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POST UTME OAU 2022 Mathematics | Objective

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Question 1 View Details

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

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

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

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

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

Correct Answer: B

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Question 2 View Details

Solve for x in the equation \(2^x = 12\).

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 3 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.

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 4 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \(\frac{1}{6}\)\)

B. \(\frac{1}{3}\)\)

C. \(\frac{2}{3}\)\)

Correct D. \(\frac{5}{6}\)\)

Correct Answer: D

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Question 5 View Details

Find the determinant of the matrix \(A = \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).

A. -120

B. 120

Correct C. 240

D. -240

Correct Answer: C

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Question 6 View Details

A rectangular tank with a length of 5m, a width of 3m, and a height of 2m is filled with water. If the density of water is \(1000kg/m\^3\\(tank with a length of 5m, a width of 3m, and a height of 2m is filled with water. If the density of water is (1000kg/m\), calculate the volume of water in the \tank in cubic meters.

A. \(10m^3\)

B. \(15m^3\)

Correct C. \(20m^3\)

D. \(25m^3\)

Correct Answer: C

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Question 7 View Details

Solve for x in the equation: \(2x^2 + 5x - 3 = 0\).

A. \(x = -3\)

Correct B. \(x = 1/2\)\)

C. \(x = 3\)

D. \(x =\)\(-1/2\)

Correct Answer: B

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Question 8 View Details

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment stops. What is the probability that the experiment will stop on the first roll?

A. \(1/2\)

B. \(1/3\)

C. \(2/3\)

Correct D. \(1/6\)

Correct Answer: D

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Question 9 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. 4π/3

B. 2π/3

C. π/3

D. π/2

Correct Answer: A

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Question 10 View Details

A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A that contain exactly three elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 11 View Details

Determine the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. \(2 3^{10}-1 \\)/\(3-1\) )

B. \(2 3^{10}+1 \\)/\(3+1\) )

C. \(2 3^{10}-1 \\)/\(3+1\) )

D. \(2 3^{10}+1 \\)/\(3-1\) )

Correct Answer: A

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Question 12 View Details

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

Correct A. \(x < -3/2\) or \(x > 1/2\)

B. \(x < -3/2\) or \(x < 1/2\)

C. \(x > -3/2\) or \(x > 1/2\)

D. \(x < -3/2\) or \(x < 1/2\)

Correct Answer: A

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Question 13 View Details

Find the area of the triangle with vertices ( A(1,2) ), ( B(3,4) ), and ( C(2,1) ).

Correct A. \(1/2\)

B. ( 1 )

C. \(3/2\)

D. ( 2 )

Correct Answer: A

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Question 14 View Details

A circle with center ( C(0,0) ) and radius 4 passes through the point ( P(3,4) ). Find the equation of the circle.

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

B. \(x^2 + y^2 = 20\)

C. \(x^2 + y^2 = 24\)

D. \(x^2 + y^2 = 28\)

Correct Answer: A

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Question 15 View Details

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

Correct A. \(64/3\)

B. \(64/5\)

C. \(64/7\)

D. \(64/9\)

Correct Answer: A

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Question 16 View Details

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

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

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

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

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

Correct Answer: A

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Question 17 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = \frac{1}{2}\) for ( x ) in the interval \([0, 2\\() for ( x ) in the interval \pi]\).

Correct A. \(\frac{\pi}{6}\)\)

B. \(\frac{\pi}{4}\)\)

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

D. \(\frac{\pi}{2}\)\)

Correct Answer: A

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Question 18 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19 View Details

A particle moves in a straight line with a velocity given by ( v(t) = \((2t^2 + 5t - 3\)\) ). Find the acceleration at time \(t = 1\\((2t^2 + 5t - 3) ). Find the acceleration at time\).

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 20 View Details

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

Correct A. \begin{pmatrix} 1 \ 1 \end{pmatrix}

B. \begin{pmatrix} 1 \ -1 \end{pmatrix}

C. \begin{pmatrix} -1 \ 1 \end{pmatrix}

D. \begin{pmatrix} -1 \ -1 \end{pmatrix}

Correct Answer: A

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Question 21 View Details

Solve the inequality (\(\frac{x}{x-2}\(> 2\)\) for \\((frac{x}{x-2} > 2\(x > 2\)\).

Correct A. \(x > 4\)

B. \(x > 6\)

C. \(x < 4\)

D. \(x < 6\)

Correct Answer: A

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Question 22 View Details

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

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 23 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

A. \(x = -2\)

Correct B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: B

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Question 24 View Details

A matrix ( A ) is given by \(A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\). Find the determinant of ( A ).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 25 View Details

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

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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