2025 Post UTME Mathematics Likely Questions and Answers

2025 Post UTME Mathematics Likely Questions and Answers

In this post, we have compiled the 2025 Post UTME mathematics likely questions and answers with detailed explanations to help you study effectively. By practicing with these questions, you will gain confidence, understand the exam structure, and improve your chances of success.

1. The sum of N140,000 is shared between Abu, Kayode and Uche. Abu has twice as much as Kayode, and Kayode has twice as much as Uche. What is Kayode’s share? (A) N80,000 (B) N10,000 (C) N40,000 (D) N20,000

Topic: Ratio and Proportion

Correct Option: (C) N40,000

Step-by-step explanation:

Step 1: Establish the relationship between the shares.
Let Uche’s share be represented by ‘x’.
Since Kayode has twice as much as Uche, Kayode’s share is 2x.
And since Abu has twice as much as Kayode, Abu’s share is 2 * (2x) = 4x.

Step 2: Set up the ratio.
The ratio of the shares for Abu, Kayode, and Uche is 4x : 2x : x, which simplifies to 4 : 2 : 1.

Step 3: Find the total number of parts in the ratio.
Total parts = 4 + 2 + 1 = 7 parts.

Step 4: Calculate the value of one part.
The total amount to be shared is N140,000.
Value of one part = Total Amount / Total Parts = N140,000 / 7 = N20,000.

Step 5: Determine Kayode’s share.
Kayode’s share corresponds to 2 parts of the ratio.
Kayode’s share = 2 * (Value of one part) = 2 * N20,000 = N40,000.

2. In a season, a club scored: $2,0,3,3,2,1,4,0,0,5,1,0,2,2,1,3,1,4,1,1$. The mean, median and mode are, respectively:

Options: (A) $1.8,\ 1,\ 1.5$ (B) $1.8,\ 1.5,\ 1$ (C) $1.5,\ 1,\ 1.8$ (D) $1,\ 1.8,\ 1.5$

Topic of the question: Averages (mean, median, mode)

Correct option: (B) $1.8,\ 1.5,\ 1$

Step-by-step explanation:

Let the data set be

$$ \{2,0,3,3,2,1,4,0,0,5,1,0,2,2,1,3,1,4,1,1\}. $$ Number of observations: $$ n=20. $$ Mean Compute the total sum $S$. It is convenient to use a frequency breakdown: $$ \begin{aligned} &0:\ 4\ \text{times} \quad (0\cdot 4=0),\\ &1:\ 6\ \text{times} \quad (1\cdot 6=6),\\ &2:\ 4\ \text{times} \quad (2\cdot 4=8),\\ &3:\ 3\ \text{times} \quad (3\cdot 3=9),\\ &4:\ 2\ \text{times} \quad (4\cdot 2=8),\\ &5:\ 1\ \text{time} \quad (5\cdot 1=5). \end{aligned} $$ Hence $$ S=0+6+8+9+8+5=36. $$ Therefore, $$ \text{Mean}=\bar x=\frac{S}{n}=\frac{36}{20}=1.8. $$ Median First, order the data: $$ 0,0,0,0,\ 1,1,1,1,1,1,\ 2,2,2,2,\ 3,3,3,\ 4,4,\ 5. $$ Since $n=20$ is even, the median is the average of the 10th and 11th terms: $$ \text{10th term}=1,\quad \text{11th term}=2 \;\Rightarrow\; \text{Median}=\frac{1+2}{2}=1.5. $$ Mode The mode is the most frequent value. From the frequency breakdown above, $1$ occurs 6 times, more than any other value. Thus $$ \text{Mode}=1. $$ Conclusion $$ (\text{Mean},\ \text{Median},\ \text{Mode})=(1.8,\ 1.5,\ 1)\ \Rightarrow\ \text{Option (B)}. $$

3. I am x years and my brother is 3 years older. How old was my brother last year?

(A) (x – 4) years (B) (x +2) years (C) (3x – 1) years (D) (3x +1) years

Topic: Algebraic Expressions

Correct Option: (B) (x + 2) years

Step-by-step explanation:

Step 1: Express the brother’s current age.
My current age is x years.
My brother is 3 years older, so his current age is (x + 3) years.

Step 2: Calculate the brother’s age last year.
To find his age last year, we subtract 1 from his current age.
Brother’s age last year = (x + 3) – 1.

Step 3: Simplify the expression.
(x + 3) – 1 = x + 2 years.

4. Divide the sum of 8, 7, 2, 6, 0, 4, 7, 2, 3 by their mean. (A) 7 (B) 9 (C) 8 (D) 6

Topic: Statistics (Mean)

Correct Option: (B) 9

Step-by-step explanation:

Step 1: Calculate the sum of the numbers.
Sum = 8 + 7 + 2 + 6 + 0 + 4 + 7 + 2 + 3 = 39.

Step 2: Count the number of values in the set.
There are 9 numbers in the set.

Step 3: Calculate the mean of the numbers.
Mean = Sum of numbers / Number of values = 39 / 9.

Step 4: Divide the sum by the mean.
(Sum) / (Mean) = 39 / (39 / 9).

Step 5: Simplify the expression.
To divide by a fraction, you multiply by its reciprocal:
39 * (9 / 39) = 9.

