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POST UTME LEAD CITY UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

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 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 derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using 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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using 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 View Details

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

Correct A. \(\frac{1}{2}\)\) \arctan(x) \Big|_\(0^1\)

B. \(\frac{1}{2}\)\) \arctan(x) \Big|_\(0^1\) + \(\frac{1}{2}\)\)

C. \(\frac{1}{2}\)\) \arctan(x) \Big|_\(0^1\) - \(\frac{1}{2}\)\)

D. \(\frac{1}{2}\)\) \arctan(x) \Big|_\(0^1\)

Correct Answer: A

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Question 8 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using 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 View Details

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 View Details

Find the standard 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 View Details

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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

Solve the equation \(x^2 + 4x - 5 = 0\) using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the circle passing 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 View Details

Solve the equation (\(1x +\)\(1x = 2\)\) for x \in \\((\(1x +\)1x = 2) for x \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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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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