POST UTME ESUT 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

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 ( 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{-2x}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 3
If $f(x) = \frac{1}{x^2 + 1}$, find $f'(x)$.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{x}{\( x^2 + 1 \)^2}
D. \frac{-x}{\( x^2 + 1 \)^2}
Question 4
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
Question 5
Solve the system of equations u\sing matrices: \begin{align*} x + y + z &= 6, \ x + 2y + 3z &= 11, \ x + 3y + 6z &= 16. \end{align*}
A. \begin{bmatrix} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 3 & 6 \end{bmatrix}
B. \begin{bmatrix} 1 & 2 & 3 \ 1 & 3 & 6 \ 1 & 6 & 11 \end{bmatrix}
C. \begin{bmatrix} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 3 & 6 \end{bmatrix}^{-1}
D. \begin{bmatrix} 1 & 2 & 3 \ 1 & 3 & 6 \ 1 & 6 & 11 \end{bmatrix}^{-1}
Question 6
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 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 vector \mathbf{a} such that \mathbf{a} \cdot \mathbf{b} = 10 and \mathbf{a} \cdot \mathbf{c} = 5, where \mathbf{b} = \begin{pmatrix} 2 \ 3 \end{pmatrix} and \mathbf{c} = \begin{pmatrix} 1 \ 4 \end{pmatrix}.
A. \begin{pmatrix} 5 \ 2 \end{pmatrix}
B. \begin{pmatrix} 3 \ 1 \end{pmatrix}
C. \begin{pmatrix} 4 \ 3 \end{pmatrix}
D. \begin{pmatrix} 2 \ 5 \end{pmatrix}
Question 9
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 10
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 11
Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \).
A. \( x = \frac{3}{2}, y = \frac{1}{2} \)
B. \( x = \frac{1}{2}, y = \frac{3}{2} \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 0 \)
Question 12
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 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
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 15
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
A. (1, 5)
B. (5, 1)
C. (2, 2)
D. (3, 3)

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