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0% found this document useful (0 votes)
951 views100 pagesMaths Rev Kit pp2
For paper 2
Uploaded by
katsosegana07Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF or read online on Scribd
/ 100
Candidate
Centre Number Number
(oy
‘THE MINISTRY OF EDUCATION BOTSWANA.
in collaboration with
UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE
. Botswana General Certificate of ‘Secondary Education
MATHEMATICS 0563/2
PAPER 2
OCTOBER/NOVEMBER SESSION 2001 2 hours
Candidates answer on the question paper.
‘Additional materials:
Etectronic calculator
Geometrical instruments
Candidate Namo __.
TIME 2 hours
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 this question paper.
working is needed for any question it must be shown below that question.
Omission of essential working will result in loss of marks.
INFORMATION FOR CANDIDATES i
‘The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 75.
It the degree of accuracy is not specified in the question and if the answer is not exact, the answer
should be given to three significant figures. Answers in degrees should be given to one decimal place.
‘many question where the value of m is required use the value from your calculator or take x as 3.142.
FOR EXAMINER'S USE |
This question paper consists of 15 printed pages and 1 blank page.
$8 (SLevsic) soaeasre
‘SUCLES 2001 [Turn over 2
‘Mathematical formulae for papers 1 and 2
Surface area and volume of solids
Total surface area
Name of solid Volume
cone marl darth
pyramid | base area height
sphere 4nr? $ar3
‘Trigonometry
Sine Rule
‘Area of a triangle 3 few
sana
1 (@)_ Mpho entered an elevator on floor number 6. He went 3 floors up then 4 floors down and got out |”
of the elevator.
‘On what floor did he get out?
(b)_ The first 3 terms of a sequence are ~5, ~2 and 1
Write down the next 2 terms of the sequence.
(i) Find an expression for the nth term of the sequence.
Answer (a). 2]
2]
Gi) 2)
|
2 Ofentse has a job which pays P20 per hour at normal rate.
‘The overtime rate is P40.50 per hour.
One week Ofentse worked 9 hours of overtime in addition to his normal working hours.
If he eared a total of P1064.50 for that week, calculate the |
(@) amount of money he earned at the normal rate,
(b) number of hours he worked at the normal rate,
Answer (a)P... 2
©), a)
[Turn over ber
te
3
4 fe
‘A helicopter leaves base B and flies 12km on a bearing of 090° to a place P.
then flies 20km to a place Q which is due North of base B.
(a) Using a scale of Lem to represent 2km, make a scale drawing to show the flights of the
helicopter from B to P, and from P to . The point B has already been marked for you.
2
(b) Using your diagram, or otherwise, find the
@ distance BQ,
) bearing of Q from P.
Answer (0) (i) a
rn Fe
te
Lorato went to buy a new outfit in Mmabatho.
She changed P1500 to Rands at a bank in Lobatse, The exchange rate was PI to R1.3241.
(a) How many Rands did Lorato receive?
(b)_ In Mmabatho she bought an outfit which cost R1200 before tax. She then paid 2% sales tax.
Calculate the sales tax she paid.
(©) Lorato brought back some Rands and she decided to change R667 to Pula,
‘The exchange rate for this transaction was PI to R1.3340.
Calculate the amount of Pula she received from the bank.
Answer (a)R
OR
(oP...
{Tum over
Pe
\Eonners
tie fu
tie
: |
A Tie Design Company fsa wide vi of wal es, Each leas em of 16 sal qos,
tnd soneo he geet shade show
Tile Tile2
(a) How many lines of symmetry does Tile 1 have?
Answer (a). sown O]
(b) @ Shade one square on Tile 1 50 that the tile will have rotational symmetry of order 2. [1]
(i) Mark, with the letter X, the centre of rotational symmetry. itt)
(6) Shade the smallest possible number of squares on Tile 2 so that both lines M and L are lines of
symmetry. a)
fw
xis
Ue Fe | 7
level ground. She found that the angle is 31°.
‘The distance from A to T is 251m as shown.
(@) Calculate the height of the radio mast, G7.
T
25m,
“mB
(b) Calculate
® 2G,
(i) the angle of elevation of the top, 7, from the point B.
Answer (a).
) @)
6 —Tebogo measured the angle of elevation of the top of a vertical radio mast, G7, from a point A on
‘Tebogo now moves 10 metres, directly towards the base G, to a point B.
wm (2)
van [3]
w.
