Grade Nine 1)Elizabeth visits her friend Andrew and then returns home by the same route. She always walks 2km/h when oin u!hill" #km/h when oin downhill and $km/h when on level round. %f her total walkin time is # hours" then what is the total distan&e she walks in km' 2)(oy&e was de&oratin her store window for a oin out of business sale. She wanted to make a ure that looks like the followin. *he shaded !ie&e is made of a di+erent material material.. ,ow mu&h material does she need n eed in metres s-uared'
$)%n 2 (oy&e needed to nd the material she would need for the shaded reion. ,ow mu&h material would she need for the unshaded reion in m2' )Geore and 0hil were !layin with their sh tank aain. *hey had a di&ult time kee!in their sh alive. *he sh tank is 1&m lon" # &m wide and &m hih. *hey tilted the tank" as shown" restin on a # &m ede" with the water level rea&hin the mid!oint of the base. 3hen they rest the tank down to a horizontal !osition" !osition" what is the de!th of the water in &m'
4)Ale5" 6red 6red and *homas run at &onstant rates. %n a ra&e of 1"m" Ale5 nished 2m ahead of 6red and m ahead of *homas. 3hen 6red nished" how far was he ahead of *homas' 7in m)
#)%f A89: is a s-uare and A8E is an e-uilateral trianle" trianle" then what is the measure of ; 869'
<)An unusual die has si5 fa&es labelled 1"2"$"4"< =. %f two of these di&e are rolled" and the numbers showin on the u!!er fa&es are added" what is the number of !ossible di+erent sums' >)*he ?uin!ool family de&ided to build a !ool of the followin sha!e. *he sides of their 12 @ = yard are trise&ted. 3hat is the !erimeter of the shaded !ool'
=)A &lassroom &ontained an e-ual number of boys and irls. Eiht irls left to !lay ho&key" leavin twi&e as many boys as irls in the &lasssroom. 3hat was the oriinal number of students !resent' 1)6lora had an averae of 4# on her rst < e5ams. 3hat would she have to make on her eihth e5am to obtain an
averae of # on > e5ams' 11)% have a broken fan belt on my &ar. *he belt oes around 2 !ulleys" whose &enters are 14&m a!art and ea&h !ulley is &m in diameter. ,ow lon should the belt be' 12)9omin out of the ro&ery store" Ebree has eiht &oins" of whi&h none is a halfBdollar" that add u! to C1.4. Dnfortunately" on the way home she loses one of them. %f the &han&es of losin a -uarter" dime or ni&kel are e-ual" whi&h &oin is most !robably lost' 1$)(oe ives Ni&k and *om as many !eanuts as ea&h already has. *hen Ni&k ives (oe and *om as many !eanuts as ea&h of them then has. 6inally" *om ives Ni&k and (oe as many !eanuts as ea&h has. %f at the end ea&h has si5teen !eanuts" how many !eanuts did ea&h have at the beinnin' 1)After a ath test" ea&h of the twentyBve students in the &lass ot a !eek at the tea&herFs rade sheet. Ea&h student noti&ed ve AFs. No student saw all the rades and no student saw his or her own rade. 3hat is the minimum number of students who s&ored A on the test' 14) 8art Sim!son oes to the &orner store and buys an e-ual number of $4 &ent and $ &ent &andies for C22.<4 7thatFs a lot of &andy) ,ow many &andies did he buy' 1#) *he 8and 9ommittee of 1 !eo!le wishes to set u! a tele!hone &all system. *he initial &onta&t !erson &alls three other !eo!le" ea&h of whom &all three others and so on" until all the !eo!le in the 8and 9ommittee have been &onta&ted. 3hat is the ma5imum number of !eo!le they need to make the &alls. 1<)Students in an elementary &lass de&ided to s!end : dollars for a !resent for their favourite tea&her" rs. 8allentine" ea&h &ontributin an e-ual amount. 8e&ause fteen students refused to &ontribute" ea&h of those remainin areed to &ontribute an additional" e-ual amount. 3hat was the additional amount ea&h had to &ontribute" in dollars' 1>)%an was enterin a ath &ontest for Grade =. ,e was workin on this !arti&ular !roblem. ,e was havin di&ulty with the answer. *his was the !roblemH *he inteers reater
than 1 are arraned" four in ea&h row" in 4 &olumns" as followsH
a 2 1
b $ = 11 1<
&
d
> 12 1#
4 < 1$ 14
e
# 1
%f he followed the !attern what &olumn would the number 12 fall in' 1=)*hree rade nine ath students were iven the followin !roblemH A three diit number 2A is added to $2= and ives 48$. %f 48$ is divisible by $" then what is the larest !ossible value of A' Ine student thouht A &ould be 1. Another student thouht A was 4. *he last student thouht A was . 3ho was &orre&t' 2)(oy" Noella and ,olly were !layin Jum! ro!e. (oy and Noella at !oints 8 and 9 were twirlin the ski!!in ro!e waitin for ,olly at !oint A to Jum! into the middle of the ro!e 7at !oint :). *he three irls formed a = deree anle. ,olly was 1m away from Noella and 1m away from (oy. ,ow far does she have to Jum! into the middle of the ski!!in ro!e' A: is
!er!endi&ular to 89.
