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POST UTME VERITAS UNIVERSITY 2022 Mathematics | Objective

Are you preparing for POST UTME VERITAS UNIVERSITY 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 determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 2

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first 5 terms of the sequence.

A. 33

Correct B. 35

C. 37

D. 39

Correct Answer: B

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Question 3

The equation of a circle is given by \( x^2 + y^2 - 6x + 4y + 4 = 0 \). Find the coordinates of the center of the circle.

Correct A. \( 3, -2 \)

B. (2, 3)

C. \( 4, -1 \)

D. (1, 2)

Correct Answer: A

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Question 4

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

A. 10

Correct B. 12

C. 15

D. 18

Correct Answer: B

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Question 5

A polynomial function is defined by ( f(x) = x^3 - 2x^2 + 3x - 1 ). Find the value of \( f\( -1 \ \) ).

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 6

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7

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

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

B. x < 1 or x > -3/2

C. x < -3/2 or x > 1

D. x < 3/2 or x > -1

Correct Answer: A

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Question 8

Find the sum of the first 5 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ... \).

Correct A. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5

B. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6

C. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7

D. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8

Correct Answer: A

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Question 9

In the diagram below, ( ABC ) is a triangle with \( AB = 5 \) cm and \( BC = 6 \) cm. Find the length of ( AC ).

A. 7

B. 8

Correct C. 9

D. 10

Correct Answer: C

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Question 10

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

Correct A. x = -2

B. x = -1

C. x = 1

D. x = 2

Correct Answer: A

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Question 11

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 12

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 13

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

A. 4

B. 8

Correct C. 16

D. 32

Correct Answer: C

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Question 14

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

A. 5

B. 10

C. 15

Correct D. 20

Correct Answer: D

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Question 15

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

A. 15

B. 25

C. 35

Correct D. 45

Correct Answer: D

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Question 16

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

Correct A. x^2 + y^2 + 4x - 8y + 5 = 0

B. x^2 + y^2 - 4x + 8y + 5 = 0

C. x^2 + y^2 + 2x - 4y + 5 = 0

D. x^2 + y^2 - 2x + 4y + 5 = 0

Correct Answer: A

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Question 17

Solve the matrix equation AX = B, where A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}, X = egin{bmatrix} x \ y \end{bmatrix}, and B = egin{bmatrix} 5 \ 6 \end{bmatrix}.

Correct A. X = egin{bmatrix} 1 \ 2 \end{bmatrix}

B. X = egin{bmatrix} 2 \ 1 \end{bmatrix}

C. X = egin{bmatrix} 3 \ 4 \end{bmatrix}

D. X = egin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 18

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

Correct A. 10

B. 12

C. 15

D. 20

Correct Answer: A

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Question 19

Solve the system of equations: x + y = 4 and xy = 6.

Correct A. x = 2, y = 2

B. x = 3, y = 1

C. x = 1, y = 3

D. x = 4, y = 0

Correct Answer: A

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Question 20

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

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 1

D. y = x - 2

Correct Answer: A

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Question 21

A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.3. If two indep\endent random variables X and Y have the same probability distribution, find the probability that X + Y = 5.

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 22

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

A. 16\pi

Correct B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: B

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Question 23

Solve the equation \sin^2 x + \cos^2 x = 1 for x in the interval [0, 2\pi].

A. \frac{\pi}{4}

B. \frac{\pi}{2}

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

Correct D. \pi

Correct Answer: D

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Question 24

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

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: A

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Question 25

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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