POST UTME CHRISTOPHER UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).
A. \( y = \frac{1}{2}x + \frac{1}{2} \)
B. \( y = 2x - 1 \)
C. \( y = \frac{1}{2}x - 2 \)
D. \( y = 2x + 1 \)
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x < -1 \) or \( x > \frac{3}{2} \)
Question 3
Find the area of the triangle with vertices ( (0,0), (3,0), (0,4) ).
A. \( \frac{1}{2} cdot 3 cdot 4 \)
B. \( \frac{1}{2} cdot 3 cdot 4 cdot \sin 60^circ \)
C. \( \frac{1}{2} cdot 3 cdot 4 cdot \cos 60^circ \)
D. \( \frac{1}{2} cdot 3 cdot 4 cdot \tan 60^circ \)
Question 4
Find the equation of the circle with center \( -2, 3 \) and radius \( 4 \).
A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
C. \left\( x + 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
D. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
Question 5
Solve the inequality [ 2x - 5 > 3x + 2 \] for [ x \in \mathbb{R} \].
A. x < -3
B. x > -3
C. x < 3
D. x > 3
Question 6
Find the surface area of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \frac{8}{3}
B. \frac{4}{3}
C. \frac{8}{5}
D. \frac{4}{5}
Question 7
Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 8
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \) u\sing the quadratic formula.
A. \frac{-5 + \sqrt{37}}{4}
B. \frac{-5 - \sqrt{37}}{4}
C. \frac{-5 + \sqrt{37}}{2}
D. \frac{-5 - \sqrt{37}}{2}
Question 9
Find the area under the curve \( y = e^x \) from \( x = 0 \) to \( x = 1 \).
A. e - 1
B. e + 1
C. e^2 - 1
D. e^2 + 1
Question 10
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant method.
A. \begin{pmatrix} 11 \ 2 \end{pmatrix}
B. \begin{pmatrix} -11 \ 2 \end{pmatrix}
C. \begin{pmatrix} 11 \ -2 \end{pmatrix}
D. \begin{pmatrix} -11 \ -2 \end{pmatrix}
Question 11
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ).
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{2}{\( x^2 + 1 \)^2}
D. \frac{-2}{\( x^2 + 1 \)^2}
Question 12
Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 4 \ 5 & 1 & 2 \ 3 & 2 & 1 \end{array} ].
A. -1
B. 1
C. 2
D. 3
Question 13
Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \) u\sing substitution.
A. x = \frac{3}{2}, y = \frac{1}{2}
B. x = \frac{1}{2}, y = \frac{3}{2}
C. x = 2, y = 1
D. x = 1, y = 2
Question 14
Find the sum of the first ( n ) terms of the geometric progression ( 2, 6, 18, ldots ).
A. \( 2 cdot \frac{6^n - 1}{5} \)
B. \( 2 cdot \frac{6^n + 1}{5} \)
C. \( 2 cdot \frac{6^n - 1}{6} \)
D. \( 2 cdot \frac{6^n + 1}{6} \)
Question 15
Solve the system of equations \( x + y = 4 \) and \( x^2 + y^2 = 16 \).
A. \( x = 2, y = 2 \)
B. \( x = 2, y = 2 \) or \( x = -2, y = -2 \)
C. \( x = 2, y = 2 \) or \( x = -2, y = -2 \) or \( x = 0, y = 4 \)
D. \( x = 2, y = 2 \) or \( x = -2, y = -2 \) or \( x = 4, y = 0 \)

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