I
BOTSWANA EXAMINATIONS COUNCIL
in collaboration with
UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE
Botswana General Certificate of Secondary Education
CANDIDATE
NAME
CENTRE
NUMBER
CANDIDATE
NUMBER
*Z
l:
ul:
-
G:
0563/02
MATHEMATICS
OctoberlNovember 2012
Paper 2
G:
u:
-*-
2 hours
Candidates answer on the Question Paper.
Additional Materials: Geometrical instruments
Electronic calculator
READ THESE INSTRUCTIONS FIRST
Write your centre number, candidate number and name in the spaces provided 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 below that question. Omission of essential working
will result in loss of marks.
Do not use staples, paper clips, highlighters, glue or correction fluid.
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.
lf 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"
ln any question where the value of TT is required, use the value from your calculator or take w as 3.142.
For Examiner's Use
This document consists of 13 printed pages and 3 blank pages.
@ BEC 2012
[Turn over
2
Mathematical formulae for papers 1 and 2
Surface area and volume of solids
Name of solid
Total surface area
Volume
cone
nrz + rlrl
ln"n
1
pyramid
5
4tr2
sphere
Trigonometry
Sine Rule
Area of a triangle
@ BEC 2012
B
sin A
sin
sinA
sinB
sin C
= )ao sinC
0563t02totNt12
base area x height
4
5""
For
For
Examinels
Use
3
1
ln March 2010, the number of goats sold for slaughter was 3650.
(a)
Express the number of goats sold in standard form.
Answer (a)
(b)
".".........
(c)
..""."............ t1l
The total amount of money paid for the goats in March 2010 was P2 682 000.
Calculate the mean selling price of a goat, correct to the nearest thebe.
Answer (b) P..........
2
Examiner's
Use
".................. l2l
ln March 2011, the number of goats sold was 16% less than that of March 2010.
How many goats were sold in March 2011?
Mr Mokone bought 375 bags of flour each of mass 12.5 kg.
(a)
Calculate the total mass of the flour bought.
He packaged all the flour into 2.5 kg packets"
(b)
a BEC 2012
Calculate the total number of packets used to package all the flour.
0563l02lolNl12
[Turn over
For
4
For
Examiner's
Use
3
Examiner's
Use
A mass of 100 g is hung at the end of a spring and the length of the spring measured.
Another mass of 100 g is added and the spring length measured again. The exercise
is repeated up to the 8th mass.
The results are shown in the scatter graph below.
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o 100 200 300 400 500 600 700 800
Mass (g)
(a)
State the type of correlation of the scatter graph.
Answer (a) . ..
(b)
(c)
Draw the line of best fit for the scatter graph.
Using the line of best fit, estimate the mass when the length of the spring
is 8.64 mm.
@BEC20't2
.
0563t02totNt12
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For
5
Examiner,s
Use
The cash price of a new
car is p11SOO0.
' '- --" There are two options,
car as shown in the table
A and 8, of paying
below"
For
for the
P1 15 000.00 cash
27%ffi
48 monthlv instalments
inctatm^^+^ ^, h^^pZAru
of
Mpho chooses option g
(a)
to pay for the car.
Calculate
(i)
the amount that she will pay
as deposit,
Answer (a)O p
(i i)
the total amount she will
t2l
have to pay.
Answer (a)(i) p
(b)
Mpho pays more ,:i1y.b{
choosing option B than
option 4.
How much more does dh"'nur"1o
tzl
p".ii
Answer (b) p
l1I
@ BEC 2012
0563t02totNt12
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Examinet
Use
Examiner's
Use
For
6
For
5
Examiner's
Use
The points L(-6, 1 1) and M(-5,8) lie on a straight line.
(a)
Find the equation of the line LM.
Answer (a)
(b)
t21
LM is extended to a point N such that LM = MN.
Find the coordinates of the point N.
Answer (b) (
6
The times, in minutes, taken by 10 competitors to complete a puzzle are
'15, 9, 23, 32, 17 , 12,27 , 19,26 and 15.
(a)
Find the difference between the time taken by the fastest competitor and the time
taken by slowest competitor.
Answer (a)
(b)
...........
....minutes t1l
..
....minutes l2l
Calculate the median of the distribution.
Answer (b) .. -.
(c)
@BEC2012
One competitor is chosen at random from the group to represent the team in a
regional competition.
What is the probability that the competitor chosen took more than 18 minutes?
0563t02totNt12
For
7
For
Examiner's
Use
Examiner's
Use
The diagram below shows a plot used for a paddock ABC .
