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Exam Review

Key Facts: UCE Mathematics Exam

456

Official UNEB subject code for UCE Mathematics

UNEB

20% / 80%

Subject result: continuous assessment / national examination

NCDC / UNEB

2h 15m

Duration of UNEB's published NLSC Mathematics sample (456/1)

UNEB / NCDC NLSC

UGX 164,000

2026 normal UCE registration fee for privately sponsored candidates

UNEB 2026 registration guidance

Grade D

Minimum competency grade required for certification

UNEB / NCDC NLSC

The UCE Mathematics examination (Subject 456) is sat at the end of Senior 4 in Uganda under UNEB and NCDC guidelines. The Mathematics result combines 20% continuous assessment with 80% national examination using written scenario-based tasks. Compulsory project achievement is reported separately. OpenExamPrep provides 100 independent English-language MCQ study questions across four practice topic groups.

Sample UCE Mathematics Practice Questions

Try these sample questions to review concepts for the UCE Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Convert the decimal number 139 into a binary number (base 2).
A.10001011_2
B.10011011_2
C.10001101_2
D.11001011_2
Explanation: To convert 139 from decimal to binary, we express it as powers of 2: 139 = 128 + 8 + 2 + 1 = 1*(2^7) + 0*(2^6) + 0*(2^5) + 0*(2^4) + 1*(2^3) + 0*(2^2) + 1*(2^1) + 1*(2^0). Reading the coefficients from 2^7 down to 2^0 yields 10001011_2.
2Evaluate the addition in base 5: 324_5 + 433_5, giving your answer in base 5.
A.1212_5
B.1312_5
C.1322_5
D.1412_5
Explanation: Adding place values from right to left: 4 + 3 = 7 = 1*5 + 2 (write 2, carry 1); 2 + 3 + 1 (carry) = 6 = 1*5 + 1 (write 1, carry 1); 3 + 4 + 1 (carry) = 8 = 1*5 + 3 (write 3, carry 1); and bringing down the carried 1 gives 1312_5. In decimal, 324_5 = 89 and 433_5 = 118, whose sum is 207 = 1*125 + 3*25 + 1*5 + 2 = 1312_5.
3Given that 24_n + 35_n = 62_n, find the value of the base n.
A.6
B.7
C.8
D.9
Explanation: Convert each term to base 10 using powers of n: (2n + 4) + (3n + 5) = 6n + 2. Simplifying the left-hand side gives 5n + 9 = 6n + 2. Subtracting 5n and 2 from both sides yields n = 7. All digits (2, 4, 3, 5, 6) are strictly less than 7, confirming base 7 is valid.
4Evaluate the arithmetic expression following the correct order of operations: 3/4 - 1/3 * (2/5 + 1/2).
A.7/20
B.9/20
C.11/20
D.3/10
Explanation: Evaluate the brackets first: 2/5 + 1/2 = 4/10 + 5/10 = 9/10. Next, perform multiplication: (1/3) * (9/10) = 3/10. Finally, subtract from 3/4: 3/4 - 3/10 = 15/20 - 6/20 = 9/20.
5Three church bells toll at intervals of 12 minutes, 18 minutes, and 30 minutes respectively. If they toll together at 8:00 a.m., at what time will they next toll together?
A.9:30 a.m.
B.10:00 a.m.
C.11:00 a.m.
D.12:00 noon
Explanation: The time until they toll together again is the Lowest Common Multiple (LCM) of 12, 18, and 30. Prime factorisations: 12 = 2^2 * 3, 18 = 2 * 3^2, 30 = 2 * 3 * 5. LCM = 2^2 * 3^2 * 5 = 4 * 9 * 5 = 180 minutes. 180 minutes equals 3 hours, so 8:00 a.m. + 3 hours = 11:00 a.m.
6Express the recurring decimal 0.272727... as a common fraction in its lowest terms.
A.27/100
B.3/11
C.9/33
D.7/25
Explanation: Let x = 0.272727... Since two digits repeat, multiply by 100: 100x = 27.272727... Subtracting the first equation from the second gives 99x = 27, so x = 27/99. Dividing numerator and denominator by their greatest common factor (9) simplifies x to 3/11.
7In a Senior Four class of 60 students, 45% are boys. How many girls are in the class?
A.27
B.33
C.35
D.38
Explanation: The percentage of girls is 100% - 45% = 55%. The number of girls is 55% of 60 = (55/100) * 60 = 0.55 * 60 = 33. Alternatively, the number of boys is 0.45 * 60 = 27, and 60 - 27 = 33 girls.
8A merchant in Masaka sold a bicycle for UGX 460,000, making a profit of 15% on the cost price. Calculate the cost price of the bicycle.
A.UGX 391,000
B.UGX 400,000
C.UGX 415,000
D.UGX 420,000
Explanation: The selling price represents 100% + 15% = 115% of the original cost price. Therefore, Cost Price = Selling Price / 1.15 = 460,000 / 1.15 = UGX 400,000.
9Divide UGX 180,000 among three siblings, Sarah, Peter, and James, in the ratio 2 : 3 : 5. How much does James receive?
A.UGX 36,000
B.UGX 54,000
C.UGX 90,000
D.UGX 108,000
Explanation: Sum of ratio parts = 2 + 3 + 5 = 10 parts. Value of one part = 180,000 / 10 = UGX 18,000. James receives 5 parts: 5 * 18,000 = UGX 90,000.
10Twelve builders can construct a school perimeter wall in 15 days working at the same pace. How many days will it take 20 builders to complete the same wall?
A.8 days
B.9 days
C.10 days
D.25 days
Explanation: This is an inverse proportion problem: more workers require fewer days. Total work = 12 builders * 15 days = 180 builder-days. Number of days required for 20 builders = 180 / 20 = 9 days.

About the UCE Mathematics Practice Questions

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