BOTSWANA EXAM I NATIONS COUNCI L

"r Botswana General Certificate of Secondary Education

MATHEMATICS 0563/03
Paper 3 OctoberlNovember 2019
2 hours 30 minutes
Additional materials: Answer paper Graph paper (2 sheets)
Electronic calculator Mathematical tables (optional)
Geometrical instruments

READ THESE INSTRUCTIONS FIRST

Write your answers on the separate answer paper provided.

Start each question on a fresh side of the page.
Write your Centre number, candidate number and name on each sheet of answer paper you use.
Answer all questions.
All working must be clearly shown. The working should be done on the same sheet as the rest of the answer.
Marks will be given for working which shows that you know how to solve the problem even if you get the
answer wrong.
At the end of the examination, fasten all your work securely together using the string provided.
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 '125.
Electronic calculators may be used,
lf the degree of accuracy is not specified in the question and if the answer is not exact, the answer should be
grven 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.

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This document consists of 14 printed pages 2 blank pages.

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Mathematical formulae for paper 3

Surface area and volume of solids

Name of solid Total surface area Volume

1^
cone xrz + xrl -3 nr'h

pyramid base area x height

3
4"
sphere 4nr2 -3 nf"

Trigonometry
(f)

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Sine Rule
sinA sinB sinC
ab c

ab c
siM sinB sinC

1
Area of a triangle = sinC
rrb
Cosine Rule a2 = bz + c'-Zbccos A

b2+c2-a2
cosA=
2bc

Statistics
rO
O
O

variance _ z$ -xY ,
vr$-xf
zf

Standard deviation (SO1 = JVariance =

z(r-rI

or Zr' _{FY
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1 During an outbreak of a certain disease, 2A427A0 babies were tested. Of these, 909060
babies were found to have the disease.

(a) (i) Calculate the number of babies that were free of the disease. I1l
(ii) Express the number of babies that were free of the disease as a percentage
of those who were tested. I2l
(b) ln order to prevent the spread of the disease, the health department administered a drug
lo 704/o of babies that were found to have the disease.

(i) How many babies did the health department administer the drug to? 12)

(ii) The cost of the drug per baby was US Dollar 11.99.
Calculate the cost, in US Dollars (US$), of the drug administered to babies that were
found to have the disease. {21

g (c) The 2A427AO babies tested for the disease represent 16.50/o of the entire population.

Calculate the entire population. t3j

2 There are2.25 x 104 of animal species in a national park. This number of animal species is
expected to double in five years.

(a) Calculate the number of the animal species that is expected in five years' time.
Give your answer in standard form. 12)

(b) After five years, the actual number of the animal species was 3.95 x 104.

{i) Calculate the difference between the actual and the expected number of the animal
species at the end of five years. Give your answer in standard form. l2l
(ii) Express the difference as a fraction of the expected number of the animal species,
Give your answer in its simplest form. t2J
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lnthediagram belowdh=-Ou anO &=-9v. f isa pointalong ORsuchthat Of: TR=1'.2.

U is a point along OS such that OU: US = 1 :2.

Express in terms of u and/or v

(a)
+
RS, 12)
--)
(b) or, t1j
-+
(c) TU. l2l

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4 The diagram below shows a circle with centre O. The points P, Q, R, S and f lie on the
circumference of the circle. The size of angle QOR = 48" and the size of angle PRS = 65'

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State, with a reason, the size of angle

(a) RSP, l2l

(b) RPQ, t2)

(c) SIP. 121

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The diagram below shows a right square based pyramid, ABCDE, of vertical height, hcm, with a
shaded top. The shaded top is also a right square based pyramid of vertical height 15.3cm.
The ratio of the base length of the shaded pyramid to the base length of pyramid ABCDE
is2:5.

E r----
I

C'

(a) Calculate the height, h.

121

(b) State the ratio of the volume of the shaded pyramid to that of pyramid ABCDE. I1l
(c) The volume of the shaded pyramid is 524cm3.

Calculate the volume of the unshaded part of pyramid ABCDE. t3I

6 A windmill is to be installed inside a farm. The farm is in the form of a triangle ABC
such that AB = 10.5 km, AC = 13.5 km and the size of angle ABC = 62" .

{a} Using a scale of 1 cm to represent 1 ,5 km, construct a scale diagram of the farm. t3l
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(b) Measure and write down the actualdistance of BC. 121

(c) The windmill must be installed such that it is the same distance from AC as it is from 8C.
It should also be 7.95km from B.

Construct the locus of points in the farm that are:

(i) the same distance from AC as they are from 8C, I1l

(ii) 7.95km from B. t1l

td) Mark and label, with letter t4l, the position of the windmill. t1l

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The diagram below shows the speed-time graph of a moving particle. The particle accelerates
for 15 seconds from a speed of 5 m/s to a speed of Vm/s. lt then decelerates for 10 seconds
to rest.

20 ---r*]-::i-i
i+ ii-'i-r:r
V
,;r 'liili :l t:ii
1E
IJ
tr;l_1i-+1
I#-[, -ti {): \iij-.,ti
t: :i1-i \i
Speed
(m/s) 10
'I i I i

. l-i l .. I t-i .,iil$ J, 1T

{_i_i i,i t:l
r,t:1'r4t ..., + l. i. . '..| )

y1fi1.,:i,,
irll" +l
"'. j-,L-j-- t; j-\l
5
:::lr.r

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Time (f seconds)

(a) What is the speed, Vmls, of the particle at f = 15 seconds? I1I

(b) Calculate the acceleration of the particle when f = 10 seconds. t21

(c) Calculate the total distance travelled by the particle in 25 seconds. I3l

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The diagram below represents part of a sports field. The field is in the form of a sector OAB with a
triangle OCD enclosed. The length OC = OD = 4.25m, CD = 2.54m, OA = OB = 90m and the
size of angle BaD = COA = 3.1".

