5 m Length Tom hs 48 metres of fening to use for the three sies of the retngulr enlosure. 1 m Whih set of imensions will use the entire 48 m of fening? with is 8 m, length is 6 m with is 12 m, length is 12 m with is 24 m, length is 12 m with is 12 m, length is 24 m Wht is the totl ost of the mteril? $75. $87.5 $15. $175. sg Consier the following tringle. sj A yliner hs volume of 4p m 3 n imeter of 2 m. 3.5 m 16 m Whih of the following is losest to the height of the yliner? Bse 1 m Whih expression n e use in the proess of etermining the length of the se? 4 m 2 m m Aemi 13

15 Multiple-Choie Gre 9 Assessment of Mthemtis, 211 sk Consier the igrm elow. Whih of the following equtions is lwys true? x x 5 1 x 5 1 x 5 2 x 5 2 sl A retngulr sign is uilt s shown elow. The four supports for the k of the sign form four ongruent tringles. 32 x Wht is the vlue of x? Aemi

16 Gre 9 Assessment of Mthemtis, 211 Open-Response Builing n Ie Rink Jke uils n ie rink s shown elow. 25 m 1 m Determine the perimeter of the rink. Show your work. Aemi 15

17 Open-Response Gre 9 Assessment of Mthemtis, 211 Shzm Prvin esigns lightning olt using two qurilterls n one tringle s shown elow. 66 y y x 25 Complete the tle elow. Justify your nswers using geometri properties. Angle mesure Justifition x y 16 Aemi

18 Gre 9 Assessment of Mthemtis 211 Smple Assessment Questions: Aemi Answer Key Respon in ooklet Respon in ooklet. 14. Respon in ooklet. 22. Respon in ooklet. 3. Respon in ooklet Respon in ooklet. 31. Respon in ooklet En of Assessment Answer Key Smple Assessment Questions

19 Applie Gre 9 Assessment of Mthemtis 211 SAMPLE ASSESSMENT QUESTIONS Reor your nswers to the multiple-hoie questions on the Stuent Answer Sheet (211, Applie). Plese note: The formt of this ooklet is ifferent from tht use for the ssessment. The questions themselves remin the sme.

20 Gre 9 Assessment of Mthemtis, The imensions of retngle re in 3:5 rtio. If the shorter sie lengths re 3 m, wht re the lengths of the longer sies? 1 m 15 m 18 m 5 m 2 The tle elow shows informtion out renting movies from four ifferent stores. Whih store offers the lowest ost per movie? Nme of store Gret Flix Net Show Movie Time DVDs R US Totl ost ($) Gret Flix 6 Numer of movies rente Net Show 12 3 Movie Time 25 1 DVDs R Us Multiple-Choie 3 The tle elow shows the prie per se of wter t ifferent stores. Evelyn is uying 12 ottles of wter. At whih store shoul Evelyn uy her wter to py the lest? Store Chepies Foosmrt Vriety Foos Super Groers Chepies Foosmrt Vriety Foos Super Groers 4 The ost of n MP3 plyer is $299. A newer moel osts 2% more. Whih of the following is losest to the sle prie of the newer moel fter 3% isount? $ $269.1 $289. $31.96 Prie per se $1.75 $2.25 $4.59 $4.99 Numer of 5 ml ottles per se Applie 1

21 Multiple-Choie Gre 9 Assessment of Mthemtis, Wht is the vlue of the expression? A nle me of wx is in the shpe of yliner. 6 m m 5 6 Whih vlue of x mkes the eqution 1 x 1 true? The eqution h represents the reltionship etween the istne,, tht person n see in n open fiel, in kilometres, n the personʼs height, h, in metres. One fternoon, Amy n see istne of 4.5 km. Whih of the following is losest to Amyʼs height? 1.1 m 1.6 m 2.1 m 2.5 m Whih is losest to the totl mount of wx to mke the nle? 226 m m m m 3 9 Whih expression is simplifie form of Hint: 8x 2 2 6x 8x 2 1 6x ]8x ]8x V 5 pr 2 h ]2x(]4x 1 3)? 2 Applie

22 Gre 9 Assessment of Mthemtis, 211 Open-Response Guzzling Gs Dvi n Shunese eh tke 45 km trip. Dvi rives r n uses 7 L of gs per 1 km. Shunese rives truk n uses 12 L of gs per 1 km. If gs osts $.9/L, how muh more will it ost Shunese thn Dvi to rive 45 km? Show your work. Applie 3

23 Open-Response Gre 9 Assessment of Mthemtis, 211 Juggling Juie Juie is sol in two ifferent ontiners, one n ue, s shown elow. 3 m 12 m 8 m Cone Volume πr2 h 3 Cue Volume l 3 Whih ontiner hols more juie? Cirle one: Cone Cue Show your work. 4 Applie

