POST UTME BSU 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let A be a 3x3 matrix with determinant 6. If A is transformed into B by multiplying each element by 2, what is the determinant of B?
A. 12
B. 24
C. 48
D. 96
Question 2
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{3}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{3}{4}
Question 3
A function is defined by ( f(x) = \frac{1}{x^2 + 1} ). Find the value of \( f\( -1 \ \) ).
A. 0
B. 1
C. 1/2
D. 1/4
Question 4
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 = 9 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )
Question 5
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 6
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. 0
B. π/2
C. π
D. 3π/2
Question 7
In the diagram below, the circle with center ( O ) has equation \( x^2 + y^2 = 4 \). What is the length of the chord ( AB )?
A. 2√3
B. 2√2
C. 2√5
D. 2√6
Question 8
Find the value of \( \log_{10} \( 1000 \ \) ).
A. ( 3 )
B. ( 4 )
C. ( 5 )
D. ( 6 )
Question 9
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first five terms of the sequence.
A. 2 + 5 + 13 + 29 + 61
B. 2 + 5 + 13 + 29 + 57
C. 2 + 5 + 13 + 27 + 57
D. 2 + 5 + 13 + 27 + 61
Question 10
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 59048
B. 59049
C. 59050
D. 59051
Question 11
Find the surface area of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. ( 32 pi )
B. ( 16 pi )
C. ( 64 pi )
D. ( 128 pi )
Question 12
In the diagram below, ( O ) is the center of the circle and ( AB ) is a chord. If \( OA = 5 \) and \( OB = 7 \), find the length of ( AB ).
A. √(74)
B. √(50)
C. √(100)
D. √(200)
Question 13
A die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. √\( 1/6 \)
B. 1/6
C. 1/3
D. 1/2
Question 14
A set of exam scores has a mean of 80 and a s\tandard deviation of 10. If a new score of 90 is added, what is the new mean?
A. 81
B. 82
C. 83
D. 84
Question 15
Find the derivative of the function ( f(x) = 3x^2 \sin(x) ) u\sing the product rule.
A. \( 6x \sin\( x \ \) + 3x^2 \cos(x) )
B. \( 6x \cos\( x \ \) - 3x^2 \sin(x) )
C. \( 6x \sin\( x \ \) - 3x^2 \cos(x) )
D. \( 6x \cos\( x \ \) + 3x^2 \sin(x) )

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