POST UTME UNIPORT 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( 2^x + 2^{-x} = 3 \) for x.
A. \( x = \log_2 2 \)
B. \( x = \log_2 3 \)
C. \( x = \log_2 4 \)
D. \( x = \log_2 6 \)
Question 2
A cylindrical \tank with a radius of 4m and a height of 6m is filled with water. If the density of water is 1000 kg/m^3, calculate the volume of water in the \tank.
A. 120 m^3
B. 150.8 m^3
C. 180 m^3
D. 200 m^3
Question 3
Find the sum of the infinite geometric series 1 + x + x^2 + ...
A. 1/\( 1-x \)
B. 1/\( 1+x \)
C. 1/\( 1-x^2 \)
D. 1/\( 1+x^2 \)
Question 4
Find the surface area of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 4 - x^2 \) about the x-axis.
A. ( 16pi )
B. ( 32pi )
C. ( 64pi )
D. ( 128pi )
Question 5
Find the surface area of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 64π
B. 128π
C. 256π
D. 512π
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
B. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
C. \( x > -\frac{5}{4} \) and \( x < \frac{3}{2} \)
D. \( x < -\frac{5}{4} \) and \( x > \frac{3}{2} \)
Question 7
Solve the equation $\log_{10}\( x^2-4 \)=2.$
A. x=\pm 2\sqrt{10}
B. x=\pm 10
C. x=\pm 2\sqrt{5}
D. x=\pm 5
Question 8
Find the volume of the solid formed by revolving the region bounded by the curves $y=x^2$ and $y=4x$ about the x-axis.
A. \frac{32}{15}\pi
B. \frac{64}{15}\pi
C. \frac{128}{15}\pi
D. \frac{256}{15}\pi
Question 9
Solve the matrix equation AX = B, where A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}, X = egin{bmatrix} x \ y \end{bmatrix}, and B = egin{bmatrix} 5 \ 6 \end{bmatrix}.
A. egin{bmatrix} 1 \ 2 \end{bmatrix}
B. egin{bmatrix} 2 \ 3 \end{bmatrix}
C. egin{bmatrix} 3 \ 4 \end{bmatrix}
D. egin{bmatrix} 4 \ 5 \end{bmatrix}
Question 10
A histogram represents the distribution of exam scores of a class of 50 students. The histogram has 5 bars, each representing a score range of 10 points. The heights of the bars are 8, 12, 15, 10, and 5 units, respectively. Find the mean score of the class.
A. 8
B. 10
C. 12
D. 15
Question 11
Find the equation of the circle with center at (2, 3) and radius 4.
A. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \text{Equation: } \( x + 2 \)^2 + \( y - 3 \)^2 = 16
C. \text{Equation: } \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \text{Equation: } \( x + 2 \)^2 + \( y + 3 \)^2 = 16
Question 12
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24π cm^3
B. 48π cm^3
C. 72π cm^3
D. 96π cm^3
Question 13
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 32π
B. 64π
C. 128π
D. 256π
Question 14
Determine the value of x in the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. 1
B. -1
C. 3
D. -3
Question 15
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. \text{Equation: } y = 1x + 1
B. \text{Equation: } y = 2x + 1
C. \text{Equation: } y = 3x + 1
D. \text{Equation: } y = 4x + 1

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