POST UTME WELLSPRING UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2 x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 2
Let X be a random variable with probability density function (pdf) given by f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X lies in the interval \( -1, 2 \).
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 3
Solve the inequality $\log_{10} \( x^2 - 4 \) > 2$.
A. $x<-2$ or $x>2$
B. $x<-2$ or $x>4$
C. $x>2$ or $x<4$
D. $x<-4$ or $x>2$
Question 4
Determine the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 2
B. 61
C. 62
D. 63
Question 5
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 6
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 104,783
B. 104,783
C. 104,783
D. 104,783
Question 7
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 13
B. 15
C. 17
D. 19
Question 8
Find the value of $\sum_{n=1}^{5} n^2$.
A. 55
B. 65
C. 75
D. 85
Question 9
A histogram has a mean of 25 and a s\tandard deviation of 5. Find the probability that a randomly selected value is between 20 and 30.
A. ( 0.8 )
B. ( 0.6 )
C. ( 0.4 )
D. ( 0.2 )
Question 10
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 2
D. y = x + 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
Find the derivative of the function f(x) = \frac{x^2}{x^2 + 1}.
A. \frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x^2}{\( x^2 + 1 \)^2}
C. \frac{2x^3}{\( x^2 + 1 \)^2}
D. \frac{2x^4}{\( x^2 + 1 \)^2}
Question 13
A histogram is shown below. Find the mean of the data.
A. 10
B. 12
C. 14
D. 16
Question 14
A set of 5 numbers has a mean of 10. Find the sum of the numbers.
A. 50
B. 50
C. 50
D. 50
Question 15
Solve the system of equations \begin{align*} x + y &= 2 \ x - y &= 1 \end{align*}.
A. x = 1, y = 1
B. x = 1, y = 2
C. x = 2, y = 1
D. x = 2, y = 2

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