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POST UTME LEAD CITY UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME LEAD CITY UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

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 derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.

A. -2x/\( x^2 + 1 \)²

Correct B. 2x/\( x^2 + 1 \)²

C. -2/\( x^2 + 1 \)²

D. 2/\( x^2 + 1 \)²

Correct Answer: B

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Question 4

Solve the system of equations \( egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} \).

Correct A. (1, 2)

B. (2, 1)

C. (3, 4)

D. (4, 3)

Correct Answer: A

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Question 5

Find the surface area of the sphere with radius 5cm.

A. 50π cm²

B. 100π cm²

Correct C. 150π cm²

D. 200π cm²

Correct Answer: C

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Question 6

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct Answer: C

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Question 7

Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).

Correct A. \frac{1}{2} \arc\tan(x) \Big|_0^1

B. \frac{1}{2} \arc\tan(x) \Big|_0^1 + \frac{1}{2}

C. \frac{1}{2} \arc\tan(x) \Big|_0^1 - \frac{1}{2}

D. \frac{1}{2} \arc\tan(x) \Big|_0^1

Correct Answer: A

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Question 8

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

Correct A. \frac{-5 \pm \sqrt{5^2 - 4(1)(6)}}{2(1)}

B. \frac{-5 \pm \sqrt{5^2 - 4(1)(6)}}{2(1)}

C. \frac{-5 \pm \sqrt{5^2 - 4(1)(6)}}{2(1)}

D. \frac{-5 \pm \sqrt{5^2 - 4(1)(6)}}{2(1)}

Correct Answer: A

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Question 9

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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Question 10

Find the s\tandard deviation of the data set: 1, 3, 5, 7, 9.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 11

In a geometric sequence with first term (a) and common ratio (r), find the sum of the first 5 terms if \( a = 2 \) and \( r = 3 \).

Correct A. 2 + 6 + 18 + 54 + 162

B. 2 + 6 + 18 + 54 + 162 + 486

C. 2 + 6 + 18 + 54 + 162 + 486 + 1458

D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374

Correct Answer: A

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Question 12

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 5. If the scores are normally distributed, find the probability that a randomly selected score is between 70 and 80.

A. 0.1587

B. 0.3413

Correct C. 0.6915

D. 0.9772

Correct Answer: C

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Question 13

Solve the equation \( x^2 + 4x - 5 = 0 \) u\sing the quadratic formula.

A. \frac{-4 \pm \sqrt{16 + 20}}{2}

Correct B. \frac{-4 \pm \sqrt{36}}{2}

C. \frac{-4 \pm \sqrt{16}}{2}

D. \frac{-4 \pm \sqrt{20}}{2}

Correct Answer: B

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Question 14

Find the equation of the circle with center (C(2, 3)) and radius 4.

Correct A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16

B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16

C. \left\( x - 4 \right \)^2 + \left\( y - 5 \right \)^2 = 16

D. \left\( x - 5 \right \)^2 + \left\( y - 4 \right \)^2 = 16

Correct Answer: A

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Question 15

A right triangle has legs of length 3 and 4. Find the length of the hypotenuse.

Correct A. 5

B. 7

C. 9

D. 11

Correct Answer: A

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Question 16

Find the sum of the infinite geometric series with first term 1/2 and common ratio 1/4.

Correct A. 1

B. 3/4

C. 1/2

D. 2/3

Correct Answer: A

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Question 17

Solve the inequality \frac{x-2}{x+1} > 0.

A. x > -1

B. x < 2

C. x > 1

Correct D. x < -1 or x > 2

Correct Answer: D

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Question 18

A set of 5 numbers has a mean of 10. If 5 is added to each number, what is the new mean?

Correct A. 12

B. 15

C. 10

D. 8

Correct Answer: A

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Question 19

In a right triangle, the length of the hypotenuse is 10 and one of the legs is 6. Find the length of the other leg.

Correct A. 8

B. 6

C. 4

D. 2

Correct Answer: A

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Question 20

Find the equation of the circle with center (2, 3) and radius 4.

Correct A. \left\( x-2\right \)^2 + \left\( y-3\right \)^2 = 16

B. \left\( x-3\right \)^2 + \left\( y-2\right \)^2 = 16

C. \left\( x-4\right \)^2 + \left\( y-5\right \)^2 = 16

D. \left\( x-5\right \)^2 + \left\( y-4\right \)^2 = 16

Correct Answer: A

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Question 21

Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).

Correct A. x^2 + y^2 - 4x - 6y + 9 = 0

B. x^2 + y^2 - 2x - 4y + 4 = 0

C. x^2 + y^2 + 2x - 6y + 9 = 0

D. x^2 + y^2 - 6x + 2y - 9 = 0

Correct Answer: A

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Question 22

Solve the equation \( \tan x + \cot x = 2 \) for \( x \in \left\( 0, \frac{\pi}{2} \right \).

Correct A. \frac{\pi}{4}

B. \frac{\pi}{6}

C. \frac{\pi}{3}

D. \frac{\pi}{2}

Correct Answer: A

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Question 23

Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.

Correct A. \frac{16}{15} \pi

B. \frac{32}{15} \pi

C. \frac{64}{15} \pi

D. \frac{128}{15} \pi

Correct Answer: A

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Question 24

Find the sum of the infinite geometric series \( \sum_{n=1}^\infty \frac{2}{3^n} \).

Correct A. \frac{2}{3}

B. \frac{4}{9}

C. \frac{8}{27}

D. \frac{16}{81}

Correct Answer: A

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Question 25

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

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 3

D. y = x - 3

Correct Answer: A

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