POST UTME OAU 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( x^4 - 6x^2 + 8 = 0 \).
A. x = \pm 2
B. x = \pm \sqrt{2}
C. x = \pm 2\sqrt{2}
D. x = \pm 4
Question 2
In the diagram below, 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 3
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 4 - x \) about the x-axis.
A. 16π
B. 32π
C. 64π
D. 128π
Question 4
A circle has a diameter of 10 cm. Find the area of the circle.
A. 25π
B. 50π
C. 100π
D. 200π
Question 5
A vector \( \vec{a} = 2\hat{i} + 3\hat{j} \) is rotated by an angle of 30 degrees. What is the magnitude of the rotated vector?
A. 3.61
B. 4.24
C. 4.47
D. 4.58
Question 6
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 7
Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).
A. 6
B. 12
C. 18
D. 24
Question 8
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.24
B. 0.36
C. 0.48
D. 0.64
Question 9
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. 24\pi cm^3
B. 48\pi cm^3
C. 96\pi cm^3
D. 192\pi cm^3
Question 10
Find the determinant of the matrix \( egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{pmatrix} \).
A. -1
B. 1
C. 2
D. 3
Question 11
In the sequence ( 1, 2, 4, 8, 16, ... ), find the next term.
A. 32
B. 64
C. 128
D. 256
Question 12
A right-angled triangle has a hypotenuse of 10 cm and one leg of 6 cm. Find the length of the other leg.
A. 8 cm
B. 4 cm
C. 12 cm
D. 16 cm
Question 13
In the diagram below, ( AB ) is a diameter of the circle with center ( O ). If \( angle AOB = 60^{circ} \), find the measure of ( angle ACB ).
A. 30^{circ}
B. 45^{circ}
C. 60^{circ}
D. 90^{circ}
Question 14
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.
A. 14
B. 16
C. 18
D. 20
Question 15
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).
A. \( egin{pmatrix} 0 \ 0 \end{pmatrix} \)
B. \( egin{pmatrix} 1 \ 2 \end{pmatrix} \)
C. \( egin{pmatrix} -1 \ 2 \end{pmatrix} \)
D. \( egin{pmatrix} 1 \ -2 \end{pmatrix} \)

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