Maths Green Book
Maths Green Book
Maths Green Book
MATHEMATICS
4008
1999-2001
-t
..'i
Candidate ,i'
Candidaie Name
INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the spaces at the top of this page.
Answer all questions.
Write your answers in the spaces provided on the question paper.
lf working is needed for any question it must be shown in the space below that question.
Omission of essentialworking willresull in ioss of marks.
Mathematical tables, slide rules and calcutators may not be brought into the examination room.
For
Exunincr's E,ru,
Ust i
'3i
iiri - trt,
.. :
ia!
/^\
tL,, frl
lrI
Calculate
(i) the total numhr of turns he makes,
(fi) the tota! distance he wal&s.
f'
I
6 ,'A motorist tlegan a journey at lu 45. The;our-*ey E$sii fiim "i
ili.tu;5;; i5r*!ui;;,"
(b) Given that he drove at an average speed of 100 km/h, calculate the distance that he
t_
.q
For
Eruminer's For
{'r;e Exambtr's
Usc
T {"
dt-1gj$' .4D is the diameter of the circle A B C D.Chords BC and C D areequal and
CAB - 33". The side CD is praduced to E.
Calcllate
i€
(a) \At:, Pri
(b) nfn,
.
(c) ,'tfi1,.
Frankfurt - t1 -J
Larnaca, 9 2A
i
London -5 0
Rome 10 13
11 All the lengths on a scale drawing irre one eighth of their actual lengths.
Calculate
(a) the actual length of a line repre sented bv a line -5.6 cnr long on the scale clrau,ing.
(b) the area on the scale drarving rvhich ieprescnts an actual arctr of ,t.i96 cnrr.
I
LA
vl
[1]
(a)(i)aquadrilateralABCDwithanglesTf'1'07o,50"and100o,
(ii) a triangle LMN with sides 11,4 cm' 52 cm and 4'7 cm'
tll
t1l
t1l
fit r lor
Exuminer's Exuntintr':
Use Use
(b) On rhe diagram in the answer space, shade the image of ABCD so that the resuiting,
complete, shape has BC as a line of symmetry.
Answer (b)
\*-
,?, A B
D C
l1I
(c) On the diagram in the answer space, shade the image which is the reflection of the
shaded shape in the line PQ.
Answer (c)
trl
{IR/l//$?wl/s9,
For I
L1 For
u*i
Ltuniner'sl Erzmircr's
Usc
I I
1.6 (a) Solve the inequaiity -7 <?* 3,r < 5.
i
(b) Illustrate your answer to part (ai on the number line in the answer space.
{b} tll
l7
* A man estimates that each side of a square {Joor has a iength,of 4 metres, correct to the
nearest metre.
Find the difference between the largest and smallest possible calculated values of the area
of the flrxrt.
,4tzsvr'*r
t3l
{llllr{l{r;wi rtst
. !r, .
Lrtll4:tl(r \
l
|
im
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$oive lher equriior:;
I
I
I llr
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l
{n} ;, i- + = !-',.
I
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I {b) .i'(l'-+ 3} - 2{t -* },'t ." i:.
I
I
I
I
I
I
I
I
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I
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I
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19
.li{ltr' l/4ttfl6r*
For I
Etaminer'sl For
,YX
Usc Examincr's
Usc
YX
20
,ilA ilA
YX ryx YX
Take n
TA t#
toba!.,
rk tt
The diagram shows a pattern used in dressmaking. It consists of six equal circles of radius
3,5 crn inscribed in a rectangle. The sides of the rectangle are tangentsto the
circles which
touch other circles as shown.
Calculate
4{lI'l/{t28n/sq)
For
T.xtmincr's
t4 For
Examhct's
U* Usc
2l
A
'u5,.L
In the diagram, ABCD und EFCDare parallelograms on the same base DC and between
the parallel lines DC and ABEF.
4ffitu{J2Efitsp)
ftr
Lruniner's
Utc
f(.r) = (2.x
- lXx - 2)(x + 3)
(i) A,
(ii) B.
