BOTSWAI.{A EXAM I NATIONS COU NCI !in collaboration with
UNIVERSITY OF CAMBfilDGE LOCAL EXAMINATIONS SYNIDICATE
Botswana General Certificate of Seconclary Edueation
CANDIDATE
NAME
CANDIDATE
GENTRE
NUMBER
NUMBER
C::
ry
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@-
&563/04
MATI{EMATICS
OcteberlFtroveral her ES08
Paper 2
2 hours
u'ffi
Candidates answer on the (iuestion Paper.
-:&
AcjditionalMaterials:
s:
Geometrical instruments
Electronic calculator
HEAO THESE INSTHUCTIONS FIHST
page'
vr/rite your centre number, candidate nunrber and name in the spaces provided at the top o{ this
Answer all questions.
Write your answers in lhe spaces provided on this question paper.
ll working is needed for any question !t must be shown below that question. Cmission of essentialworking will
result in loss of rnarks.
Do not use staples, paper clips, higtrhlighters, glue or correction fluid.
The nurnber of marks is given in brackets [ ] at the end of each question or part questionThe lotal of the marks for this paper is 75.
should be
lf the degree of accunacy is not specified in the question and if the answer is not exact, the answer
given to ihree signilicant figures" Answers in degrees should be given to one decimal place.
ln any question where the value of r is required, use the value from your calculator or take n as 3-142'
For Exarnimer's Use
This documenl consisls ol 15 printed pages and 1 blank page"
sP {sLMlcGW)Ts6068/5
o
BEC 2008
[Turn over
2
Mathematical fonnulae for papers I and 2
Surface area afld volume of solids
Name of solid
Total surface area
nrZ +
nrl
\r12h
{ base arca x height
Trigonornetry
Sine Rule
A _=_
sin B
obc
sin
dbc
srn
-=
Area of a rriangle
I
4
sin
sin C
= ;clr
I
B
sin C
sin C
5------t
Irrrr
3
I'or
Enfltilt{,ri
f.rrraiarrri
IJse
I
Use
In January 2008, the cost
(a)
of I litre of petrol lvas P6.16.
Horv much did 60 lires of petlol cost?
Ailstver (a)
(h)
P',..........
l2l
In August of the same year, Tiro paid P420 for 60 litres of petrol'
Calculate the percentage increase in the price of petrol betlveen.lanuary and,{ugust.
2
A salad is made using cabbage, carrots and garden peas in the ratio
(a) What percel:tage
by mass'
of the salad mass ls garden peas?
rbrswer
(b)
5:3:4
(a).............
l2l
A salad of mass l0kg is to be rnade'
ti)
Calculate the tnass of cabbage tequired for the salad.
Ansu'er
(ii)
(lrxi)...........
Cabbage costs i'6.35 Per kg.
Calculate the cost of cabbage required for the l0kg salad.
.'-..--..kg l2l
Far
4
Evnniner':t
Ct'e
(a)
Given the sequence 17, 14, I l, g, 5. ..,
(i)
lvrite dolvn the next tlvo terms of the sequence,
Answ,er
(ii)
find an exprcssion for the ltth term of the sequence.
Ansv,er (aXii)
(b) Two sequences whose nrh terms are given by 2n55 ancr g0 -
(i)
Find the value of
ru
t2t
rr
have a common lerm.
at lvhich the common term occurs.
Answer {[t)\i)
(ii)
tu
Write dorvn tlre eommon term.
Answ,er
(Irxii)........,.
lll
fin
5
Erominer's
Use
A friangular plot PQR is such that PR = ?5m, QR = 68m and PRC = 83o.
(a)
Using a scale
(b) Measure
(i)
(ii)
of
I cm to represent l0m, construct a scale diagrarn of the plot.
artd rvrite dorvn
the size ot
g4n.
the actual length of PQ.
t2t
l-$
ftnfieri
5
Use
i*!ffi
ilfi =xi['.',ffi
,:1o*::E;ffi,,ffi Hl,,oH**JHlbierresambe,orv
The height
2mnr and.4B
?ns
=
316:
=;;=
Dz{ =
J6p-
_
D
(a)
(b)
Caiculate the volurne
of the diamond.
Answer
The mass of the dianrond
is 0.0212g.
Calculate the dcnsity
of diamond in g/mm3.
(c)
Shorv thar the height,
12t
Afisy,er
() ,lE/- rtub
Tfw
7
Errrrrracri
Use
A square ABCD is such thnt the coordinates of A and B are (3, -2) and ( l, 2) respectively.
(a)
Calculate the area of the square.
(b) D is the point (7,0).
Find the coordinates of the centre of the square.
{c)
Answer
(b) (......,............,....-..............)
