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POST UTME UNILAG 2019 Mathematics | Objective

Are you preparing for POST UTME UNILAG exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the value of x in the equation \( \sin\( 2x \ \) = \frac{1}{2} ) given that ( 0 leq x leq 2pi ).

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 2

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

Correct A. \frac{32\pi}{3}

B. \frac{64\pi}{3}

C. \frac{128\pi}{3}

D. \frac{256\pi}{3}

Correct Answer: A

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Question 3

Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 11 \end{bmatrix} \).

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 4

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the value of \( a_{10} \).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 5

A circle has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 ). Find the equation of the \tangent line at the point ( (4, 7) ).

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 7

D. y = x - 7

Correct Answer: A

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Question 6

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

Correct A. 13

B. 15

C. 17

D. 19

Correct Answer: A

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Question 7

Solve the inequality 2x^2 - 5x - 3 > 0.

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -3 \) \cup \( 1, \infty \)

C. \( -\infty, 1 \) \cup \( 3, \infty \)

D. \( -\infty, 3 \) \cup \( 1, \infty \)

Correct Answer: A

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Question 8

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 9

Solve the 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 10

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

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = 2x - 3

D. y = 2x + 3

Correct Answer: A

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Question 11

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. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 12

Solve the differential equation \frac{dy}{dx} = \frac{x^2 + 1}{y^2} with the initial condition y(0) = 1.

Correct A. y = \sqrt{x^2 + 1}

B. y = \frac{x^2 + 1}{x}

C. y = \frac{x^2 + 1}{x^2}

D. y = \frac{x^2 + 1}{x^3}

Correct Answer: A

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Question 13

Find the area of the triangle formed by the points (0, 0), (3, 0), and (0, 4).

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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Question 14

A vector \vec{a} has a magnitude of 5 units and makes an angle of 60\circ with the positive x-axis. Find the x and y components of \vec{a}.

Correct A. \vec{a} = 2.5 \hat{i} + 4.33 \hat{j}

B. \vec{a} = 4.33 \hat{i} + 2.5 \hat{j}

C. \vec{a} = 2.5 \hat{i} - 4.33 \hat{j}

D. \vec{a} = 4.33 \hat{i} - 2.5 \hat{j}

Correct Answer: A

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Question 15

Solve the inequality x^2 + 4x + 4 > 0.

Correct A. x < -2 or x > 0

B. x > -2 or x < 0

C. x < 0 or x > 2

D. x > 0 or x < 2

Correct Answer: A

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Question 16

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{array} ].

Correct A. -2

B. 4

C. 6

D. 8

Correct Answer: A

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Question 17

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

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 18

Solve for x in the equation [ \sin^2 x + \cos^2 x = 1 ].

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

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

C. x = \frac{\pi}{6}

D. x = \frac{\pi}{3}

Correct Answer: A

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Question 19

Find the volume of the solid formed by revolving the region bounded by the curve [ y = x^2 ] about the x-axis.

Correct A. \frac{\pi}{3}

B. \frac{\pi}{2}

C. \frac{\pi}{4}

D. \frac{\pi}{6}

Correct Answer: A

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Question 20

A vector [ \vec{a} = 2\hat{i} + 3\hat{j} \] is given. Find the magnitude of the vector.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 21

A circle has a diameter of 10 cm. Find the area of the circle in terms of π.

A. 50π

Correct B. 25π

C. 75π

D. 100π

Correct Answer: B

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Question 22

A histogram is constructed from the following data: 2, 4, 5, 6, 8, 9, 10. Find the mean and median of the data.

Correct A. 5.5, 6

B. 6, 5.5

C. 6.5, 6

D. 7, 6

Correct Answer: A

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Question 23

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

A. 32π

B. 64π

Correct C. 128π

D. 256π

Correct Answer: C

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Question 24

A 3x3 matrix is given by A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. Find the determinant of the matrix.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 25

Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).

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

B. \( x - 4 \)^2 + \( y - 5 \)^2 = 9

C. \( x - 5 \)^2 + \( y - 6 \)^2 = 16

D. \( x - 6 \)^2 + \( y - 7 \)^2 = 25

Correct Answer: A

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