POST UTME LAUTECH 2025 Mathematics | Objective

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Question 1 View Details
Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)
Correct A. 10
B. 100
C. 1000
D. 10000

Correct Answer: A

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Question 2 View Details
Solve for y in the equation \(y = \frac{1}{2} \left x + \frac{1}{x} \right \\) ).
A. x + \(\frac{1}{x}\)\)
B. \(\frac{1}{2}\)\) \(x^2\)
C. \(\frac{1}{2}\)\) x
Correct D. \(\frac{1}{2}\)\) \left\(x + \frac{1}{x} \right\)

Correct Answer: D

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Question 3 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{x^2}\)\)\) \) using the chain rule.
Correct A. -\(\frac{2}{x^3}\)\)\)
B. \(\frac{2}{x^3}\)\)\)
C. -\(\frac{1}{x^3}\)\)\)
D. \(\frac{1}{x^3}\)\)\)

Correct Answer: A

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Question 4 View Details
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 5 View Details
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
Correct A. 6
B. 12
C. 18
D. 24

Correct Answer: A

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Question 6 View Details
In the diagram below, the graph of \(y = \frac{1}{2} $12x \\) ) is shown. What is the value of ( x ) at the point where the graph intersects the line \(y = 2\)?
Correct A. π/4
B. π/2
C. π/6
D. π/3

Correct Answer: A

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Question 7 View Details
A random variable ( X ) has a probability distribution given by \(P X = k \\) = \(\frac{1}{2^k}\)\)\) ) for \(k = 1, 2, 3, \ldots \\() for (k = 1, 2, 3, \\). What is the expected value of ( X )?
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 8 View Details
The equation of a circle is given by \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) ). What is the distance between the center of the circle and the point ( (5, 7) )?
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 9 View Details
A sequence is defined by \(a_n = \frac{1}{n} + \frac{1}{n + 1}\) for \(n = 1, 2, 3, \ldots \\() for (n = 1, 2, 3, \\). What is the sum of the first five terms of the sequence?
A. 1
B. 2
C. 3
Correct D. 4

Correct Answer: D

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Question 10 View Details
The area under the curve \(y = x^2\) from \(x = 0\) to (x = 2\) is given by the definite integral \(\\((x = 2) is given by the definite integral \int_0^2 x^2 dx \\). What is the value of the integral?
A. 4
B. 6
Correct C. 8
D. 10

Correct Answer: C

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Question 11 View Details
Let X be a random variable that takes values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with probabilities 0.1, 0.2, 0.3, 0.1, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05 respectively. Find the probability that X is greater than 4.
Correct A. 0.45
B. 0.55
C. 0.65
D. 0.75

Correct Answer: A

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Question 12 View Details
Solve for x in the equation \(x^2 - 6x + 8 = 0\).
Correct A. 2
B. 3
C. 4
D. 5

Correct Answer: A

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Question 13 View Details
Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).
Correct A. 16
B. 32
C. 64
D. 128

Correct Answer: A

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Question 14 View Details
A circle has a radius of 5 cm. Find the area of the circle.
A. 50π
Correct B. 100π
C. 150π
D. 200π

Correct Answer: B

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Question 15 View Details
A histogram shows the distribution of exam scores. Find the mean of the scores.
A. 50
B. 60
Correct C. 70
D. 80

Correct Answer: C

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