LESOTHO GENERAL CERTIFICATE
OF SECONDARY EDUCATION
At the end of the examination, fasten all your work securely together.
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 70.
Examiners use
This document consists of 12 printed pages
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Examinations Council of Lesotho
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2
1.
The price of a Mathematics book is M132.50.
(a)
Calculate the amount received when 32 books are sold.
Answer (a) M……………………………. [1]
Write your answer to part (a) in standard form.
(b)
Molise changes Pula (P) 700 into Maloti(M). The
exchange rate is P 1 = M 1.11
e exchan
Calculate the amount he receives.
(1
3
$
2.
3(
5
Answer (b) M…………
M……………………………. [1]
Factorise completely.
63
15p2 + 24pt
(&
3.
,0
Answer M ……………………………….. [2]
A
Answer ……………………………………. [2]
4.
Arrange the following numbers in order of size, starting with the smallest.
ʹ͵
0.47ͷͲ
ξͲǤʹʹ
4.66 xͳͲ-1
Answer …………… ൏ …………. ൏ …………. ൏ ………….
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Examinations Council of Lesotho
[2]
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3
5.
NOT TO
SCALE
30 cm
x cm
sin 53.20 = 0.801
cos 53.20= 0.599
tan53.20 = 1.34
3
$
3(
5
53.2o
You may use this information
Calculate the value of x.
Answer
nswer x = .………………………….cm [2]
Mpho scores the following marks in 5 tests.
tests
(1
6.
63
(&
Her mean mark is 44.
,0
28, 40, 52,
2,, yy,, 60.
Calculate the value of yy..
Answer y = ..……………………………. [2]
7.
The number of spectators at the World Cup match was 82 000 correct to the nearest
thousand. If each spectator paid M 750, what is the lower bound for the total amount
paid?
Answer M ………………………………. [2]
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Examinations Council of Lesotho
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4
8.
A cylindrical water pipeline has the radius of 0.5 metres and length 84 kilometres
ଶଶ
takeɎ as
଻
84 km
NOT TO
SCALE
0.5m
3
$
3(
5
Calculate the volume of water the pipeline contains when it iss full.
fu
ful
Give your answer in cubic metres.
ଵ
Tefetso invests M920 at a rate of 2 % pe
per year simple interest.
ଶ
,0
9.
(1
Answer
Answer
nsw ……………………………… m3 [3]
63
(&
Calculate the total amount Tefetso h
has after 5 years.
AnswerM…………………………………. [2]
10.
Solve the simultaneous equations.
3x + 4y = 6
x + 5y = 13
Answer x = ……………………………….
y = ………………………………. [3]
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Examinations Council of Lesotho
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5
11.
y is inversely proportional to x2.
When x = 4, y = 3.
Find y when x = 5.
య
12.
(a)
ଷ ఴ
ቀ଼ቁ
3
$
3(
5
Answer y = ……………………………….
……
[3]
భ
x
ଷ ఴ
ቀ଼ቁ = pq
Answer (a) p = ………………………….
q = ………………………….. [2]
2-3 + 2-4 = k22-4
63
(b)
(&
,0
(1
Find the value of p and the value of q.
alue of k.
Find the value
Answer (b) k = …………………..………. [2]
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Examinations Council of Lesotho
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6
13.
The diagram shows three straight lines.
7
6
5
4
3
1
-8
-7
-6
-5
-4
-3
-2
-1
0
-1
1
3
$
3(
5
2
2
3
4
5
6
7
On the grid, shade the unwanted region and label
el with the letter R, the region
which satisfies the inequalities:
ଵ
y൑ x + 4,
(1
y൒3
an
and
x + y൒ 6.
14.
M=
5
െ͵
63
(&
,0
ଶ
2
4
N=
[3]
െͳ െ ʹ
2 6
Calculate
(a)
MN
Answer (a) MN = …………….…………. [2]
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Examinations Council of Lesotho
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7
M-1, the inverse of M.
(b)
Answer (b) M-1= ………………….…….
Make w the subject of the formula.
c=
ସା‫ݓ‬
‫ݓ‬ାଷ
0
(1
3
$
3(
5
15.
[2]
Answer w =……………………………….
[3]
…………
16.
The diagram shows the speed-time graph
p for the first 120 seconds of a car
ph
journey.
20
15
Speed
(m/s)
10
5
0
10
20
30
40
50
60
70
80
90
100
110
120
Time(s)
(a)
Calculate the acceleration of the car during the first 25 seconds.
Answer (a) ……………………… m/s2
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Examinations Council of Lesotho
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8
(b)
Calculate the distance travelled by the car in the first 120 seconds.
Answer (b) ……………………………. m [3]
17.
f(x) = x2 + 1
g(x) =
௫ାଶ
ଷ
3
$
3(
5
(a) Work out f (- 1).
Answer
………………………………. [1]
er (a) …
Find g-1(x).
[1]
63
(c)
Answer (b) gf(3x) …………………...….
(&
,0
(1
(b) Find g(3x), simplifying your answer as far as po
possible.
Answer (c) g-1(x) = ……………………… [2]
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Examinations Council of Lesotho
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9
Three figures ABCD, AI BICI DI and AIIBIICIIDII’ are shown on the diagram.
18.
y
3
2
1
D
C
A
B
DI
AI
CI
BI
x
0
-1
2
3
6
5
4
AII
7
8
BII
3$
3(
5
1
-2
DIIII
9
CII
a) Describe a single transformation which maps
ABCD onto AI BICI DI
map A
,0
(1
Answer (a) ……………………………………………………………………….
[3]
……………
63
(&
II II II II
b) A single transformation maps AI BICI DI onto A B C D .
h represen
Find the matrix which
represents this transformation.
© ECoL 2013
Examinations Council of Lesotho
Answer (b)……………….
[2]
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10
19.
In this question, give all your answers as fractions.
A box contains 3 red pencils, and 2 blue pencils.
Neo chooses 2 pencils at random, without replacement.
Calculate the probability that
(a)
they are both red,
they are of different colours,
exactly one of the
pencils is green.
he two pe
63
(c)
Answer (b) ………………………………. [2]
(&
,0
(1
(b)
3
$
3(
5
Answer (a) ……………………………….
[2]
………
Answer (c) ………………………………. [1]
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Examinations Council of Lesotho
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11
20.
R and T are points on a circle centre O, with radius 5 cm.
PR and PTare tangents to the circle and reflex angle ROT=225(degrees)
and OP = 13(centimeters)
R
NOT TO
SCALE
2250
13cm
O
5cm
P
3$
3(
5
T
A thin rope goes from P toR, around the major arc RT
T and then
t
from T to P.
Calculate the length of the rope. Express your
urr answe
answer in terms of ߨ
Answer ………………………….…cm
21.
(a)
[4]
The two lines
ines y = 2x + 8 and y = 2x – 12 intersect the x-axis at P and Q.
Work out the distance PQ.
Answer (a) PQ = …………………..……. [2]
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Examinations Council of Lesotho
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12
(b)
Write down the equation of the line with gradient -4 passing through (0, 5).
Answer (b) ……………………………………… [1]
Find the equation of the line parallel to the line in part (b) passing
through (5, 4).
3
$
3(
5
(c)
Answer (c)
…………………………….…. [2]
c)) …………
………
(&
,0
(1
22. The diagram shows a triangular field ABC
C
Scale 1cm : 1m
63
B
A
60ι
C
6 cm
i.
The treasure is hidden in the field such that it is
Equidistant from A and B.
ii. 40 m from A
By construction, find the position of the treasure and label it with the letter T.
[4]
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Examinations Council of Lesotho
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