POST UTME LAUTECH 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. 1023
B. 1024
C. 1025
D. 1026
Question 2
Solve the equation: \( x^2 + 5x + 6 = 0 \)
A. -2
B. -1
C. 2
D. 3
Question 3
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 4
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 5
Find the determinant of the matrix $\begin{bmatrix} 2 & 1 & 1 \ 1 & 2 & 1 \ 1 & 1 & 2 \end{bmatrix}$.
A. 4
B. 6
C. 8
D. 10
Question 6
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 7
Find the value of ( x ) in the equation \( 2^x + 5^x = 7^x \) u\sing \logarithms.
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 8
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}}
C. f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 9
A sequence is given by \(a_n = 2n^2 + 3n - 1\). Find the sum of the first 5 terms of the sequence.
A. 50
B. 55
C. 60
D. 65
Question 10
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the s\tandard error of the mean.
A. 2.083 cm
B. 2.5 cm
C. 3.125 cm
D. 3.75 cm
Question 11
Solve the equation \tan x + \cot x = 2, where x is an acute angle.
A. \frac{\pi}{4}
B. \frac{\pi}{6}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 12
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 13
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 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
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \frac{1}{2}.
A. \frac{1023}{512}
B. \frac{1024}{512}
C. \frac{1025}{512}
D. \frac{1026}{512}

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