POST UTME UI 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center ( (3, 4) ) and radius 5.
A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 )
B. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 25 )
C. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 9 )
D. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 9 )
Question 2
Find the mean and s\tandard deviation of the random variable X with probability mass function \begin{align*} p(x) = \begin{cases} \frac{1}{3} & \text{if } x = 1 \frac{1}{2} & \text{if } x = 2 \frac{1}{6} & \text{if } x = 3 \end{cases} \end{align*}.
A. \text{Mean: } 1.5, \text{ S\tandard Deviation: } 1.1
B. \text{Mean: } 2, \text{ S\tandard Deviation: } 1.2
C. \text{Mean: } 1, \text{ S\tandard Deviation: } 1.3
D. \text{Mean: } 2.5, \text{ S\tandard Deviation: } 1.4
Question 3
Find the matrix product AB, where A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} and B = \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}.
A. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
B. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
C. \begin{bmatrix} 17 & 20 \ 39 & 46 \end{bmatrix}
D. \begin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix}
Question 4
A random variable ( X ) has a probability distribution given by the table below. Find the expected value of ( X ).
A. 2.5
B. 3.5
C. 4.5
D. 5.5
Question 5
In a survey of 100 students, 60 students preferred Mathematics, 30 students preferred Science, and 10 students preferred both Mathematics and Science. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. 0.6
B. 0.7
C. 0.8
D. 0.9
Question 6
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 7
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. \frac{2x\( x^2 + 1 \) - 2x^3}{\( x^2 + 1 \)^2}
B. \frac{2x^2 - 2x^4}{\( x^2 + 1 \)^2}
C. \frac{2x^3 - 2x}{\( x^2 + 1 \)^2}
D. \frac{2x^2 + 2x^4}{\( x^2 + 1 \)^2}
Question 8
Evaluate the definite integral \( int_{0}^{1} x^2 , dx \).
A. \( \frac{1}{3} \)
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{4} \)
Question 9
A company produces two products, A and B. The profit from producing x units of product A and y units of product B is given by the function ( P(x, y) = 2x + 3y - xy - 10 ). Find the partial derivative of P with respect to x when y = 2.
A. 2 - y
B. 2 + y
C. 2y - 1
D. 2y + 1
Question 10
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \).
A. \( egin{pmatrix} -15 \ 10 \end{pmatrix} \)
B. \( egin{pmatrix} 10 \ -15 \end{pmatrix} \)
C. \( egin{pmatrix} 15 \ -10 \end{pmatrix} \)
D. \( egin{pmatrix} -10 \ 15 \end{pmatrix} \)
Question 11
A circle has its center at ( (2, 3) ) and passes through the point ( (6, 5) ). Find the equation of the circle in the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ).
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 64
Question 12
A random variable X has a probability distribution given by the following table:
A. 0.5
B. 1.0
C. 1.5
D. 2.0
Question 13
A vector ( mathbf{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of the vector.
A. x = 4, y = 3
B. x = 3, y = 4
C. x = 2, y = 5
D. x = 5, y = 2
Question 14
Find the determinant of the matrix \begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}.
A. 0
B. 1
C. 2
D. 3
Question 15
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{3pi}{4} \)
C. \( x = \frac{5pi}{4} \)
D. \( x = \frac{7pi}{4} \)

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