(b) The point Pt-2, f ) lies on the curve. Calculate the value of n'.
Ansv,er trl
lrl
t2l
Frequency
density
0l020JU
Time in minutes
Anotherwaytorepfesentthesameinformationisshownbelow.
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j., a;.-t{'i il .J{iillji;1:}i.
i ii.'.; r.in'::ii :i{J.i/l i'. itri,iiir?,i, t't-;i'.{' f,; iilifii.rt <ji :.3, /,-.
l
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,
rli'.',:r.'l i'l
i:,; t,l,,t;ti rji,li.,
", ?i.,i anei r', i-,, isavir;H, )/*ilf fftirtwr-,i' it iiirr.l !*l;ti.
tii:.<7: {71
i,r: j Lt z I"rl
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tT-,.--,,.,,,-
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il' rrnir:rr'r
f.rrr lr lrtr'r'-r
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Inthediag,rarn,P,Bancl/trepresentpcintsonlevelgrounclwithl"O=13{}m,Pft=24m'
eFg = B7i and Qf n = 4ff' T.he bearing of I from.P is 042''
use as much of the information given belcrv as is ne.cessar-v'
(a) Caiculate
(i) the bearing of .R fram fr,
(a) Mr Mogo paid cash and was allowed 157o discount. caiculate the discount.
(b) bought t\e television set through a lay-by scheme. In rhis scheme he paid an
Y.t P-*9"
initial deposit of fr ol the marked price and then 3 equal monthly insraiments,
before he collected the television set. calculate each monihly instalmint.
{c) The marked price in 1999 was a result of a L0% increase over the marked price of the
previous year. calculate the marked price of the television set in 199g.
(c) $ {.21
For
fur
Eumintr's
Use
Use
27 (a)
1 2 J 4
1 3 5 7
Table 1
Consider the pattern of the numbers shown in Table L above, which is incomplete.
1 I 1
.tA
z 1,3
J 1,3,5 t
4 1.3.5,7
i
Table 2
(iii) Write down the sum ot rn" terms in line 30 of the table.
f r I
(ut) Irl
ITilATHS JUilE {999
4008/1
POSSIBLE ANSWERS
9. (a) 5 (b) 92
12. (a) -5
5 tbi
It
13. (a) (i) the sum of the angles
is less than 360o
(ii)the sum of the two shorter sides is less ihan the third side.
(b) hvo angles which add uP to 90o
23.(a)4(b)rectangleofheightl,8and
interval3oct<4'
(c) 3o<t<40
24. (a) kD L
(b) 10 (c) ZJi orJn
Wfit{: ,',1 ,r i.i rri\-,rrrS r''ft thC SgiJ;{iilt(.: ,iri$,//er Li"llr-iti ylOVid*,1
if irci: r-;;r, 'iri)ir,l iir;i.r: *rir. l:ircfi i:f ;16n*r, ii*t*n !ii+ sit+:lis loceihei'.
fiigr:ti,*i:il ,.i;li;4!91g1.r! r?lrJt:it f!Ot he Uegd.
,lii '*rl:,'l!;,i'.r'rr:;.;i i:r, ti,,;-,,';,;'::i.:.,!1:r iish*uldh.*lji,'trleCInth{::;amesh**tA$thgieStCf theanSwer.
{lmiSS;,tit ,.ti , ..: t_ri"::; ii , r.:1i..., . ,..,'ill :r:lit;lt !fr li:*lt *t i'**fkl;.
if the dei;i'i:{,r i}; ::i;l.i-ii;.i*i. ir: I,i,t ::;-iiscilied iri ti;t; qUeStiCn anrj if th*: ;tli:;yye;' iS r:Ct eXaet, t}:e anSWer ShOUld
he 5;i,l*ri t.'": lilrr:* t-iirf,iiri,::l::t, ri,a:riirl:. lini:UJi:l'S ir-'' degrees SirOUld lle r;iVen tr,: i-rne eje*lrlrai plaCe.