(Torn over
fe
the fe 8 fe
enter ties
te the
7 The extemal dimensions of some cylindrical tins of jam are diameter 8cm and height 12cm.
(a) Calculate the volume of one tin of jam,
‘The tins are packed in a rectangular box with internal dimensions 40 em by 32cm by 25cm as shown.
25cm
32cm
40cm
(©) @ How many tins will il the bottom of the box completely?
(8) How many tins will fill the box completely?
ii) Calculate the volume of space in the box that will not be occupied by the tins.
Answer (a). 2
| oOo 2
| Gi. a
| Gi)... 8) fe
Ue
9
‘A bus left Kanye at 8.15a.m. and arrived in Tsabong at 1.45 p.m
(8) How long did the joumney take?
‘The following morning the bus left Tsabong for Kanye, It took 5 hours 45 minutes and arrived in
Kanye at 1610,
(b) At what time did the bus leave Tsabong?
(©) Ifthe 5 hours 45 minutes is given to the nearest 5 minutes, what is
(the Least time the bus could have taken,
i) the maximum time the bus could have taken?
Answer (a). a
® see a
ow a )
Gi) cresennnnneen m
enone. (Turn over
fer
te % | 9 ‘The masses of 300 students in & Junior School were recorded. The results are shown in a grouped |“
frequency table below. |
i
Mass (rkg) | Frequency | euiee
| 30 4.
Answer (b) «. 2
3 (@) Mrs Lefatshe bought 15 metres of cloth. The cost of one metre is P69.95.
Cc (How much did she have to pay?
Answer (a)(i) P. uy
(ii) She cut out 2 pieces, each 6.13 metres long, from the cloth,
How long, in centimetres, is the remaining piece?
Answer (a\(ii) . em [2}
(b) Ina science laboratory a student measured the thickness of four types of cardboard
Paper using a micrometer. The results of the measurements in metres were:
2x10%, 6x10, 1.2107, 7% 104.
Arrange the measurements in order of size starting with the smallest,
Answer (b) Q]
(8632 Nov 0 [Turn over For
saminer
4
‘Ata regional Mathematics and Science Fair, 10 students’ projects were seen by 2 judges.
The scores, in percent, given by Judge 1 and Judge 2 are represented in the scatter graph as
shown,
80
70
60
Score given °°
by Judge 2
40
30
20
10
10 2 30 4 50 60 70 80 90 100
Score given by Judge |
‘The scores given by the two judges correlate positively.
(a) Draw the line of best fit. 0
(b) Use your line to answer the following questions.
(i) One project was seen by Judge 1 only and she gave 45%. What score do you
expect Judge 2 would have given for the same project?
Answer (b)(i) % (1)
(i) Another project was seen by Judge 2 only and given 55%. What score do you
expect Judge 1 would have given?
Answer (b)(ii)
1612 Nov 00
For
Examiners For
Examiner
5
5 (a) Ina sequence, the next term is found by multiplying the previous term by 4 and then
subtracting 1. Starting with 3, write down the next 3 terms of the sequence.
Answer (a). [2]
(b) The nth term of another sequence is given by Sn + 3. Ifthe nth term is 498, what is the
value of n’?
Answer (6). fe)
6 (a) The equation of a straight line is 3x Sy-15=0.
(Write this equation in the form y = mx +c.
Answer (a)(i) RI
(ii) Write down the coordinates of the point where the line crosses the y-axis,
Answer (a)(ii) ..
0}
(b) A line segment CD has endpoint coordinates C(-~1,2) and Dp, q). M(2, ~2) is the
‘midpoint of the line segment CD.
(Find the coordinates of the endpoint D,
Answer (bY) D (
(ii) Calculate the distance between points C and M.
Answer (bY i
2)
056372 Now 00 {Turn over
For
Exanin For 6 For
vaminer’s Ezaminer®
7 The following containers are each filled with water at a steady rate.
A B c
The graphs below represent the depth of water against time for each of the containers.
1 2 3
Depth Depth Depth
of of of
water water water
- ~ ~
Time Time Time
(a) Match the graphs with the containers.
Answer (A) A. as
c
1 5642 No 09 For
Beaminer
(b) The container below is also filled with water at a steady rate.
7
——|
[|
On the axes provided, sketch the graph of the depth of water against time for the
container.
Depth
water
Time
(84372 Nor 0
R]
{Turn over
For 8
(a) The volume of the cuboid shown is given by V = x?y,
Find the volume if x= 1.2 em and y= 3.7 em.
