POST UTME PAN-ATLANTIC UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. 2 < x < 4
B. x > 4
C. x < 2
D. x = 4
Question 3
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 100.48
C. 200.96
D. 400.96
Question 4
A circle has a radius of 4 cm. Find the area of the circle.
A. \pi r^2
B. \pi r^2 + \pi r^2
C. \pi r^2 - \pi r^2
D. \pi r^2 + \pi r^2 + \pi r^2
Question 5
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -1 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) if ( mathbf{a} ) and ( mathbf{b} ) are orthogonal.
A. \( egin{pmatrix} 3 \ -2 \end{pmatrix} \)
B. \( egin{pmatrix} -3 \ 2 \end{pmatrix} \)
C. \( egin{pmatrix} 0 \ 0 \end{pmatrix} \)
D. \( egin{pmatrix} 1 \ 2 \end{pmatrix} \)
Question 6
A particle moves in a straight line with an initial velocity of 5 m/s. If the acceleration is 2 m/s^2, find the velocity after 3 seconds.
A. 13
B. 15
C. 17
D. 19
Question 7
Solve the equation \( 2^x + 2^{-x} = 3 \).
A. x = 1
B. x = 2
C. x = \log_2 2
D. x = \log_2 3
Question 8
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 9
A circle has equation \( x - 1 \ \)^2 + \( y - 2 \)^2 = 4 ). Find the equation of the \tangent line at point ( (3, 5) ).
A. y - 5 = -\frac{1}{2}\( x - 3 \)
B. y - 5 = \frac{1}{2}\( x - 3 \)
C. y - 5 = \( x - 3 \)
D. y - 5 = -\( x - 3 \)
Question 10
Solve the system of equations $x + y = 2$ and $xy = 1$.
A. (1, 1)
B. \( 1, -1 \)
C. \( -1, 1 \)
D. \( -1, -1 \)
Question 11
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the expected value of ( X ).
A. ( 2 )
B. ( 3 )
C. ( 4 )
D. ( 5 )
Question 12
Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.
A. 4/3
B. 2/3
C. 1/3
D. 1/2
Question 13
Solve the inequality $|x - 2| > 3$.
A. \( -∞, -1 \) ∪ (4, ∞)
B. \( -∞, 1 \) ∪ (4, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 4 \) ∪ (1, ∞)
Question 14
Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).
A. \(x < -3\) or \(x > 2\)
B. \(-3 < x < 2\)
C. \(x < -3\) or \(2 < x < 3\)
D. \(x > 3\)
Question 15
Find the sum of the first 10 terms of the geometric series \(\sum_{n=1}^{10} 2^n\).
A. 2047
B. 2048
C. 2049
D. 2050

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