POST UTME BSU 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \( \frac{16}{15} pi \)
B. \( \frac{32}{15} pi \)
C. \( \frac{64}{15} pi \)
D. \( \frac{128}{15} pi \)
Question 2
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 3
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{16}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{64}{3} \)
D. \( \frac{128}{3} \)
Question 4
Find the value of $\log_{10} \( x^2 \) = 4$.
A. 10
B. 100
C. 1000
D. 10000
Question 5
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \)
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, -3 \) \cup \( 3, \infty \)
Question 6
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 7
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 8
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. 123.5
B. 124.5
C. 125.5
D. 126.5
Question 9
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. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )
Question 10
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = \frac{1}{2}e^{-|x|}$ and $f_Y(y) = \frac{1}{2}e^{-|y|}$, respectively. Find the probability that $X+Y>0$.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. 1
Question 11
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. \( y = \frac{4}{2} \( x - 1 \ \) + 2 )
B. \( y = \frac{4}{2} \( x - 3 \ \) + 4 )
C. \( y = \frac{2}{2} \( x - 1 \ \) + 2 )
D. \( y = \frac{2}{2} \( x - 3 \ \) + 4 )
Question 12
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 13
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 14
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 15
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\( 3^{13}-1 \ \)/\( 3-1 \) )

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