Answer (a) em? [1]
(b) A rope has length x metres. Two pieces each of length y metres are cut off and the
length of the remaining piece is given by (x - 2y) m as shown,
Find the length of the remaining piece given that x= 17} mand y=6} m.
Answer (b) «. 2)
(©) Factorise
6p+p?+9.
Answer (c)
(2)
For
Examiners For
Examiners
9
9 The diagram shows the positions of 3 villages: Keaga, Molapo and Sekgwa, The bearing
of Molapo from Kgaga is 056°.
NORTH
Molapo
NORTH q
Keaga E
Sekgwa
(a) Find the bearing of Kgaga from Molapo.
Answer (a) 2
The three villages are joined by 3 straight roads. The acute angle at Molapo is 30° as shown
on the diagram. The distance from Kgaga to Molapo is the same as the distance from
Molapo to Sekgwa.
(b) Calculate the acute angle at Sekgwa,
Answer (b) Q)
‘The distance from Kgaga to Molapo is 40 km.
(©) Calculate
(the distance from Kgaga to Sekgwa,
Answer (c)(i) RQ)
(ii) the area of the triangular region enclosed by the 3 roads.
Ansiver (cil) 2
36372 Nov 00 (Turn over
For
Buamine 10
10 The diagram shows a mirror ABCDEF,
in which BCEF is a square of side
62cm.
ABF is a sector of a circle of radius
62cm, centre F, and CDE is a sector of
a circle of radius 62 cm, centre E.
‘Angle AFB = angle CED = 30°.
(@) Calculate
(the length of the arc AB,
Answer (ai) rR
(i) the perimeter of the mirror.
Answer (aXii) em [1]
(b) Calculate the area of
@ sector CDE,
Answer (bX) .. (2)
(the mirror ABCDEF.
Answer (b)(i (2)
(©) Given that the length 62cm in the diagram is correct to two significant figures,
complete the statement below to show the lower and upper bounds for this length.
Answer (0) vorneon ES length < em [1]
3642 Now 00 For
miners
’
11 A stone is dropped from the top of a building. The height, h metres, of the stone above the
‘ground is given by h = 45 ~ 51, where f seconds is the time after the stone is dropped.
(a) Complete the table below to find the values of A corresponding to the given values
iu
oft.
1) | 0 os J is] 2 [a5] 3
him) |
[21
(b) On the axes provided below, draw the graph of h against t.
G3)
(© _ Using your graph or otherwise, find the value of when the stone is 10m above the
‘ground.
Answer (c)
056372 Now 00
For
Examiners
{Turn over For
2
12 (a) In January 1997 the number of pupils at a school was 450.
Given that the number of pupils at the school in January 1998 was 645, find the
percentage increase in the number of pupils correct to 3 significant figures.
AMsWeF (Gd) ones % [2]
(b) (Kagiso invested P5000 at 9% simple interest for 3 years. How much money will
she have in her account at the end of 3 years?
Answer (by(i) P a (2)
(ii) Setshogo invested the same amount of P5000 at 9% compound interest for 3
years. How much money will he have in his account at the end of 3 years?
Answer (by(ii) P. von (2
(iil) Who will have more money in the account at the end of 3 years and by how
much?
Answer (b)(iii a)
(6372 Nov 00
For
Examine For
3
13 (@) Construct triangle ABC where AB = 6 cm, BC = 4.cm and AC = 8 cm.
‘The point A has been marked for you.
(21
(b) On your diagram above, construct the locus of the points which are equidistant from
Aand C.
Label it 21
(©) On your diagram above, construct the locus of all points that are 4cm fromA. [1]
(4) What is the geometric relation between the locus in part (b) and the locus in part (e)?
Answer (d) m4
3642 Nov 00 [Turn over
For For
14
14 One thousand people employed by a company were asked to state the amount of money
they spend on food daily. The cumulative frequency curve shows the results.
1000
800
Cumatative 600
frequency
200
o
1.40 1.60 180 20020 2.40
‘Amount spent (Pula)
(@)_Use the curve to find an estimate for
(i) the median amount of money spent,
Answer (a)(i) P
Gi) the interquartile range.
Answer (a\(i) P
Bl
(b) The company announced that it would bear the expenses of those who spent P2,00 or
Jess. How many employees will benefit from this?
Answer (B) .. uy
(©) Whatis the probability that an employee picked at random will spend P2.00 or less per
day?