This *uestinn paper eonsists r:i 'i 1 printecl pages and t blank page.
ibl42) LiF:t:: t 16
Sectir.rn A ii:4 n:rarksl
Tendai is paid gi2,40 atr haur {or a basic week d{ 4fi hours. }ic is
paici $18,6{i an irour for
tb)
*vertime. clui.uior*. his pay {or a rveek in rvhich he works for 48 ho*rs. i3l
are giris.
ic) There are 1500 pupils ar Fundd Secondary Schaoi. One third of the pupils
{i} Find the number of boYr;'
uumber of berys studying
tii) Given that i of the boys are stuclying,.Agricuitit;:e, express the
Agriculture as a percentage of the tctiril tumb*r of pupiis at the schocL
\'
14l
id) Caiculate the simple interest earned on $l2i:X) invcstcd at a rate of 15% per annum
for
6 months. L21
'fhe table below shows the number cf pupils fronl eactrr fqrrm who went on a trip io {ireat Zimtrabrve.
-"**1
Irrirm Nnr nber of pupils i
(ai Using a i cm-wide bar tc represent each form and a vertical seale o{ -2 ern to rcpresent i0 pupils"
<lralia labelled trar chart fcr the given clat:r. i3i
ie) [f twq pupiis are shoscn ar riirlclom from those wh* rvent on the trip, lind the probatrility that
they were both in Form .i. tZl
(6) t.iivcri that tire totai nunrber of pupils rit ilic sch,:tii iva:; 108ii, lirrc!" as a single fraction in its
lorvcst lcrms, the probabilitv thirt a pupil ehosen at randcm from the rvhcle sehcc;l, went on the
triir aucl wls in eiihcr f;orln 2 nr Form 4' IZI
! r' ?,1\
(r) Fin'.1 tht: vaiui: cf r fr.:r vrhich the
{
.
rnatlix _
.. l
in stngular. i2i
{ci 11". }' ztntl )li:t'i: io;ur i:aints rvith coort}inates {*'2,1)' (4.6). {n9- l) arrd (1. * 2) resp€ctiv()ly.
'Y.
>
{i} ljind .\ }' ',t 3 t:triittttti vccl(}!".
(ii) t iricl 1Yf I.
{a) (i) Construct a quadrilateral ABCD in which AB = 9,0 cm. DiB = gA", AfrC = 60",
AD =7.5 cm and BC = 6.3 cm. t4]
' (ii) Measure and write down the size of ne O. '{1]
(c) Mark and label points X and Y which are 5.0:m from B and equidistant from DA
and DC. t2l
) --i
----\
6 In a survey, 200 people were asked which of three meats - beef, chicken or pork - they liked. The
results are displayed in the table below.
Beef ,80
Chicken n0
Pork 50
Beef and Chicken 6U
Chicken and Pork 46
Pork and Beef .32
All three '28
None.of the three' h
M l-x
r+4 3r+ I
The diagrarn shows a rectangle right-angled triangle..The lengths of the sides of the rectangle
;1f are ft + e) *a (z I rj "n{"
fire iengthi of two of the sides of the triangle N are x cm and
"*
(3* + 1) crr as shoryn. "*.
(r) Write down an expression, in terms of r, for the area of
G) rectangle i?f,
(ii) trianglc tV.
t2l
in r and
O) Givcn that the arca of reatangle M is twicc tlp area of trianglc JV' form art €quation
show that it redues to
2x2-x*14=0. t3l
(c) Solve the equation in (b), giving your ails*€fti correct to 3 signif€nl fgtrres' t5l
(.) write down tlre dimenslons of rectangle JU mrrect to the tsf€st millimDaf€. I2l
7
Triangle dBC has verrices A{- 3,2), B{- l, 2) and C{_ l, 3).
Triangle A p $ thas verrices A,(- Z,
- r, ll,,{_ Z, _i) and'C,(_ 3, _ l).
