POST UTME CALEB UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 5 terms of the geometric series \( 1 + 2 + 4 + 8 + ldots \).
A. 31
B. 32
C. 33
D. 34
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
C. \( x < -\frac{1}{2} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 4
Find the value of \( \sin 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \).
A. \( \frac{24}{25} \)
B. \( \frac{16}{25} \)
C. \( \frac{20}{25} \)
D. \( \frac{12}{25} \)
Question 5
A matrix A has the following elements: \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}. Find the determinant of A.
A. 0
B. 1
C. 2
D. 3
Question 6
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \frac{-2 \pm \sqrt{0}}{2}
B. \frac{-2 \pm \sqrt{4}}{2}
C. \frac{-2 \pm \sqrt{8}}{2}
D. \frac{-2 \pm \sqrt{16}}{2}
Question 7
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 10
B. 12
C. 14
D. 16
Question 8
Find the magnitude of the vector \( \vec{a} = \langle 3, 4 \rangle \) and the vector \( \vec{b} = \langle -2, 1 \rangle \).
A. \sqrt{3^2 + 4^2} = 5
B. \sqrt{\( -2 \)^2 + 1^2} = \sqrt{5}
C. \sqrt{3^2 + \( -2 \)^2} = \sqrt{13}
D. \sqrt{4^2 + 1^2} = \sqrt{17}
Question 9
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 - 2x + 1 \) and the x-axis about the x-axis.
A. \( \frac{1}{3} pi \)
B. \( \frac{2}{3} pi \)
C. \( \frac{3}{2} pi \)
D. \( \frac{4}{3} pi \)
Question 10
Find the area under the curve y = x^3 from x = -1 to x = 1.
A. \frac{2}{3}
B. \frac{4}{3}
C. \frac{6}{3}
D. \frac{8}{3}
Question 11
Find the equation of the circle with center (C(2, 3)) and radius 4.
A. \left\( x - 2\right \)^2 + \left\( y - 3\right \)^2 = 16
B. \left\( x - 3\right \)^2 + \left\( y - 2\right \)^2 = 16
C. \left\( x - 4\right \)^2 + \left\( y - 2\right \)^2 = 16
D. \left\( x - 2\right \)^2 + \left\( y - 4\right \)^2 = 16
Question 12
Solve for x in the equation \( 2^x + 2^{x+1} = 3 \cdot 2^{x+2} \).
A. -2
B. -1
C. 0
D. 1
Question 13
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).
A. \( \frac{pi}{4} \)
B. \( \frac{3pi}{4} \)
C. \( \frac{5pi}{4} \)
D. \( \frac{7pi}{4} \)
Question 14
Solve the system of equations \( egin{cases} x + y + z = 6 \ x + 2y + 3z = 12 \ 2x + 3y + 5z = 20 \end{cases} \) u\sing matrices.
A. \( egin{cases} x = 2 \ y = 2 \ z = 2 \end{cases} \)
B. \( egin{cases} x = 3 \ y = 2 \ z = 1 \end{cases} \)
C. \( egin{cases} x = 1 \ y = 3 \ z = 2 \end{cases} \)
D. \( egin{cases} x = 4 \ y = 1 \ z = 1 \end{cases} \)
Question 15
Solve the equation $\frac{1}{2}x^2 + 3x - 4 = 0$.
A. 4
B. -2
C. -4
D. 2

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