Mathematics Examination Paper
Combined Mathematics Exam Paper
Item 1: Dimensions and Area Growth
A poultry farmer builds a rectangular enclosure measuring 15 m by 10 m. He wants to
expand it by adding the same length to each side so the area doubles.
Task:
(a) What should the new dimensions be?
(b) If the enclosure holds 300 hens and each lays one egg daily, how many eggs are collected
in 3 weeks?
Item 2: Dimensions Application (Crop Garden)
A farmer has a rectangular garden of 20 m by 12 m. He wants to expand it so that its area is
tripled by adding equal length x on all sides.
Task:
(a) Find the value of x.
(b) What will the new dimensions be?
Item 3: Playground Expansion
A rectangular playground measures 25 m by 18 m. To accommodate more children, it must
be increased so that its area becomes 1.5 times the original.
Task:
(a) Determine how many meters must be added equally to each side.
(b) What is the area of the new playground?
Item 4: Ratio & Proportion (Fees)
Akibuwa pays UGX 3,600,000 in a 5:3:4 ratio for fees, accommodation, and meals.
Task:
(a) How much does he pay for accommodation?
(b) If he pays 85% of fees in first installment, a third of the rest in the second, how much is
left for the last installment?
(c) Convert base-10 number 194 to base 5.
Item 5: Income Distribution
A family receives UGX 2,400,000 monthly. They spend it in the ratio 4:2:1 on food, rent, and
savings.
Task:
(a) How much is spent on rent?
(b) If rent increases by 25%, what's the new amount?
Item 6: Project Resource Allocation
A builder divides 60 workers in ratio 3:2:1 to design, construct, and inspect.
Task:
(a) How many workers are in each category?
(b) If 20% of the inspectors are reassigned to construction, how many are left?
Item 7: Statistics - Water Purification (Grouped Data)
Data (liters of water per household): [20, 40, 60, ..., 39] (use original table)
Task:
(i) Create frequency distribution table (class interval 10)
(ii) Find median volume
(iii) How many households are below 44.5 L?
(iv) Plot a histogram
(v) Plot an ogive
Item 8: Class Test Scores (Grouped Data)
Scores: [35, 45, 67, 88, 54, 69, 72, 43, 66, 78, 50, 62, 84, 59, 91, 39, 48, 55, 60, 87, 41, 36, 74,
80, 58]
Task:
(i) Form frequency distribution (class interval 10)
(ii) Draw histogram
(iii) Construct ogive
(iv) Estimate median score
Item 9: Factory Output (Grouped Data)
Number of items: [105, 112, 120, 118, 110, 130, 128, 135, 107, 142, 150, 125, 138, 145, 123,
140, 132]
Task:
(i) Create a frequency table (class width 10)
(ii) Plot a histogram
(iii) Draw cumulative frequency graph (ogive)
(iv) Find median class
Item 10: Sets - Ice Cream Flavours
Chocolate: 158, Vanilla: 130, Strawberry: 188
Chocolate & Vanilla: 40, Vanilla & Strawberry: 80, Chocolate & Strawberry: 88, None: 10
Chocolate & Vanilla only = learners who like all three
Task:
Find number who like all 3 flavours. Should Simon invest?
Item 11: Set Theory - Library Users
Out of 200 students:
- 120 read newspapers
- 90 read magazines
- 70 read journals
- 60 read both newspapers and magazines
- 40 read newspapers and journals
- 30 read magazines and journals
- 20 read all three
Task:
Use Venn diagram to determine:
(a) Number who read only newspapers
(b) Number who read none
(c) Number who read only one category
Item 12: Set Membership - Sport Participation
In a school of 100 students:
- 60 play football
- 40 play volleyball
- 25 play both
Task:
Use a Venn diagram to find:
(a) Number who play only football
(b) Number who play neither sport
Item 13: Sets Application - Movie Preferences
Out of 300 people:
- 180 like action
- 150 like comedy
- 100 like both
Task:
(a) Represent in Venn diagram
(b) How many like only one genre?
(c) How many like none?
Item 14: Bearing & Speed
Juma travels 71 km on N45E, then Eastward at 45 km/h for 80 mins using a car with 14L
fuel (20 km per liter).
Task:
(a) Draw and label the path
(b) How far did he travel in total?
(c) Was fuel enough?
Frequency Table for Item 8: Class Test Scores
Score Range Frequency
30-39 3
40-49 4
50-59 5
60-69 5
70-79 3
80-89 4
90-99 1
Frequency Table for Item 9: Factory Output
Output Range Frequency
100-109 2
110-119 3
120-129 4
130-139 4
140-149 3
150-159 1
