POST UTME DELSU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 = 20 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 24 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 28 )
Question 2
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. -1
C. 2
D. 3
Question 3
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. ( f'(x) = 6x + 2 )
B. ( f'(x) = 6x - 2 )
C. ( f'(x) = 6x + 4 )
D. ( f'(x) = 6x - 4 )
Question 4
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = -\frac{1}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{1}{\( x^2 + 1 \)^2} )
Question 5
Evaluate the definite integral \( int_{0}^{1} x^2 \sin x , dx \).
A. \frac{1}{2} - \frac{1}{3}
B. \frac{1}{2} + \frac{1}{3}
C. \frac{1}{2} - \frac{1}{4}
D. \frac{1}{2} + \frac{1}{4}
Question 6
Find the sum of the infinite geometric series with first term 1/2 and common ratio 1/4.
A. 1
B. 3/4
C. 5/8
D. 7/16
Question 7
Find the area under the curve \( y = x^2 \) from 0 to 2.
A. 2
B. 4
C. 6
D. 8
Question 8
Determine the mean of the following data set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
A. 5
B. 6
C. 7
D. 8
Question 9
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) 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 10
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 5x + 3} ) u\sing the quotient rule.
A. \( \frac{-2x + 5}{\( 2x^2 + 5x + 3 \ \)^2} )
B. \( \frac{2x + 5}{\( 2x^2 + 5x + 3 \ \)^2} )
C. \( \frac{2x - 5}{\( 2x^2 + 5x + 3 \ \)^2} )
D. \( \frac{-2x - 5}{\( 2x^2 + 5x + 3 \ \)^2} )
Question 11
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 12
A histogram shows that the heights of students in a class are normally distributed with a mean of 165 cm and a s\tandard deviation of 5 cm. Find the probability that a randomly selected student is taller than 170 cm.
A. \( P\( X > 170 \ \) = 0.1587 )
B. \( P\( X > 170 \ \) = 0.3413 )
C. \( P\( X > 170 \ \) = 0.5 )
D. \( P\( X > 170 \ \) = 0.6827 )
Question 13
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{14}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{18}{3} \)
D. \( \frac{20}{3} \)
Question 14
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 15
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and (6, 7).
A. x^2 + y^2 - 12x - 8y + 35 = 0
B. x^2 + y^2 - 10x - 6y + 25 = 0
C. x^2 + y^2 - 14x - 10y + 49 = 0
D. x^2 + y^2 - 16x - 12y + 64 = 0

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