POST UTME AAUA 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \log_{10} \( x^2 \) = 4.
A. 10
B. 100
C. 1000
D. 10000
Question 2
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) if it exists.
A. \begin{pmatrix} 6 \\ -4 \end{pmatrix}
B. \begin{pmatrix} -6 \\ 4 \end{pmatrix}
C. \begin{pmatrix} 0 \\ 0 \end{pmatrix}
D. \begin{pmatrix} 3 \\ -2 \end{pmatrix}
Question 3
Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}.
A. 0
B. 1
C. 2
D. 3
Question 4
Find the equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).
A. \( y = \frac{1}{2}x + \frac{1}{2} \)
B. \( y = \frac{1}{2}x - \frac{1}{2} \)
C. \( y = 2x - 1 \)
D. \( y = 2x + 1 \)
Question 5
Let \( A = \{ 1, 2, 3, 4, 5 \} \) and \( B = \{ 2, 3, 5, 7, 9 \} \). Find the symmetric difference of sets ( A ) and ( B ).
A. \{ 1, 4 \}
B. \{ 1, 2, 3, 4, 5, 7, 9 \}
C. \{ 2, 3, 5, 7, 9 \}
D. \{ 1, 2, 3, 4, 5, 7, 9 \}
Question 6
Find the value of \( int_{0}^{2} \( 2x^2 + 3x - 1 \ \) dx ).
A. 4
B. 6
C. 8
D. 10
Question 7
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
B. 32\pi
C. 48\pi
D. 64\pi
Question 8
Solve the inequality \frac{x}{2} - 3 > 2.
A. x > 10
B. x < 10
C. x > 4
D. x < 4
Question 9
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?
A. \frac{1}{3}
B. \frac{1}{6}
C. \frac{2}{6}
D. \frac{3}{6}
Question 10
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
C. \left\( x - 4 \right \)^2 + \left\( y - 3 \right \)^2 = 16
D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16
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 = 25
C. \( x-2 \)^2 + \( y-3 \)^2 = 36
D. \( x-2 \)^2 + \( y-3 \)^2 = 49
Question 12
Find the value of \( \frac{d}{dx} \( x^3 - 3x^2 + 2x - 1 \ \) ).
A. 3x^2 - 6x + 2
B. 3x^2 - 6x + 1
C. 3x^2 - 6x - 1
D. 3x^2 + 6x - 1
Question 13
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. 6x + 2
B. 6x - 2
C. 3x^2 + 2
D. 3x^2 - 2
Question 14
Find the volume of the cylinder with radius 6 cm and height 8 cm.
A. 768\pi \text{ cm}^3
B. 512\pi \text{ cm}^3
C. 384\pi \text{ cm}^3
D. 256\pi \text{ cm}^3
Question 15
A histogram is constructed from the following data: 2, 4, 6, 8, 10. Find the mean of the data.
A. 5
B. 6
C. 7
D. 8

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