Answer ().. a)
56372 Nor 00
For
Examiners
~~ For
,
11. Some cylindrical tins have radius 4 cm and height 11 em,
(@) Calculate the volume of one tin.
cm? [2)
(b) As many tins as possible are packed in a rectangular box measuring 48 cm by 32.cm
by Lem,
@ How many tins are in the box?
(i) What percentage of the volume of the box is filled by the tins?
Answer (b) (i).
~% [2]
3680 W 199 (Turn over
For For
6 Inthe diagram, TA and 7D are B
tangents to the circle, touching
the circle at A and D respectively.
DC is a diameter which meets TA ct
produced at 2.
Angle TDA = 64°.
gle Ef
Calculate
(@) Dac,
(b) DCA, @
© AfD, T = D
@ TBD.
Answer (a) DAC =
(&) DEA =
(AD =
(@) TBD = 0
7
In a survey of a group of people, j said “Yes”, said “No”.
‘The remainder were “Undecided”.
(8) What fraction of the group was “Undecided”?
Answer (a) ..
() 11 more people said “Yes” than said “No”.
How many people said “Yes”?
Answer (b) ..
5637. W 1999, {Turn over
For Fors
13. A village A is 25 km from O on a bearing of 050°.
Another village B is 45 am from O on a bearing of 120°,
(a) Using a scale of Lem to Sim, complete the diagram below, showing clearly the
Positions of A and B. ‘
Answer (a)
North
2)
(b) Use your diagram to find
(® the distance of A from B,
(ii) the bearing of A from B.
Answer (6) (i) .. km [1]
Gi). Q
(5642 W 199 [Turn over
For ,
()_On the grid below draw the graph of y against x for 0 10
ed
10 The selling price of a car is P72 000. .
(a) The dealer is willing to sell the car for a deposit of 30%, followed by 24 equal monthly
payments, .
() How much is the deposit?
(i) How much is each monthly payment?
Answer (a) (i) P fet) P
GP a
(b) The cost of renting the car is an initial, non-returnable P2000 for administration costs,
plus P1750 per month.
(@ Calculate the total cost of renting the car for 3 years.
Gi) Calculate the number of months after which it becomes more expensive to rent
the car than to buy it for P72.000.
Answer (b) (i) P
ie}
Gi) 2}
ox Wie 16
15 One day Pako ran from his home to a nearby river.
He rested by the river and then walked home.
The graph of his journey is shown below.
st
4
Distance
from home
om a
1
0 10 20 30 40 50 0 70 80
‘Time (minutes)
(a) For how many minutes did he rest by the river?
(b) How fast did he run from his home to the river? Give your answer in km/h,
©) 10 minutes after Pako started from home his brother, Kabo, set off from home,
Kabo walked towards the river at a steady speed of 4 km/h until he met Pako.
The two brothers walked home together.
(@ On the diagram draw the travel graph for Kabo's journey from his home until he
met Pako,
(i) Use your graph to find the total distance that Kabo walked.
Answer (a) ..
©).
ckan/h
ow on the diagram
(i kom
a)
(2
(2)
2)
657. W 1559
For 4
A small picture measures 30 cm by 20cm.
‘The picture is to be mounted onto a larger piece of card which will produce a border, x cm
wide, around the picture.
‘The area of the border is y cm?.
(a) Show that y= 100x+ 4x2,
Answer (a)
(21
(b) For the function y = 100x+ 42°, some values of x, and the corresponding values of y
are given in the table below.
x | o 1 2 3 4 5 6
y | o | 108 | 216 | 336 | 464 p | 744
() Calculate the value of p.
Answer (b) (i), a)
Ea
5632 1959 For
> R
12 (@) Intriangle ABC, BAC = 74°, ABC = 48°,
ACB = 58° and AB = 6.5 cm.
Calculate the length of BC.
Answer (a) ..
(b) In triangle XYZ, Y2Z = 57°, XY = 10cm
and XZ =8 cm.
Calculate the area of triangle XYZ.
Answer (b)
Bl
[2]
ese W 1958
cB For
if
8 The diagram below shows the cumulative frequency curve of the heights of 80 girls.
Cumulative
frequency
140 145 150 155 160 165 170
Height (em)
Use this curve to estimate
(a) the median,
(b) the interquartile range,
(©) the number of girls whose height is greater than 162 cm.
