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POST UTME OAU 2022 Mathematics | Objective

Are you preparing for POST UTME OAU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing 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

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

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

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

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

A rec\tangular \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, 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

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

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

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

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

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

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

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

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

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

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing 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

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

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

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

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

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 20

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

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

Correct A. x > 4

B. x > 6

C. x < 4

D. x < 6

Correct Answer: A

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Question 22

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

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

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

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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