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138
163
WS W ffs-nrq) ot
No
For examineFliG- -
I 100
+?+ h 4i
Candidate
Mathernatics
Date:Duration:
01l'10120132 hour 30 min
CHUNG CHENG HIGH SCHOOLrvsxur,rr
End-of-Year Examination {2Ol 3): Secbndary 2 Express
Name
t. .(l)
(b)
164
it is given that tr/ is directly proportional to ,j--When r = 5, V = 108.
(D Find an equation connecting tr/and r.(ii) Find the value oi V wheo r = 4.
Given that forty-iwo workmen can build d horse in I 8 days, find the number of workmenrequired to build the hoqse in 27 days, assuming that all the workmen are working at the samerate.
Answer (a)(i)
Class
Additional Material: .1 sheet of graph paper (to be submitted separaGly)
READ THESf INSTRUC I IONS FIRST ]
Wrile your name, register number and class on the space provided above.Wrile in dark blue or black pen,You may use a pencil for any diagrams or graphs.Do not use paper clips, highlighters, glue oi coreclion ftuid.
Answer all questions.lf working is needed for any question, it must be shown with the answer.Omission of essential working will result in loss of marks_Calculators should be used where appropriate.
Give your answer in the simplest form. Leave your answer in fraction whereapplicable- Give non-exacf numgricar answers correct to 3 significant figures,or 1 decimal plai-e in the case of angtes in degrees, unress a different rever ofaccuracy is specified in the question
For z, use your c;'lculator value, unless the question requtres lhe answer interms of 7r
I he number of marks is given in brackels [ ] at the end of each qr."iion oipart question.
The total of lhe marks for this paper is 100
Setter: Ms. Lin Xiaoying
Ti)is paper snsists of 13 priDted pages, INCLUOING the over page.
t2l
trl
trlo)
2. Expand and simplify each of the lbllowing.(^) 5p(-2p+ 5q)-3p(2q -7 p)(b) Qx +3)(x -7)-(3.r - 5)?
Answer(q)____ 12)
(b) ll1
CCE( EOY Eren 2013 Malllenalcs / Sec ? Exptess
1"1
Page 1 ol 13
CCHY EOY Eram 2013 tttalrtemetics./ Sec 2 E p.ess Page 2 ol 13
Danyal Education
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\140
166
l, . Factorise each ofthe following expressions completely.
(a) 3a2 -ob-6oc+2bc(b) 60plq+6pzq2 -t26pg;
Ansy,er (a)
'o)
4. Given that e -- 5o$ -. y. , make -r rhe subjecr of the iormula-
Answer
5. .The table shows the numbei ofpets owned by each ofthe 25 families.
(a) Drarv a dot diagram to represent the infomration in the table.
(b) Find the modal number ofpels.
(c) A family is chosenat random. Find theprobability that itowns 3 pets.
(d) A pet is chosen al random. Find the probability thar it belongs to a family which owns at most2 pets.
Answer (a): t21
2A34r0r L)
23610120i234171
{21
13l
Answer (b)
k)
(d)
trl
tll
12)
lx9
Page 3 ot 13 . tco
Page 4 ol 13
CaHY EoY Exan ioi3 Mal}@nais,/ Sic 2 E\p/ess
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' $r::n'rCCHYEOYE aamt3 Matbemalics / Sec 2 Exqess
Danyal Education
142
167168
6. [Diagram is not drawrr to seale]:- In the fig,ure, AABC and AIED are simil ar- AE: g crn, BD
= 7 cm and lD = 9 cm,
Find t-he lengrh of EC. 8. - A figure IOB of radius 7 cm and perimeter of 25
of bise radius r cm, as shou'n in Diagrdm 2-
cm, as shown in Diagram 1, is folded irito a cone
9
a7cn
7cm
Diagcm I
the value ofr,the curved surface area of the cone'
cm
7cm
B
Solve the following equalions.