(a) ti) De;cribe fulry the singre transformation that maps AAgc
onto /,A p tc t. tzl
(ii) write Jown the matrix that represents this transformation.
pt
{b) onto triangle A zB zc 2by a transformation which is represenred by the
:::T?ijt
mainxt lluootd
o _2J
(i) Find the coordinates of Ar, B, and Cr.
(ii) tzl
Write down the matrix which represents the transformation
which maps A.4rgrC, onto
AABC.
tr I
(iii) Find the marrix which represenrs the transformdtion which
LAptCr maps LArBrC, onto
l2l
(c) Triangle
4i{3cr has vertices 4 r(3. 2), B1(5. 2) and C,r(g, 3).
Describe fully the singre transformation tirat maps n,4Bc
onto a.4.rBlc.r.
13l
fTurn over
9 (at
tii) Given that,,{C --Ieg and that the area of triangle ABC is 2 square units, find the area of
PQEC.
t4i
(b)
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El!rccti** g:*lpeltii,;:.llet'!,',r i-rtrc *f ihr: fa,:,;:; r'f iitc ir.ii:,', :i'- .,liil:",vii ai;()r.'i:.
{*} i.alcuiitt* llir: r,cliri:rc *i tiit: lrte tai il:itirrl';:i!. llj
{ii; F)xpress thc vt;iunr* r:i ihc r;l*{rii r(:I}1{ivf{l ii.i:-i i)rrrcent;,t{e ti' tlie .,'rrlunri: oi th.: r.rrip.iitiri
r'rih,'
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{ivi ,',,1 tt-,, tii.'iltl i'(';!tiivt(1 \-1 iji {:lijiir'ti;i,r,i i-ir:trir'iirirr +" ,rli::iirr:;ti :i'.'riltI rlrlrrr',:l {'llclrI;itr*: thr:r
'.,iiil!s<rf t.;t,-ii rllhr.rr.,. i.it'ilrl \.(rr.rr .it:..,,1 i,t i(,ir{.rji iu iirt'iii'.it...i1. ;l lr.:niir cJ',it n:iilitrre ii"rt.
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r'r-;1..1.{,i i-
'fh* tabL: i:r:icrv tirl*s st':l:lri tor:'esill}ilr'iiitg gaitii.r:l 'rt t' 'ri;ri
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'I'aking t:*r lr.: rljl resellt i rr:*<.'tr{1. tir;rlv ir i';*:'iZE.r::i::i:'t;.".i: fq.;i ii -- i '.:,, {:
tt]) "l
'Iiakinp12 cm tr-r i'illlreserll f n'i:'s, tji;ir',';t l'tl-ilc:ii;1xis f'.it'- 11 '::' ;; ':, I'j.
Llratrv thr-'. Egapir ;{ 1' ,'. 'i + 5l ' t'. ili {} <. ,":', i';-
e
{ci
r"J I isc fhe if"pra.Dh
_I-__' f r-r rrslitrt;itr:
iiii) ihil elistance i:l}vt:rcil L;y thi: h:rll rn tlte lirri I ri:r:guds.
i.x i
{d} ii} i:i3,' ilrarvipg i1 iirlisrnt finri tiri: gri:.cii*nt {if ihe traph wlle1l I-""i'
iii) g1;11s $viq:i'ir,r 1v!13i- ll"ii.e traeiitrtli i i'-llir;ceilIs-
!
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'i'; r\*lfily*r ths: wir*i* of fhir qriestion or; :l single sfueet *f grapir t?ap*r.
'l i',..,'
r rii.".: !..- i}tr:,r i' ,.r r,,-..,....f
i.ili'S ()i i(-triitnzily
r-.1:-.,-.,.,....
:s,-:;iis :iilti 1, t'tlr,vs <ll' Sttlrcri{tf S*ztt-.; fftf ;i sCil{}ijl ;ria\,.
iAi F,Aqh n"rw,ri'i,ttlilarr.' ?i s*;ri.r:ii;ri citch ritw *f Sirpciirif
:,i:rlt-S itari
"rr:itf:,;
liAel ?il scl].t:i.