24 Gre 9 Assessment of Mthemtis, 211 Multiple-Choie s The grph elow represents the reltionship etween the numer of lories n the volume for vrious rinks. N Numer of Clories vs. Volume Numer of lories 4 Q 3 2 R 1 P T V Volume (ml) Whih of the following points represents rink with more lories thn expete for its volume? P Q R T Applie 5

25 Multiple-Choie Gre 9 Assessment of Mthemtis, 211 A plumer hrges n initil fee of $5, plus n itionl $25 per hour. Totl Cost vs. Time C Whih grph represents this reltionship? Totl ost ($) Totl ost ($) Totl Cost vs. Time C Time (h) Totl Cost vs. Time C t t Totl ost ($) Totl ost ($) Time (h) Totl Cost vs. Time C Time (h) t t Time (h) 6 Applie

26 Gre 9 Assessment of Mthemtis, 211 Multiple-Choie f A snowstorm lsts for seven hours. Dt is reore for the epth of snow for the first five hours. g In whih of the following ptterns is there liner reltionship etween the numer of she squres n the term numer? Time (h) Depth of snow (m) Term 1 Term 2 Term 3 Term 4 Whih grph elow est moels the epth of snow uring the five hours? H Term 1 Term 2 Term 3 Term 4 Depth (m) Time (h) t Term 1 Term 2 Term 3 Term 4 H Depth (m) Term 1 Term 2 Term 3 Term 4 Time (h) t H Depth (m) Time (h) t H Depth (m) Time (h) t Applie 7

27 Multiple-Choie Gre 9 Assessment of Mthemtis, 211 h An online musi store provies musi tht memers n ownlo. The store hrges memership fee n ost per song. k The totl ost for printing lssifie vertisement in lol newspper is me up of $3 fee, plus $.1 per wor. The hrt elow represents the reltionship etween the totl ost n the numer of songs ownloe. Numer of songs Totl ost ($) Whih eqution elow moels the reltionship where C is the totl ost to ple the vertisement n w is the numer of wors? C w 1 13 C w C w C w Whih of the following is not true out this reltionship? It is non-liner. It hs n initil ost. It hs onstnt rte of hnge. It n e represente y stright line. j At her fitness lu, Jonne is hrge $15 per month. The totl ost for 12 months is $27. Is the reltionship etween the totl ost n the numer of months iret or prtil vrition, n wht is the initil fee? iret vrition, $ iret vrition, $18 prtil vrition, $15 prtil vrition, $9 l s Plo hs ellphone. The reltionship etween his totl monthly ost, C, in ollrs, n the numer of minutes he uses the phone, t, is represente y the eqution C t. Whih of the following is not true out this reltionship? The ost per minute is $.25. The vlue of the rte of hnge is.25. The totl monthly ost for 1 minute is $2. The grph of the reltionship hs C-interept of 2. The eqution C 5 15n 1 1 represents the reltionship etween the totl ost of gym memership, C, in ollrs, n the numer of months of memership, n. Whih sttement out this gym memership is true? It hs n initil ost of $15. It osts $115 per month. It hs n initil ost of $15 n fee of $1 per month. It hs n initil ost of $1 n fee of $15 per month. 8 Applie

28 Gre 9 Assessment of Mthemtis, 211 Multiple-Choie s The following esries Ih s rive from Winsor to Toronto: One hour fter leving Winsor, he stops for 15 minutes to hve snk. Distne from Toronto vs. Time D He then rives for two more hours n then stops to visit frien for one hour. He then ompletes his rive to Toronto t fster rte thn ny other segment of his trip. Distne from Toronto (km) Whih grph est esries his trip? Distne from Toronto vs. Time Time (h) t D Distne from Toronto vs. Time Distne from Toronto (km) Time (h) t Distne from Toronto (km) D Distne from Toronto vs. Time Time (h) t D ss Dn nees to get his r fixe. Distne from Toronto (km) Time (h) t Fst Freie hrges $44 for mterils, plus $5 per hour for lour. Rpi Ron hrges $36 for mterils, plus $6 per hour for lour. Whih repir shop hrges less for 5-hour jo, n how muh less? Rpi Ron hrges $8 less. Fst Freie hrges $3 less. Rpi Ron hrges $3 less. Fst Freie hrges $1 less. Applie 9

