POST UTME DELSU 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let ( f(x) = \frac{1}{x^2 + 1} ). Find the value of \( int_{-1}^{1} f\( x \ \) , dx ).
A. \( \frac{pi}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{8} \)
D. \( \frac{pi}{16} \)
Question 2
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 = 32 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 64 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 128 )
Question 3
A vector ( vec{A} ) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x and y components of ( vec{A} ).
A. x-component: 4, y-component: 3
B. x-component: 3, y-component: 4
C. x-component: 4, y-component: 4
D. x-component: 3, y-component: 3
Question 4
Find the equation of the \tangent line to the curve \( y = x^2 - 2x + 1 \) at the point ( (1, 0) ).
A. y = x - 1
B. y = x + 1
C. y = 2x - 1
D. y = 2x + 1
Question 5
Let \( mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \). Find the vector ( mathbf{c} ) such that ( mathbf{c} ) is perp\endicular to both ( mathbf{a} ) and ( mathbf{b} ).
A. \( egin{pmatrix} -12 \ 10 \ 6 \end{pmatrix} \)
B. \( egin{pmatrix} 12 \ -10 \ -6 \end{pmatrix} \)
C. \( egin{pmatrix} 0 \ 0 \ 0 \end{pmatrix} \)
D. \( egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \)
Question 6
Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).
A. ( 4 )
B. ( 6 )
C. ( 8 )
D. ( 10 )
Question 7
The polynomial ( P(x) = x^3 - 6x^2 + 11x - 6 ) has a root at \( x = 1 \). Find the other two roots.
A. 2, 3
B. 1, 2
C. 1, 3
D. 2, 4
Question 8
Find the value of \( \frac{d}{dx} \( x^3 - 6x^2 + 11x - 6 \ \) ).
A. 3x^2 - 12x + 11
B. 3x^2 - 12x + 6
C. 3x^2 - 12x - 11
D. 3x^2 - 12x + 5
Question 9
Find the volume of the solid formed by revolving the area under the curve \( y = x^2 - 2x + 1 \) about the x-axis from \( x = 0 \) to \( x = 2 \).
A. \( \frac{1}{3} pi \times 2^3 \)
B. \( \frac{1}{3} pi \times 3^3 \)
C. \( \frac{1}{3} pi \times 4^3 \)
D. \( \frac{1}{3} pi \times 5^3 \)
Question 10
Solve the inequality \frac{x-2}{x+1}>0
A. x<-1 or x>2
B. x<-1 or x<2
C. x>1 or x>2
D. x<-1 or x<2
Question 11
Find the volume of the solid formed by revolving the region bounded by y = x^2 and y = 4 - x^2 about the x-axis
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 12
Solve for x in the equation \( 2^x + 2^{x+1} = 3 cdot 2^x \).
A. \( x = -1 \)
B. \( x = 0 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 13
A circle has a radius of 4 cm. Find the area of the circle.
A. 16π cm^2
B. 32π cm^2
C. 64π cm^2
D. 128π cm^2
Question 14
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = 90
C. x = 180
D. x = 270
Question 15
Given that ( f(x) = \frac{1}{x^2 + 1} ), find \( lim_{x \to infty} f\( x \ \) ).
A. 0
B. 1
C. ∞
D. undefined

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