Answer (a)
) (2)
1)
ss30 W 1959 “11 Bananas are sold at PI.SO per kg,
(a) Calculate the cost of 1.8kg of bananas,
‘An exercise book costs P1.35.
(b) Calculate the largest number, N, of exercise books that can be bought for P12.
note,
How much change did she get?
Answer (a) P..
@8EC 2004 oseuezorvns
(©) Lorato bought 1.8kg of bananas and that number, N, of exercise books. She paid using a P20
)
2]
B)
[Turn over
fer
tie 4
2. Ima football competition, for each game played, a team got 3 points for winning, | point for drawing
01 0 for losing.
(@)_ Team A played 18 games.
(What is the maximum number of points the team could have got?
‘Team A won 4 of the games, lost 4 and drew the rest.
(ii) How many games did the team draw?
Gi) How many points did the team get?
(iv) What percentage of the maximum number of points did the team get?
(b) Team B obtained 29 points. Ifthe team drew 8 games, how many did it win?
Answer (a) (i)
Wi.
| Gi). 2
(iv) 2)
| ® Ry
enec 2004 osssmaonos fr 5 be
ter soit
“© | 3 Acylindrical container of diameter 42cm is filled with 180 litres of milk. “
(a) Express 180 titres in em?,
(b) Calculate the cross-sectional area of the container.
(©) What is the depth of the mitk in the container’?
A fall carton can hold 1.15 of milk,
(d) How many full cartons can be filled from 1807
(©) How much milk, in litres, will be left after filling the cartons?
Answer (d)... em? [I]
.. 2
Om re
Doren 2
©. ol (2)
© BEC 2008 ossxoonvo (Turn over fe 6
4 The total cost of servicing a car is the sum ofthe cost of labour and the cost of spare pars. The labour
‘costs P8S per hour, and the spare parts cost Py.
(a) Ifa garage took x hours to service a car, form an expression in terms of x and/or y for
(the total labour cost,
(i) the total cost of servicing the car.
(by The cost of spare parts used in servicing a car was PA75.
Calculate the bill if it took 3 hours to service the car.
(©) The bill for servicing a Toyota Corolla was P890. The cost of spare parts was PS50.
How many hours di it take to service the car?
Answer (a) (i) P.. uw
qd P. uw
() P.. . Q)
Ry
‘©BEC 2004 sexo
fe
te fr 1
tain
te
5 The diagram shows a solid wooden cone of base radius 25cm and slant height of 32.S¢m,
325
(a) Show that the vertical height of the cone is 20.8cm, correct to I decimal place.
Cc (b) Calculate the volume of the wood used to make the cone.
‘The mass of the cone is 11 000g.
(©) Calculate the density of wood in g/cm’.
(4) Calculate the total surface area of the cone,
Answer (a)
enec 2004 seaman
(2)
21
2
BI
[Turn over
fw
te fo
Examiner] 8
"16 (@) Drawaline AB Bem. The point A has already been marked for you. nm
Ae
(b) (i) Showing all the construction lines, construct the locus of points equidistant from points A
and B and label it /. 2)
Gi) ‘The points C and D lie on { such that SC = SD = 3m, where S is the mid-point of AB,
Mark and label the points C and D. io
ii) Draw and name the quadrilateral ACBD.
Answer (b) (ii ty
| © @_ Construct the focus of points 41cm from point A. 2
| (i) What is the name of the line CD in relation to the locus in part (c(i)?
| Answer (6) (ii) w
i
|
'
ec 2004 ossezano4 br
tie
© BEC 2004
9
7 Ina survey, 50 families were asked to state the number of cars they own,
‘The results are displayed in a bar chart below.
‘Number of cars owned by 50 families
Number of
families
Number of cars
(@) the modal number of cars per family,
Gi) the total number of cars in the 50 families,
Gi) the mean number of cars per family
(b) What is the probability that a family picked at random has no car?
(©) One of the cars is picked at random.
‘What isthe probability that it belongs to a family with 2 cars?
Answer (a) (i)
Gi) a
(ii
(Bor
©.
oseanzorNed
au
2)
2)
iu
2}
[Turn over
far fee
tie
10
‘The diagram shows the positions of three airports A, 8 and C. Airport B is 200km due North of A.
Airport C is on a bearing of 050° from A and 110° from B.
North
[a2 North
B
c
200
A
Calculate
(a) the bearing of B from C,
(b) the size of angle BCA,
(©) the length of BC.
Answer (a).
(),
©.