21)Kou are iven this ra!h of a trianle :E6 and you are asked its area. 3hat do you think it is'
22)9onstable 8ob is drivin alon the *ransB9anada ,ihway at 1 km/h. ,e is !assed by elissa who is drivin in the same dire&tion at a &onstant s!eed. *en se&onds after elissa !assed 8ob" their &ars are 1m a!art. 3hat is the s!eed of elissaFs &ar in km/h'
2$)
*rianle A89 is an isos&eles riht anled trianle with 89 L A8 L 2. A &ir&ular ar& of radius 2 with &entre 9 meets the hy!otenuse at :. A &ir&ular ar& of radius 2 with &enter a meets the hy!otenuse E. 3hat is the area of the shaded reion' 2)6red !i&ked four numbers out of a hat. *he averae of the four numbers is =. %f three of the numbers are 4" = and 12" then what is the fourth number' 24)Ste!hanie wasnFt very keen on Alebra. ,er tea&her ave her an Alebra !roblem and told Ste!hanie to solve it. She was
havin !roblems" &an you hel! her' $5 M < L 5 2 M k L <5 M 14 3hat is the value of k' 2#) 9hris asked oretta her ae and she saidH O
Py ae'P she asked" PyouFll have to uessP P(ust let me think" A," thatFs itH yesP PQeverse my ae" divide by three" add thirtyBfour" my ae youFll seeP ,ow old was oretta' 2<)Geore (e+erson !lans to drive from his home to Edmonton" a tri! of 22km. ,is &ar has a 2 allon tank and ets 2)9an you uess this number'
R R R R R R
*he number is not an odd number. %t has e5a&tly four fa&tors. %f you reverse the diits" a !rime number is formed. *he sum of the diits is a two diit !rime number. *he number is less than the s-uare root of 1. Ine of the diits is a s-uare number. 3hat number are we thinkin of' 2=)P3as that your bike om'P asked 9harlene in awe. ,er mother looked at the faded old !hoto and re!lied" Py rst" and % earned it. % ot a Job that summer with a &y&le dealer and he was to !ay me thirty dollars and this new bike for seven weeks of work. 8ut % didnFt enJoy the Job so % -uit after four weeks. ,e ave me three dollars and % ke!t the bike.P ,ow mu&h was the bike worth' $)A &ubi& metre of water weihs 1k. 3hat is the weiht of a waterbed mattress that is 2 metres by $ metres by 2&m if the &asin of the mattress weihs 1k' $1)elissa and 9rai were doin their math homework. *hey had a disareement on one of the !roblems. *he !roblem read" P3hat is the value of 7)72 1==#)' elissa found it to be 7> 1==#)" but 9rai disareed and felt it was 72 1==>). 3ere either of them riht' %f so" who was riht' $2)A farmer found an advertisment for a !lot of land with very ood soil and an askin !ri&e of C124.. *he !lot of land
looked like thisH 3hy didnFt the farmer buy the land'
$$)%n a re&ent survey" of houses &ontained two or more !eo!le. If those homes &ontainin only one !erson" 24 &ontained a male. 3hat is the !er&entae of all houses whi&h &ontain e5a&tly one female and no males' $)%n a re&ent ele&tion at the :r. (ohn ,uh Gillis ,ih S&hool" Susie 9ook re&eived 42 votes" Gre a&:onald re&eived $ votes and *ravis Austen re&eived 1$ votes. %f = of those eliible to vote did so" what was the number of eliible voters' $4)%f the ure shown is folded to make a &ube" then what is
the letter o!!osite the S'
$#)Jill loves math but she hates this !roblem. 9an you hel! her' *he sum of four numbers is #. %f you add $ to the rst number" $ is subtra&ted from the se&ond number" the third is multi!lied by $ and the fourth is divided by three" then all the results will be e-ual. 3hat is the di+eren&e between the larest and the smallest of the oriinal numbers' $<)%f the ve e5!ressions 25 M 1" 25 B $" 5 M 2" 5 M 4" and 5 B $ &an be arraned in a di+erent order so that the rst three have a sum 5 M $" and the last three have a sum 5 M " what would the middle e5!ression be' $>)%n our volleyball leaue" the numbers on the Jerseys may be
formed usin one or two diits &hosen from 1" 2" $" " 4. Numbers with re!eated diits are allowed but the sinle diit numbers are not allowed. 3hat is the total number of !ossible Jersey numbers for ea&h team' $=)ark has C.4 and (eanBartin has C$.. ark s!ends twi&e as mu&h as (eanBartin and now sees that he has half as mu&h money left as (eanBartin has left. ,ow mu&h money did ark s!end' ,ow mu&h money did (eanBartin s!end' ,ow mu&h do ea&h of them have left' )A motor&y&le and a tru&k left a roadside diner at the same time. After travellin in the same dire&tion for one and a -uarter hours" the motor&y&le had travelled 24km farther than the tru&k. %f the averae s!eed of the motor&y&le was #km/hour" nd the averae s!eed of the tru&k. 1)Similar re&tanles are &onstru&ted on the sides of a riht trianle as shown. 6ind their areas and a relationshi! amon those areas. ,ave you seen a similar relationshi!'
