POST UTME FUTA 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}.
A. \left\{ \left\( - \frac{5}{7}, \frac{27}{7} \right \) \right\}
B. \left\{ \left\( - \frac{5}{7}, - \frac{27}{7} \right \) \right\}
C. \left\{ \left\( \frac{5}{7}, - \frac{27}{7} \right \) \right\}
D. \left\{ \left\( \frac{5}{7}, \frac{27}{7} \right \) \right\}
Question 2
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. \( \frac{4}{3} pi \)
B. \( \frac{8}{3} pi \)
C. \( \frac{16}{3} pi \)
D. \( \frac{32}{3} pi \)
Question 3
Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ... ).
A. ( 62 )
B. ( 64 )
C. ( 66 )
D. ( 68 )
Question 4
In the diagram below, $ABCD$ is a rec\tangle and $E$ is the midpoint of $AD$. If $AB = 6$ and $BC = 8$, find the area of triangle $ADE$.
A. 12
B. 16
C. 24
D. 32
Question 5
Solve the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 2 \)
Question 6
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 3 \)
D. \( y = 2x + 3 \)
Question 7
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \( -3, -1 \) \cup (1, 3)
B. \( -3, -1 \) \cup (1, 3) \cup \( 4, \infty \)
C. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -4 \)
D. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -4 \) \cup \( 4, \infty \)
Question 8
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \ \)
B. \( x = 0 \ \)
C. \( x = -1 \ \)
D. \( x = 1 \ \)
Question 9
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 = 4
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
Question 10
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ 11 \end{bmatrix} \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 11
Find the volume 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{16}{15}\pi
B. \frac{32}{15}\pi
C. \frac{64}{15}\pi
D. \frac{128}{15}\pi
Question 12
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 13
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 14
Find the area of the triangle formed by the points ( A(2, 3), B(4, 5), C(6, 7) ).
A. ( 10 )
B. ( 12 )
C. ( 15 )
D. ( 20 )
Question 15
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. \( x > 3 \ \)
B. \( x < 3 \ \)
C. \( x = 3 \ \)
D. \( x = 2 \ \)

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