(a) 8.:2 - 7x = 0(b) 2xz -6=26(c) l0-l9x-15r2 =0
A'
Find
Diagram 2
Answer (a)
(b)
(u)
(b)Answer cm t2)
c, tt2
l2l
l2l
9. (u) Let(=lx:xisaninteger, \<x<71,A={x:risexacllydivisibleby3}and B=\7'3'5\
ti) Express set B in set-builder nolation'
(ii) Find n(l)-(iii) Write down all the proper subsets of l'
(b) L"i 4 = lrff students in a class), C = {students who like cooking} and
D = (studenls who like drawing)-
Describe each of the following in words'
(D CnD+0(iD Cc.D
e
Answer (a)(i)
(b)(t
Ansu,er (a) x:
(b)r=
(c)*-
frlLL)
12)
l2l
ul
t1l
t2)
tll
ir l
tltPage 5 ol 13 !!
CCHY EOY Exarn 2ot3 Mathenatrcs / Sec Z E\press
CCHYEOYE on2013 Mathenot:Es / Se2 t:aryess Page 6ol 13
Danyal Education
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169
10. It is given that 4 cm on a map represents;an actual length of, I km-
G) Express the scale ofthe map in the form I : r_
(b) The dislance benveen 2 shopping mars on rhe map i-s 9-5 cm- Fiird rhe acrual distance in krn.(c) The actual area of a park is 1 .6 km2. Iind the area of the park on rhe map.
12, 'Express ;XG. frurusingle
fraction in is sirnplesl fonn.
t70
ijl
Answe.r (a)
:ol(c)
Answer (o)
km
cm2
trl
trl
t2)
IL Simplify rhe following expressions.
. 1^1 35x6y'
n--,- tx y
(b) :!:t--(2b\'crla-t1r'\c )
Answer
13. Given tlnt p2 +7 p = qz +7q and p * g , find rhe value of 5(p+ 9)?
Answer
trl
Page 8 ol 13
CCHY EOY Exam 2Ot3 Mathewtid/SecZEx4ess
o)
Page 7 of 13
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CCHY EoY Exam 201i Mathemalix/ Sec 2 E\pre$
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Danyal Education
146
t7r
l4' _ Raymond has- 42 coins i, his piggy banlg of which x are twenty-cent coins, y are lilly-cent coins and
-(x + 2y) arc one-dollar coins.
(a) Form an equalion in x andy, leaving your answer in simplest form
(b) A coin is chosen at random. The prob.ability ofchoosinga one-dollar coin is EForm an equation in -r and y, leaving your answer in simplest forrri.
21
(c) Hence, solve rhe simulraneous equations in (a) and (bJ.
(d) A one-dollar coin is removed znd 5 tw€nty-cent coins are praced back into the piggy bank,Calculare the probability of choosing a one-dollar coin frorn ,f_," piggy UrnL. .'
772
I5. A remote toy car moves at an average spied of -x nvs tor (.r + 5) seconds from point u4 to 8. Wilhoutstopping, the toy then moves from point .B to C at an average speed ol2x m/s for (2x + t ) seconds-
G) Write down, in terms of-qrhedislance coverecl
(D frompointl toB,(ii) from foint I to C.
(b) It is given that the total distance covered from poinr I to C is 4,75 m.
(D Form an equation in r and shoiv rhat it simplifies to 20x2 + 2&x - I 9 = 0.(ii) Solve the equation.
(c) Hence, calculate the average speed ofthe toy from pointl torC,
Answer (b)(i): t2l
trl
Ir]
t3ltll
tll
t3l
[1]
Answer (a)(i)
@(i0
(b)(i,
m
m/s
CCHY EOY Eram 2013 M athe fiatcs / Sec 2 Expie ss
(d)
Page 9 ol 13
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CCHY EOY Enm 2013 Mathemetics / Sec 2 E prees
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(c)x:Danyal Education
148
173
l6' Figr;re I shorvs a vertical cross section ofa furii:cl. The funnel was made by cutting olfthe tip ofacircular cone ard joining. the-remaining part to a cylindrical tube- The l"ngii oiriJ"yrindrical tubeis 6 cm and its diameter is I -5 cm- The ione originaily had a height of g 9m and a base diameter ofl2-cm- Figure2showsrheverricarcrosssecrionoftheripofthe-conethirwascut, Ir;;;;;;g;'",I cm and a base diameter of l-5 cm.
12 cm
174
17. The rdbie below sbows the number of children in each family that visiis rhe Universal Studio on a
particular daY.