BI
ence 2004 ossannx0nv
ele 9
a
The
Calculate
@) vio,
(b) 7R,
(©) _ the distance between the centres P and U/ of the circles,
Answer (a)
@)
Oo
© BEC 2004 os6anz0NVO
iagram shows two circles with centres P and U of radii Sem and 15cm respectively. TVW and.
TOR are straight lines touching the circles at Vand W and at Q and R respectively. TQ = 12cm.
[Turn over fw
Ue
‘© BEC 2004
10 (@)_ Solve the simultaneous equations
2
Answer x=.
(b)_ The diagram below shows the graph of 2x + 3y = 12.
In the same diagram, draw the graphs of
@ x=2,
) 4x—Sy=20.
essovonvot
a)
Q
fo
uc
te fe
cour B
\ (©) @._ Show, by shading the unwanted regions, the set of points satisfying the inequalities
x22,
2e4 3y < 12 and
4n—5y $20.
in part (e)(i).
Answer (c(i
(@) (Draw a line parallel to 2x + 3y = 12 and passing through the point (3,4).
‘Write down the equation of the line in part (d)(j).
Answer (d) (i).
© BEC 2004 ossvensonvos
ul
(Gi) Write down the coordinates of one point with integer coordinates satisfying the inequalities
ul
ol
fer
te te
3
‘A supermarket sells a packet of biscuits for P3.95, a flask for P14,95 and a cereal server for P17.05.
(a) How much more does the cereal server cost than the flask?
its?
(b) How much will a customer pay for 6 packets of
(©) The nutritional information on the packet of biscuits states that in one
1.2g protein, 8.4 g carbohydrates and 4.3 g fat.
(@) Calculate the nutritional mass of one biscuit.
il) What percentage of the nutritional mass is carbohydrate?
(@)_ The nutritional mass is 95% of the total mass of the biscuit,
Calculate the total mass of the biscuit.
Answer (a) P sun
DP vresmnns
© @.
@ ..
‘©ec 2005, ossxomonves (Turn over
fw ber 4 fir
te tie
2A box of washing powder is in the form of a cuboid of length 24cm, width 10cm and height 30cm.
(@) How much washing powder, in em?, does the box hold when full?
‘A ull cup holds 360cm? of washing powder.
(b) How many cups of washing powder can be obtained from the box?
(©) A slightly soiled shirt requires 2 of a cup of washing powder.
How much washing powder, in cm?, does a slightly soiled shirt require?
Answer (a) .. em? [2]
® Ul
©
© B8C 205, ossaenonos fr 5
“* | 3. The diagrams below form part ofa pattem of rods held by bolts on a wall
A ft) AAA
Diagram 1 Diagram 2 Diagram 3
(@) In the space provided below, sketch the next diagram.
(b) The table below shows the number of rods and the corresponding number of bolts.
Diagram number ry2}3a][a].. a
‘Number of rods 5|9 . r
Number of bolts 3/5 |b 7
a (@) Complete the table for diograms 3 and 4,
(i) Express
(a) rinterms of n,
(b) bin terms of n.
(il) Find the number of rods needed for 19 bolts,
Answer (b) (i) (@) ..
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4 The diagram below shows the model of a steel girder whose cross-section is trapezium ABCD.
AB =Scm, DC = 7cm, and the height AE = 3m.
(@) Calculate the area of the cross-section ABCD.
(b) ‘The mode! has a volume of 224cm?,
Calculate its length.
(©) Anhole with a rectangular cross-section, PORS, is cut vertically through the model as illustrated
below. PORS is on the top Face of the girder. PQ = 4.2cm and QR = 1.8cm.
Calculate the volume of the remaining metal,
Answer (a) ..
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mf) 3 ho ‘On the axes below, draw the graphs of
ysx+2 and
y
for values of x from -3 to 3, 2)
(b) On the diagram, show, by shading the unwanted regions, the set of points satisfying
ysx42,
ys3-x and
yo.
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T] 6 Tecoordinates of the vertices of triangle ABC are A(2, 6), B(-2, -3) and C(12, p).
(@) Calculate the length of AB.
(b) The coordinates of the mid-point of BC are (5, 4).
Calculate the value of p.
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Answer (a)
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7 The diagram illustrates a cylindrical container and a solid sphere.
‘The container is open at the top, has an internal radius of 10cm and has height 11 em. The radius of
the sphere is 4em.
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‘The cylindrical container is completely filled with water. The sphere is placed inside the container
and rests at the bottom.
