POST UTME ACHIEVERS UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x^2 - 8 \) - \( x^2 - 4 \)\( 2x^2 + 4x \)}{\( x^2 - 4 \)^2}
C. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x^2 + 8 \) - \( x^2 - 4 \)\( 2x^2 - 4x \)}{\( x^2 - 4 \)^2}
D. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x^2 - 8 \) - \( x^2 - 4 \)\( 2x^2 - 4x \)}{\( x^2 - 4 \)^2}
Question 2
A fair six-sided die is rolled. If the number 4 is rolled, a second die is rolled. If the number 6 is rolled, a third die is rolled. What is the probability that at least one 5 is rolled?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 3
Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} \)
C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)
D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. x < -\frac{5}{4} \text{ or } x > \frac{3}{2}
B. x > -\frac{5}{4} \text{ or } x < \frac{3}{2}
C. x < -\frac{5}{4} \text{ and } x > \frac{3}{2}
D. x > -\frac{5}{4} \text{ and } x < \frac{3}{2}
Question 5
Determine the value of x in the equation \( 2^x + 5^x = 3^x \) if x is a positive integer.
A. 1
B. 2
C. 3
D. 4
Question 6
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \).
A. ( 1 )
B. \( \frac{1}{2} \)
C. \( \frac{1}{3} \)
D. \( \frac{1}{4} \)
Question 7
Determine the value of the determinant of the matrix \( egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )
Question 8
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = -\frac{2}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
Question 9
Solve the system of linear equations \( 2x + 3y = 7 \) and \( x - 2y = -3 \) u\sing substitution.
A. \left\{x = \frac{17}{5}, y = \frac{14}{5}\right\}
B. \left\{x = \frac{17}{5}, y = -\frac{14}{5}\right\}
C. \left\{x = -\frac{17}{5}, y = \frac{14}{5}\right\}
D. \left\{x = -\frac{17}{5}, y = -\frac{14}{5}\right\}
Question 10
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. \left[\frac{x^3}{3} + x^2 - 3x\right]_0^2
B. \left[\frac{x^3}{3} + x^2 - 3x\right]_2^0
C. \left[\frac{x^3}{3} + x^2 - 3x\right]_0^1
D. \left[\frac{x^3}{3} + x^2 - 3x\right]_1^0

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