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POST UTME UNIOSUN 2025 Mathematics | Objective

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Question 1

Determine the volume of the frustum of a cone with height 10cm, lower base radius 6cm, and upper base radius 4cm.

A. 60π cm^3

Correct B. 80π cm^3

C. 100π cm^3

D. 120π cm^3

Correct Answer: B

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Question 2

Solve for x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 3

Find the area under the curve $ y = x^2 + 2x - 3 $ from x = 0 to x = 4.

A. 40

B. 60

Correct C. 80

D. 100

Correct Answer: C

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Question 4

A sequence is defined by the formula $ a_n = 2n^2 + 3n - 1 $. Find the sum of the first 5 terms of the sequence.

A. 55

B. 65

C. 75

Correct D. 85

Correct Answer: D

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Question 5

A polynomial function is defined by the equation ( f(x) = x^3 - 2x^2 + x - 1 ). Find the value of f$ -2 $.

Correct A. -9

B. -7

C. -5

D. -3

Correct Answer: A

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Question 6

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

A. -120

B. 120

Correct C. 0

D. -60

Correct Answer: C

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Question 7

A sequence is defined by the recurrence relation [ a_n = 2a_{n-1} + 3 ] with initial term [ a_1 = 2 ]. Find the sum of the first 5 terms of the sequence.

A. 65

B. 70

Correct C. 75

D. 80

Correct Answer: C

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Question 8

Find the volume of the frustum of a cone with radii 6 and 4 and height 8.

A. 256\pi

B. 512\pi

Correct C. 768\pi

D. 1024\pi

Correct Answer: C

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Question 9

A histogram has class boundaries 0, 5, 10, 15, 20 and class marks 2.5, 7.5, 12.5, 17.5. If the frequency of the class 5-10 is 8, find the mean of the histogram.

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 10

Solve the equation [ x^2 + 4x + 4 = 0 ].

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 11

Find the equation of the circle pas\sing through the points (2,3), (4,5), and $ -1,2 $.

Correct A. $ x^2 + y^2 - 4x - 6y + 5 = 0 $

B. $ x^2 + y^2 + 4x + 6y + 5 = 0 $

C. $ x^2 + y^2 - 4x + 6y + 5 = 0 $

D. $ x^2 + y^2 + 4x - 6y + 5 = 0 $

Correct Answer: A

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Question 12

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \ \end{cases} ). Find the mean and s\tandard deviation of X.

Correct A. $ \text{Mean} = 2.1, \text{S\tandard Deviation} = 0.8 $

B. $ \text{Mean} = 2.3, \text{S\tandard Deviation} = 0.9 $

C. $ \text{Mean} = 2.5, \text{S\tandard Deviation} = 1.0 $

D. $ \text{Mean} = 2.7, \text{S\tandard Deviation} = 1.1 $

Correct Answer: A

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Question 13

Solve the system of linear equations $ egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -2 \ 3x + y + 2z = 5 \end{cases} $.

Correct A. $ x = 1, y = 2, z = 3 $

B. $ x = 2, y = 3, z = 4 $

C. $ x = 3, y = 4, z = 5 $

D. $ x = 4, y = 5, z = 6 $

Correct Answer: A

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Question 14

Find the equation of the line pas\sing through the points (1,2) and (3,4).

Correct A. $ y = 2x - 1 $

B. $ y = 2x + 1 $

C. $ y = -2x + 1 $

D. $ y = -2x - 1 $

Correct Answer: A

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Question 15

A histogram of a random variable X is given below. Find the mean and s\tandard deviation of X.

Correct A. $ \text{Mean} = 2.1, \text{S\tandard Deviation} = 0.8 $

B. $ \text{Mean} = 2.3, \text{S\tandard Deviation} = 0.9 $

C. $ \text{Mean} = 2.5, \text{S\tandard Deviation} = 1.0 $

D. $ \text{Mean} = 2.7, \text{S\tandard Deviation} = 1.1 $

Correct Answer: A

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Question 16

Determine the sum of the first 10 terms of the geometric series $ 2x^2, 4x^3, 8x^4, ldots $ with common ratio $ r = 2x $.

Correct A. 2x^{20} - 1

B. 2x^{20} + 1

C. 2x^{20} - 2

D. 2x^{20} + 2

Correct Answer: A

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Question 17

A histogram of exam scores is shown below. If the mean score is 70, what is the median score?

A. 65

Correct B. 70

C. 75

D. 80

Correct Answer: B

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Question 18

Solve the inequality $ 2x^2 + 5x - 3 > 0 $ u\sing the quadratic formula.

Correct A. \left$ -\frac{3}{2}, \frac{3}{4} \right $

B. \left$ -\frac{3}{4}, \frac{3}{2} \right $

C. \left$ -\frac{3}{2}, \frac{3}{2} \right $

D. \left$ -\frac{3}{4}, -\frac{3}{2} \right $

Correct Answer: A

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Question 19

A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. $2500

Correct B. $3000

C. $3500

D. $4000

Correct Answer: B

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Question 20

A car travels from city A to city B at an average speed of 60 km/h. On the return trip, the car travels at an average speed of 40 km/h. What is the average speed for the entire trip?

A. 48 km/h

B. 50 km/h

Correct C. 52 km/h

D. 54 km/h

Correct Answer: C

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Question 21

Find the volume of the frustum of a cone with height $h$, base radii $r_1$ and $r_2$, and slant height $l$.

Correct A. \frac{1}{3}\pi h$ r_1^2+r_2^2+r_1r_2 $

B. \frac{1}{3}\pi h$ r_1^2-r_2^2+r_1r_2 $

C. \frac{1}{3}\pi h$ r_1^2+r_2^2-r_1r_2 $

D. \frac{1}{3}\pi h$ r_1^2-r_2^2-r_1r_2 $

Correct Answer: A

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Question 22

Solve for $x$: $\log_{10} $ x^2 $ = 4$.

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 23

Find the area under the curve $y = \sin x$ from $x = 0$ to $x = \frac{\pi}{2}$.

Correct A. 1

B. 2

C. \frac{1}{2}

D. \frac{1}{4}

Correct Answer: A

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Question 24

Solve the equation $\sqrt{x^2-4} = 2x-2$.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 25

Find the value of $\tan 60^\circ$.

A. 1

Correct B. \sqrt{3}

C. 2

D. \sqrt{2}

Correct Answer: B

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