2)*rianle 0?Q is e-uilateral. ?Q L $ units" 8 is the mid!oint of ?A. ?A is !er!endi&ular to 0Q. 3hat is the lenth of 08'
$)% have sold 2/$ of my !en&ils for C.14 ea&h. %f % have > !en&ils left" how mu&h money did % &olle&t for the !en&ils % sold' )*he minute hand of a &lo&k is #&m lon. *o the nearest &entimeter" how far does the ti! of the minute hand move in $4 minutes' 4)*he numerator of a &ertain fra&tion is $ less than the denominator. %f the numerator is tri!led and the denominator is in&reased by <" the value of the resultin fra&tion is $/2. 3hat was the oriinal fra&tion' 5 L denominator 5B$ L numerator #):arryl ate 1 !eanut butter &u!s in ve days. Ea&h day he ate si5 more than he ate the !revious day. ,ow many !eanut butter &u!s did :arryl eat on the rst day' <)3hat is the ne5t term in the se-uen&e' 2" 1" 22" . >)A Qoman boy was iven this !uzzleH *ake one hundred one" and to it a5 the half of a dozen" or if you !lease si5T 0ut fty to this" and then you will see what every ood boy to others should be. =)Solve the mai& s-uareH
2 U
U
BBBBMBBBBMBBBB U U BBBBMBBBBMBBBB $> U $ U $# 4)illy had a math !roJe&t to do for her eometry &lass. ,er tea&her wrote" PA &ubo&tohedren is a !olyhedron that &an be formed by sli&in a &ube at the mid!oints of its edes.P illy
had to nd the surfa&e area of the &ubo&tobedren formed by a &ube havin a side of lenth &m' GQA:E N%NE ANS3EQS
1) ANS3EQH 5 B :istan&e of D!hill K B :istan&e of :ownhill V B :istan&e evel Ground *otal walkin timeL#L75/2My/#Mz/$)M75/#My/2Mz/$)7*his is used for her walkin ba&k BBB u!hill turns to down hill and downhill turns to u!hill) #75/2My/#Mz/$My/2M5/#Mz/$)L$# $#L75MyMz) LLLW 5MyMzL$#/L= LLLLW She walks 1>km in total. 2) ANS3EQH Area of half 9ir&le
Area of radius 2BW AL0i@r2 L0i 71)2 L0i
0i/2 L 0i/2
Area of little &ir&le. AL0i2 L0i7.4)2 L0i7.2$) L0i/ 0i/ @ 1/2 L 0i/> 0i/2 B 0i/> L area of one 0i/> B 0i/> L $0i/>
$0i/> @ 2 L #0i/> L $0i/ m 2 $) ANS3EQH Area of lare &ir&le AL0i@r2 L0i71.4)2 L2.240i 2.240i B area shaded L 2.240i B .<470i)m 2 L $0i/2m2 ) ANS3EQH Xolume of the water L Xolume of 1/2 of tank L 1/2 1&m @ &m @ #&m L 12" 1/2 712") L #" #" L 1 &m @ # &m @ d 1 &m L d 4) ANS3EQH BW24m ahead et 5 L time for Ale5 to nish et t L time for 6red to nish Ale5 6red *homas BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB dist at 5 1m >m #m S!eed
1m/5
>m/5
#m/5
6ind the time it will take 6red to nish 2m/s!eed76red)Lt 2m / >m / 5 2 @ 5 / > L t 5/ L t ,ow far &an *homas o in that time76red was 2 ahead and will o antoher 2) t@s!eed7*homas) #m/5 @ 5/ L 14m in that time
B 14 L 24m *homas has 2m left to o. #) ANS3EQH Anle 6 L 14 derees <) ANS3EQH 1 1M1" 1M2" 1M$" 1M4 1M<" 1M=" 2M$" 2M4" 2M<" 2M=" $M=" 4M=" ) AnswerH
2 M $2 L &2 1# M = L & 2 24 L &2 &L4
72 @ ) M 72 @ $) M 7 @ 4) L $ =) ANS3EQH et the number of irls or boys L 5
275B>) L 5 25 B 1# L 5 5L1# *here are 25 students in the &lass" therefore there are $2 students. 1) ANS3EQH et 5 L the mark on the eihth e5am. 4# L .4# 7.4# @ < M 5)/> L .# $.=2 M 5 L .# @ > $.=2 M 5 L .> 5 L .>B$.=2 5 L .>> L >> 11) ANS3EQH
