POST UTME LASU 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. \( x = -\frac{5}{4} \)
B. \( x = \frac{3}{2} \)
C. \( x = -\frac{3}{2} \)
D. \( x = \frac{5}{4} \)
Question 2
Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)
Question 3
Solve the equation \( \log_2 \( x^2 + 1 \ \) = 3).
A. x = 7
B. x = 5
C. x = 3
D. x = 1
Question 4
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 5
Solve the system of equations u\sing matrices:\n\( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 6
Find the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).
A. \( \frac{4\pi}{3} \ \)
B. \( \frac{5\pi}{6} \ \)
C. \( \frac{7\pi}{6} \ \)
D. \( \frac{11\pi}{6} \ \)
Question 7
Solve the equation \log_{10} \( x^2 \) = 4.
A. 10
B. 100
C. 1000
D. 10000
Question 8
Find the area of the triangle with base \( b = 8 \) and height \( h = 12 \).
A. ( 48 )
B. ( 60 )
C. ( 72 )
D. ( 80 )
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 inequality \( x + 2 \ \)^2 - 4\( x - 1 \)^2 > 0).
A. x < -3 or x > 2
B. x < -1 or x > 3
C. x < -2 or x > 1
D. x < -4 or x > 4
Question 11
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 12
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366
B. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098
C. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098 + 354294
D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366
Question 13
Find the surface area of the sphere with radius \( r = 5 \).
A. ( 100pi )
B. ( 50pi )
C. ( 25pi )
D. ( 10pi )
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 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. \( x = 4, y = 0 \)

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