Number of children 0 l 2 J 4
FreQtiency -t* I 9 1l t0 2x+1
Given tlrat.r is a positive integer, find
(") the value of-r when I07 families visit the Universal Studiq
(b) the value ofx when thc nrean number ofchildren is 2-5,
G) the rnaimum value of x when the modal number of children is no1 4,
(d) the minimum vzrlue of x when rhe median number of children is 3-
Calculale,(a) the volume ofihe cone before it rvas cur,(b) the volume ofrhe cone in Figure 2,(c) the volume of the finnel,(d) the total exlemal surface area of the furmel,
6cm
l-5 cm
Figrrre I
I.5 cm
\ ./ I rcm
Figurc 2
Aniwer (a) t2l
t2l
ttl
{21
(b)
k)
(d)
cmr tI lcm3 tllcmr : [2]
cm2 t5l
(a)
(b)
k)(d)
Answer
I,t?
Pqe 11 ol 13t.t8CCHi Eoy Erain 2a13
CCHY EOY Exan 2013 Malhemalics./ Sec 2 Exryess Page 12 o, t3
Mathen atics/ Sec 2 E $ess
Danyal Education
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17s
18- !rtlrq.d'iagrar.,1,4BC:zBcD=90",AB:Bcn\cD:rscm,AD=27cmandBD=(3-t_4)cm.' Calculate the value ofx, giving your answer to 2 decimal places.
r5
Anjwer
21
C
t3l
19 Ansrvcr the rvlrsle of this question orr a piece ofgraph papcr
The following table gives the conesponding varues ofx and y which are connecled by rbe equationy=4x2 -4x-15.
x -t 0 l 7 3 4
v 33 a -7 -]5 b -7 9 ,J
G) Caiculate rhe value of a and of D_
(b) using a scale of2 cm ro represent I unil on lhe x-axis and 2 cm to rcpresent 5 units onrhey-axis, draw rhe graph of y = 4n? - 4x - I 5 for - 3 S t.S 4 -(") Draw and write down lhe equatton of the line of symmetry of the cur ve y = 4 xz * 4x _15.
(d) From yourgraph, 6nd(i) the minimum value of7,(iD tht values of;r when y = I 7,(iii) thevalue of.Twhenx=-l-3.
(e) (i) Draw the lin! y = 5 on lhe same axes.
/;;\ Hence, write downr-coordinates ofthe porn(sofintersection between rhe 2ttU' grapns.
[End ofPaper]
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176
CCHY EO{ Etan} 2013 Melhemat rcs ,/ Sec 2 ExTess
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Page 13 oI 13 t:(,
Danyal Education
,e*vd WS W 6tuLrqoCHUNG CHENG HIGH SCHOOL ryrsxuNr
End-of-Year Examination (201 3)Secondary 2 Express
Ir) [t is given that Z is directly proportional to l. When r. = 6, V = l0B,(i) Find an equation connecling I/and r,
(ii) Find the valus of V whqn 7 = 4,
(b) Given that fo(y'two workmcn csn build a house in I 8 days, iind the number of workmenrequired to build the house in 27 days, assuming thal all the workmen are w6y[ing at the samerate.
(a) (i) v.lcrtWhenr=6,V-'1Q8.I 0g = k(6))
108 a216k
. r08 rk.-=-1\ Z aLtv a
."v =!,'2
(a) (ii) When r = 4,
v = !141tz"Y =32
(b) 4?. men, I 8 days
l+r.s lxr.sYY28 men, 27 days (lnverso Proportion)
B1
Expand and simplify each of the following.(a) s p(-2p + sg)-3p(2(t -7 p)(b) (2x+3)(x17)-(3.r-5)r
(,I /6
ti+ h ti
Ca nd idate
Math ematics
Da toiDura tion
I
I
I
I
I
Naote No Class
01 / 10/20132 hour 30 min
For examtncr's use
/100M1
A1
B1
Additional Materia l; 1 sheet of grsp6 paper (to be sutrmiled separatety)
READ THESE INSTRUCTIONS FIRST
\l/rite your name, regrster number and class on the,space provided above.Write in dark blue or black pen,You may use a pencil for any diagrams or graphs,Do not use paper clips, highllghlers, giue oi correction flujd,
Answer all quostions.lf working is needed for any question, it must be shovrn with the answer.Omission of essential working will result in loss of marks,Calcrrlators should be used where appropriate,
Give your answer in the simplesl form. Leave your answer in fraction vrhereapplicable. Give non-exact numericar answers correct to 3 significant iigures,or'1 decimal placeinlhecaseof angresindegrees,unressa-differentre'ver oiaccuracy is specified in the question
FOr n, use your calculator value, unless the guestion requires the anSwer interms of
The numberof marks is given in bracketi []ar the end of each question orpart question.
