POST UTME AAUA 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let X and Y be indep\endent events with P(X) = 0.4 and P(Y) = 0.6. Find P(X ∩ Y).
A. 0.24
B. 0.48
C. 0.64
D. 0.72
Question 2
Solve the equation \frac{3x - 2}{2x + 1} = \frac{x + 2}{x - 1}.
A. 0
B. 12
C. 6
D. 4
Question 3
A set of 5 consecutive integers has a median of 10. If the sum of the integers is 50, what is the value of the smallest integer?
A. 5
B. 8
C. 10
D. 12
Question 4
Find the derivative of ( f(x) = \frac{1}{2} \log_{10} \( x^2 + 1 \) ) u\sing the chain rule.
A. \frac{1}{2} \cdot \frac{1}{x^2 + 1} \cdot 2x
B. \frac{1}{2} \cdot \frac{1}{x^2 + 1}
C. \frac{1}{2} \cdot \frac{2x}{x^2 + 1}
D. \frac{1}{2} \cdot \frac{1}{\( x^2 + 1 \)^2} \cdot 2x
Question 5
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 6
Find the area under the curve \( y = \sin^2\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{2} \)
D. \( \frac{3pi}{4} \)
Question 7
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 8
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 = 16
D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16
Question 9
Solve the system of 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. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 10
Find 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 11
Find the area under the curve y = \sin(x) from x = 0 to x = π/2.
A. 1
B. 2
C. 3
D. 4
Question 12
Determine the value of $x$ in the equation $2x^2 + 5x - 3 = 0$ u\sing the quadratic formula.
A. -1
B. 1
C. 2
D. 3
Question 13
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. \frac{64}{3}
B. \frac{32}{3}
C. \frac{16}{3}
D. \frac{8}{3}
Question 14
Solve for ( x ) in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 15
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the chain rule and limits.
A. ( f'(x) = 2x + 2 \)
B. ( f'(x) = 2x - 2 \)
C. ( f'(x) = x^2 + 2 \)
D. ( f'(x) = x^2 - 2 \)

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