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(a) Calculate the size of angle

(i) Doc, l2l

(ii) BoA. t1l

(b) The triangular part, OCD, of the field is surfaced with concrete and the remaining part is
to be surfaced with synthetic fibre.

Calculate the area of the field that is

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(i) surfaced with concrete, 121

(ii) to be surfaced with synthetic fibre. 121

(c) The cost of buying synthetic fibre is P95.99 per square metre excluding 12%VAT.

Calculate

(i) the amount of money, including VAT, for buying one square metre of the fibre. 121

(ii) the total amount of money that would be used to buy enough fibre for surfacing
the remaining part of the field. 12)

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I The frequency table below shows shoe sizes for a group of 18 football players.

Shoe size Number of players

7 Z

I b

a_
1
3

v tr

IU 2

(a) A player is chosen at random from the group to attend a coaching clinic.

What is the probability that the player chosen wears size 8? I1l

H (b) The player who is chosen to attend a coaching clinic wears sizeL From the remaining
players in the group, two more are chosen at random to attend a regionaltraining camp.

Calculate the probability that

(i) they both wear size 9, 121

(ii) one wears size I and the other wears size 10. l3l

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10 The diagram below represents a rectangular cloth of length (4p - 1) m and width (p + 2) m.
An isosceles triangular decoration of base length (4p - 3)m is painted on the cloth. The base
vertices of the decoration are 1 m from the edges of the cloth.

I
p+2

f,
1
j
u
C) K- 1 ->r
6r 4p-1

(a) Express, in terms of p,

(i) the height of the triangular design, t1I

(ii) the area of the triangular design, I1l
(iii) the area of the cloth that is not painted. 121

(b) The area of the cloth that is not painted is 13 m2.

Form an equation, in terms of p, to represent this information and show that it reduces to
4p'+ 13p-27 =0. t3l
(c) (i) Solve the equation 4p2 + 13p - 27 = 0, giving the answers correct to two decimal
places.
I5l
ro (ii) Hence calculate the area of the triangular design. l2l

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11 A supermarket sells two types of capacitors, type A and type 8. A capacitor of type A costs
Px and a capacitor of type B costs Py.

(a) A customer bought 25 capacitors of type A and 35 capacitors of type B.

(i) Express, in terms of x and y, the total cost of these capacitors. l2l
(ii) The total cost of these capacitors is P60.75.

Form an equation, in terms of x and y, to represent this information, t1l

(b) Another cusiomer bought 30 capacitors of type A and 75 capacitors of type B and paid
P112.50.

Form an equation, in terms of x and y, to represent this information. 121

(c) (i) Solve the equations in (a)(ii) and (b) simultaneously. l3l

R (ii) Calculate the total cost of buying 105 capacitors of type A and 46 capacitors of
5 type B. 121

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12 The table below shows the number of people who entered a shopping mall at different time
intervals during the first 2 hours of opening.

Time (f minutes) Frequency

0sf<15 60

15 s t < 30 30

30<t<45 75

45<t<75 90

75=t<120 135

(a) State the range of the times for the people entering the shopping mall. t1l

(b) The midpoint of 0 s t < 15 is 7.5.

(,
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Calculate an estimate of the time, in minutes, for the

(i) mean, t3l

(ii) variance, t3l

(iii) standard deviation. t1l

(c) Without drawing a cumulative frequency curve, calculate an estimate of the

(i) median, t3l

(ii) 85th percentile. t3l

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{3 Answer the whole of this question on a sheet of graph paper.

The table below shows some values of x and corresponding values of y f or the equation
1^
Y=2-;
-l x'.

x *4 *3 -2 _t 0 0.s 1 2 3 4

v 34 15.5 6 1tr 2 19 1.5 -2 *11^5 d

(a) Calculate the value of d. t1l

(b) Using a scale of 2 cm to represent 1 unit on the x-axis and Zcm to represent 10 units on
y- r. ; x3 for -4 =x <4.
the y-axis, drawthegraph of t4I

(c) On the same axes, draw the graph of y' -7x + 1. t1I
o)

(d) Use the graphs in (b) and (c) to estimate the values of x satisfying both y = 2 - *xt
and Y ='7x + 1. t3l

(e) By drawing a tangent atx= 2, estimate the gradientof y=r-;f at(2,-2). t3I

u)
(f

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14 Answer the whole of this question on a sheet of graph paper.

Using a scale of '1 cm to represent 1 unit on each axis, draw the x-axis for -8 x < 7 and the
y-axisfor-4sys6. =

(a) Draw and label

(i) triangle A with vertices (*1, 4), (3, 4) and (7, 0), t1I

(ii) triangle B with vertices (-4,4), (-6, 4) and (-8, 6). I1l

(b) Describe fully the transformation that maps triangle A onto triangle B. t3l

(c) Triangle C is an image of triangle B after a 90" anticlockwise rotation using the
centre (-2,3).

Draw and label triangle C. t2)

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15 The diagram below represents a floor mat in the form of a trapezium TUVW.
IX is the height of the trapezium, UV = 9.5m, TW = 6.7 m and TX = 4.4rn.
All the measurements are correct to 1 decimal place.

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i4.4
I
I
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(a) Write down the upper bound for the length of UV. t1l

(b) Calculate the upper bound for the area of the floor mat. t3l

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