The total of the marks for this paper is 100.
Setter:.Ms Lin Xiaoyirrg
This paper conslsls o, 1 3. prioted pages, |NCLUOING lhe covgr p3gg.
(b) Qx +3)(x -7)-(3x-5)'i zxz -l4x + 3x -21 - (9r' -30x + 25)
= 2x1 - 1 lx :21 - gxz + 30x.- 25
= -7x1 *l9x-46 .
28 mpn are required.
t.
(a) 5p(*2p +5q)-3p(zq -7 p)
' = *10 p2 + 25 pc1 * 6 pq.+ 21p2
=1.1.p2 +19pqir
M1
M2
A1
CCHY EOY Erafr 20tJ Molhinslics / Soc 2 Etpress Page 1 ol t3CCI|Y tOY Exam 2013 MolhunalulSec2E pmss
I
I
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Danyal Education
(\t'19
l. Facrorisc each olrhe following expressions compietely3a2 - ab -6oc +2bc60p)q +6p2q1 -l26pqt
(a)
(b)
5. The table shorvs the number olpels owned by each of the 25 lomilies.
203-4 )
0 t23236 0
t 2 ! 0 3 2
34t2
I80
B1
A1
N,J
(a) ia1 - ab -6ac +2bc
= a(3a - b) - 2c(3a * b)
= (a _ 2c)(3a - b)
M1
-y1
'I
(b) t6O f g + 6p1 q1 -t26pq)=6pq(10p7 + pq-21q2)
=6pq(|p-?q)(2p+3q)
4. Civen rhat I = Sr.lT$ ,make -r. rhe subjecr of the fornula,
t1
2s7M1
a.-1 -v'
(a)
(b)
(c)
(d)
'tDraw a do( diagram (o represcnt the informotion ilr the rable,
Find the ruodal nurnber of pets.
A family is chosen at randorn. Find the probability that it orvus 3 pets.
A pet is chosen at randorn, Find the probability thirt it belongs to a farnily which orvrrs at nros(2 pcts.
M1
Attstvu (o)
No, ofPets
(b) Mode = I Bl.
(c)5rlJlownsJDelst=_=-' 25.5
A1
(d) Total no. ofpets =(0 x 4) +(l x 7) + (2 x 6)+(l x 5) +(4 x 2) +(6 x I)=48
.19P(betongs to a family which owns at.rnost 2 pets) = l!
v
A ,4)5n) A1
NLO
A1t Corrcct termsA1: Correct slgn
Molhoni(cs / Soe 2 E ptoss Poio 3 ot.i3ccHY EOY Ersd 20t3 MhlhomAli.s I sh, Ftath.c
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Danyal Education
,.A figure z{OB of radius 7 cnr and perirneleroI base radius i'cm, as shown in Diagram 2.
182
of 25 crn, as shown in Diagram t, is lolded into a cone
(,l(,6. IDiagram is nol drawrr to scale]
' In the figure, MBC and LAED are sirnirar. l[ = g cnr, BD = 7 cm and AD = 9 cm.Find thc lengrh of IC.
8.
98cm
7cm c
Solvc thc lollowing cquations.
(a) Sxr-7r=0(b) Lxt -6=26(c) I0-l9x-1Sx']=0
(a) 8x1-7r=or(8x-7)=0
-7r=U or r=-B
(b) zxl -6 = 26
t-2 - rr.a - )a
xr - 16
--Lj
98lC=l8cnr,'. EC= l8-8
= l0cnr
AT
ADAC
M1
M1
A1
AB.AEI6
MI
A1
cm
?cm
DieSrsm I
Find(a) the value ofr,(b) the curved surface alea ofthe cone.
