POST UTME PAN-ATLANTIC UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \( \sin (2x) \) when \( x = \frac{\pi}{6} \).
A. \frac{1}{2}
B. \frac{\sqrt{3}}{2}
C. \frac{\sqrt{2}}{2}
D. \frac{\sqrt{6}}{2}
Question 2
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1
Question 3
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 )
A. 6x + 2
B. 3x^2 + 2
C. 6x - 2
D. 3x^2 - 2
Question 4
Solve the equation \( \log_2 (x) = 3 \).
A. 8
B. 16
C. 32
D. 64
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 6
Find the magnitude of the vector \( \vec{a} = \langle 3, 4 \rangle \ \) and the vector \( \vec{b} = \langle -2, 1 \rangle \ \).
A. \( \sqrt{29} \)
B. \( \sqrt{5} \)
C. \( \sqrt{2} \)
D. \( \sqrt{3} \)
Question 7
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )
Question 8
A rec\tangular box has dimensions 5 cm, 8 cm, and 3 cm. Find the volume of the box in cubic centimeters.
A. 120
B. 150
C. 180
D. 200
Question 9
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 10
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 6 \) and \( mathbf{a} cdot mathbf{c} = 3 \), where \( mathbf{b} = egin{bmatrix} 2 \ 3 \end{bmatrix} \) and \( mathbf{c} = egin{bmatrix} 1 \ 4 \end{bmatrix} \)
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \ 2 \end{bmatrix}
D. \begin{bmatrix} 4 \ 3 \end{bmatrix}
Question 11
A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even and the coin lands heads up, find the probability that the number on the die is greater than 3.
A. 1/4
B. 1/6
C. 1/2
D. 2/3
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( -\frac{5}{4}, \frac{3}{2} \right \)
B. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( -\frac{5}{4}, \infty \right \)
C. \left\( -\infty, -\frac{5}{4} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
D. \left\( -\frac{5}{4}, \frac{3}{2} \right \)
Question 13
A circle has an equation of the form \( x^2 + y^2 + Dx + Ey + F = 0 \). If the circle passes through the points ( (1,2) ) and ( (3,4) ), find its equation.
A. \( x^2 + y^2 - 4x - 6y + 5 = 0 \)
B. \( x^2 + y^2 + 4x + 6y + 5 = 0 \)
C. \( x^2 + y^2 - 6x - 4y + 5 = 0 \)
D. \( x^2 + y^2 + 6x + 4y + 5 = 0 \)
Question 14
A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 15
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \)
A. 1
B. -1
C. 2
D. 3

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