Area of &ir&le L 70i)r2 L 70i)&m2 L 0i&m2 14 M 14 M 0i &m"su!W2 L 2.# &m 12) ANS3EQH %f or fewer are -uarters and the rest dimes and ni&kels" it wouldnFt brin the total to C1.4 with the dimes or ni&kels. 4 are -uarters BW C1.24 Ither $ dimes or ni&kels make u! 2 &ents. 0QI8A8%%*%ESH osin a -uarter L 4/> &han&es osin a dime L 1/>
osin a ni&kel L 2/> L 1/ Greatest !robability BW -uarter ;B Answer 1$) ANS3EQH t (oe
Ni&k
*om
1#
1#
1#
$
>
>
$2
2
2>
1#
1
2#
1
>
(oe Ni&k *om
B 2# B 1 B > 0eanuts
1) ANS3EQH # students QEASINH %f e5a&tly 4 AFs were iven in the &lass" then the students who s&ored these AFs saw their own rade. %f si5 AFs had been iven then ea&h of the A students &ould have seen the other 4 AFs in the &lass. # is the minimum. 14) ANS3EQH Y L I6 $ &ent &andy L of $4 &ent &andy .$ 5 M .$4 5 L 22.<4 5 L $4 &andies total of &andies L 25 L < 1#) ANS3EQH 2< M 2< M # M # L ## 1<) ANS3EQH s B Students d B :ollars
ea&h &ontributes d/s 14 donFt &ontribute d/s L 14d/s to be s!lit amon sB14 students 714d/s)/7s B 14) L 14d/s @ 1/sB14 14d/7s2 B 14s) ea&h student must &ontirbute this amount e5tra 1>) ANS3EQH 9anFt be in row b or d Not divisible by BW therefore not in & 2 M >5 L 12 >5 L 1 5 L 124
# M >5 L 12 5 L 12.4 ;B not a whole
*herefore 12 lies in a. 1=) ANS3EQH A L B *he last student. 2A M$2= BBBBB 48$
AM1M2L8 4AM$$ A L 1 or A L AM$L8 BBBBBBBBBBB A is not e-ual to 2" $ 4" $" # or <
2) ANS3EQH
Y2 L 71)2 M 71)2 Y L 21/2
21/2/2 L 8: 721/2/2)2 M 78:)"su!W2 L 1m 2 78:)2 L 1 B 1/4 78:) L 71/2) 1/2 m L .<) a L 1 Dnits 2
bL>B1L< hL4B1L
22) ANS3EQH 8obFs s!eed 71km/h)@71h/$#se&)@71m/km) L 2<.<<<>m/se& %n 1s 8ob travels 1s@2<.<<<>m/se&L2<<.<<>m *herefore elissa must have travelled 2<<.<<> m M 1m L $<<.<<>m elissaFs s!eed is $<<.<<>m/1sL$<.<<<>m/s 7$<.<<<>m/s)@71km/1m)@7$#s/1h)L1$#.km/h elissa ot a very bi s!eedin ti&ket. 2$) ANS3EQH BW 1.=# units 2
1/ of &ir&le rL2
A L 70i@r2)71/#) 1/#@0i@22 1/$ 0i Area of trianle L 1/2 bh L 1/2 @ 2 @ 2 L 2 2 B 1/$ 0i L one !art of shaded area L .=4$ @ 2 ;B two e-ual !arts L 1.=# units 2 2) ANS3EQH 75 M 4 M = M 12) / L = 75 M 2#) / L = 5 M 2# L $# 5 L 1 24) ANS3EQH $5 M < L <5 M 14 B5 L > 5 L B2 7B2)2 M k L < 7B2) M 14 M k L B1 M 14 kL1B k L B$ 2#) AnswerH 2 BW use trial and error 2 L 2/$ M $ 2<) AnswerH 22km/2km for 2 allons sto! 1 after #> km sto! 2 after 12=# km sto! $ after 1= km
$7 tanks of as be&asue he starts full) sto!s to &om!lete his tri!' 2>) AnswerH Even" less than 1" four fa&tors Qeverse the diits BW !rime number < L 11 < BW !rime fa&tors L 1" 2" $<" < is a s-uare number 2=) AnswerH < weeks of work BW C$ and the bike weeks of work BW C$ and the bike $ weeks of work BW C2< C2 $2) AnswerH
*he sum of the two sides L $ M 2 L 4 *he sum of the two sides of a trianle has to be reater than the third side. *herefore" the !ie&e of land was a line" not a trianle and had no area $$) AnswerH # 24 14 4
&ontain two or more !eo!le &ontain one !erson of # &ontain a male of total &ontain a male. of houses &ontain sinle females.
