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POST UTME COVENANT UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

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

A. 0

B. -1

Correct C. 1

D. 2

Correct Answer: C

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Question 2 View Details

If (f(x) = \(\frac{1}{\(x^2 + 1}\)\)\), find \\((f(x) = frac{1}{x^2 + 1}\(f'(x)\).

A. \(\frac{-2x}{x^2 + 1\) ^2}\)\)

Correct B. \(\frac{2x}{x^2 + 1\) ^2}\)\)

C. \(\frac{1}{x^2 + 1\) ^2}\)\)

D. \(\frac{-1}{x^2 + 1\) ^2}\)\)

Correct Answer: B

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Question 3 View Details

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

Correct A. 0.693

B. 0.693

C. 1.098

D. 1.098

Correct Answer: A

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Question 4 View Details

Solve the inequality \(2x^2 + 5x - 3 \geq 0\).

Correct A. \left( -\infty, \(\frac{-5 - \sqrt{61}\)}{4}\) \right] \cup \left[ \(\frac{-5 + \sqrt{61}\)}{4}\), \infty \right]

B. \left( -\infty, \(\frac{-5 + \sqrt{61}\)}{4}\) \right] \cup \left[ \(\frac{-5 - \sqrt{61}\)}{4}\), \infty \right]

C. \left( -\infty, \(\frac{-5 - \sqrt{61}\)}{4}\) \right] \cup \left[ \(\frac{-5 + \sqrt{61}\)}{4}\), \infty \right]

D. \left( -\infty, \(\frac{-5 + \sqrt{61}\)}{4}\) \right] \cup \left[ \(\frac{-5 - \sqrt{61}\)}{4}\), \infty \right]

Correct Answer: A

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Question 5 View Details

Find the value of (x\) in the equation \(2^x + 3^x = 5^x\\((x) in the equation\).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 6 View Details

Solve for x in the quadratic equation \(x^2 + 5x + 6 = 0\).

A. \(x = -2\)

Correct B. \(x = -3\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: B

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Question 7 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 8 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. x < -1 or \(x > 3\)

B. \(x < 1\) or \(x > 3\)

C. x < -1 or \(x < 3\)

D. \(x > 1\) or \(x > 3\)

Correct Answer: A

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Question 9 View Details

Find the sum of the first 5 terms of the geometric series \(2 + 6 + 18 + ..\)..

Correct A. 62

B. 64

C. 66

D. 68

Correct Answer: A

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Question 10 View Details

Solve the system of linear equations \(x + y = 4\) and \(x - y = 2\).

Correct A. \(x = 3\), \(y = 1\)

B. \(x = 1\), \(y = 3\)

C. \(x = 2\), \(y = 2\)

D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 11 View Details

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

Correct A. 2x/\(x^2 + 1\)^2

B. -2x/\(x^2 + 1\)^2

C. 2/\(x^2 + 1\)^2

D. -2/\(x^2 + 1\)^2

Correct Answer: A

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Question 12 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 13 View Details

The equation of a circle is given by \((x^2 + y^2\) = 4\). Find the equation of the \tangent line to the circle at the point \\((x^2 + y^2 = 4). Find the equation of the \(1, \sqrt{3} \\) ).

Correct A. \(y = -\)\(\sqrt{3}\) x + 2\sqrt{3}

B. \(y =\)\(\sqrt{3}\) x + 2\sqrt{3}

C. \(y = -\)\(\sqrt{3}\) x - 2\sqrt{3}

D. \(y =\)\(\sqrt{3}\) x - 2\sqrt{3}

Correct Answer: A

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Question 14 View Details

A histogram is shown below. Find the mean of the data.

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 15 View Details

Evaluate the definite integral \(\int_0^1 x^2 dx\).

A. \(1/3\)

Correct B. \(1/2\)

C. \(2/3\)

D. 1

Correct Answer: B

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Question 16 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{1 - \(x^2}}\)\) ) using the chain rule.

Correct A. \(\frac{-x}{1 - x^2 \\)^{\(3/2\)}} )

B. \(\frac{x}{1 - x^2 \\)^{\(3/2\)}} )

C. \(\frac{1}{1 - x^2 \\)^{\(3/2\)}} )

D. \(\frac{-1}{1 - x^2 \\)^{\(3/2\)}} )

Correct Answer: A

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Question 17 View Details

Solve for ( x ) in the equation \(\sin^2 x \\) + \\(\cos^2(x)\)\(= 1 ).\)

Correct A. \(x = \frac{\pi}{4}\)

B. \(x = \frac{3\pi}{4}\)

C. \(x = \frac{\pi}{2}\)

D. \(x = \frac{5\pi}{4}\)

Correct Answer: A

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Question 18 View Details

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

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

B. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 4\) )

C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 9\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 25\) )

Correct Answer: A

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Question 19 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 90.

Correct A. 0.1587

B. 0.3413

C. 0.5

D. 0.8413

Correct Answer: A

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Question 20 View Details

Simplify the expression \(\frac{2^3 \cdot 3^2}{2^2 \cdot 3^4}\).

Correct A. \(\frac{1}{3}\)

B. \(\frac{1}{9}\)

C. \(\frac{1}{27}\)

D. \(\frac{1}{81}\)

Correct Answer: A

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Question 21 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \(1/2\).

Correct A. \(1023/512\)

B. \(2047/1024\)

C. \(4095/2048\)

D. \(8191/4096\)

Correct Answer: A

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Question 22 View Details

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, calculate their total daily profit in naira.

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: A

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Question 23 View Details

In the diagram below, what is the area of the triangle ABC?

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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Question 24 View Details

Solve for x in the equation \(2^x\) + \\((2^x\)\(= 128.\)\)

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 25 View Details

A car travels from city A to city B at an average speed of 60 \(km/h\). If the distance between the two cities is 240 km, how long does the journey take in hours?

A. 4

Correct B. 4.5

C. 5

D. 5.5

Correct Answer: B

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