POST UTME UNIPORT 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 1234
B. 2345
C. 3456
D. 4567
Question 4
Solve the quadratic equation \begin{align*} x^2 + 4x + 4 &= 0 \end{align*}.
A. \text{Solution: } x = -2
B. \text{Solution: } x = -1
C. \text{Solution: } x = 0
D. \text{Solution: } x = 1
Question 5
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 6
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 7
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
Question 8
Find the volume 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. \( \frac{16pi}{3} \)
B. \( \frac{32pi}{3} \)
C. \( \frac{64pi}{3} \)
D. \( \frac{128pi}{3} \)
Question 9
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}} )
B. ( f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}} )
C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}} )
D. ( f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}} )
Question 10
Find the volume of the sphere with radius 4 cm.
A. 256π cm³
B. 512π cm³
C. 768π cm³
D. 1024π cm³
Question 11
Let X and Y be indep\endent events with P(X) = 0.4 and P(Y) = 0.6. Find P(X ∩ Y).
A. 0.24
B. 0.36
C. 0.48
D. 0.60
Question 12
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 13
Find the equation of the plane pas\sing through the points $A(1,2,3)$ and $B(2,3,4)$ and perp\endicular to the line $\vec{r}=\begin{pmatrix}1\ 2\ 3\end{pmatrix}+t\begin{pmatrix}1\ 1\ 1\end{pmatrix}.$
A. x+y+z=6
B. x-y+z=4
C. x+y-z=2
D. x-y-z=0
Question 14
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 15
Solve the system of linear equations u\sing matrices: \[ \begin{array}{ccc} x+2y-3z&=&7\ 2x-y+z&=&5\ -x+3y-2z&=&1\ \end{array}\]
A. x=1, y=2, z=3
B. x=2, y=1, z=4
C. x=3, y=2, z=5
D. x=4, y=3, z=6

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