POST UTME WELLSPRING UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( \frac{x}{x+1} > \frac{1}{x+1} \) for \( x in mathbb{R} setminus {-1} \).
A. \( x > 0 \)
B. \( x < -1 \)
C. \( x > 1 \)
D. \( x < 0 \)
Question 2
A vector ( mathbf{a} ) has components \( a_1 = 2 \) and \( a_2 = 3 \). Find the magnitude of ( mathbf{a} ).
A. 5
B. 10
C. 15
D. 20
Question 3
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 4
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( y = 4 \) about the x-axis.
A. 32\pi
B. 16\pi
C. 64\pi
D. 128\pi
Question 5
A set of 5 integers has a mean of 10. If 2 is added to each integer, what is the new mean?
A. ( 12 )
B. ( 10 )
C. ( 11 )
D. ( 9 )
Question 6
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \( x = -2, x = -3 \)
B. \( x = 2, x = 3 \)
C. \( x = -1, x = -4 \)
D. \( x = 1, x = 4 \)
Question 7
Find the sum of the first 10 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = 3 \).
A. 3199
B. 3198
C. 3197
D. 3196
Question 8
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)
B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)
C. \( x = \frac{-5 pm \sqrt{25 + 24}}{2} \)
D. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)
Question 9
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 10
Solve the system of equations \begin{align*} x+y+z &= 3 \ x+2y+3z &= 7 \ x+3y+6z &= 12 \end{align*}
A. \begin{align*} x &= 1 \ y &= 1 \ z &= 1 \end{align*}
B. \begin{align*} x &= 1 \ y &= 1 \ z &= 1 \end{align*}
C. \begin{align*} x &= 1 \ y &= 1 \ z &= 1 \end{align*}
D. \begin{align*} x &= 1 \ y &= 1 \ z &= 1 \end{align*}
Question 11
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 80?
A. 0.68
B. 0.85
C. 0.95
D. 0.99
Question 12
Solve for x in the equation \log_{10}\( x^2 \) = 4.
A. \pm 10
B. \pm 100
C. \pm 1000
D. \pm 10000
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)
Question 14
In a probability experiment, two events A and B are indep\endent. If ( P(A) = \frac{1}{4} ) and ( P(B) = \frac{1}{3} ), find ( P(A cap B) ).
A. \( \frac{1}{12} \)
B. \( \frac{1}{6} \)
C. \( \frac{1}{8} \)
D. \( \frac{1}{10} \)
Question 15
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 = 25
C. \( x-2 \)^2 + \( y-3 \)^2 = 36
D. \( x-2 \)^2 + \( y-3 \)^2 = 49

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