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POST UTME UNIOSUN 2025 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

Correct A. -9

B. -7

C. -5

D. -3

Correct Answer: A

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Question 6 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the circle passing 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 View Details

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

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 View Details

Find the equation of the line passing 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 View Details

A histogram of a random variable X is given below. Find the mean and standard 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 View Details

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 View Details

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 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$ using 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 View Details

A company produces two products, A and B. The profit from product A is 10 per unit, and the profit from product B is15 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 View Details

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 $km/h\\((km/h). On the return trip, the car travels at an average speed of 40$. 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 View Details

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 View Details

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 View Details

Find the area under the curve $y = $1x$ 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 View Details

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 View Details

Find the value of $$160^\circ$.

A. 1

Correct B. $\sqrt{3}$

C. 2

D. $\sqrt{2}$

Correct Answer: B

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