POST UTME CALEB UNIVERSITY 2020 Mathematics | Objective

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Question 1
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 2
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 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 4
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 5
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 6
Find the sum of the first 10 terms of the geometric series ( 2, 6, 18, ldots ).
A. ( 2040 )
B. ( 2050 )
C. ( 2060 )
D. ( 2070 )
Question 7
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 8
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 9
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
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 10
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. Find the expected value of X.
A. 1.1
B. 1.3
C. 1.5
D. 1.7
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
Find the determinant of the matrix [egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}].
A. 0
B. 1
C. 2
D. 3
Question 13
Find the value of $\sqrt{16} + \sqrt{9}$.
A. 5
B. 7
C. 8
D. 10
Question 14
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 15
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

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