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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

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CCHY EOY Eram 2013 tttalrtemetics./ Sec 2 E p.ess Page 2 ol 13

Danyal Education

165

\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

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Page 4 ol 13

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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

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CCHY EOY Exarn 2ot3 Mathenatrcs / Sec Z E\press

CCHYEOYE on2013 Mathenot:Es / Se2 t:aryess Page 6ol 13

Danyal Education

144

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

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Page 7 of 13

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CCHY EoY Exam 201i Mathemalix/ Sec 2 E\pre$

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Danyal Education

146

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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

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Ir]

t3ltll

tll

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[1]

Answer (a)(i)

@(i0

(b)(i,

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(d)

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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?

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Mathen atics/ Sec 2 E $ess

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150

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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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

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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

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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

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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

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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

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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

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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)

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ccHY eoY exhn 2013 Malheiladct / Sec 2 Ail)Gss Pogc I al 13

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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.

iI

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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,

21

(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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