Ansn'er
(c:)
l2l
Write down the coordinates of the point C'
) tll
I
For
Ltttutitti,r.\
llse
The diagram below shows a cylindrical can of base radius 3.35cm and height 2cm.
G-----
(a) Calculate
3.35-
the volume of the cylindrical can,
Ansx'er
(b)
(c)...............
.......
cnt3 l2l
cans identical to the above can are to be fiiled completely witlr dough.
(i)
How many cans would be completery fiiled from 4550cm3 of clouglr?
Artswer
1ii)
(/r(i)........,..
Calculate the volunre of the dough that woulci be left after
filling
the cans.
l2l
T=r
I
fhr
tv*riu:r\
Ttre diagrarn belorv shorvs triangle LMN inrvhich
LlilN = g5., LM = I l.6cm antl LN = 2l.8cm.
Uv
Ii/
Calculate thc size af MN L.
Attsfi,etr
tll
The diagrarn below shows part of a parallclogranl pfRS.
PJr= 6cnr and
P,S
= 3.5cm.
{a}
Locate the point ,t ancl conrplete the parirllelogram.
(b)
on
{c)
What is thc geornetrical name of thc locLrs in part (b),?
the cliagram, rlrarv the locus of points rvhich are equiclistant
frcm pT.ancl ps.
Attsn er
(t)
l2t
lzt
ttl
7
frrr
f-rerrainer's
Lt*
t0
The table belorv shows the number of units,
rr,
of electricity consumed and the ccrresponding
charges, E, in Pula.
Number of units,
l
Eleclricity charge, E (Pula)
(a) On the diagranr
100
200
300
45
80
il5
belorv, plot the points from the tahle and join thern rvith a straight line.
125
E (pula)
0
100
200
3t)0
Number of units, ll
(b)
Use your graph to fin<.! the electricity charge rvhen 260 units are used.
il
(c) (i)
Frrr'
flrarrtirrrri
Lirr:
Find the gradient, ,,,, of rhe graph.
Atswer
(ii)
(c)(i).........".
ll
Write down the equation shorving the relationship between the number of urrits used ald
form E = nut + c.
the electricity charge in the
(iii)
I
What dors the intercept, c, lcplesent?
Att.sw,er
(cXiii)
Ilt
lit
l2
Etaminer\
Ute
ll
The cumulative frequency curye below shorvs the ages of 50 ernployees of a company.
-:
i- i-
r-.,]_
50
jl
+
-
'il
i
45
.t
4G -+-f
ii
.i-I r_
u
I I
t_ l-T
-L
..{..
Number
of
25
enrployces
tl
,,,.jI
l++!
20
t- i-
fl
r1-
j-
!l-r'l
..i
I
30
;l
*4
rl
'.i.f-:i
1*'i-:
f.'
35
-!-+
iiii
Use the graph to estinrate
(D
the rnedian,
(iil
the lorver quartile,
(iii)
the upper quartile.
tr
ii'/
l_L
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i.+-1-
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(a)
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70
l
(b)
Calculate the interquartile range.
Artsv,er
(e)
(#),..............
What is the probability that an employee selected at random is aged less than 40 years?
Ansv'er (c)
(d)
.... years
The company offers a rctircment package to the oldest lUvo of its employees.
State the age of the youngest employee r,r,ho qualifies for this ofi,er.
III
far
t4
flronnaeri
Lire
t2
The diagram belorv shows the frame of a church rvindorv. It is in the form of an arc pLS of a circle
centre O, radius 40cnr joined to a pentagon \ORSO.
QR =76.1cm, PQ = SR = 6$cm and POS
=
ts
(a)
Wdte down the size of the reflex angle
1440.
76'l
fdS.
Ans*t'er {a)
(b)
Calculate the length r:f arc PIS.
Answer
(c)
(lr)..............
A strip of ribbon is to be rur once along the outer frame pORSTp.
Calculate the length of the ribbon required.
..........cm l2l
|-
ltw
liranrirrtl
Ltrr
l5
i
13
seditse bought a total
I'tu'
flralriilri'l
of I9 tickets for children and for
Usr
aclults.
The numbel'of tickets bought for chitdren is .y.
(a)
Write down an expressiotr, in terms of
for the number of rickets bought for adults.
.1',
Attswer (c)
(f,)
Tickets cost P20 each firr a child and
pj5
write doivn an expressiori, in tenrrs of
(i)
._r',
each for an adult.
for the total cost of tickets for
children,
A,rtsr+,er
(i0
(l,Xi).....
Seditse paid a total
(i)
lrt
adults.
Artsy,er (I,lxii)
(c)
III
of F500 for
lll
atrl the tickers.
Form air equation in 1 and solve it.
.Aasu,cr (cXi)
)'-
(ii)
l3t
How much rnotrey rvas used to buy tickets for adults?
Arrsv,cr (r'Xii) P
t2l
i