POST UTME UNILAG 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 ). Find the equation of the \tangent line at the point ( (4, 7) ).
A. y = x + 1
B. y = x - 1
C. y = -x + 7
D. y = x - 7
Question 2
A 3x3 matrix is given by A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. Find the determinant of the matrix.
A. 0
B. 1
C. 2
D. 3
Question 3
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 5 \) and \( mathbf{a} cdot mathbf{c} = 3 \), where \( mathbf{b} = \( 2, 1, 3 \ \) ) and \( mathbf{c} = \( 1, 2, 1 \ \) ).
A. (1, 2, 3)
B. (2, 1, 3)
C. (3, 2, 1)
D. (1, 3, 2)
Question 4
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. \( 4 \ \)
B. \( 6 \ \)
C. \( 8 \ \)
D. \( 10 \ \)
Question 5
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{pi}{2} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = pi \)
Question 6
Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} \)
C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)
D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)
Question 7
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 13
B. 15
C. 17
D. 19
Question 8
Solve the system of linear equations \( egin{cases} x + y + z = 6 \ 2x - 3y + z = 3 \ x - 2y + 3z = 2 \end{cases} \) u\sing substitution.
A. \left\( 1, 2, 3 \right \)
B. \left\( 2, 1, 3 \right \)
C. \left\( 3, 2, 1 \right \)
D. \left\( 1, 3, 2 \right \)
Question 9
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. \left[ \frac{x^3}{3} + x^2 - 3x \right]_0^2
B. \left[ \frac{x^3}{3} + x^2 - 3x \right]_1^2
C. \left[ \frac{x^3}{3} + x^2 - 3x \right]_0^1
D. \left[ \frac{x^3}{3} + x^2 - 3x \right]_1^3
Question 10
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If 75% of the scores lie within 2 s\tandard deviations of the mean, what is the lower limit of the range of scores?
A. \( 40 \ \)
B. \( 50 \ \)
C. \( 60 \ \)
D. \( 70 \ \)
Question 11
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = 2x - 3
D. y = 2x + 3
Question 12
A vector \vec{a} has a magnitude of 5 units and makes an angle of 60\circ with the positive x-axis. Find the x and y components of \vec{a}.
A. \vec{a} = 2.5 \hat{i} + 4.33 \hat{j}
B. \vec{a} = 4.33 \hat{i} + 2.5 \hat{j}
C. \vec{a} = 2.5 \hat{i} - 4.33 \hat{j}
D. \vec{a} = 4.33 \hat{i} - 2.5 \hat{j}
Question 13
Find the volume of the solid formed by revolving the region bounded by the curve [ y = x^2 ] about the x-axis.
A. \frac{\pi}{3}
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{\pi}{6}
Question 14
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the quotient rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{1}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^2} )

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