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POST UTME UI 2024 Mathematics | Objective

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Question 1

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

Correct A. -14

B. 14

C. -28

D. 28

Correct Answer: A

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Question 2

A histogram is constructed from the following data: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23. What is the class width of the histogram?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 3

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is P(A ∩ B)?

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 4

Solve the equation [ x^2 + 4x + 4 = 0 ].

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 5

A circle has a radius of 5 cm. What is the area of the circle?

A. 25\pi

Correct B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: B

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Question 6

Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 7

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

Correct A. \( x = -2 \)

B. \( x = -3 \)

C. \( x = 2 \)

D. \( x = 3 \)

Correct Answer: A

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Question 8

Find the derivative of the function ( f(x) = 3x^2 - 2x + 1 ) u\sing the power rule.

Correct A. ( f'(x) = 6x - 2 )

B. ( f'(x) = 6x + 2 )

C. ( f'(x) = 3x^2 - 2 )

D. ( f'(x) = 3x^2 + 2 )

Correct Answer: A

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Question 9

Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. \( x = 1, y = 2 \)

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

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 10

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 11

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the prism in cubic centimeters?

Correct A. 72

B. 48

C. 36

D. 24

Correct Answer: A

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Question 12

In a certain number base, the number 1011 represents the value 5. What is the value of the number 1101 in this base?

A. 11

B. 13

Correct C. 15

D. 17

Correct Answer: C

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Question 13

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. \frac{1}{6}

B. \frac{1}{3}

Correct C. \frac{1}{2}

D. \frac{2}{3}

Correct Answer: C

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Question 14

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

Correct A. 6x + 2

B. 3x + 1

C. 2x - 1

D. x - 2

Correct Answer: A

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Question 15

A vector \mathbf{a} has a magnitude of 5 units and points in the direction of the positive x-axis. A vector \mathbf{b} has a magnitude of 3 units and points in the direction of the positive y-axis. What is the magnitude of the sum of these two vectors?

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 16

Determine the probability of the event that a randomly selected student from a class of 30 students is a female, given that 15 students are females and 8 students are males.

Correct A. \frac{1}{2}

B. \frac{2}{3}

C. \frac{3}{4}

D. \frac{4}{5}

Correct Answer: A

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Question 17

Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...

A. 195

B. 205

Correct C. 215

D. 225

Correct Answer: C

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Question 18

Solve for x in the equation \sin(x) = \cos(x) u\sing the identity \sin^2(x) + \cos^2(x) = 1.

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

B. \frac{\pi}{2}

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

D. \frac{\pi}{6}

Correct Answer: A

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Question 19

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

A. ₦1,250

Correct B. ₦1,500

C. ₦1,750

D. ₦2,000

Correct Answer: B

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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 + 2

D. 3x^2 - 2

Correct Answer: A

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Question 21

Find the equation of the circle with center at ((2,3)) and radius 4.

Correct A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )

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

C. \( x-4 \ \)^2 + \( y-3 \)^2 = 16 )

D. \( x-2 \ \)^2 + \( y-3 \)^2 = 64 )

Correct Answer: A

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Question 22

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

Correct A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)

B. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)

C. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)

D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)

Correct Answer: A

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Question 23

Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \).

Correct A. \( ln 2 - ln 1 \)

B. \( ln 2 - ln 2 \)

C. \( ln 1 - ln 2 \)

D. \( ln 2 - ln 3 \)

Correct Answer: A

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Question 24

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

Correct A. \( x = 1, y = 1 \)

B. \( x = 2, y = 0 \)

C. \( x = 0, y = 2 \)

D. \( x = 1, y = 2 \)

Correct Answer: A

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Question 25

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

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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