POST UTME ABU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{3} ) for \( x = 1, 2, 3 \). Find the expected value of ( X ).
A. ( E(X) = 2 )
B. ( E(X) = 3 )
C. ( E(X) = 4 )
D. ( E(X) = 5 )
Question 2
Solve for x in the equation \( 2^x + 5^x = 3^x \).
A. 1
B. 2
C. 3
D. 4
Question 3
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 4
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.8413
B. 0.6827
C. 0.6915
D. 0.9772
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 1 \) to \( x = 4 \).
A. \( \frac{1}{2} left[ \frac{x^3}{3} + \frac{3x^2}{2} - 2x \right] \)
B. \( \frac{1}{2} left[ \frac{4^3}{3} + \frac{3 cdot 4^2}{2} - 2 cdot 4 \right] - \frac{1}{2} left[ \frac{1^3}{3} + \frac{3 cdot 1^2}{2} - 2 cdot 1 \right] \)
C. \( \frac{1}{2} left[ \frac{4^3}{3} + \frac{3 cdot 4^2}{2} - 2 cdot 4 \right] \)
D. \( \frac{1}{2} left[ \frac{1^3}{3} + \frac{3 cdot 1^2}{2} - 2 cdot 1 \right] \)
Question 6
A set of data has a mean of 25 and a s\tandard deviation of 3. Find the z-score of the value 32.
A. 1
B. 2
C. 3
D. 4
Question 7
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. ( f'(x) = \frac{\( x - 2 \)(2x) - \( x^2 - 4 \)(1)}{\( x - 2 \)^2} )
B. ( f'(x) = \frac{\( x - 2 \)(2x) + \( x^2 - 4 \)(1)}{\( x - 2 \)^2} )
C. ( f'(x) = \frac{\( x - 2 \)(2x) - \( x^2 - 4 \)(1)}{\( x - 2 \)^2} )
D. ( f'(x) = \frac{\( x - 2 \)(2x) + \( x^2 - 4 \)(1)}{\( x - 2 \)^2} )
Question 8
Solve for x in the equation: \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{\pi}{6}
Question 9
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 10
A polynomial function is defined as \( f(x) = x^3 - 6x^2 + 11x - 6 \). Find the value of f(2).
A. 0
B. 2
C. 4
D. 6
Question 11
Solve the system of equations u\sing matrices: [ egin{cases} x + 2y = 6 \ 3x - 2y = -3 \end{cases} ].
A. \( x = 3, y = 1.5 \)
B. \( x = 1.5, y = 3 \)
C. \( x = 2, y = 2 \)
D. \( x = 4, y = 1 \)
Question 12
Find the sum of the first 10 terms of the geometric progression 3, 6, 12, 24, ...
A. 1230
B. 1240
C. 1250
D. 1260
Question 13
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x > \frac{3}{2}
D. x > -1 or x < \frac{3}{2}
Question 14
A function ( f(x) ) is defined as ( f(x) = \sin^2(x) + \cos^2(x) ). Find the derivative of ( f(x) ) u\sing the chain rule.
A. ( f'(x) = 2\sin\( x)\cos(x \) )
B. ( f'(x) = 2\cos\( x)\sin(x \) )
C. ( f'(x) = 2\sin^2(x) + 2\cos^2(x) )
D. ( f'(x) = 2\sin(x) - 2\cos(x) )
Question 15
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, what is their total daily profit?
A. ₦1,250
B. ₦1,500
C. ₦1,750
D. ₦2,000

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