POST UTME UI 2024 Mathematics | Objective

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Question 1 View Details
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 View Details
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 View Details
Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, what is P(\(A \cap B\))?
Correct A. 0.12
B. 0.24
C. 0.36
D. 0.48

Correct Answer: A

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Question 4 View Details
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 View Details
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 View Details
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 View Details
Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using 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 View Details
Find the derivative of the function ( f(x) = \(3x^2 - 2x + 1\) ) using 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 View Details
Solve the system of linear equations using 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 View Details
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 View Details
A rectangular 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 View Details
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 View Details
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 View Details
Find the derivative of the function f(x) = \(3x^2 + 2x - 5\) using 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 View Details
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 View Details
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 View Details
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 View Details
Solve for x in the equation sin(x) = \cos(x) using the identity \\\(sin(x) = cos(x) using 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 View Details
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 View Details
Find the derivative of the function f(x) = \(3x^2 + 2x - 5\) using 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 View Details
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 View Details
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 View Details
Find the area under the curve \(y = \frac{1}{x}\) from \(x = 1\) to \(x = 2\).
Correct A. \(\(12 -\)11\)
B. \(\(12 -\)12\)
C. \(\(11 -\)12\)
D. \(\(12 -\)13\)

Correct Answer: A

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Question 24 View Details
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 View Details
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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