POST UTME WELLSPRING UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. \[ y = \frac{2}{2}x + 1 \]
B. \[ y = \frac{2}{2}x - 1 \]
C. \[ y = \frac{2}{2}x + 2 \]
D. \[ y = \frac{2}{2}x - 2 \]
Question 2
A particle moves in a straight line with an initial velocity of 5 m/s and an acceleration of 2 m/s^2. Find the velocity after 3 seconds.
A. 7
B. 9
C. 11
D. 13
Question 3
A rec\tangular garden measures 10m by 5m. Find the area of the garden.
A. 50m^2
B. 75m^2
C. 60m^2
D. 40m^2
Question 4
Solve for x in the equation [ \log_{10} \( x^2 \) = 4 ].
A. 10
B. 100
C. 1000
D. 10000
Question 5
Let ( f(x) = \frac{1}{\log_{10} x} ). Find \( f^{-1}\( x \ \) ) and simplify.
A. 10^x
B. \log_{10} x
C. 1/x
D. x^2
Question 6
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{2}{3}
C. \frac{1}{2}
D. \frac{1}{6}
Question 7
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].
A. -1
B. 1
C. 2
D. 3
Question 8
Find the derivative of the function f(x) = 3x^2 + 2x - 5 u\sing the chain rule.
A. 6x + 2
B. 6x^2 + 2
C. 6x^2 + 2x
D. 6x + 2x^2
Question 9
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x+2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-2 \ \)^2 + \( y+3 \)^2 = 16 )
C. \( x+2 \ \)^2 + \( y+3 \)^2 = 16 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )
Question 10
A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed for the round trip?
A. 45
B. 48
C. 50
D. 52
Question 11
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 12
A right circular cone has a height of 20 cm and a base radius of 10 cm. Find the volume of the cone.
A. 1000 \pi
B. 2000 \pi
C. 3000 \pi
D. 4000 \pi
Question 13
Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2, & 0 leq y leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that \( X + Y leq 1 \).
A. \frac{1}{3}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{3}{4}
Question 14
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. -1.5
B. 1.5
C. 3
D. -3
Question 15
Find the derivative of ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. -\frac{1}{\( x^2 + 1 \)^2}
D. \frac{1}{\( x^2 + 1 \)^2}

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