5. A chord of length 6cm is drawn in a circle of radius 5cm. Find the distance of the chord from the centre of the circle. (A) 2.5cm (B) 3.0cm (C) 3.5cm (D) 4.0cm

Topic: Geometry (Circles and Chords)

Correct Option: (D) 4.0cm

Step-by-step explanation:

Step 1: Visualize the problem.

Step 2: Form a right-angled triangle.
The radius of the circle is the hypotenuse of the right-angled triangle (5 cm).
The perpendicular distance from the center to the chord is one leg of the triangle.
Half the length of the chord is the other leg of the triangle (6 cm / 2 = 3 cm).

Step 3: Apply the Pythagorean theorem.
Let ‘d’ be the distance of the chord from the center.
The theorem states: a² + b² = c²
d² + 3² = 5²

Step 4: Solve for ‘d’.
d² + 9 = 25
d² = 25 – 9
d² = 16
d = √16
d = 4 cm.

6. A rectangular picture 6cm by 8cm is enclosed by a frame ½ cm wide. Calculate the area of the frame. (A) 20sq.cm (B) 15sq.cm (C) 13sq.cm (D) 16sq.cm

Topic: Mensuration (Area of a Rectangle)

Correct Option: (B) 15sq.cm

Step-by-step explanation:

To find the area of the frame, calculate the area of the outer rectangle (picture + frame) and subtract the area of the inner rectangle (the picture).

Step 1: Calculate the dimensions of the outer rectangle.
The width of the frame is ½ cm on each side.
New Length = 8 cm + ½ cm + ½ cm = 8 + 1 = 9 cm.
New Width = 6 cm + ½ cm + ½ cm = 6 + 1 = 7 cm.

Step 2: Calculate the area of the outer rectangle.
Area_outer = New Length * New Width = 9 cm * 7 cm = 63 sq. cm.

Step 3: Calculate the area of the inner rectangle (the picture).
Area_inner = 8 cm * 6 cm = 48 sq. cm.

Step 4: Calculate the area of the frame.
Area_frame = Area_outer – Area_inner = 63 sq. cm – 48 sq. cm = 15 sq. cm.

7. Seven (7) pupils of average age 12 years leave a class of 25 pupils of average age of 14 years. If 6 new pupils of average age 11 years join the class, what is the average age of the pupils now in the class? (A) 13 years (B) 12 years 7 ½ months (C) 13 years 5 months (D) 13 years 10 months

Topic: Statistics (Averages)

Correct Option: (D) 13 years 10 months

Step-by-step explanation:

Step 1: Calculate the initial total age of the class.
Total age of 25 pupils = 25 * 14 years = 350 years.

Step 2: Calculate the total age of the pupils who left.
Total age of 7 pupils who left = 7 * 12 years = 84 years.

Step 3: Calculate the new total age after the 7 pupils left.
New total age = 350 – 84 = 266 years.
Number of pupils remaining = 25 – 7 = 18 pupils.

Step 4: Calculate the total age of the new pupils who joined.
Total age of 6 new pupils = 6 * 11 years = 66 years.

Step 5: Calculate the final total age and the final number of pupils.
Final total age = 266 + 66 = 332 years.
Final number of pupils = 18 + 6 = 24 pupils.

Step 6: Calculate the new average age.
New average age = Final total age / Final number of pupils = 332 / 24 years.
332 / 24 = 13 with a remainder of 20.
So, the average age is 13 and 20/24 years.

Step 7: Convert the fractional part of the year to months.
(20/24) * 12 months = 20 * (12/24) = 20 * (1/2) = 10 months.

The new average age is 13 years and 10 months.

8. By selling an article for N45.00 a man makes a profit of 8%. For how much should he have sold it in order to make a profit of 32%? (A) N180.00 (B) N58.00 (C) N55.00 (D) N63.00

Topic: Percentages and Profit/Loss

Correct Option: (C) N55.00 is not correct. The correct selling price to make a 32% profit is N55.13. There may be a rounding consideration in the provided options.

Step-by-step explanation:

Step 1: Find the Cost Price (CP).
Let the Cost Price be CP.
Selling Price (SP) = CP + Profit
Profit = 8% of CP = 0.08 * CP
SP = CP + 0.08 * CP = 1.08 * CP
We know SP = N45.00
45 = 1.08 * CP
CP = 45 / 1.08 ≈ N41.67

Step 2: Calculate the new Selling Price for a 32% profit.
New Profit = 32% of CP = 0.32 * 41.67
New SP = CP + New Profit
New SP = 41.67 + (0.32 * 41.67)
New SP = 41.67 * (1 + 0.32)
New SP = 41.67 * 1.32 ≈ N55.00

A group of 14 children received the following scores in a reading test: 35, 35, 26, 26, 26, 29, 29, 29, 12, 25, 25, 25, 25, 17. What was the median score? (A) 29 (B) 26 (C) 25 (D) 23

Topic: Statistics (Median)

Correct Option: (B) 26

Step-by-step explanation:

Step 1: Order the scores from least to greatest.
12, 17, 25, 25, 25, 25, 26, 26, 26, 29, 29, 29, 35, 35.

Step 2: Identify the middle value(s).
There are 14 scores, which is an even number. The median will be the average of the two middle scores.
The middle scores are the 7th and 8th values in the ordered list.

Step 3: Find the 7th and 8th scores.
7th score = 26
8th score = 26

Step 4: Calculate the average of the two middle scores.
Median = (26 + 26) / 2 = 52 / 2 = 26.

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  2025 Post UTME English Language Likely Questions and Answers
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