Diogrom 2
(b) Curved surface area of the cone
=rl7
(a) Perimeter - 25 cm*Arc.{8= ll cm2rr =ll cm
l1f*-
2rr = 1,75 (3 s,0
="(*},,
of
ft)(i) Some students rvho like cooking and drarving
(c)00 All students who likc cooking also Iike dravring,
lvtl
-38.5 crn: (exact value) A1
B1
b-t
M1
A1
9. (a) Lctf={.r:xisaninteger, lSx<7J,4-(x:xisexactlydivisiblebyl)andp*{2,3,5\(i) Express set B in sefbuilder notation.(ii) Find n(21).
(iii) Write down all the proper subscts of I.Let I * (ali students in a class), C = (students wlro like cooking) and
D = {students who like drawing},Describe each of the following in words.(i) CnD*$(ii) CcD
Anstuer (a)(i) B - lx i x is a prime number,x < 7)
'.(a) (ii) n(A) = z
t1o11iii1Prop", subsets ofzl = t3), {5}, I BZI -1 for,any grlor
(b)
(c) lo-r9r-15.r.2.0I5r2 +l9r*10=0(3r+5)(5x-2)=0
aI = -t- or
3A1
t.
x2
5
!
rcm
M1 Bl.l Any logical answe/s
CCHY EOY Exam 2013 nlalhomalics / Soc 2 EtgBis Pago 5 ot t3CCHY €OY Exoq ?0t3 Mdlhenallcs / Soa 2 et prcss Psqo 6 al 13
L
1
Danyal Education
1B3ra4
t0, ll is given that 4 cm on a map represenrs an actual lengh of I krn.
(a) Express the scale ofthe map in rhe lorm I : r,
(b) The distance belween 2 shopping malls on the map is 9.5 cm, Find rhe actual disrance in km(c) The acrual area ofa park is 1.6 km2. Find rhe area oflrhe park on the map.
i 2. ' Express13 -2x
;rlTx + 16
13 -2x 4
*2 -8-r+16' 4-xli-2.r 4
=-+-(x-4)' 4-xIt -2x 4
=_+_(x - 4)' [- (.. - +11
13 *2x 4= G;jr - *-4
13*2x-a$-4)=-.-1;p-13-2x-4x+16
(, - 4)'
29 - 6.r'G-17
pl*?p=g2+?q
P''q'=-'tp+7q(p + q)(p - q) -- -7(p - q)
:.P+q-'7
5(p+q)'=5(-7)2- at<
* - 1-
o, o single fraction in its sirnplest form
(o) Scale=4cmr Ikm= I cm:0.25 km= I I 25000
(b) Actual distance - 9.5 x 0.25 km= 2.375 k:rr (exact value)
(c) r\rea Scale o I cm2 : 0.0625 krn2
ot
B1
[41
M1
lvl1
AI
M1
A1
Altemarivc Solurionl
l3-2.t 4
r! -8r+16 4 -rl3-2.t 4,
=--+-(,.--a)' 4-xll-2x 4=p6:;7* 4-,
13 -2x 4= j : +-'(4-x)' 4-x
't
Aiea on map - =!L = 25.6 crnl' 0.0625
I I . Siniplify the following expressions.
rdl.Trty
I ab^b'
;(,, -rt35x6 y2
lx' y
B1
l3-2x+(4 *.r)
l3-2x+16-4.t(4 - x)t
29-6x(4-;T
(a)
(b)
(a)
26 \';l
35 xb vl=_X-X<-'Jx"y
5u
.r2
.(13. Civertthat p1 +7p=qt*7q and p+q,findtltevalue of 5(p-rg)r.
(b) ab - b1 (zt\,,.r...-+1.-lt'(a-b), \ c J
b(o - b\ c)'T+x-c'(q-b)! 8b!' bct(a-b\'8b'cl
7a :- 61t
c=+, 862(a -E) A1
$tr)
ccHi Eoy Eran zot3 . Mathel,dt;cs/ Sac'2 ixptoss Foge 7 ot 13
ccHY eoY exhn 2013 Malheiladct / Sec 2 Ail)Gss Pogc I al 13
I
MDanyal Education
187
l6' Figure I shows a vertical closs section ofa funnel. The fururel was rxade by curring ofirhe tip ola'circularconeandjoininglhe.remainingparttoacylinaricainrbe. Thelengrrr ofrhecyiindrical rrrbeis 5 cm and its diameter is r.5 cm..TnIioi.