Firer reg,ulations limit thr: Irrt*i nunibi:r li s,*r*ts fi:.4iij.
\I/".it,,,1^,,,:. .,., 1,.......^i1r....,1.: rvrri{iii
.r, .,,. i -!. .. .r
vvtttii Liulvu.3!r !ucqu(rrlr-y cXa}i-erisfs ri.i.. -...r..i-r. .'-
fhis restr'iction;r.nr"j shi;w ill;ii ii l't:iii:t:es lri
-1.'{ i- 1&, ,,., ii{}. i2j
{hl fltclr.' rs:ipiice irt ihe hirll li,r'r1., lnorc tlrarr lE r',.lrvs i;isciri;.
'fhe F{oadmastet' j.nsi.itt-:El lhat iherr: u:i:rc at ir:llli1 ji lotys gf {irriil'tlii"!' :{i--':iiii.
Writc riown twt: f*rlhcr incquaiitic:. otht-::' Iii;rn ./ ,.i- wr'icir cxnre,qs
.-";
''. ii ariei ,:: Ii1csd]
restricti$tis. l:i I
-t'he poinr yi
{c} {-t" rr:present"q .{ r+ws c{ Orclinary seats and }' i*trvs oi Superic:'s{ra:i;.
LJsing a scale af 2 cni la represcn{ 2 rorvs *rt i:iii;}; axis, ilraw.r" ilnd.v,axes taking valries 1rf -r an6
,'t l'-,,*.
tl trrtl tI
t/ r., flt
tt, 1-\/,
Constnrct. and indicate clearlv Lrv shading ilic snwanted r*gionr. thc ri:I.:ion in which i;r, y) musf
iie. Uj
{{i} All al llic reats rvr:rc ,:ceilpi*tj.
Write rieirvn the coordinaics of thc ilcints tririr:h.represenr t.hc larse.-t pe rmitte.ci ar:rilencr:.
t2j
{*) liiich (}rdinary sc;il cr}}i .1{iculrts irriii '.:tic}t 5riiii.i-iot iiiii eosr 51.
Writ* d*wn, in t*rms cf ; anli.'l,,lir exllirssir>n f<,.r the totai incc.rul*:. ip <jcliltrs. I1l
i$ Find the greatest p*:;sil:le irrcclrrc. givcn tirrrt irll tti* cr.rnrliti()n:; rili.::;alis,ficri" ii]
hIATHEUATIGS JUNE 1999
4008t4028t02
posstBLE AiUSULERS
(a) r;-
'1
1.
3
'1 a
J^]
-
''-2
o-L
-_*A-
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c') 1-
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=1,6 or 1 ;J A1
fi100
% of totai =
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x i00 Mj
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=B- -t
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0f 8,333% 41
i200x15x6
{d) M1
11itt x l2
$90 A1
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2F=5 tvt-t
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RA[) =90'*2b with correct construction arc$
seen C1
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For For
'
Examiner's
Use
Etaminer's
Use
7 The cost of 5 rulers is $1L,25. The cost of 3 rulers and a pen is $9,35.
Calculate the cost of
(a) a ruier,
{b) a pen.
(b) $ I2l
I
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Examiner's Examiner's
Use Use
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Answer x =
v- t3l
10 The exchange rate on a certain day was 3,8 dollars for 1 rand.
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Eramirc/sl lEnninr's
Use I
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diagram atrove shows poinrs I,('1. S). (.l{9. 3) and S(12. l0).
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(ii) {21
Fer For
Exsmlner's
Ihe Ennincr's
Usr
2I Two of the angles of? pentagon are 3.ro and 11.r" respectively. Their sum is 1.680.
(b) Given that the remaining three angles a!:e ful the ratio of 3 : 4 : 5, calculate the size of
rL^ t^--^^+
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(h) 121
22 .)5 that
(a) Given
-*- *. i,q
x-3p express r in terms of p and q.
