POST UTME KSU 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve y = x^2 + 2x - 3 from x = 1 to x = 3.
A. 20
B. 30
C. 40
D. 50
Question 2
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for (x).
A. \( x = \frac{\pi}{4} \)
B. \( x = \frac{3\pi}{4} \)
C. \( x = \frac{5\pi}{4} \)
D. \( x = \frac{7\pi}{4} \)
Question 3
A polynomial function f(x) has a root at x = -2 and a root at x = 3. If f(x) has a degree of 4, find the product of the roots of f(x).
A. -6
B. 6
C. 12
D. -12
Question 4
Find the derivative of the function ( f(x) = x^2 \sin x ).
A. ( f'(x) = 2x \sin x + x^2 \cos x )
B. ( f'(x) = 2x \sin x + x^2 \cos x )
C. ( f'(x) = 2x \sin x + x^2 \cos x )
D. ( f'(x) = 2x \sin x + x^2 \cos x )
Question 5
Find the area of the triangle with vertices ((2,3)), ((4,5)), and ((6,7)).
A. ( 10 )
B. ( 20 )
C. ( 30 )
D. ( 40 )
Question 6
Solve the equation \( \sin^2 x + \cos^2 x = \frac{3}{4} \) for ( x in [0, 2pi] ).
A. \( x = \frac{pi}{6} \) or \( x = \frac{5pi}{6} \)
B. \( x = \frac{pi}{4} \) or \( x = \frac{3pi}{4} \)
C. \( x = \frac{pi}{3} \) or \( x = \frac{2pi}{3} \)
D. \( x = \frac{pi}{2} \) or \( x = \frac{3pi}{2} \)
Question 7
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 8
If ( f(x) = \frac{1}{x^2 - 4} ), find \( f^{-1}\( x \ \) ).
A. \( f^{-1}\( x \ \) = \frac{1}{x^2 + 4} )
B. \( f^{-1}\( x \ \) = \frac{1}{x^2 - 4} )
C. \( f^{-1}\( x \ \) = \frac{1}{x^2 + 2} )
D. \( f^{-1}\( x \ \) = \frac{1}{x^2 - 2} )
Question 9
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis from \( x = 0 \) to \( x = 2 \).
A. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx )
B. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx + pi int_{0}^{2} \( x^2 \)^2 - (2x)^2 , dx )
C. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx - pi int_{0}^{2} \( x^2 \)^2 - (2x)^2 , dx )
D. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx )
Question 10
Find the equation of the line pas\sing through the points (1, 2) and (3, 4).
A. y = 2x - 1
B. y = 2x + 1
C. y = 3x - 1
D. y = 3x + 1
Question 11
A particle moves in a straight line with an initial velocity of 5 m/s. After 2 seconds, its velocity increases to 10 m/s. Find the acceleration of the particle.
A. 2.5 m/s^2
B. 5 m/s^2
C. 10 m/s^2
D. 15 m/s^2
Question 12
If \( A = egin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix} \) and \( B = egin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} \), find ( AB ).
A. \( AB = egin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix} \)
B. \( AB = egin{pmatrix} 3 & 1 \ 1 & 3 \end{pmatrix} \)
C. \( AB = egin{pmatrix} 2 & 2 \ 2 & 2 \end{pmatrix} \)
D. \( AB = egin{pmatrix} 3 & 2 \ 2 & 3 \end{pmatrix} \)
Question 13
Simplify the expression \sqrt{48} \times \sqrt{18}.
A. 12\sqrt{3}
B. 24\sqrt{2}
C. 36\sqrt{3}
D. 48\sqrt{2}
Question 14
Find the sum of the infinite geometric series with first term 2 and common ratio 1/2.
A. ( 4 )
B. ( 8 )
C. ( 16 )
D. ( 32 )
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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