POST UTME LAUTECH 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the trigonometric equation \sin^2 x + \cos^2 x = 1.
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \frac{3\pi}{4}
D. x = \pi
Question 2
Find the value of x in the polynomial equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 3
A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.
A. y = x + 1
B. y = x - 1
C. y = -x + 1
D. y = -x - 1
Question 4
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/3
B. 1/2
C. 2/3
D. 1/6
Question 5
The equation of a circle is given by \(x^2 + y^2 + 4x - 6y + 9 = 0\). Find the coordinates of the center of the circle.
A. (2, 3)
B. \( -2, 3 \)
C. \( 2, -3 \)
D. \( -2, -3 \)
Question 6
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)² + \( y - 3 \)² = 16
B. \( x - 2 \)² + \( y + 3 \)² = 16
C. \( x + 2 \)² + \( y + 3 \)² = 16
D. \( x - 2 \)² + \( y - 3 \)² = 16
Question 7
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 7.07 cm
C. 10 cm
D. 15 cm
Question 8
Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{1}{2}
D. \frac{2}{5}
Question 9
Solve the equation \( x^2 - 4x + 4 = 0 \) u\sing the quadratic formula.
A. x = 2
B. x = -2
C. x = 1
D. x = -1
Question 10
A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. 2500
B. 3000
C. 3500
D. 4000
Question 11
Find the value of ( x ) in the equation \( 2^x + 3^x = 5^x \) u\sing \logarithms.
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 12
Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 6cm.
A. 100π cm³
B. 150π cm³
C. 200π cm³
D. 250π cm³
Question 13
A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.
A. 20
B. 25
C. 30
D. 35
Question 14
A histogram represents the distribution of exam scores in a class. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 70?
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 15
A histogram represents the distribution of exam scores in a class. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 70?
A. 0.25
B. 0.5
C. 0.75
D. 0.9

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