Uganda certificate of education
Test 2
Mathematics
Paper 1
Duration 2 hours and 15 minutes
Instructions:
This paper has two sections A and B. it consists of six examination items
Section A has two compulsory items
Section B has two parts I and II. Answer one item from each part.
Answer four examination items in all
Start each item on a fresh page.,
Section A (COMPULSORY)
Item 1
John plans to visit the shop that is 12 km south of his home and then the boutique that is 5km east of the
shop and after drive back home using a direct route from the boutique to home. He is to use his
motorcycle that consumes 0.035litres of fuel per km and he wants to know how much fuel he will need
for the whole journey. He has seven hundred fifty thousand Uganda shillings. He plans to use part in the
shop and part in the boutique in the ratio of 3:2 respectively. He wants to spend ugx 210,000 on shirts and
ugx 120,000 to buy trousers. However he is not sure if his budget for the boutique will be enough for the
shirts. He is to buy 24 packets of cooking oil, 12 packets of sugar and 30 packets of salt. All of these are
to be used to make packages for some of his family members in the village. He wants each package to
have an equal number of items in it. He needs to know the highest number of packages he can make from
these.
Task
a. How much fuel will he need for whole journey?
b. Will the money he plans to use in the boutique be enough for what he plans to buy? Justify your
answer.
c. How many packages will he make from the items he plans to buy?
Item 2
A private car park is designed in such a way that it can accommodate x-pickups and y- mini buses at any
given time. Each pick up is allowed 15m2 of space and each minibus is allowed 25m2 of space. There is
only 400m2 of space available for park. Not more than 35 vehicles are allowed in the park but atmost 10
minibuses are allowed at a time.
Task
I. Write down all the mathematical statmates to represent the above information
II. On the same axes plot the graphs of all the statmates
III. If the packing charges for a pickup is shs 500 and that for a minibus is shs 800 per day. Find how
many vehicles of each type should be packed in order to get maximum parking income. Hence fine
the maximum parking income per day.
Section B( PART 1)
Item 3
Gulu is 138km from lira through Kamudini. Peter leaves Gulu for lira cycling at a steady speed of
24km/hr. when he had travelled a distance of 18km from Gulu, john setts off from the same spot peter
started from cycling at a steady speed of 30km/hr.
Task
a. Find when and where john over took peter?
b. If john maintained his speed ever after overtaking peter, determine how long it took him waiting for
peter to join him.
c. Given that peter then increased his speed such that they arrived in lira at the same time, by how much
did peter increase is speed immediately after he was overtaken?
Item 4
Mr Muyanja was preparing for a wedding and he wanted to know the quantities of different kinds of
drinks that his guests would take. On consultations mr Namigo gave him the following information.
He needs to buy soda, juice and water depending on the preferences of the people. The number of people
to drink both soda and juice only should be one fifth of those who are to drink all the three categories.
Those who are to drink all the three categories are also to be 20times those to drink juice and water only
and 10 times those to drink soda and water only. Also the number of people to drink soda only, are to be
1
2 times those to drink water only. Suppose that 41 people won’t drink any type of drink and 200 people
2
are expected, of whom 24 people are likely to take only one type of drink.
Task
a. Help mr muyanja to determine the number of bottles of each type of drink that would be taken.
b. Determine the type of drink that would be most taken. What would be the cause for this
preference?
c. If a guest would be picked at random from the group, determine the probability that he/she would
drink atmost one of drink.
(PART II)
Item 5
A certain island has been having a serious problem of poor network for a long period of time. The
government with the network providers is planning to establish a mast with a frequency that can
cover the whole island. The island is in the shape of a triangle ABC with AB=10km, as the main
landing site. Side BC=8km and AC=6km.
Task
I. Determine the angle ABC
II. Two points P and Q are 1000m apart. The angle of elevation of the top of the mast from
points P and Q are 60o and 30o respectively. Calculate the height of thye mast if the points are
on the same side of the mast.
Item 6
A bucket of homogeneous paint is in the shape of a frustrum with open end of diameter 28cm, bottom
diameter of 18cm and 22cm deep. The bucket of paint is used to paint a cylindrical pillar of storied
building. The pillar measures a diameter of 100m and is 140m high. Two hundred thirty five liters of the
paint is made by mixing three paints A, B, C. the ratio by amount of paint A to B is 4:5 and that of B to C
is 6:8. Paint A costs shs 7200 per liter, paint B costs shs 18000 per liter and paint C costs shs 6375 per
liter. (take π=22/7, 1 liter of paint can paint 440m2).
Task
Determine
I. The number of liters of paint needed to paint the cylindrical pillar
II. The capacity of the bucket in liters
III. The number of buckets of paint required to paint the pillar.
IV. The amount of each paint in the mixture
V. How much is 1 liter of mixture.
END
