POST UTME ESUT 2017 Mathematics | Objective

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Question 1
Find the area of the triangle with vertices (2, 3), (4, 5), and (6, 7).
A. 9
B. 10
C. 11
D. 12
Question 2
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. f'(x) = 6x + 2
B. f'(x) = 6x - 2
C. f'(x) = 3x^2 + 2
D. f'(x) = 3x^2 - 2
Question 3
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. x > 4
B. x > 2
C. x < 4
D. x < 2
Question 4
Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].
A. -120
B. 120
C. 0
D. -60
Question 5
Solve the system of equations \begin{align*} x + y &= 2 \ x - y &= 1 \end{align*}.
A. \left\( 1, 1 \right \)
B. \left\( 1, -1 \right \)
C. \left\( -1, 1 \right \)
D. \left\( -1, -1 \right \)
Question 6
Find the derivative of the function f(x) = x^3 - 2x^2 + x - 1.
A. 3x^2 - 4x + 1
B. 3x^2 - 4x - 1
C. 3x^2 + 4x - 1
D. 3x^2 - 4x + 2
Question 7
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
Question 8
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 2 \cdot \frac{3^{10} - 1}{3 - 1}
B. 2 \cdot \frac{3^{11} - 1}{3 - 1}
C. 2 \cdot \frac{3^{12} - 1}{3 - 1}
D. 2 \cdot \frac{3^{13} - 1}{3 - 1}
Question 9
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. \( -1 \)
B. ( 0 )
C. ( 1 )
D. ( 2 )
Question 10
Find the equation of the circle with center $(2, 3)$ and radius $4$.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
Question 11
Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0.
A. \left\( -\infty, -1 \right \) \cup \left\( 1, \infty \right \)
B. \left\( -\infty, -3 \right \) \cup \left\( 1, \infty \right \)
C. \left\( -\infty, -3 \right \) \cup \left\( -1, 1 \right \) \cup \left\( 1, \infty \right \)
D. \left\( -\infty, -3 \right \) \cup \left\( 1, \infty \right \)
Question 12
Find the derivative of the function \( f(x) = \frac{1}{x^2 + 1} \).
A. \( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} \)
B. \( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} \)
C. \( f'(x) = \frac{x}{\( x^2 + 1 \)^2} \)
D. \( f'(x) = \frac{-x}{\( x^2 + 1 \)^2} \)
Question 13
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).
A. \( x \leq -1 \) or \( x \geq \frac{3}{2} \)
B. \( x \geq -1 \) or \( x \leq \frac{3}{2} \)
C. \( x \leq -1 \) or \( x \geq -\frac{3}{2} \)
D. \( x \geq -1 \) or \( x \leq -\frac{3}{2} \)
Question 14
A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?
A. \frac{1}{3}
B. \frac{1}{4}
C. \frac{1}{6}
D. \frac{1}{12}
Question 15
Find the equation of the \tangent line to the curve y = x^2 + 2x - 3 at the point (1, 2).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1

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