POST UTME FUTA 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 = 32
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 64
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 128
Question 2
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 3
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 4
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 5
Find the derivative of the function ( f(x) = \frac{1}{2} \log_{10} \( x^2 + 1 \) ) u\sing the chain rule.
A. \( \frac{1}{x^2 + 1} \)
B. \( \frac{1}{2} cdot \frac{2x}{x^2 + 1} \)
C. \( \frac{1}{2} cdot \frac{2x}{x^2 + 1} cdot \log_{10} \( x^2 + 1 \ \) )
D. \( \frac{1}{2} cdot \frac{2x}{x^2 + 1} cdot \log_{10} \( x^2 + 1 \ \) + \frac{1}{x^2 + 1} )
Question 6
Find the volume of the solid formed by revolving the region bounded by the curve $y = \sqrt{x}$, the $x$-axis, and the line $x = 4$ about the $x$-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 7
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 8
Find the equation of the circle with center $(0, 0)$ and radius $5$.
A. x^2 + y^2 = 25
B. x^2 + y^2 = 50
C. x^2 + y^2 = 75
D. x^2 + y^2 = 100
Question 9
Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ... ).
A. ( 62 )
B. ( 64 )
C. ( 66 )
D. ( 68 )
Question 10
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 11
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 12
In the diagram below, $ABCD$ is a square and $E$ is the midpoint of $AD$. If $AB = 8$, find the area of triangle $ADE$.
A. 16
B. 32
C. 64
D. 128
Question 13
Find the derivative of the function ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the power rule.
A. ( f'(x) = 3x^2 - 4x + 3 \)
B. ( f'(x) = x^2 - 2x + 1 \)
C. ( f'(x) = 3x^2 - 4x + 1 \)
D. ( f'(x) = x^2 - 2x - 1 \)
Question 14
Find the equation of the circle with center at ( (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 15
Find the vector ( mathbf{b} ) such that \( mathbf{a} cdot mathbf{b} = 10 \) and \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \).
A. \( egin{pmatrix} 5 \ 2 \end{pmatrix} \)
B. \( egin{pmatrix} 2 \ 5 \end{pmatrix} \)
C. \( egin{pmatrix} 5 \ -2 \end{pmatrix} \)
D. \( egin{pmatrix} -2 \ 5 \end{pmatrix} \)

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