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MATHEMATICS
Paper 1
September 2012
2
1
hours
2
POST MOCK EXAMINATION
Uganda Certificate of Education
MATHEMATICS
PAPER ONE
DURATION: 2hrs. 30mins.
Instructions:
i)
ii)
iii)
Attempt all questions in section A and not more than 5 in section B.
All necessary working must be shown on the same sheet of paper as the rest of
the answer.
Simple, silent non-programmable calculators may be used.
SECTION A 40 MARKS 


1 2
b  2a , evaluate  7 * 5 *  2 .
3
3x  5 y   9
1.
Given that a * b 
2.
Use matrix method to solve the equations:
3.
A solid cone has a base radius of 5cm and height 12cm . Calculate the total
surface area.
(4 marks)
4.
Solve the equation: log 10 10 x  50  log 10 x  4  2
5.
A function is defined by g x  
i)
ii)
6.
2 y  5 x  16
(4 marks)
(4 marks)
(4 marks)
x2  4
. Find:
x 2  5x  6
values of x for which g x  0
values of x for which g x is not defined.
(4 marks)
P varies as Q and inversely proportional to the square of R , given that P  3
when R  2 and Q  6 , find the value of Q when P   2 and R   3 .
7.
Given that A1, 3 and B13, 12 , the point X divides AB in the ratio 1 : 2 , find
the length of AX .
(4 marks)
© MATHEMATICS DEPT @ RGSS
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8.
Edward wanted to exchange Kenyan shillings Ksh 540,000 to Tanzanian shillings
(TZsh ) . It is given that 1 Ug sh  1.8 TZsh and 1 Ksh  25 Ugsh . Calculate how
much (TZsh ) Edward got.
(4 marks)
9.
In the figure above, angle OQP  40 o , find the length OQ and OP .(4 marks)
10.
The line through the points A1, 3 and B 3,  5 is perpendicular to the line
through Q1,  4 . Determine the equation of the line through Q .
SECTION B (60 Marks)
Attempt only (FIVE) questions in this section
11.
a)
b)
c)
d)
12
The marks below were obtained by some students in a Math test.
5.1 5.6 6.7 3.0 2.1 4.2 3.4 3.8 8.3 3.8 7.5 4.5 3.4 3.8 5.8 5.0
5.6 7.6 9.1 8.7 2.5 5.6 2.7 6.4 6.1 9.2 9.0 6.4 4.0 4.9 7.7 5.4
5.8 4.6 7.5 5.2 6.0 6.6 2.2 9.4 4.4 5.2 3.4 6.4 7.2 8.0 5.2 4.4
Draw a frequency distribution table of equal class intervals of 10 beginning with
2.0
Using a Working mean of 5.45, calculate the average mark.
Draw a histogram and use it to estimate the mode.
Calculate the median.
A triangle ABC with vertices A2,  5 , B2,  1 and C5,  1 is rotated through a
half turn by a matrix M to form the image A' B' C ' .
a) Determine the matrix M and the coordinates of A' B' C ' .
b) A' B' C ' is then reflected along the line x  0 by a matrix of transformation N to
form triangle A' ' B' ' C ' ' . Determine matrix N and the coordinates of A' ' B' ' C ' ' .
c) Plot triangle ABC and its images on the same axes and describe fully the
transformation that maps A' ' B' ' C ' ' back to ABC .
© MATHEMATICS DEPT @ RGSS
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13a)
b)
c)
14.
i)
ii)
iii)
iv)
15.
a)
b)
c)
d)
Using a ruler and pair of compasses only, construct a quadrilateral ABCD in
which AB  5cm , BC  6cm , , CD  9cm angle ABC  60 o and BCD  135 o .
Drop a perpendicular from D to meet BC at M.
Construct the circumference of triangle CDM and determine:
i)
the length of AD
ii)
the radius of the circle.
Mrs Opio bought 3kg of sugar, 2 loaves of bread and 3litres of milk. Mrs
Musoke bought 4kg of sugar, 3 loaves of bread and 3litres of milk. Mrs Dubai
bought 2kg of sugar, 4 loaves of bread and 5litres of milk. The prices at the local
shop for 1 kg sugar, 1 loaf of bread and 1 litre of milk are shs 2000, shs 1400 and
shs 800 respectively, while at the super market the corresponding prices are
shs1700, shs1000 and shs 700 respectively. The return journey for each lady is
shs 1400.
Write down a 3 X 3 matrix for the commodities bought.
Write down a 3 X 3 matrix for the prices of the commodities.
Determine by matrix multiplication the total expenditure for each person from
each of the shops.
Calculate the percentage savings Mrs Musoke makes by buying the commodities
at the super market.
A tailor makes two types of dresses: Casual wear and Party wear. Two materials
A and B are used. Material A is limited to 20 metres and material B is limited to
15 metres. The table below shows the size for each material takes for a dress and
the profit made.
Dress
Material A
Material B
Profit
Casual
2m.
3m.
$12
Party
4m.
1m.
$10
Write down all the inequalities that satisfy this information.
Represent these inequalities on a graph.
Find the maximum profit.
Find how many dresses of each type should be made to maximize the profit.
© MATHEMATICS DEPT @ RGSS
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16a) If hx  nx  m , and h4  19 and h5  22 , find n and m , and hence h 6 .
b)
Given that f 1 x  
3x
, find f x  and hence f 5 and f  5 .
4x  5
17a) A balanced die and a balanced tetrahedron are tossed together. The faces of the
die are marked 1 to 6 while those of the tetrahedron are marked 1 to 4.
i) Make a table to show the possible outcomes of the experiment.
ii) Find the probability that the numbers appearing on top are the same or the sum
of the numbers appearing on top is greater than 7.
b)
i)
ii)
Gabriella picks two balls in succession from a basket containing 4 white balls and
5 Yellow balls without replacement. Find the probability that the two balls
picked are:
of the same colour.
of different colours.
SUCCESS
END
© MATHEMATICS DEPT @ RGSS
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