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POST UTME UNILORIN 2024 Mathematics | Objective

Are you preparing for POST UTME UNILORIN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 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^2 + 1}} ) u\sing the chain rule.

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

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

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

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

Correct Answer: A

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Question 2

Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix} \).

A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)

Correct B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} \)

C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} -1 \ 3 \end{bmatrix} \)

D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ -2 \end{bmatrix} \)

Correct Answer: B

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Question 3

Find the area under the curve \( y = \sin\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \) u\sing integration.

Correct A. \( \frac{pi}{2} \)

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

C. \( \frac{pi}{6} \)

D. \( \frac{pi}{8} \)

Correct Answer: A

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Question 4

A particle moves along the x-axis with its position given by ( x(t) = 2t^2 + 3t - 1 ). Find the velocity of the particle at time \( t = 1 \).

Correct A. ( v(1) = 5 )

B. ( v(1) = 7 )

C. ( v(1) = 9 )

D. ( v(1) = 11 )

Correct Answer: A

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Question 5

A company produces two products, A and B. The profit from producing x units of A and y units of B is given by ( P(x,y) = 2x + 3y - xy ). Find the maximum profit when x = 10 and y = 20.

A. ( P(10,20) = 100 )

Correct B. ( P(10,20) = 120 )

C. ( P(10,20) = 140 )

D. ( P(10,20) = 160 )

Correct Answer: B

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Question 6

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 48\pi cm^3

B. 64\pi cm^3

Correct C. 80\pi cm^3

D. 96\pi cm^3

Correct Answer: C

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Question 7

A particle moves in a straight line with a velocity of 5 m/s. Find its acceleration after 2 seconds, given that its initial velocity is 2 m/s.

A. 1.5 m/s^2

B. 2 m/s^2

Correct C. 2.5 m/s^2

D. 3 m/s^2

Correct Answer: C

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Question 8

Find the equation of the \tangent to the curve y = x^2 + 2x - 3 at the point (1, 2).

Correct A. y - 2 = 4\( x - 1 \)

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

C. y - 2 = 3\( x - 1 \)

D. y - 2 = 5\( x - 1 \)

Correct Answer: A

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Question 9

A histogram has a mean of 25 and a s\tandard deviation of 5. Find the probability that a randomly selected value lies between 20 and 30.

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 10

Solve the inequality x^2 - 4x - 5 > 0.

Correct A. x < -1, x > 5

B. x < -1, x < 5

C. x > -1, x > 5

D. x < -1, x < 0

Correct Answer: A

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Question 11

In the vector equation \( mathbf{r} = mathbf{a} + t mathbf{b} \), where ( mathbf{a} ) and ( mathbf{b} ) are vectors, and ( t ) is a scalar, find the vector ( mathbf{r} ) when \( mathbf{a} = 2 mathbf{i} + 3 mathbf{j} \), \( mathbf{b} = mathbf{i} - 2 mathbf{j} \), and \( t = 3 \).

Correct A. 9\mathbf{i} + 5\mathbf{j}

B. 6\mathbf{i} + 7\mathbf{j}

C. 8\mathbf{i} + 9\mathbf{j}

D. 10\mathbf{i} + 11\mathbf{j}

Correct Answer: A

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Question 12

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

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 13

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25

B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25

C. \( x - 5 \)^2 + \( y - 3 \)^2 = 25

D. \( x - 3 \)^2 + \( y - 5 \)^2 = 25

Correct Answer: A

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Question 14

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

A. x = \frac{\pi}{2}

Correct B. x = \frac{\pi}{4}

C. x = \frac{3\pi}{4}

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

Correct Answer: B

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Question 15

Find the volume of the cylinder with radius ( 4 ) and height ( 6 ).

Correct A. 48\pi

B. 64\pi

C. 72\pi

D. 80\pi

Correct Answer: A

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Question 16

A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the s\tandard error of the mean.

A. 2.5 cm

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 17

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 18

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Calculate its volume.

A. 400 cm^3

B. 500 cm^3

Correct C. 600 cm^3

D. 800 cm^3

Correct Answer: C

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Question 19

A sequence is defined as \( a_n = 2n + 1 \). 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 20

Find the derivative of the function \( f(x) = 3x^2 + 2x - 5 \) u\sing the power rule.

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 21

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 22

A fair six-sided die is rolled. What is the probability that the product of the numbers on the two dice is a multiple of 3?

A. \frac{1}{3}

B. \frac{1}{2}

Correct C. \frac{2}{3}

D. \frac{5}{6}

Correct Answer: C

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Question 23

Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 1.

A. \frac{1}{2}

B. \frac{3}{2}

Correct C. \frac{5}{2}

D. \frac{7}{2}

Correct Answer: C

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Question 24

A vector \vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k} and a vector \vec{b} = -1\hat{i} + 2\hat{j} - 3\hat{k}. Find the cross product of \vec{a} and \vec{b}.

Correct A. \hat{i} - \hat{j} + \hat{k}

B. \hat{i} + \hat{j} + \hat{k}

C. \hat{i} - \hat{j} - \hat{k}

D. \hat{i} + \hat{j} - \hat{k}

Correct Answer: A

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Question 25

Solve the system of linear equations: 2x + 3y = 7 and x - 2y = -3.

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 3, y = -1

D. x = -1, y = 3

Correct Answer: A

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