POST UTME LAUTECH 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 2
A histogram shows the distribution of exam scores. Find the mean of the scores.
A. 50
B. 60
C. 70
D. 80
Question 3
A circle has a radius of 5 cm. Find the area of the circle.
A. 50π
B. 100π
C. 150π
D. 200π
Question 4
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.
A. 0.45
B. 0.55
C. 0.65
D. 0.75
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)
Question 6
Find the area under the curve \( y = x^2 \) from x = 0 to x = 4.
A. 16
B. 32
C. 64
D. 128
Question 7
Solve for x in the equation \( x^2 - 6x + 8 = 0 \).
A. 2
B. 3
C. 4
D. 5
Question 8
In the diagram below, the graph of \( y = \frac{1}{2} \tan \( 2x \ \) ) is shown. What is the value of ( x ) at the point where the graph intersects the line \( y = 2 \)?
A. π/4
B. π/2
C. π/6
D. π/3
Question 9
A random variable ( X ) has a probability distribution given by \( P\( X = k \ \) = \frac{1}{2^k} \) for \( k = 1, 2, 3, \ldots \ \). What is the expected value of ( X )?
A. 1
B. 2
C. 3
D. 4
Question 10
The area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) is given by the definite integral \( \int_0^2 x^2 dx \ \). What is the value of the integral?
A. 4
B. 6
C. 8
D. 10
Question 11
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
D. \frac{1}{2} \left\( x + \frac{1}{x} \right \)
Question 12
A sequence is defined by \( a_n = \frac{1}{n} + \frac{1}{n + 1} \ \) for \( n = 1, 2, 3, \ldots \ \). What is the sum of the first five terms of the sequence?
A. 1
B. 2
C. 3
D. 4
Question 13
The equation of a circle is given by \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 ). What is the dis\tance between the center of the circle and the point ( (5, 7) )?
A. 1
B. 2
C. 3
D. 4
Question 14
Find the derivative of the function ( f(x) = \frac{1}{x^2} \) u\sing the chain rule.
A. -\frac{2}{x^3}
B. \frac{2}{x^3}
C. -\frac{1}{x^3}
D. \frac{1}{x^3}
Question 15
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 12
C. 18
D. 24

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