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MATHEMATICS
Paper 1
Feb. 2025
2 hours :15 minutes
Page | 1

UGANDA CERTIFICATE OF EDUCATION

MULAGO HIGH SCHOOL
MATHEMATICS PAPER ONE

INSTRUCTIONS:
≈ This paper has two sections A and B. it consists of six examinations 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
≈ Use a graph when needed and a silent non-programmable calculator
≈ Start each question on a fresh page.
≈ Additional questions will not be marked

Make you own luck, work harder

 SECTION A
ITEM 1
Okello, who is a retailer at Alero trading Centre, 50km away from Gulu city, wishes to re-
stock his hop but due to the growing number of customers he receives during business
Page | 2 hours he does not have time to close his shop. He decided to send Nobert a boda-boda
man to purchase new stock from Gulu city with two million two hundred fifty thousand
shillings.
Nobert’s motorcycle consumes 0.045 litres of fuel per kilometer. One-third of the money is
to be used to buy Beer, soda and water in the ratio of 5 : 2 : 1 respectively, and 62.22% is to
be used spent on groceries. The cost of the items are as follows;

Item Unit Cost(shs)

Fuel Litre 5,700
Beer Crate 62,500
Soda Carton 10,000
Water carton 5,000
Task:
a) Help Nobert know how much fuel he needs to buy for the whole journey to and fro.
b) How much is spent on groceries and drinks respectively?
c) How many crakes of soda, cartons of soda and water he needs to buy?
d) How much is left?

ITEM 2
Wallace owns a small bakery and plans to bake two types of loaves of bread; whole wheat
bread and white bread. Due to the bakery’s own capacity, he can bake at most 15 loaves of
bread a day.
He wants to bake at least 3 loves of whole wheat bread. Additionally, he wants to bake at
least 3 loaves of whole wheat bread. Additionally, he wants to bake more whole what bread
than white bread because it is more popular among his customers.
They are sold at UGX.6500 per loaf for whole wheat bread and white bread at UGX.5000.
To cover his costs and make a profit, he needs to earn more than Shs 30,000 from sales each
day.
Task:
a) How many loaves of each type should he bake in order to make a maximum profit?
b) What is the minimum number of loaves he can bake and still make a profit?

SECTION B
PART I (answer one item)
ITEM 3

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 In preparation for the sports day, Margie and Jessica went to the market to buy some items.
Margie went with Shs. 33,500 while Jessica went with Shs. 39,500. Margie bought 2 loaves
of bread, 3kg of sugar and 4 pencils. Jessica bought 3 loaves of bread, 4kg of sugar and
2pencils. A loaf of bread, a kg of sugar and a pencil was sold at shs.5500, 3800 and 400
respectively.
Page | 3
On the sports day, Maria, Tracy and Molly participated in a game where each of them
picked 2 identical marbles from a box, one after the other without replacement. The box
contained 7 green and 8 red marbles. Maria picked marbles of the same colour, Tracy picked
marbles of different colours and Molly picked the second marble as red. The prize was for
one who scores the highest probability from after the picking.
A commissioner from the Ministry of education and sports as special guest during his
speech gave details about the region having 60 schools where 30 schools participate in both
Sports(T) and MDD(M) and that 6 schools participate in sport but not MDD ad 14
participate in neither. And he is not sure about the those who participate in MDD but not
Sport.
Task
(a) Using matrix knowledge, help Margie and Jessica to know the balance they have after
buying?
(b) Who of Maria, Tracy and Molly won the prize?
(c) Help the commissioner find the actual percentage of schools that participate in Only
MDD?

ITEM 4
A farm school carried out a survey on the yields of maize grains in relation to the heights
of maize plants and were measured in centimeters and sample result are recorded below.
The farm school admin decided that plants of height below 586cm be uprooted on the
yields
607 562 638 602 576 615 621 590 632 609 598 599 596 597 583 604 582 596 624 618
595 603 555 588 615 618 597 627 597 622 622 616 563 610 592 571 630 610 560 589
580 599 581 593 600 602 595 575 598 594:
Task: using classes with equal class with of 10 cm.

a) Show the number of plants that should be uprooted using a statistical diagram
hence also estimate the median height of these plants.
b) As math students determine the average and modal heights of the crops
PART II (answer one item )
ITEM 5

Make you own luck, work harder

 Mary usually set off from a landing site that Is located on coordinate 𝑂(−9, 7) on her grid
map to island A which is located at coordinate 𝐴(−6, 3) on her grid map during her day
off. Island A is southeast of landing site O. this time she plans to extend her tour from island
A to island B that is 9km northeast of island A and then sails back to the landing site through
the direct route.
Page | 4
She plans to tour island A for 3 hours and around island B for 4 hours. Her journey is to
start at10:00am. She hopes to be back by20:00 hours since she has to work the following
day. She wants to know if it’s possible to return by that time but she does not know the
time the ship will take to sail the whole journeys. The boat is usually ridden at ana average
speed of 64km/hr.
She is in charge of paying her fellow worker. Some workers were given the salary increment
to 650,000. this includes allowances of 120,000. She needs to know how much income tax
she is to deducted from them and the net amount she is to pay them using the tax bands
below.

Taxable income Tax rates (%)

0 - 200,000 0
200,001- 400,000 10
400,001 – 600,000 15
Task:
a) What is the total distance they are to sail? Hence find the total time for visits and sail
for the whole journey?
b) Will she be back at the planned time?
c) How much will she pay her fellow worker?
ITEM 6
Your brother wants to design a children’s playground. It will have a triangular garden and
a circular fence around the garden. The two sides of the triangular garden will measure 50
m and 70m, and the angle between them will be 450.
Your brother also wants to construct a circular fence around the garden such that the
circular fence perfectly touches the three vertices of the triangular garden.
Your brother intends to put pavers in the region outside the triangular garden but inside
the circular fence. Each square meter of pavers costs shs35000.
Your brother needs help in identifying the type of triangular garden, coming up with an
accurate design of the playground as well as the cost of buying the pavers.
Task: Help your brother to;
a) Construct an accurate design of the children playground.
b) Identify the type of triangle represented by the triangular garden and give reason for
your answer.
c) Determine the amount of money needed to buy the pavers.
END.

Make you own luck, work harder