(8) How much water will flow out of the container?
(b) The sphere is then removed from the container.
Calculate
() the volume of the remaining water,
(i) the height of the remaining water,
Answer (a) cm? [2]
O@ em? (3]
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‘Two girls, Lorato and Chawa, work in a restaurant where they wrap lunch boxes,
Lorato wraps 20 boxes in ¢ minutes.
(@) Express, in terms of r, the number of boxes she wraps in one minute,
(©) Chawa wraps 30 boxes and takes 8 minutes more than the time Lorato takes to wrap 20 boxes,
Express, in terms of
(@ the time, in minutes, Chawa takes to wrap the 30 boxes,
(i) the number of boxes she wraps in one minute.
(©) Lorato and Chawa wrap the same number of boxes in one minute,
(@ Express this information in an equation.
i) Solve the equation in part (e)().
(lil) Find the number of boxes each girl wraps in one hour.
Answer (a)
i.
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10
‘The diagram below shows a vertical flagpole, BE, and a raised flag. The distance from the bottom of
the pole to the top of the flag, BA, is 4.2 m. The point Cis 6.2m away from B on level ground.
42
B
62
(@) Describe the locus of C.
(b) Calculate the angle of elevation of A from C.
(©) The angle of elevation of the bottom of the flag, D, from Cis 28°.
Calculate AD.
a
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‘The centre of the window is 0.
ec (@)_ Write down a single geometrical term that best describes the relationship between the triangular
window panes.
(©) Calculate AGB.
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10 The diagram shows a regular octagonal window, ABCDEFGHA, of a church.
(b) State the order of rotational symmetry of the window.
(@)_ Given that 08 = 60cm, calculate the area of one triangular window pane.
(©) Hence calculate the area of the church window.
‘Answer (a)
@)
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I The frequency table below shows the heights of 700 millet plants.
Height (cm) | Frequency | Cumulative
frequency
1000.
(Wi) The graph crosses the x-axis at three points (r, 0), (1, 0) and (s, 0).
Write down the value of r and the value of s.
Answer (a)
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"141 A heap of sand is in the form of a cone of base radius 1.5 m and height 1.8mas shown in the diagram | ™
below.
18
© (@) Calculate the volume ofthe sand.
(©) The sand was dug out from a level surface creating a rectangular cross-sectional pit with base
measuring 2.3m by 1.7m.
Calculate the depth ofthe pit.
(©) Ifthe 2.3 min part (b) is given correct to the nearest tenth of a mete, state its upper bound,
c
Answer (a) ... vam? [2]
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12 Inthe diagram, AT represents a side of a vertical building 18m high. The angle of depression of a car
at B from the top of the bui
1 T, is 33° and angle TAB = 90°.
(a) Calculate AB, the distance of the car from the foot of the building,
(b) The car now moves in a straight line, a distance of 13m from B to C as shown in the diagram |
below.
T.
18
A
Calculate
() the angle of depression of C from 7,
i) the distance of the car from the top of the building T-
Answer (A) sorrrne
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B
(by (i)
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13 The diagram below shows the positions of three locations, Phaleng, Kgwakgwe and Newtown in a
city. Kgwakgwe and Newtown are joined to Phaleng by straight roads R/ and R3 respectively.
North
{ Kewakgwe
Scale: 1m to 1km
RL
i
Phaleng. Newtown
(@) A police patrol tower is such that itis the same distance away from the two roads
Showing all construction lines, construct, on the diagram, all the possible positions of the
tower. 2
(b) A -cinema hall is to be constructed south of the R3 road such that it is 2km away from the road.
Construct, on the diagram, all the possible positions of the hall 2
(©) Write down the geometrical term used to describe the relationship between the construction in
part (b), and the 3 road.
Answer (6) sn.
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© BEC 2006 osexronves [Turn over ™ | 14° The diagram shows a hexagon ABCDEF on a grid made of equilateral triangles.
(8) Draw all the lines of symmetry of the hexagon on the diagram above.
(b) Write down the size of angle FBD.
(©-REC 2005 es63M/01N6 (©). The hexagon ABCDEF is
AB =p, FB =9 and CB = as shown below.
such that ed.
A itis given that m=
(@) Find the value of ¢ when m= 1l,1=-3andd=4,
Answer (a)...
(b) Express d in terms of m, ¢ and
Answer (b)..
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/| 2 _Ancleetric cooker can eitheF be bought for cash or through hire purchase,
instalments of PI71 each.
