BOTSWANA EXAMI NATIONS COUNCI L

Botswana General Certificate of Secondary Education

CANDIDATE
NAME

CENTRE CANDIDATE
NUMBER NUMBER

*
o\
MATHEMATICS 0563/02
AJ
N)
Paper 2 OctoberlNovember 2016
(x
u 2 hours
5 Candidates answer on the Question Paper.
cl Additional Materials: Geometrical instruments
o. 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 n is required, use the value from your calculator or take n as 3.142.

For Examiner's Use

T This document consists of 14 printed pages and 2 blank pages.

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 2

Mathematical formulae for papers 1 and 2

Surface area and volume of solids

Name of solid Total surface area Volume

4
t^
cone nr2 + xrl ;J n('h
1
pyramid base area x height
5
4e
sphere 4nr2
3't'

Trigonometry

sinA
- silB - sinc
sine Rure abc
abc
sinA sinB sinC

Area of a triangle = 1ab sinc

2

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 For
3
Examiner's
Use
Tshepo had P80 to spend. He spent P20 on video games, P30 on comic books and P5 on
candy.

Express, as a ratio in simplest terms, the total amount of money spent to the amount of
money left.

Answer (a) ..... . t3l

2 A memory card used to store photographic images has 128 units of storage capacity.
A total of 36 images are stored on the memory card and 54 units of storage capacity
remain.

(a) Calculate the average amount of storage capacity used for each image.

Answer (a). . ................... l2l

(b) The cost of processing the 36 images into photographs is P156.60. A discount of
5% is given on the cost of processing the images.

Calculate the actual cost of processing all the images.

Answer (b)P ... ,...". tzl

The number of people, to the nearest ten, in a village is 46 960.

(a) Write down the upper bound of the number of people in the village.

Answer (a) .

(b) Write down the number of people in the village in standard form, correct to two
significant figures.

Answer(b)... l2l

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 For
4 Examiner's
Use
Thato drove 320 km from Molapo to Karaga. She started off at 08 00 and drove 200 km in
2 hours. She stopped for 30 minutes and then drove the remaining 120 km in t hour.

(a) Calculate the average speed for the entire journey.

Answer (a) . .........km/h

(b) Draw a distance-time graph to represent Thato's journey on the pair of axes
provided below.

Karaga

Distance
(km)

Molapo
0800 0900 1000 1100 '1200
Time (hours)

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 For
5
Examiner's
Use
The diagram below shows the points A and B on the circumference of a circle, centre O.
The chord AB = 14cm and the size of OAB = 32o.

Calculate

(a) the radius of the circle,

Answer (a) ....cm

(b) the shortest distance of the chord AB from the centre of the circle.

A customer had P3000 to exchange to Euros.

The exchange rate between the Pula and the Euro was P1 to e0.08456 .

How much in Euros, was P3000 worth?

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(a) Solve the inequality 4x + 15 > 6x + 2 .

Answer (a)

(b) Write down the prime numbers which satisfy the inequality 4x + 15 > 6x + 2 .

Answer (b) l2l

9 The points S(2, 1) and U(x, y) are two vertices of a square STUV. The point R(4, 3) is the
midpoint of SU.

(a) What are the coordinates of the vertex U?

Answer(a) ( , ) I2I

(b) The coordinates of the vertex f are (6, 1).

Calculate the length of a side of the square.

Answer (b) .12)

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 7

The diagram below shows a triangle KLM. KL = 90m, LM = 61m and the size of
KML =82.3'.

Calculate the size of MkL.

Answer t3l

11 The diagram below shows triangle H and a line /.

On the same diagram, draw the image of triangle H, alter a reflection in the line i. 121

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 I
(a) The capacity of a fuel tank of a car is 55 litres. The cost of fuel is P9.60 per litre.

Calculate the cost of filling up the tank when it is completely empty.

Answer (a) P ..... .. ............ . . .. t2l

(b) The rate of fuel consumption of the car is 7.4litres per 100 km.

Calculate the maximum possible distance, in km, that the car could cover on
one full tank of fuel.

Answer (b) .km [2]

(c) The cost of fuel is increased from P9.60 to P9.70 per litre.

Calculate the percentage increase.

Answer(c) . . 121

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 For
I Examiner's
Use
The results of an election show that Maatla got 210 votes, Thato 84 votes and Motheo
56 votes. The total number of votes is 350 .

(a) The information is to be represented in a pie chart.

Calculate the angle of the sector representing the number of votes that Thato got.

Answer (a) ........... .. 121

(b) Calculate as a percentage the number of votes that Maatla got.

Answer (b) ,^ t2l

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 Far
10
Examiner's
Use
The diagram below shows a sector of a circle of radius 1 5 cm. The sector angle is 200".

Calculate

(a) the length of the arc,

(b) the perimeter of the sector.

g
Solve the equation ": = !5
2x-1

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 11

The table below shows the shoe sizes of 40 students in a class.

Shoe size Number of students

4 4

5 7

6 10

7 11

8 6

I 2

(a) What is the range of the shoe sizes?

Answer (a) .. . t1I

(b) Calculate the mean shoe size.

Answer (b)

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 For
12
Examinels
Use
The table below shows some values of x and the corresponding values of yfor the equation
y=f-6x+8.
X 0 1 2 a 4 5 b

v I 3 0 -1 0 3 8

(a) What is the minimum value of y?

Answer (a)........
(b) On the pair of axes provided below, draw the graph of y - x2 - 6x + I for
0<x<6.

i
:ii
tii
ii;
I
-7 l
I

i;i
.1
i

A I 1 l
1' -.
I
i
rii
i
t

lli I
t::
I I

tl
l
i i l
,l l 1 I

l
i

I I
f iI'
.f,
I
.l,il
I I I

,' I ;,;
+ l
I

I
t
li l I1
1li
I
i
]G
lr
II
l,i
rl!

' 4 ii I
],, i
)

rl
'l i
1f

(c) On the same pair of axes, draw the graph of y = x - 1. l2l

(d) Use the graphs in (b) and in (c) to estimate the values of x that satisfy the equations

y=f -6x+8and y=x-1.

Answer (d)x= orx=

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 13

The diagram below shows a regular tetrahedron made of aluminium.

The length of the edge is 5 cm and the vertical height is 4.08 cm.

;i+oa
t\
t\

(a) Show that the area of the base is 10.8 cm2, correct to three significant flgures.

Answer (a).. ..... ........cm' 121

(b) Volume of a tetrahedron = I5 O"r" area x height .

Calculate the volume of the tetrahedron.

Answer (b) ............cm3 121

(c) The density of aluminium is 2.7 gtcm3.

Calculate the mass of the tetrahedron.

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 14

The table below shows the distribution of /Q scores, s, of 30 people.

Number of
lQ score (s) people
130ss<135 4

135ss<140 7

140ss<145 8

145<s<150 5

150ss<155 4

155ss<160 2

(a) What is the mid-point of the class 130 s s < 135?

Answer (a)

(b) On the pair of axes provided, draw a frequency polygon to represent the
distribution.

Number of
people

125 130 140 145 150

lQ score (s)

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