The length of the boundary AB is 100 m"
The size of BAC = 35 o and the size of ABC = 61"
"
100
A
Calculate
(a)
the size of ACB,
(b)
the length of the boundary AC,
(c)
the area of the plot for the paddock.
0563t02tatNt12
@ BEC 2012
ffi
[Turn over
For
Examinefs
Use
I
8
For
Examiner's
Use
The diagram below shows trapeziums P and Q.
z-
4
I
o
0
-l
\
-z
P
-c
(a)
Describe fully the single transformation that maps trapezium P onto
trapezium Q.
Answer (a)
(b)
@ BEC 2012
Trapezium R is the image of trapezium P under enlargement of scale factor 2,
centre (0, -4).
Draw trapezium R on the same pair of axes.
o563t02lotNt12
l2l
Examiner's
Use
For
Examiner's
9
For
9
Use
The table below shows some values of x and the corresponding values of y for the
equation Y=-f-3x+5.
(a)
X
_(
4
-3
-2
-1
0
1
2
v
-5
1
5
7
7
5
1
-5
On the axes provided below, draw the graph of y = -* - 3x + 5
for -5sx32.
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]t
!.i...i.-,1.
1-"i
&A*t--i
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1"i
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Use the graph to find values of x such that
i-t ' 1"-
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i1
j i.i
ili
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'i-'!"
ii
"i-e
t.
l'
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-f - gx + 5 = 0
.
Answer (b) x =............... or x = ................. l2l
(c)
On the same pairof axes, drawthe graph of y = 1 x +
(d)
Write down values of xforwhich
2 for -5 < x< 2.
-f -gx* 5=;x+2.
Answer (d) x =.............. or x =
o BEC 2012
l2l
0563/02lO/N/12
l2l
[Turn over
10
For
Examiner's
Use
10
For
Examiner's
Use
The diagram below shows a table top TUVWXYZ in the form of a regular heptagon
with centre O. The length of each side is 140cm.
XW
(a)
State the order of rotational symmetry of the table top.
Answer (a)
(b)
............
.....:......c1r1 12)
The table top is to be decorated using triangular tiles.
Calculate
(i)
the area of the tile that is needed to cover fOU,
Answer (d)O .
(ii)
@ BEC 2012
l2l
Calculate the perpendicular distance from O to TU.
Answer (c) ..... ..
(d)
t1l
Show that the size of f1V ts 128.6', correct to one decimal place.
Answer (b)
(c)
............
"......
the total area of the table top to be decorated.
0563102/o/N/12
............cm' 121
11
For
For
Examiner's
Use
Examiner's
11
The diagrams below show a pattern of small triangles.
Diagram 1
(a)
Diagram 2
Use
Diagram 3
Show, by shading, the small triangles that represent Diagram 4 in the grid
provided below.
t1l
The table below shows the number of small triangles in each diagram.
(b)
Diagram
1
2
3
Number of
smalltrianqles
b
10
14
(i)
4
How many triangles are in Diagram 4?
Answer (b)(i). .. .
(
ii)
n
.
Write down an expression, in terms of n, for the number of small
triangles in Diagram n.
Answer (b)(ii) ........
(c)
o BEC 2012
I1l
t2l
A diagram has a total of 106 small triangles.
What is its diagram number?
0563l02lolNl12
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For
Examinefs
Use
For
12
12
Examiner's
Use
A cup costs Px and a plate costs P3 more than a cup.
(a) Write down an expression, in terms of x, for the cost of a plate.
Answer (a) ". .. .
.......t11
(b) Martha buys 4 cups and 2 plates.
Write down an expression, in terms of x. for the total amount of money Martha
used.
Answer (b) ..... ... ..
(c) The total amount of money Martha used is P27.
Write down an equation, in terms of x, for this information.
(d) Solve the equation in part (c).
(e) How much money does a plate cost?
@ BEC 2012
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.......t11
Examiner's
Use
For
13
For
13
The diagram below shows a solid wooden ornament in the form of a cone of base
radius 4.3 cm. The height of the cone is 6.2 cm and the slant height is I cm.
I
I
6.2
(a)
Show that the slant height, {, is 7.55 cm, correct to 3 significant figures.
Answer (a)
(b)
............
...........cm2 l2l
............
...........cm2 t3l
The ornament is to be varnished
Calculate the total surface area to be varnished.
Answer (c)
(d)
............cm l2l
Calculate the curved surface area of the cone.
Answer (b)
(c)
............
Calculate the volume of wood used to make the ornament.
o BEC 2012
0563/02/O/N/12
Eilft
t!=:
Examiner's
Use