POST UTME LASU 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and \( -1, 2 \).
A. \( x-1 \)^2 + \( y-2 \)^2 = 4
B. \( x+1 \)^2 + \( y-2 \)^2 = 4
C. \( x-1 \)^2 + \( y-2 \)^2 = 9
D. \( x+1 \)^2 + \( y-2 \)^2 = 9
Question 2
Find the vector (mathbf{a}) such that \( mathbf{a} cdot mathbf{b} = 3 \) and \( mathbf{a} cdot mathbf{c} = 2 \), where \( mathbf{b} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \) and \( mathbf{c} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \).
A. egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}
B. egin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}
C. egin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}
D. egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}
Question 3
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 4
Find the area of the triangle with base \( b = 8 \) and height \( h = 12 \).
A. ( 48 )
B. ( 60 )
C. ( 72 )
D. ( 80 )
Question 5
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = x + 1
B. y = x - 1
C. y = x + 2
D. y = x - 2
Question 6
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 1 \ 4 & 3 & 2 \ 1 & 2 & 3 \end{bmatrix} \).
A. -1
B. 0
C. 1
D. 2
Question 7
Find the surface area of the sphere with radius \( r = 5 \).
A. ( 100pi )
B. ( 50pi )
C. ( 25pi )
D. ( 10pi )
Question 8
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \)
B. \( x = -3 \)
C. \( x = 2 \)
D. \( x = 3 \)
Question 9
In a circle with center ( O ) and radius ( 4 ), a chord ( AB ) is drawn. If \( angle AOB = 60^{circ} \), find the length of ( AB ).
A. 4
B. 6
C. 8
D. 10
Question 10
Solve the system of linear equations \( egin{cases} x + y = 4 \ 2x - y = 3 \end{cases} \).
A. \( x = 2, y = 2 \)
B. \( x = 1, y = 3 \)
C. \( x = 3, y = 1 \)
D. \( x = 4, y = 0 \)
Question 11
Solve the equation \( \log_2 \( x^2 + 1 \ \) = 3).
A. x = 7
B. x = 5
C. x = 3
D. x = 1
Question 12
Find the area under the curve y = \( \frac{1}{x^2 + 1} \) from x = 0 to x = 1.
A. 0.46
B. 0.56
C. 0.67
D. 0.78
Question 13
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.
A. \( 6x + 2 \ \)
B. \( 6x - 2 \ \)
C. \( 6x + 1 \ \)
D. \( 6x - 1 \ \)
Question 14
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 15
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. x = 10^2
B. x = 10^4
C. x = 10^{-2}
D. x = 10^{-4}

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