5m 2nt u-j
(b) Flxrrrcss :-:': -:::- a as a single fraction in its sinrplest form.
'94
Answ'er {n) .r ==
Izj
(h)
lzl
f Turn over
For
For Exanbtr's
Erg,rdt'Et's
Usc
In the diagram n6c = g0: A68 = B6C, AD =15 em, DB =8 cm and DC =L0 cm.
For '
For -t:*a*incr's
Emminzr's Usc
Use
?A {s} If the matrix {3t ,: } ,"or*r"nts an enlargement, with the origin as centre,
\0 -i'i
find the value of -r.
lTrrrn over
,-
llr l)xtminer's
llraurtt'r'.1 I I;se
{a) Write rl61wn, in terms of n, rhe nurntrcr of passengers in the btts as it left Gweru'
(h) Give n that it trrrivecl in Krvekwe with 2n passenge rs, torm an equation in n and use it to
find the value of rl.
(c) Did the bqs gain or lose passengers in Gweru? Explain your answer'
ill
Explanation:
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A:'gniwr't Exumin*'s
Utt Uv
26 A cyclist starts a 30 km journey at 09 00. She maintains an average speed of 20 km/h for the
tirst threc-quzlrters of an hourand then rests. Subsequentlyshecontinues herjourneyatan
averags speed of 2-5 knrlh, arriving at her destination at 11 00.
(b) C--alculate. in hours. the time taken to cover thc last part of the journey.
. (d) 'fhe graph shown in the answer space is an incomplete distance-time graph for the
cyclist. Complete the graph.
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40081r
POSSIBL$ ANSWERS
.-
1 1-\ 9
i" (a) -2^. -l^.
125. \/ 10 - 5
.
2. (a) 6,026o, a;f,
1000
(b) 0,0e o. 310 (c)
\'/ A
-1,9 or -t'10
50t)
1,
lt.
s+jn s*Jzt
22
12. (a) (i) 0?2' (b) 288" (ci 324"
tB (a) I -i
rs\ (b) R(12:5) (c) 'l (6;0)
1 \ 2q+15P (b) rn -6
ra, --T-* l-
l
/.). \a) 6
(b) - or 0.8 tc) 97
3 /c\ ?Q
26. (a) ls (b) cr 0,6
=5
(d)
27. (a) 1.6 990 (b) (i) 0.6 9e0 1 iii 1.3 e7e
A:4008-l -n99/cs
-+ *? 4"d .rt* t'lr'ea. ".*
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'
{ :d .r } ti$ 4 'E .
MATHEiNATICS
*T ;
I f'rrrn n--s:'
Secdon A [64marksJ
o) Given thatp =3w2-J'?, find thE value of p when w = -2,x = 6 and ! ='3' tzl
(c) During a sale the price of a radio was reduced by 28% to $486.
Calculate the original price of the radio. t3l
that air
^diagram,
= nfc = Cio =25".
(i) State the reason whY AB - gg = CD' tll
(ii) ialculate
. (a) Afir, l1l
(b) reD, 121
IJse rvler and compasses only. Nl.construction lines and arcs mtrt be clearly shown.
(i) Construct, on a single diagram,
(a) a triangle XYZ inwhich XY = 9,5 cm' Y*Z = 45o and J{Z = 6,3 cm, t3l
(b) 6e iocus of points equidisiant from X and Y, t1l
(c) the locus of points equidistant from Y and Z, l1l
(d) the circle passing through X,Y andZ. f ' 121
(ii) Measure and write down the radifis of the crclb i4 (bxixd). lll
[Tirm over
l2l
s ta) Find the LCM of
ga2b3 and tSasb'
(b)
and
which DC= 6,4cm' BD=9cm,,48 =ZDC
In the diagram, ABCD is a traPezium in
gf6=34".
Find
t1l
(i) A6o,
t3l
(ii) the area of triangle ABD'
(c) ThetablebelowshowspartofMrBanda'stelephonebillforJanuary.
