POST UTME MOUNTAIN TOP UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 - 5x + 3 > 0 \) u\sing the quadratic formula.
A. x < 1
B. x > 1
C. x < 3
D. x > 3
Question 2
Solve the system of equations: \( egin{cases} x + y = 2 \ 2x - 3y = - 1 \end{cases} \).
A. \( x = 1, y = 1 \)
B. \( x = 2, y = 0 \)
C. \( x = 0, y = 2 \)
D. \( x = 1, y = 2 \)
Question 3
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24 cm^2
B. 50.24 m^2
C. 50.24 mm^2
D. 50.24 km^2
Question 4
Solve the equation [ x^2 + 4x + 4 = 0 ] u\sing the quadratic formula.
A. 0
B. -2
C. 2
D. -4
Question 5
Solve for ( x ) in the equation \( \frac{x^2 - 4}{x + 2} = 2 \).
A. \( x = 2 \)
B. \( x = -2 \)
C. \( x = 4 \)
D. \( x = -4 \)
Question 6
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 7
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > 3 \)
B. \( x < -1 \) or \( x < 3 \)
C. \( x > -1 \) or \( x > 3 \)
D. \( x > -1 \) or \( x < 3 \)
Question 8
A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.
A. 10
B. 20
C. 30
D. 40
Question 9
Find the value of \( \sin 2x \) if \( \sin x = \frac{1}{2} \) and ( x ) is in the first quadrant.
A. \( \frac{1}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
C. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{\sqrt{2}}{2} \)
Question 10
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{1}{2} \)
B. ( 3 )
C. ( 4 )
D. ( 5 )
Question 11
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 32π/3
B. 64π/3
C. 128π/3
D. 256π/3
Question 12
Find the value of ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. 1
B. -1
C. 2
D. -2
Question 13
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ].
A. 1
B. -1
C. 2
D. 3
Question 14
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the chain rule and limits.
A. ( f'(x) = 2x + 4 )
B. ( f'(x) = 2x - 4 )
C. ( f'(x) = 2x^2 - 4 )
D. ( f'(x) = 2x^2 + 4 )
Question 15
Solve the matrix equation: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 2 \)

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