POST UTME BSU 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. ( 0.9544 )
B. ( 0.8413 )
C. ( 0.6915 )
D. ( 0.5244 )
Question 2
Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. x = 0
B. x = \frac{pi}{2}
C. x = \frac{pi}{4}
D. x = \frac{3pi}{4}
Question 3
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 4
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 5
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{pi}{2} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = pi \)
Question 6
Find the vector ( mathbf{v} ) that satisfies the equation \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = 4 \).
A. \( mathbf{v} = 3mathbf{i} + 4mathbf{j} \)
B. \( mathbf{v} = 4mathbf{i} + 3mathbf{j} \)
C. \( mathbf{v} = 3mathbf{i} - 4mathbf{j} \)
D. \( mathbf{v} = 4mathbf{i} - 3mathbf{j} \)
Question 7
Determine the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. \( 2\( 3^{10}-1 \ \)/\( 3-1 \) )
B. \( 2\( 3^{11}-1 \ \)/\( 3-1 \) )
C. \( 2\( 3^{12}-1 \ \)/\( 3-1 \) )
D. \( 2\( 3^{13}-1 \ \)/\( 3-1 \) )
Question 8
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
Question 9
A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.3. What is the expected value of X?
A. 1.2
B. 1.5
C. 1.8
D. 2.1
Question 10
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 11
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.
A. 0.3413
B. 0.3415
C. 0.3417
D. 0.3419
Question 12
Find the value of $\sqrt{\frac{1}{2}} + \sqrt{\frac{1}{3}}$.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{1}{\sqrt{6}}
D. \frac{1}{\sqrt{10}}
Question 13
Solve the equation \( 2^x = 16 \) for x.
A. x = 4
B. x = 2
C. x = 1
D. x = 3
Question 14
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^2 \)
B. \( x = 10^4 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)
Question 15
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 + x^2}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( 1 + x^2 \)^{3/2}}
B. f'(x) = \frac{x}{\( 1 + x^2 \)^{3/2}}
C. f'(x) = \frac{1}{\( 1 + x^2 \)^{3/2}}
D. f'(x) = \frac{-1}{\( 1 + x^2 \)^{3/2}}

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