"Jgi'";iry had a.height of g cir and a base dianrerer of
:i ;h ;'1,:.o?,,jilltfff l:,fl:" ,..,ion"oili. tip oi ir,i?o^..,r,.;il ill rr rras a hei_phr
I 88
l'l . Tlretablebelowshowsllrcnunrberofchiidrenineach{'amilyrhatvisirsrlrr:Univelsal Srudioonapanicular day.
€Number of children 0 I L J 4
Frequency r+ I 9 t!II l0 2.r+ I
Calculale,(a) the volume ofthe cone before it was cut,(b) rhe volrrme of rhe cone in Figure 2,(c) the volume of the funrrel,(d) rhe rotal cxternal surface area ofrhe funnel.
(a) Volume of cone,,frt ht
= 96r
=302 crn! (3s.0
(b) Volume of cone
UI
,r(0,75)1 (t)
= 0,1875r.
; 0.589 cm, 13 s.g
l2 cm
6 crn
I .5 crn
Figr:rc I
(d) Using pythagor.as' Thcorenr,/,2 =61 +81
/,2 = I0o
/, =10 cm
'tL5 cnr
(8)6)tr(
I
3
I
3
*rt h,I
3
1
3
'P1 ,.'
Figtrrc 2
(a) (r+ l)+9+ ll+ l0+(2.r+ l)= 1073.r+12=1073.r = 75
x=25
M1
A1
81 /12.0.752 +lllzl - L5525
lr = 1.2) cm
(b) Mean - 2.5
F*LIiF.i- = l.J>tS.,r+65 ,.)x +328x+65o7.5x+80U.)x=l),r=J0
B1
B1
M1
A1
B1
(c) Volume of funnel
= (962r - 0,1875 x) + mrl h
= (96;r - 0, I 875 n) + x(O,7 5)1 (6)
= 95.8125r +3.3?Sxl= 99.,1875n
= 312 cm, 13 s,g
M1 Total Surface Area
= mrl, - mr!, +2mrh
= n(6)(l 0) - :r(0 .? S)(t ,25) + 2n (0.7 s)(6)
=:60r'.A.93?5n +9n '
';68J625n
= 214 cm2 (3 s.0 (d) (.rr. l)+9+ 11=9+(2.r+ l)x+21 =2I+ I0.t- ll
M1
A1
(c) 2.r+l<ll2.r < l0t <.5
Max.t - 4
(o|r)-
CCH'/ EOy Exan ZOr3 L,lalheffiatlcs/ Sec Z Exptoss Pogb 11 ol 13
CCHY EAY Eroil 2013 i4olhefraics,/ 9oc 2 etDrors
I
Civen that x is a posirive integer, find(a) the value of r.when 107 families visir'the Universat Srudio,(b) the value ofx rvhen rhe mean number ofchildren ip 2.5,(c) the rnaximum value of .t rvhen the nrddal number of clrildren is not 4,(d) the minimum valtre of.r when the rirediarr nunrber of passenger.s is 3.
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li Danyal Education
I86
15. ..{ remore toy car moves ar an average speed olx nr/s for (x + 5) seconds from point I (o B',Without
siopping, rhi toy then moves from point B to C at an average speed of2v rrr/s fot (2:r + I) seconds.
(a) Wrile down, in lerms olx, ths litl3pqs cpvered
(i) lronr pointl to 8,
(ii) fiom Point B to C.
(b) lt is given tha( the total distancc covered from point,4 to C is 4,75 nt'
(i) Form an equation in x and show that it simplities to 20x2 + 28x - l 9 = 0.
(ii) Solve the cquation.