Balori buys the cooker on hire purchase.
(@) Calculate the total amount of money that he pays for the cooker.
Answer (a) P.
() How much money would he have saved if he bought it for cash?
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(2)
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(@) At the end of the first month the mass of the puppy had increased by 28%,
Calculate the mass of the puppy at the end of the first month,
Answer (a), akg [2]
(b) At the end of the second month, the mass of the puppy had increased such that it was now 15%
‘more than that at the end of the first month.
(® Calculate the mass of the puppy at the end of the second month,
Answer (b)(i)..
kg {2}
(ti) Whats the percentage increase in its mass since birth?
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‘Thato saves PS in the first month, P8 in the second month, P11 in the third month, P14 in the fourth
‘month, and continues with the same pattern up to twenty four months.
(@) How much money will Thato save inthe fifth month?
Answer (a)...
(b) Calculate the total amount of money that Thato would have saved in the first five months.
Answer (B) Poems Ri
(©) Describe, in words, the pattern of Thato’s monthly savings.
m
(@)_ Write an expression, in terms of n, for the amount of money saved in the nth month, where nis
such that 1 = n= 24,
Answer (d) Perea. (2)
(©) How much does he save in the last month?
Answer (e) Paw. a
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(a) What is the capacity of the drum in
@ cm,
Answer (aX).
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(i) litres.
(b). The oil is shared by a group of people.
Each person gets 25 litres.
How many people are in the group?
Answer (b). a
| 6 The distance, d, between Gaborone and Molepolole is 50km correct to the nearest 5 km.
Complete the statement below for the distance d.
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7 The diagram shows a semicircle, centre O, inscribed in a rectangle,
‘The radius of the semicircle is 7.6em.
16 o
Calculate the area of
(a) the rectangle,
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| () the semicircle,
Answer (6).
(©) the shaded part,
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“* | & The ble below shows the number of points obtained by a group of 30 candidates inthe BGCSE |
‘examination. i
|
‘Number of points | Number of candidates
35 4
36 6
37 7 |
i 38 8
39 3
40 2
(2) Calculate the range of the numberof points
4
Answer (a). mw] >
(©) Find the median numberof points.
Answer (B). uw
(©) Calculate the mean number of points.
Answer (c) 8)
(@) Those candidates who obtained atleast 38 points were admitted at an institution of higher .
| learning
| (How many candidates in the group were admitted?
Answer (d)(i). a
(ii) A candidate is chosen at random from the group
Find the probability thatthe candidate will not be admited
Aner (AN) one m) -
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|
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(@) Express AB as a column vector.
Answer (Gd) eos a
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(On the grid above represent the vector CD by a line segment. wi}
(©) Work out 4B - B.
ANSWEF (Close uw
(@ Calculate the magnitude of CD.
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10 The diagram shows a rectangular plot with length (3p - 4) metres and width 2p metres.
3p-4
2p
(@) Write down an expression, in terms of p, for the perimeter of the plot.
Answer (0) so
shown in the diagram below.
Ed
3p-3
3p45
(b) Write down an expression, in terms of p, for the perimeter of this plot.
Answer (b)..
(©) The perimeter of the rectangular plot is equal to that ofthe triangular plot.
(®) Form an equation in p to show this information,
Answer (e)(i)
(i) Solve the equation formed in part (¢)(1) to find the value of p.
Answer (Mii) p=.
lily Write down the length of the longest side of the triangular plot.
' Answer (c(i)
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Another plot is triangular and has sides measuring 3p metres, (3p - 3) metres and (3p + 5) metres as
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ue m A straight line, , passes through the points P(4, 3) and Q(-2, 6). ‘
~~ (@) Find the equation of the line /
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Answer (a). Q)
(b) Calculate the distance between P and 0.
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Cc (©) Find the coordinates of the mid-point ofthe line segment PQ.
Answer (0) (umm yrnceneen) — (2
(@)_ Ris another point on U such that PQ = QR.
Find the coordinates of R
Answer (d) ( : ~)
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12 The diagram shows the speed-time graph of a train over a period of 50 seconds.
16)
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! 0 10 20 30 0 50
{ Time (s)
| (@)_ Write down the highest speed the train reached in 50 seconds.
Answer (a)
@) Calculate
| @ the acceleration of the train during the first 10 seconds,
Answer (by)
(i) the distance covered by the train in the 50 seconds
Answer (bXii).
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