POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x - 5 > 3x + 2 \).
A. x < -3
B. x > -3
C. x < 3
D. x > 3
Question 2
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ).
A. x = \frac{\pi}{2}
B. x = \frac{\pi}{4}
C. x = \\frac{3\\pi}{4}
D. x = \\frac{5\\pi}{4}
Question 3
A right-angled triangle has a hypotenuse of length 10 units and one leg of length 6 units. Find the length of the other leg.
A. 4
B. 6
C. 8
D. 10
Question 4
Solve the equation \( 2^x + 2^x = 64 \).
A. 3
B. 4
C. 5
D. 6
Question 5
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. -1
C. 2
D. 3
Question 6
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and (6, 7).
A. x^2 + y^2 + 4x + 6y - 11 = 0
B. x^2 + y^2 + 2x + 4y - 9 = 0
C. x^2 + y^2 + 6x + 2y - 13 = 0
D. x^2 + y^2 + 8x + 10y - 15 = 0
Question 7
Find the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...
A. 2
B. 4
C. 8
D. 16
Question 8
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = \frac{2}{2}x + \frac{1}{2}
B. y = \frac{1}{2}x + \frac{3}{2}
C. y = 2x - 1
D. y = 2x + 1
Question 9
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{x}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-x}{\( x^2 + 1 \ \)^2} )
Question 10
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).
A. \frac{1}{2} \times 3 \times 4 = 6
B. \frac{1}{2} \times 3 \times 4 = 12
C. \frac{1}{2} \times 3 \times 4 = 18
D. \frac{1}{2} \times 3 \times 4 = 24
Question 11
Find the area of the triangle with vertices \( A(0, 0), B(3, 0), C(1, 2) \).
A. 3 square units
B. 6 square units
C. 9 square units
D. 12 square units
Question 12
A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.8 & \text{if } X = 2 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 1.
A. 0.2
B. 0.8
C. 1
D. 0.6
Question 13
Find the derivative of the function ( f(x) = \frac{1}{x^2} ).
A. f'(x) = \frac{-2}{x^3}
B. f'(x) = \frac{2}{x^3}
C. f'(x) = \frac{-1}{x^3}
D. f'(x) = \frac{1}{x^3}
Question 14
A rec\tangular box has dimensions 5 cm x 3 cm x 2 cm. Find the volume of the box.
A. 30
B. 40
C. 50
D. 60
Question 15
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. 4
B. 6
C. 8
D. 10

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