(O Hence, ca)cu)ate tho average sPeed ofths loy lrom point,4 to C'
i
(a) (i) Distance coversd lronl point I tc B = x(r'- 5) B1
(a) (ii) Distance covered irorn point B to C - 2x(2r + l)B1
(b) (i)
B1
(Jl(,l4 Raynrond Jras 42 coins in his piggy bank, of rvltich.r arc lwenty-cenl.coins,Tare fifty,ceni coi;rs and
(.r + 2y) are one-dollar coins.
(a) Form an cquation in x andy, leaving your ansrver in simp)est form,
(tr) A coin is chosen at randonr. The proh.ability olchooslng a one.doilar coin is E.Fornr an equation in.r and y, leaving yorrr ansrvcr in sinrplesr fonn,
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(c) Hcncc, solve lhc simultoncous equarions in (a) and (b).
(d) A onc-dollar coin is rc.moved.and 5 rwenty-cent coins are placed back into the piggy bank.calculale the probabiriry ofchoosing'a one-doilar coin lroin tho piggy uank.
(lr) P(choosing a onc-dollar "oinl = I I'21
:'.i.?l =,lL
(a) .y +.1, + (r + 2.1,) = 4J
2y +jy = 42
42 ?.1
x+2),=26
(c) ?x +31,* 4lx+2)'=?6.t =26-2;,
Bi
B1
-(t)
-(2)
M1
'A2
B1
x(x+5)+2r(Zx+l)-4,25x: + 5x + 4rl a)s = 4,15
5x7 +1x -4.75 = 0
2O.rt +28x-19 = 0 (shown)
(b) (ii) 20rr +28x-t9=0(2x - l)(l0x + l9) = Q M1
Az
B1
,=- or , * -r1 (rciected)l0Subst. (2) into (l)
2(26-2y)+31, = 42
52-4y+3y=4?,! = l0Using(2),*=6
Therefore,r=6andy= l0
(c)
)
Ayerage speed
D
T
4.7 5
5,5+2
(d) Total.no. of coins + 46
P(choose a St coirrj = I.46m/s or 0.633 m/s (3 s,0
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3x-4
lS lnrhediagrinr, ztrBC=IBCD=90',rB=gcm,cD=15cm,ApnzTcmandgD=(3x_4)cm..Calculare the vaius ofx, giving your answcr to 2 decirnal placcs.
21
D UsingPlrhagoras,Theorem,277 = trgt *7tAE'1 = 68Q
BCz = ,,16,' =699(jx'a)r =8Cr+15'(3x-4)2 =680+22S(3r-4): =965
3r-4=.ffi, =
Jffi*13
r = l l.i6 (z d,p)
EI5
M1
A1
8
C
19, Arrsrvcr. tlrc wlrolc ot(his qucstion ou a picccof gr-nph papcr
Thc foliorving table givcs tlre concsponrlirrg volucs ofr ancl.1, u,hich are corrnected by thc eqrrationy=4xt -4x-15.
(a) Calcuiate thc value of a arrd of 6.(b) Using a scalc of2 cnr to rcprossnr I unir on the x-axis ancl 2 cm to represent 5 unrrs on
the;,.axis, draw ttre graph of ! = 4x1 *4x * l5lor * j S.r S 4 .(c) Drarv and write dorvn the eqrral,ion of rhc line of syntmctry ol(he curvcY=4x'-qr-15.
(d) Fronr your glaplr, find(i) (he rninirnum value ofy,(ii) thc valucs of .r wiren,,r s 17,(iii) thc valuc ofy rvhen x = *1.3,
Drarv the liney = 5 on thc same axes,Hencc, write clown x,coordir:alcs of:the
ir -3 -Z -t 0 I?. l 4
), 3l a -7 _t5 b -7 9 11
intersection between ihe z
ilI[4]
ttl
[]L2_)
trlillirlI' l.
(e) (i)(i i)
graphs.
a=9 &=-15Scalc and axesConcct plotting oi pointsSmooth cuwE with cquation
(c) Line of symmetry is .r'= 0,5
d(i)' lvtin,y--16 (*.0.2s)
d(ii) x=-2,4 or x=3.4 (*0.05)
d(iii) /=-l (10.25)
c(ii) . x. -1.8 or . r = 2.8 (*0.0S)
(a)
(b)
BI
B1
n,
B1
BI
B1
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