$) AnswerH et 5 L the number of eliible voters 42 M $ M 1$ L 112 .= @ 5 L 112 5 L 122 *here were 122 eliible voters. $4) AnswerH 8 $#) AnswerH a M $ L b B $ L $& L d/$ et k e-ual the number all of them e-ual kLaM$
kLbB$
k L $&
k L d/$
aLkB$
bLkM$
& L k/$
d L $k
k B $ M k M $ M k/$ M $k L # 4k M k/$ L # 1#k/$ L #
k L 12 a L 12 B $ L = $# B = L 2<
d L $712) L $#
$<) AnswerH 5M4 25 B $" 5 M 2" 5 M 4" 25 M 1" 5 B $ $>) AnswerH 2> 474) M $ L 2> 12 1$ 1 14 11
21 22 2$ 2 24
$=) AnswerH arkH C.4 ark s!ends 25 27.4 B 25) L =. B 5 L $5 L 5 L
(..H C$. (. s!ends 5 $. B 5 $. B 5 #. 2.
(eanBartin s!ends C2. and has C1. left. ark s!ends C. and has C.4 left ) AnswerH #km/hr @ 1.24hr L <4km L distan&e the motor&y&le travelled 4km/1.24hr L km/hr *he averae s!eed of the tru&k is km/hr 1) AnswerH
1=.4 @ 2# L 4< <.4 @ 1 L <4 1> @ 2 L $2 $2 M <4 L 4< *he sum of the areas of the re&tanles on the les e-uals the area of the re&tanle on the hy!oteneuse. Qelates to the 0ythaorean *heorem. 2) AnswerH 0r L $ units 08 L 1=.> 2
2
2
$ L 14 M 5 $2 B 142 L 52 #<41/2 L 5 #<41/2 / 2 L 8A 7#<41/2 / 2)2 M 142 L 2 $=$.<41/2 L 1=.> L $) AnswerH 1/$ @ 5 L > 5 L 2 2/$ 72) L 1# @ .14 L C2. ) ANS3EQH
9 of 9lo&k L 20i 7#) L 120i 71/2)120i L #0i 71/12)120i L 0i *herefore #0i M 0i L <0i &m
4) ANS3EQH $75B$)/5M< L $/2 27$5B=) L $75M<) #5 B 1> L $5M21 $5 L $= 5 L 1$ 1/1$ #) ANS3EQH 1 in 4 days. 5 5M# 5M12 5M1> 5M2
;B ;B ;B ;B ;B
st day 2nd day $rd day th day 4th day
5 M 5M# M 5M12 M 5M1> M 5M2 L 1 45 M # L 1 45 L 5L> 1st day he ate > <) ANS3EQH 22 @ 2 M 2 L 1 12 @ 2 M 2 L 22 222 @ 2 M 2 L >1#1 >) ANS3EQH 9% X% =) ANS3EQH 2 U $4 U BBBBMBBBBMBBBB $< U $= U 1 BBBBMBBBBMBBBB $> U $ U $#
4) ANS3EQH
Si5 6a&es BW ENG*, I6 S?DAQE A L >1/2 @ >1/2 L > *herefore # @ > L > *rianles
,eiht' 7>1/2)2 L 7>1/2/2)2 M 52 > L 2 M 52 # L 52 5 L #1/2 Area If Ine *rianle 1/2 @ # 1/2 @ >1/2 L 7>1/2)/2 L @ 7> 1/2) AnswerH > M @ 7> 1/2)
