POST UTME OAU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
A rec\tangular box has dimensions 5 cm, 8 cm, and 3 cm. Find the surface area of the box.
A. \( 2\( 5 \times 8 + 8 \times 3 + 3 \times 5 \ \) )
B. \( 2\( 5 \times 8 + 8 \times 3 + 3 \times 5 \ \) + 2\( 5 \times 3 + 8 \times 3 + 5 \times 8 \) )
C. \( 2\( 5 \times 8 + 8 \times 3 + 3 \times 5 \ \) + 2\( 5 \times 3 + 8 \times 3 + 5 \times 8 \) + 2\( 5 \times 8 + 5 \times 3 + 8 \times 3 \) )
D. \( 2\( 5 \times 8 + 8 \times 3 + 3 \times 5 \ \) + 2\( 5 \times 3 + 8 \times 3 + 5 \times 8 \) + 2\( 5 \times 8 + 5 \times 3 + 8 \times 3 \) + 2\( 5 \times 5 + 8 \times 8 + 3 \times 3 \) )
Question 3
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 7
C. 8
D. 9
Question 4
A random experiment has two indep\endent events A and B. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events A and B occur?
A. 0.24
B. 0.48
C. 0.64
D. 0.76
Question 5
Solve the system of equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \).
A. 1, 1
B. 1, -1
C. -1, 1
D. -1, -1
Question 6
In a histogram with 5 classes, the mean of the data is 25 and the s\tandard deviation is 3. If the class width is 5, what is the value of the class mark of the class containing the mean?
A. 22.5
B. 25
C. 27.5
D. 30
Question 7
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism in cubic centimeters.
A. 30
B. 30
C. 30
D. 30
Question 8
Find the surface area of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. 16π
B. 32π
C. 64π
D. 128π
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{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2}{\( x^2 + 1 \ \)^2} )
Question 10
A circle has a diameter of 10 cm. Find the area of the circle in square centimeters.
A. 78.5
B. 78.54
C. 78.5
D. 78.54
Question 11
Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).
A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 )
B. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 25 )
C. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 9 )
D. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 9 )
Question 12
In the diagram below, the graph of \( y = \frac{1}{2} \tan^{-1} \( 2x \ \) ) is shown. What is the value of ( x ) at the point where the graph intersects the line \( y = 2 \)?
A. 1
B. -1
C. 0
D. 2
Question 13
A set of 5 numbers has a mean of 20 and a s\tandard deviation of 2. If the numbers are 18, 22, 25, and 28, what is the fifth number?
A. 20
B. 22
C. 25
D. 28
Question 14
Solve the inequality \( |2x - 1| > 3 \).
A. \( x < -1 \) or \( x > 2 \)
B. \( x < -2 \) or \( x > 1 \)
C. \( x < -3 \) or \( x > 2 \)
D. \( x < -1 \) or \( x > 3 \)
Question 15
A polynomial function is defined as ( f(x) = 2x^3 - 5x^2 + 3x - 1 ). Find the derivative of the function.
A. ( f'(x) = 6x^2 - 10x + 3 )
B. ( f'(x) = 4x^2 - 6x + 1 )
C. ( f'(x) = 2x^2 - 5x + 3 )
D. ( f'(x) = x^2 - 2x + 1 )

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