POST UTME OSUSTECH 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )
Question 2
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for x.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{3\pi}{4}
D. \pi
Question 3
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?
A. 0.68
B. 0.73
C. 0.83
D. 0.93
Question 4
Determine the value of x in the equation \( \frac{x}{2} + 5 = 11 \).
A. 4
B. 6
C. 8
D. 10
Question 5
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 6
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. 6x + 2
B. 6x - 2
C. 3x + 2
D. 3x - 2
Question 7
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 8
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. ( f'(x) = 6x + 2 )
B. ( f'(x) = 6x - 2 )
C. ( f'(x) = 6x + 4 )
D. ( f'(x) = 6x - 4 )
Question 9
A population of 1000 bacteria is growing at a rate of 20% per hour. What is the population after 3 hours?
A. ( 1000(1.2)^3 )
B. ( 1000(1.2)^2 )
C. ( 1000(1.2)^4 )
D. ( 1000(1.2)^5 )
Question 10
In a 3D coordinate system, the equation of a plane in the form \( Ax + By + Cz = D \) is given by \( 2x - 3y + 4z = 7 \). Find the dis\tance of the point \( P\( 1, -1, 2 \ \) ) from the plane.
A. \( \frac{1}{2} \)
B. \( \frac{3}{2} \)
C. \( \frac{5}{2} \)
D. \( \frac{7}{2} \)
Question 11
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?
A. 30
B. 40
C. 50
D. 60
Question 12
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{8}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)
Question 13
A vector ( mathbf{a} ) is given by \( egin{bmatrix} 2 \ 3 \ 4 \end{bmatrix} \). Find the magnitude of the vector.
A. ( 5 )
B. ( 6 )
C. ( 7 )
D. ( 8 )
Question 14
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 4\text{ cm}
B. 6\text{ cm}
C. 8\text{ cm}
D. 10\text{ cm}
Question 15
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. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)

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