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POST UTME AAUA 2025 Mathematics | Objective

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Question 1 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. \(\frac{1}{2}\)

B. ( 3 )

C. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

Correct D. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

Correct Answer: D

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Question 2 View Details

A histogram of exam scores is shown below. What is the mean score?

A. ( 50 )

Correct B. ( 60 )

C. ( 70 )

D. ( 80 )

Correct Answer: B

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Question 3 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 4 View Details

Find the volume of the solid formed by rotating the region bounded by \(y = x^2\) and \(y = 4\) about the x-axis.

A. \(\frac{16\pi}{3}\)

B. \(\frac{32\pi}{3}\)

Correct C. \(\frac{64\pi}{3}\)

D. \(\frac{128\pi}{3}\)

Correct Answer: C

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Question 5 View Details

A quadratic equation has roots \(x = 1\) and \(x = 2\). Find the equation of the axis of symmetry.

A. \(x = 0.5\)

Correct B. \(x = 1.5\)

C. \(x = 2.5\)

D. \(x = 3.5\)

Correct Answer: B

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Question 6 View Details

In a random experiment, two events A and B are independent. If P(A) = 0.4 and P(B) = 0.3, what is the probability that both events occur?

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 7 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 + \(y + 3\)^\(2 = 16\)

C. \(x + 2\)^2 + \(y + 3\)^\(2 = 16\)

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

Correct Answer: A

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Question 8 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find its volume.

Correct A. 400 \(cm^3\)

B. 500 \(cm^3\)

C. 600 \(cm^3\)

D. 800 \(cm^3\)

Correct Answer: A

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Question 9 View Details

Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...

A. 50

Correct B. 55

C. 60

D. 65

Correct Answer: B

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Question 10 View Details

Solve the system of equations using matrices:\n\\(n2x + 3y = 7\)\\(nnx - 2y = -3\)

Correct A. \(x = 1\), \(y = 2\)

B. \(x = 2\), \(y = 1\)

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 3\)

Correct Answer: A

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Question 11 View Details

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

A. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )

Correct B. ( f'\((x) =\)\(\frac{2x^3 + 2x}{\) \(x^2 + 1\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{2x^3 - 2x}{\) \(x^2 + 1\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{2x^3 + 2}{\) \(x^2 + 1\) ^2}\)\) )

Correct Answer: B

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Question 12 View Details

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

Correct A. 1.2

B. 1.5

C. 1.8

D. 2.0

Correct Answer: A

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Question 13 View Details

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

A. 16π

Correct B. 32π

C. 64π

D. 128π

Correct Answer: B

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Question 14 View Details

A vector ( mathbf{a} ) is given by \(\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}\). Find the magnitude of ( mathbf{a} ).

A. 1

Correct B. \(√5\)

C. \(2√5\)

D. 5

Correct Answer: B

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Question 15 View Details

Solve the equation \(x^2 + 2x + 1 = 0\) using the quadratic formula.

Correct A. 0

B. -1

C. 1

D. -2

Correct Answer: A

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Question 16 View Details

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

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 17 View Details

A random variable (X\) has a probability distribution given by \(P X = x\\((X) has a probability distribution given by\) = \(\frac{1}{x^2}\)\))\) for \(x = 1, 2, 3, \\()) for \dots\). Find the probability that \(X\) is greater than 2.

A. 0.25

B. 0.5

Correct C. 0.75

D. 1

Correct Answer: C

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Question 18 View Details

Solve the system of equations \(\begin{align*} x + y + z & = 6 \ x + 2y + 3z & = 11 \ x + 3y + 6z & = 16 \end{align*}\).

Correct A. [1, 2, 3]

B. [2, 3, 1]

C. [3, 1, 2]

D. [1, 3, 2]

Correct Answer: A

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Question 19 View Details

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

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 20 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. Find the probability that a randomly selected score is greater than 70.

A. 0.25

B. 0.5

Correct C. 0.75

D. 1

Correct Answer: C

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Question 21 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\).

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 22 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 23 View Details

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

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 24 View Details

Solve the inequality \(x^2 - 4x + 4 > 0\).

Correct A. \(x > 2\)

B. \(x < 2\)

C. \(x > 0\)

D. \(x < 0\)

Correct Answer: A

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Question 25 View Details

Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. \(y = 2x + 1\)

B. \(y = 2x - 1\)

C. \(y = x + 1\)

D. \(y = x - 1\)

Correct Answer: A

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