29 Multiple-Choie Gre 9 Assessment of Mthemtis, 211 s The urrent pln for ownloing musi is me up of flt fee of $2 n fee of $.5 per ownlo. A new pln is me up of flt fee of $1 n fee of $.5 per ownlo. Whih grph represents oth plns? sf Two helth lus, Super Fit n Boy Plus, offer monthly memerships. The totl monthly ost for eh lu is represente y the grphs elow. C Totl Monthly Cost vs. Numer of Visits Cost ($) Cost ($) Cost ($) C 5 4 Current pln New pln n Numer of ownlos C Current pln New pln n Numer of ownlos C n Numer of ownlos Current pln New pln Totl monthly ost ($) Whih of the following is true? Super Fit Boy Plus Numer of visits Boy Plus is lwys heper. Super Fit is lwys more expensive. Super Fit is heper if the numer of visits is fewer thn 7. Boy Plus is more expensive if the numer of visits is greter thn 9. n Cost ($) C 5 Current pln 4 3 New pln n Numer of ownlos 1 Applie

30 Gre 9 Assessment of Mthemtis, 211 Multiple-Choie sg Corrin wnts to rent snowmoile for y n onsiers two rentl ompnies. The reltionship etween the totl ost of renting from Trils-R-Us n the numer of kilometres trvelle is represente y the grph elow. C Totl Cost vs. Numer of Kilometres Trvelle 12 Trils-R-Us 1 Totl ost ($) Numer of kilometres trvelle n Off-Ros hrges flt rte of $9 for y with unlimite kilometres. At how mny kilometres is the totl ost the sme t oth rentl ompnies? 7 km 8 km 9 km 1 km Applie 11

31 Open-Response Gre 9 Assessment of Mthemtis, 211 sh Stk It Jun rws the first three terms of pttern s shown elow. Term 1 Term 2 Term 3 The pttern ontinues to grow in the sme wy. Complete the following tle oring to the pttern. N Numer of Dots vs. Term Numer Term numer, n 1 2 Numer of ots, N Numer of ots n Term numer Grph the t from the tle on the gri ove. A sle for the N-xis. Drw line or urve of est fit for the t. 12 Applie

32 Gre 9 Assessment of Mthemtis, 211 Open-Response sj Blloon Rie The reltionship etween the height of hot-ir lloon, H, in metres, n time, t, in minutes, is represente elow. H Height of Blloon vs. Time Height of lloon (m) Time (min) Determine n eqution to represent the reltionship etween the height of the lloon n time. t H = Show your work. Applie 13

33 Open-Response Gre 9 Assessment of Mthemtis, 211 sk Wlk This Wy Muro tkes wlk. The grph elow shows the reltionship etween Muro s istne from home n his wlking time. Distne from Home vs. Time Distne from home (m) D Time (min) t In the tle elow, ompre Muro s istne from home, his spee n the iretion in whih he is trvelling in the vrious segments of his wlk. Segment of grph Comprison to other segments 14 Applie

34 Gre 9 Assessment of Mthemtis, 211 Multiple-Choie sl Whih imensions proue the smllest perimeter for retngulr re of 12 m 2? 2 m 3 6 m Use the Pythgoren theorem to fin the length of the igonl in the retngle elow. 3 m 3 4 m 4 m 3 3 m 6 m 3 2 m Digonl 8 m Two squre grens re shown elow. A welome nner extens from orner of Gren A to orner of Gren B. Gren A re 42 m 2 Bnner Gren B re 36 m 2 Whih is losest to the length of the igonl? 135 m 97 m 66 m 58 m 55 m Whih is losest to the length of the nner? 6 m 9 m 12 m 78 m Applie 15

35 Multiple-Choie Gre 9 Assessment of Mthemtis, 211 s Hnn works pinting selnt on rivewys. She hrges $7.5/m 2. Consier the squre elow. 5 m 5 m 9 m 2.5 m 6 m Wht is the re of the she prt of the squre? 36 m 2 How muh will she hrge to pint the rivewy shown ove? $215. $ m 2 18 m 2 9 m 2 $28. $337.5 f Consier the igrm elow x Wht is the vlue of x? Applie

36 Gre 9 Assessment of Mthemtis, 211 Multiple-Choie g Consier the igrm elow. x w y z Whih eqution is true? x = z w = y y 1 z = 188 w 1 z = 188 Applie 17

37 Open-Response Gre 9 Assessment of Mthemtis, 211 h Win in My Sils A sil for silot is represente elow. 8 m 4 m 4 m 6 m The unshe prt of the sil is me with mteril tht osts $32/m 2. The she prt of the sil is me with mteril tht osts $125/m 2. Determine the totl ost of the sil. Show your work. 18 Applie

38 Gre 9 Assessment of Mthemtis, 211 Multiple-Choie j Designing Consier the esign elow. x y Complete the tle elow with the vlues of x n y. Justify your nswers using geometri properties. Vlue Justifition using geometri properties x y Applie 19

39 Gre 9 Assessment of Mthemtis 211 Smple Assessment Questions: Applie Answer Key Respon in ooklet Respon in ooklet. 36. Respon in ooklet Respon in ooklet. 37. Respon in ooklet Respon in ooklet En of Assessment 1. Respon in ooklet Answer Key Smple Assessment Questions

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