$ .........................
January monthlY rental
Cost of metered calls irom 010561 to
A12177 $ 886,40
Sub total
Sales tax atl7to/o
Calculate
t1l
ti) the January rPnthlY rental,
(ii) the number df units used, lrl
[1]
(iii) the charge Per unit in cents'
t1l
(iv) tle sales tax,
t1l
(v) tle total amount due.
4ffiruw99
(s) An agriculture class picked tomatoes.
t
x pupils picked more than 49 tomatoes,
3.r pupilJ picked fewer than 51 tomatoes and
5 pupils picked exactiy 50 tomatoes.
It is given that
ciass'
t = the set of pupils in the agriculrure
B=thesetofpupilswhopicKedlewerthan5lt9matoca.
(i) Illustrate this information on a clearly iabelled Venn diagram' t3l
x.
(ii) Given that the total number of pupils who picked tomatoes was 47, find [21
(b) There are 30 red balls and r yellow balls in a bag. A ball is drawn at random from the bag.
(i) Write down, in terms of r, an expression for the probability that the ball drawn 15
l1l
Yellow.
7
(ii) Given that this probability tt ,find 'r' l2l
,3
(e) The sets Pand Q atesuch that n(P) = 6' n(Q)= 9 and P n Q * a'rind
(i) the smallest possible value of n{P v Q}' t1I
[Turn over
Section B [36 marks]
7 (a)
-O and O is the
ln the diagram, is the origin.. PQ is a straight line with a gradient "t --'
point (4,0).
(i) Find the coordinates of P' l1l
{n8fftt$
Answerthe whole of this question on a shest of graph PrPen
Using a scale of 2 cm to represent 2 units on both axes, draw the x and y-axes for the ranges
0<.r<14and-2<y<16.
(s) Show the region in which all the inequalities grven below are satisfied, by ghading the
UntWANfED regions.
(i'l y >.2,
(ii) y <b,
(lti) 2y-x>-2,'
Gv) 5y+8x<80.'
I8I
O) At midday Peter set out to walk from I- towards N at an average speed of 5 km/h.
Calculate the time at which he arrived at N. l3l
(c) At N he changed the direction of his walk to due east until he reached a point D which is due
north of M.
lTurn over
10
(i) VT
w,
l1l
(ii) vR t21
PS'
(c) Taking the area of triangle VRI to be 4 cmz, calculate the area of
(i) triangle PRf,, 121
Marks scored (r) 15 <.r < 30 30<r<40 40 <.r < 50 50 <.r < 60 6O <"r < 80 80 <x < 100
Number of
candidates (fl 45 20 s5 N 30 10
(q) Draw a histogram for this distribution using a horizontal scale of 2 cm to represent l0 marks
and a scale of 2 cm to represent 1 unit on the vertical frequency density axis.
t5I
(b) Copy and complete the following table, which uses an assumed mean of 45.
Marks scored (r) Number of candidates (f) ("r - as) f(r -a5)
?2,5 _,45 _'r) <
-to12s
35 2A
45 55
55 N
70 30
90 10 45 450
rn.-
n (a) It is given that.r varies directly as y and inversely as the square of z'
(i) Write down an equation that expresses x in terms of y, s and a constant &. tll
(ii) Calculate the v'alue of the constant k when x = 15, ! =?jl and e = 3' tll
Gii) calculatethevalueof ewhen-r=3Oandy =294. l2l
pattern has not beeri drawn after the
(b) study the tiling pattern in the table given opposite. (The
pattern on line 4')
use the information given in this table to
(i) find the values of a,b, c and d,
(ii)expresst,thetotalnumberoftilesusedinPatternnumbern,intermsofn'
t8l
{n8n \irg,
Pattera Pattern Number of Numher of Totel nr:mber
nurnber biack tiies tvltrcv tiloo
",hito Lrl!J of tiles
I : CI t
t::r:l:. t
Eli.il
I, 4 s
2
t1
3
tt* 25
4
t1:
I 49 r\4